WEBVTT

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<v Speaker 0>Hi, everyone, and welcome to this demonstration video on how

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<v Speaker 1>to use the quizes in this.

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<v Speaker 1>Central to the philosophy of this module is the view

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<v Speaker 1>that the best way to learn Mazzara to revise maths

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<v Speaker 0>is through exercise.

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<v Speaker 1>And in order to enable you to get as much

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<v Speaker 1>exercise as you want in the context of your revision.

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<v Speaker 1>This module is to a very large degree structured around

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<v Speaker 0>quizzes, in particular for every section of this class.

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<v Speaker 1>Whenever you open a particular section, you will see that

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<v Speaker 1>the model pages structured in a way around a number

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<v Speaker 1>of different types of quizzes.

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<v Speaker 0>For example, this is the page of the model page

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<v Speaker 1>on topic two point three univariate calculus.

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<v Speaker 1>And as you can see, as you scroll down the

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<v Speaker 0>page, one of the first resources that you'll see here

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<v Speaker 1>is a diagnostic quiz that I will be a diagnostic

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<v Speaker 1>quiz on every topic.

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<v Speaker 1>Then further to this, there are a sequence of tutorial

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<v Speaker 1>videos on topics related to the rules of differentiation.

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<v Speaker 1>And together with every with each one of these videos,

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<v Speaker 1>there is an associated many ways that look specifically at

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<v Speaker 1>the number of exercises related to the topic of the

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<v Speaker 1>video.

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<v Speaker 1>Further down, typically, for most topics, there is an economic

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<v Speaker 1>application of discussion of some economic example of the mathematical

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<v Speaker 0>concepts studied in this topic.

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<v Speaker 1>Together with there an associated economic application.

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<v Speaker 1>Squiz, which goes over, allows you to practise through some

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<v Speaker 0>examples, the contents discussed in The View.

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<v Speaker 1>And finally, there is an advanced quiz of consisting of

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<v Speaker 1>somewhat more difficult questions that you are able to look

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<v Speaker 0>at if you have done the diagnostic quiz already and

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<v Speaker 1>you want some further exercise.

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<v Speaker 0>So it is our intention that this quizzes are fairly

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<v Speaker 0>easy to use.

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<v Speaker 1>It should be fairly self-explanatory how to use the quizzes

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<v Speaker 1>and there should be no technical difficulty in accessing and

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<v Speaker 1>playing around with the quizzes.

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<v Speaker 1>However, since the quizzes are made in a platform known

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<v Speaker 0>as numbers, which allows for a relatively versatile type of

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<v Speaker 1>question types rather than just the usual and secure types,

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<v Speaker 1>it is also understood that you might on occasions find

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<v Speaker 1>it a little bit challenging how to improve your answers

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<v Speaker 1>to these quizzes.

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<v Speaker 1>And there might be a scope for explaining further what

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<v Speaker 1>is the best way to use this quiz.

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<v Speaker 1>So the purpose of this short video will be to

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<v Speaker 0>walk you over one practise quiz and through this question

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<v Speaker 1>to demonstrate the possibilities of numbers and how and advice

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<v Speaker 1>on how best to use these quizzes in order to,

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<v Speaker 1>you know, support your learning.

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<v Speaker 1>Now, in order to get there, I am going to

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<v Speaker 0>open the page on how to use quizzes on the

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<v Speaker 1>model page.

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<v Speaker 1>And as you can see here on this page, there

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<v Speaker 1>is a practise quiz, which I am now going to

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<v Speaker 1>open in a new top.

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<v Speaker 1>And once you open a quiz, you are going to

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<v Speaker 1>see a page that looks something like this.

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<v Speaker 1>There will be a statement on the number of questions

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<v Speaker 1>and the number of marks that are distributed.

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<v Speaker 1>There will be a statement on the bus percentage.

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<v Speaker 1>In this case, it's set to be 80 percent and

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<v Speaker 1>some introductory statement.

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<v Speaker 0>Once you have this page open, if you click on

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<v Speaker 0>start, you are opening the quiz.

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<v Speaker 0>And now the way in which the quiz is structured

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<v Speaker 1>is through a sequence of questions that you can see

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<v Speaker 0>on the left.

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<v Speaker 1>In this particular example, in this particular quiz, there are

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<v Speaker 1>only three questions.

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<v Speaker 1>And at that point, by clicking on different questions on

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<v Speaker 1>the left hand side, you can jump between questions and

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<v Speaker 1>other things you can observe.

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<v Speaker 1>Is that associated with each question?

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<v Speaker 1>There is a score, for example, question why?

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<v Speaker 1>Yes, a maximum score of one.

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<v Speaker 1>Currently my score is zero because I have not yet

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<v Speaker 1>attempted, let alone correctly, answer the question.

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<v Speaker 1>So similarly in question three, in fact, there are twenty

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<v Speaker 1>four marks currently my score.

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<v Speaker 1>Zero altogether and question three, yes, far marks and that

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<v Speaker 1>far in Tokyo, there are 29 marks that can be

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<v Speaker 1>obtained from the case.

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<v Speaker 1>The total scar that one obtains from the case consists

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<v Speaker 1>of the scars that you get divided by the total

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<v Speaker 1>scar available, expressed in percentage terms.

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<v Speaker 0>Now, let's start by taking a look at the first

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<v Speaker 1>question on the quiz, which is indeed one very basic

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<v Speaker 1>question whose purpose is simply to allow us to explore

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<v Speaker 0>the what is possible within the case and how best

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<v Speaker 1>to use this resource in order to support learning.

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<v Speaker 1>So I'll consider the question.

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<v Speaker 1>I eat nine apples per day and then the question

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<v Speaker 1>is how many apples Dwight Burwick associated with the question?

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<v Speaker 1>There is an answer box here and inside the centre

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<v Speaker 1>answer box.

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<v Speaker 1>I can type stuff in this particular example.

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<v Speaker 1>The question is, if I eat nine apples per day,

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<v Speaker 1>how many apples?

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<v Speaker 1>Right, Burwick?

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<v Speaker 1>Well, since there are seven days in one week, if

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<v Speaker 1>I eat nine apples per day, then the total number

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<v Speaker 1>of apples eight Burwick is nine times seven equals to

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<v Speaker 0>sixty three.

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<v Speaker 1>If I type in my answer here.

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<v Speaker 1>Note is that to the right of the answer box,

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<v Speaker 1>a new box appears which renders the answer that I've

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<v Speaker 1>typed into mathematical notation.

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<v Speaker 1>In this particular case, there is nothing unusual in the

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<v Speaker 0>rendering of the number.

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<v Speaker 0>Once I have typed my answer, I can click on

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<v Speaker 1>submit answer and page immediately tells me that this answer

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<v Speaker 1>is correct or not.

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<v Speaker 1>It turns out that sixth tracing the correct answer to

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<v Speaker 1>this question.

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<v Speaker 1>Surprisingly, and therefore I also predict one mark for my

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<v Speaker 1>answer.

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<v Speaker 1>As you can see my scar on the left for

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<v Speaker 0>question one change from zero out of one to one

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<v Speaker 1>out of one on account of me correctly answering this

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<v Speaker 0>question.

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<v Speaker 0>Now, of course, this question is fairly easy and it

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<v Speaker 1>is unlikely that in practise I'm going to make a

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<v Speaker 1>mistake in answering the question.

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<v Speaker 1>But suppose that I get that an incorrect answer.

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<v Speaker 1>For example, 50, this is still something I can do

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<v Speaker 1>if I now click on submit answer, I receive immediately

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<v Speaker 1>the feedback that my answer is incorrect.

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<v Speaker 1>Now, there is no problem with this because once I

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<v Speaker 1>have entered it and come back to the answer box

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<v Speaker 1>and as long as I haven't submitted the quiz, I

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<v Speaker 0>can try another answer.

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<v Speaker 1>For example, the correct answer 63.

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<v Speaker 1>And once I click on Submit Answer, this is immediately

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<v Speaker 0>seen as numerically correct.

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<v Speaker 1>Now something I can do inside the question.

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<v Speaker 1>So I suppose that I made a mistake in answering

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<v Speaker 0>fifty and I don't actually know how to tackle this

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<v Speaker 1>question.

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<v Speaker 1>Something I can do is click on a button at

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:08:12.580 --> 00:08:14.590
<v Speaker 0>the bottom right called to reveal answers.

NOTE CONF {"raw":[100,100,100,84,70,87,100]}

00:08:15.010 --> 00:08:18.310
<v Speaker 1>If I click on this button, I receive this notification

NOTE CONF {"raw":[100,100,100,100,100,100,100,96,100,100]}

00:08:19.060 --> 00:08:19.870
<v Speaker 0>rate through it.

NOTE CONF {"raw":[48,100,100]}

00:08:19.870 --> 00:08:25.210
<v Speaker 1>Then once I click on OK here in a box

NOTE CONF {"raw":[51,100,100,100,90,98,100,100,100,100]}

00:08:25.240 --> 00:08:28.780
<v Speaker 1>near the answer box, I get another box known as

NOTE CONF {"raw":[93,100,100,100,100,100,100,100,76,76]}

00:08:29.050 --> 00:08:30.430
<v Speaker 1>which says expected answer.

NOTE CONF {"raw":[98,47,100,99]}

00:08:30.430 --> 00:08:33.930
<v Speaker 1>That is what is the correct answer to that question?

NOTE CONF {"raw":[100,83,100,100,100,100,100,100,100,100]}

00:08:33.940 --> 00:08:35.919
<v Speaker 1>And in fact tells me that the correct answer was

NOTE CONF {"raw":[97,99,99,100,100,98,100,100,100,94]}

00:08:35.919 --> 00:08:36.580
<v Speaker 1>six to three.

NOTE CONF {"raw":[72,68,98]}

00:08:37.270 --> 00:08:40.659
<v Speaker 1>Further down the page, I receive feedback or advice that

NOTE CONF {"raw":[100,100,100,90,100,99,100,100,100,100]}

00:08:40.659 --> 00:08:43.090
<v Speaker 1>is typically a work solution to the problem.

NOTE CONF {"raw":[100,100,97,85,100,100,100,100]}

00:08:43.510 --> 00:08:45.550
<v Speaker 1>And in this case, the work solution tells me that

NOTE CONF {"raw":[99,100,100,100,100,45,100,100,100,100]}

00:08:45.550 --> 00:08:48.130
<v Speaker 1>since there are seven days per week, if I eat

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,80]}

00:08:48.130 --> 00:08:52.540
<v Speaker 1>nine apples every day, then I will wait seven times

NOTE CONF {"raw":[100,100,96,96,100,100,81,95,100,100]}

00:08:52.540 --> 00:08:54.910
<v Speaker 1>ninety six to sixty three apples.

NOTE CONF {"raw":[90,90,100,89,100,100]}

00:08:55.750 --> 00:09:00.400
<v Speaker 1>Now notice that whilst I have clicked on review answers,

NOTE CONF {"raw":[100,87,100,45,100,100,100,100,100,100]}

00:09:00.790 --> 00:09:03.280
<v Speaker 1>my car is locked to zero.

NOTE CONF {"raw":[100,51,100,97,100,100]}

00:09:03.880 --> 00:09:04.830
<v Speaker 1>For this question.

NOTE CONF {"raw":[100,100,100]}

00:09:05.170 --> 00:09:08.980
<v Speaker 1>However, I receive the option to try another question like

NOTE CONF {"raw":[100,100,98,100,100,100,100,100,100,100]}

00:09:08.980 --> 00:09:09.340
<v Speaker 1>this.

NOTE CONF {"raw":[100]}

00:09:09.790 --> 00:09:11.950
<v Speaker 1>And if I click on this question, the on this

NOTE CONF {"raw":[100,100,100,100,100,100,100,77,66,66]}

00:09:11.980 --> 00:09:15.220
<v Speaker 1>option and if I click OK, I am back at

NOTE CONF {"raw":[99,100,100,100,100,88,100,100,100,100]}

00:09:15.220 --> 00:09:19.930
<v Speaker 1>the beginning where I am given a slightly different but

NOTE CONF {"raw":[100,100,100,100,100,98,100,100,100,100]}

00:09:19.930 --> 00:09:22.510
<v Speaker 1>in fact similar type of question where I am now,

NOTE CONF {"raw":[100,100,100,100,100,91,100,100,100,100]}

00:09:22.510 --> 00:09:25.660
<v Speaker 1>I suppose that I ate for apples birthday.

NOTE CONF {"raw":[64,100,100,100,52,99,90,73]}

00:09:25.660 --> 00:09:27.970
<v Speaker 1>Remember that previously I had nine apples per day.

NOTE CONF {"raw":[100,100,89,100,99,100,100,51,50]}

00:09:28.390 --> 00:09:30.400
<v Speaker 1>Now suppose that I eat four apples per day.

NOTE CONF {"raw":[100,90,100,100,64,80,100,100,100]}

00:09:30.670 --> 00:09:32.500
<v Speaker 1>How many apples die per week?

NOTE CONF {"raw":[100,100,100,97,98,98]}

00:09:32.740 --> 00:09:35.290
<v Speaker 1>And now the correct answer is twenty eight.

NOTE CONF {"raw":[100,100,100,100,100,100,100,100]}

00:09:35.710 --> 00:09:39.400
<v Speaker 1>I can submit this answer and notice that my score

NOTE CONF {"raw":[100,100,100,100,100,95,77,100,100,51]}

00:09:39.400 --> 00:09:40.620
<v Speaker 1>becomes one out of one.

NOTE CONF {"raw":[100,100,100,100,100]}

00:09:41.830 --> 00:09:46.000
<v Speaker 1>Therefore, one possibility of this quiz is if you get

NOTE CONF {"raw":[99,100,100,100,100,100,97,100,100,100]}

00:09:46.000 --> 00:09:48.250
<v Speaker 0>the question that you don't know how to answer something

NOTE CONF {"raw":[100,98,100,100,100,100,100,100,100,100]}

00:09:48.250 --> 00:09:50.030
<v Speaker 1>that is revealed the answers.

NOTE CONF {"raw":[100,72,46,99,100]}

00:09:50.410 --> 00:09:53.230
<v Speaker 1>This is going to give you some feedback, including countless

NOTE CONF {"raw":[100,100,100,100,100,100,97,100,100,96]}

00:09:53.230 --> 00:09:54.460
<v Speaker 1>other questions like this.

NOTE CONF {"raw":[91,100,100,100]}

00:09:54.760 --> 00:09:57.010
<v Speaker 1>And then you have the option to try another question

NOTE CONF {"raw":[100,100,100,100,100,100,99,100,100,100]}

00:09:57.010 --> 00:09:59.440
<v Speaker 1>like this one now, of course.

NOTE CONF {"raw":[100,100,100,100,100,100]}

00:10:00.050 --> 00:10:02.450
<v Speaker 1>You have the option to try another question like this

NOTE CONF {"raw":[99,100,100,100,100,100,100,100,100,100]}

00:10:02.450 --> 00:10:04.440
<v Speaker 1>one, even if you do not reveal the answer.

NOTE CONF {"raw":[100,100,100,100,100,100,98,100,100]}

00:10:04.460 --> 00:10:06.860
<v Speaker 1>So, for example, I'm going to click on try another

NOTE CONF {"raw":[100,100,100,97,100,100,100,74,60,100]}

00:10:06.860 --> 00:10:08.810
<v Speaker 1>question like this again.

NOTE CONF {"raw":[100,100,100,100]}

00:10:09.200 --> 00:10:11.570
<v Speaker 1>And now I receive yet another question.

NOTE CONF {"raw":[100,100,100,96,100,100,100]}

00:10:11.580 --> 00:10:14.090
<v Speaker 1>My car is reverted back to zero, and now I

NOTE CONF {"raw":[100,62,100,93,100,100,100,51,100,100]}

00:10:14.090 --> 00:10:15.990
<v Speaker 1>have to answer the question again.

NOTE CONF {"raw":[100,100,100,97,100,100]}

00:10:16.430 --> 00:10:19.520
<v Speaker 1>Now, the correct answer to this variety of the question,

NOTE CONF {"raw":[100,100,100,100,100,97,100,100,100,100]}

00:10:19.880 --> 00:10:22.370
<v Speaker 1>if I ate apples per day, then within a week

NOTE CONF {"raw":[100,100,94,94,91,91,100,100,100,100]}

00:10:22.370 --> 00:10:26.020
<v Speaker 1>I'm going to eat eight times seven fifty six apples.

NOTE CONF {"raw":[99,99,99,98,100,100,100,99,99,100]}

00:10:26.630 --> 00:10:29.270
<v Speaker 0>And now if I submit the answer, I get the

NOTE CONF {"raw":[100,100,100,100,79,100,100,100,100,98]}

00:10:29.270 --> 00:10:32.090
<v Speaker 0>score of one out of one note is that there

NOTE CONF {"raw":[78,67,100,100,100,100,63,63,100,100]}

00:10:32.090 --> 00:10:34.790
<v Speaker 1>is no penalty from tranqs.

NOTE CONF {"raw":[100,100,100,100,47]}

00:10:34.790 --> 00:10:37.250
<v Speaker 1>And other questions like this are revealing the answers to

NOTE CONF {"raw":[98,98,98,100,100,100,100,100,97,100]}

00:10:37.250 --> 00:10:37.880
<v Speaker 1>the question.

NOTE CONF {"raw":[100,98]}

00:10:38.480 --> 00:10:42.020
<v Speaker 1>And the only difference is that if you click on

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:10:42.020 --> 00:10:45.980
<v Speaker 1>one of these options, rather than answering the question, your

NOTE CONF {"raw":[100,100,70,76,100,100,100,100,98,100]}

00:10:45.980 --> 00:10:49.120
<v Speaker 1>original score will be reverted to zero yet.

NOTE CONF {"raw":[100,100,99,100,97,100,100,46]}

00:10:49.820 --> 00:10:53.840
<v Speaker 0>So, for example, it was one out of one zero

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:10:53.840 --> 00:10:54.590
<v Speaker 1>out of one.

NOTE CONF {"raw":[100,100,100]}

00:10:54.600 --> 00:10:57.400
<v Speaker 1>And now the question is eight five apples per day.

NOTE CONF {"raw":[100,100,100,100,100,99,100,100,100,100]}

00:10:57.440 --> 00:10:58.790
<v Speaker 1>How many like Burwick?

NOTE CONF {"raw":[100,100,39,56]}

00:10:58.820 --> 00:11:00.310
<v Speaker 1>Well, the answer is thirty five.

NOTE CONF {"raw":[100,100,100,100,90,90]}

00:11:02.230 --> 00:11:05.250
<v Speaker 1>Notice that in some cases there will be the option

NOTE CONF {"raw":[48,100,100,100,100,93,100,100,100,99]}

00:11:05.250 --> 00:11:06.290
<v Speaker 1>of shelf steps.

NOTE CONF {"raw":[81,40,100]}

00:11:06.980 --> 00:11:10.670
<v Speaker 1>Usually clicking on shelf steps is going to reveal some

NOTE CONF {"raw":[100,100,100,41,100,73,100,100,86,79]}

00:11:10.830 --> 00:11:12.430
<v Speaker 1>reveal, some sort of hint.

NOTE CONF {"raw":[93,100,100,100,95]}

00:11:13.790 --> 00:11:17.000
<v Speaker 1>In this case, the hint is that there are seven

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:11:17.000 --> 00:11:18.240
<v Speaker 1>days in a week.

NOTE CONF {"raw":[100,100,100,100]}

00:11:18.980 --> 00:11:23.660
<v Speaker 1>Notice that again, there is no penalty from revealing the

NOTE CONF {"raw":[98,100,100,100,100,100,100,100,98,100]}

00:11:23.660 --> 00:11:27.710
<v Speaker 1>steps, which I can again hide after I have revealed

NOTE CONF {"raw":[100,100,99,98,100,90,100,100,100,98]}

00:11:27.710 --> 00:11:31.340
<v Speaker 0>once and in some cases you might want to click

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:11:31.340 --> 00:11:35.090
<v Speaker 1>on this shelf steps button in order to review a

NOTE CONF {"raw":[100,100,60,100,62,100,100,100,90,91]}

00:11:35.090 --> 00:11:38.870
<v Speaker 1>potentially useful hint about how to answer a question.

NOTE CONF {"raw":[100,100,76,100,100,100,100,100,100]}

00:11:40.370 --> 00:11:46.640
<v Speaker 0>Now, this is the basic structure of a quiz question,

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:11:47.300 --> 00:11:52.460
<v Speaker 0>and one of the good things about the squillace is

NOTE CONF {"raw":[100,100,100,100,100,100,100,82,99,100]}

00:11:52.460 --> 00:11:56.390
<v Speaker 1>that you can use them to learn by clicking on

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,96]}

00:11:56.390 --> 00:11:59.990
<v Speaker 0>if you feel and even if you know what the

NOTE CONF {"raw":[100,100,94,55,100,100,100,100,98,100]}

00:11:59.990 --> 00:12:02.990
<v Speaker 1>correct answer is, if you feel that you can benefit

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:12:02.990 --> 00:12:06.020
<v Speaker 1>from more exercise, you can get this exercise simply by

NOTE CONF {"raw":[100,94,100,100,100,100,100,100,100,100]}

00:12:06.410 --> 00:12:06.890
<v Speaker 1>clicking on.

NOTE CONF {"raw":[100,100]}

00:12:06.890 --> 00:12:09.260
<v Speaker 1>Try another question like this as many times as you

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:12:09.260 --> 00:12:09.620
<v Speaker 1>like.

NOTE CONF {"raw":[100]}

00:12:09.930 --> 00:12:12.740
<v Speaker 1>And in this way you can recreate a particular type

NOTE CONF {"raw":[100,99,100,100,100,100,99,100,100,100]}

00:12:12.740 --> 00:12:13.850
<v Speaker 1>of exercise menotti's.

NOTE CONF {"raw":[100,100,26]}

00:12:13.850 --> 00:12:16.400
<v Speaker 1>For example, if there is a question on the power

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:12:16.400 --> 00:12:19.970
<v Speaker 1>rule and you answer the first draught of the question,

NOTE CONF {"raw":[74,100,98,100,100,100,49,56,100,100]}

00:12:20.150 --> 00:12:23.330
<v Speaker 0>well, but you want to exercise more on the power

NOTE CONF {"raw":[99,100,100,99,99,100,100,100,100,100]}

00:12:23.510 --> 00:12:25.670
<v Speaker 1>than by clicking on try another question like this.

NOTE CONF {"raw":[60,100,100,100,99,100,100,100,100]}

00:12:25.670 --> 00:12:30.230
<v Speaker 1>You are going to get more and more dros of

NOTE CONF {"raw":[93,93,100,100,100,100,100,100,20,99]}

00:12:30.230 --> 00:12:31.100
<v Speaker 1>a similar question.

NOTE CONF {"raw":[100,100,100]}

00:12:31.100 --> 00:12:35.800
<v Speaker 1>And in this way you can you can, you know,

NOTE CONF {"raw":[100,99,100,100,100,100,100,100,70,70]}

00:12:35.900 --> 00:12:38.600
<v Speaker 1>get as much exercise as you like.

NOTE CONF {"raw":[100,100,100,100,100,100,100]}

00:12:39.920 --> 00:12:43.610
<v Speaker 0>Now I'm going to move to question two from the

NOTE CONF {"raw":[71,100,100,100,100,100,100,99,100,100]}

00:12:43.610 --> 00:12:49.310
<v Speaker 1>quiz, which is a helper on how to input your

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:12:49.310 --> 00:12:51.240
<v Speaker 1>answers to this question.

NOTE CONF {"raw":[100,100,87,95]}

00:12:52.220 --> 00:12:56.480
<v Speaker 1>Now, given the versatility of numbers as a system for

NOTE CONF {"raw":[100,98,100,100,100,97,58,58,100,98]}

00:12:57.830 --> 00:13:02.870
<v Speaker 0>quizzes, the types of questions that could be asked spend

NOTE CONF {"raw":[93,100,100,100,100,100,100,100,87,97]}

00:13:02.870 --> 00:13:07.610
<v Speaker 1>not only the usual multiple type questions, where the answers

NOTE CONF {"raw":[100,99,100,100,100,100,100,100,63,100]}

00:13:07.610 --> 00:13:11.300
<v Speaker 1>are to be picked from a list of alternatives by

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:13:11.300 --> 00:13:11.900
<v Speaker 1>clicking.

NOTE CONF {"raw":[100]}

00:13:12.290 --> 00:13:15.120
<v Speaker 1>But in addition to this, there are the possibilities that

NOTE CONF {"raw":[100,100,100,100,100,100,100,98,99,100]}

00:13:15.120 --> 00:13:17.600
<v Speaker 1>the answer to a question will be a number, just

NOTE CONF {"raw":[74,100,100,96,100,100,100,99,97,100]}

00:13:17.600 --> 00:13:20.630
<v Speaker 1>like was the case in question, one that we discussed

NOTE CONF {"raw":[100,98,100,100,100,100,100,100,99,100]}

00:13:21.290 --> 00:13:24.110
<v Speaker 0>just now, or in fact, it could be an algebraic

NOTE CONF {"raw":[100,100,60,99,99,90,100,100,99,100]}

00:13:24.110 --> 00:13:28.670
<v Speaker 1>expression that is some sort of expression involving variables or

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,95]}

00:13:28.910 --> 00:13:29.780
<v Speaker 1>an equation.

NOTE CONF {"raw":[100,100]}

00:13:29.780 --> 00:13:32.060
<v Speaker 1>And inequality are in fact, the matrix.

NOTE CONF {"raw":[69,100,92,100,100,100,99]}

00:13:32.510 --> 00:13:38.120
<v Speaker 1>And even though the syntax of how these types of

NOTE CONF {"raw":[100,100,100,100,100,100,100,95,100,100]}

00:13:38.120 --> 00:13:44.000
<v Speaker 1>expressions are input into numbers is generally quite user-friendly, there

NOTE CONF {"raw":[100,100,71,82,100,99,100,100,62,100]}

00:13:44.000 --> 00:13:47.960
<v Speaker 1>is some sense in which certain rules have to be

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:13:47.960 --> 00:13:48.470
<v Speaker 1>followed.

NOTE CONF {"raw":[100]}

00:13:48.470 --> 00:13:50.390
<v Speaker 1>And the purpose of this part of the value will

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,52,100]}

00:13:50.390 --> 00:13:54.080
<v Speaker 1>be to walk you through the different types of questions

NOTE CONF {"raw":[100,100,100,54,100,99,100,100,100,100]}

00:13:54.080 --> 00:13:56.060
<v Speaker 1>that could happen on a number of squares.

NOTE CONF {"raw":[100,100,100,100,98,99,67,73]}

00:13:56.270 --> 00:13:58.790
<v Speaker 1>And how are the answers to these questions given?

NOTE CONF {"raw":[100,100,100,100,100,100,98,100,100]}

00:14:00.140 --> 00:14:03.710
<v Speaker 1>So we're going to go over a sequence of possible

NOTE CONF {"raw":[100,84,100,100,100,100,100,100,100,100]}

00:14:03.710 --> 00:14:07.040
<v Speaker 1>questions, starting with the simplest case.

NOTE CONF {"raw":[100,100,100,100,100,100]}

00:14:07.040 --> 00:14:09.980
<v Speaker 1>That is, suppose that a question that is being cast

NOTE CONF {"raw":[100,100,100,96,100,100,100,100,100,57]}

00:14:09.980 --> 00:14:12.380
<v Speaker 1>on equity, some multiple choice question.

NOTE CONF {"raw":[93,60,91,100,100,99]}

00:14:12.950 --> 00:14:14.810
<v Speaker 1>So it could be that in some cases you are

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:14:14.810 --> 00:14:21.020
<v Speaker 1>asked multiple choice question and suppose that, you know, there

NOTE CONF {"raw":[100,100,100,74,100,100,100,100,100,100]}

00:14:21.020 --> 00:14:24.200
<v Speaker 1>is a multiple choice question with exactly one answer.

NOTE CONF {"raw":[82,75,100,100,94,88,100,100,100]}

00:14:24.320 --> 00:14:28.100
<v Speaker 1>For example, suppose that your question such that the correct

NOTE CONF {"raw":[100,100,100,100,44,63,100,100,100,100]}

00:14:28.100 --> 00:14:31.460
<v Speaker 1>answer to this question is five and then you are

NOTE CONF {"raw":[100,100,100,100,100,90,100,100,97,95]}

00:14:31.460 --> 00:14:32.780
<v Speaker 1>asked to choose the correct answer.

NOTE CONF {"raw":[97,73,100,100,100,100]}

00:14:32.780 --> 00:14:36.560
<v Speaker 1>And there is a list of options, one of which

NOTE CONF {"raw":[100,100,100,74,100,100,100,100,100,100]}

00:14:36.710 --> 00:14:38.210
<v Speaker 1>is the correct option.

NOTE CONF {"raw":[100,100,100,98]}

00:14:38.240 --> 00:14:40.550
<v Speaker 1>So in this case, we know that the correct option

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:14:40.550 --> 00:14:41.150
<v Speaker 1>is five.

NOTE CONF {"raw":[100,100]}

00:14:41.780 --> 00:14:44.750
<v Speaker 1>And how do we choose this option is simply by

NOTE CONF {"raw":[100,100,100,100,100,100,100,50,100,100]}

00:14:44.750 --> 00:14:46.610
<v Speaker 1>clicking on the correct option five.

NOTE CONF {"raw":[100,94,100,100,100,98]}

00:14:47.030 --> 00:14:50.480
<v Speaker 1>And once you click on submit part, you see that

NOTE CONF {"raw":[100,100,100,100,100,100,82,95,100,100]}

00:14:50.780 --> 00:14:53.000
<v Speaker 1>you are getting the feedback that we have chosen a

NOTE CONF {"raw":[95,95,100,100,100,100,100,100,100,100]}

00:14:53.000 --> 00:14:53.810
<v Speaker 1>correct answer.

NOTE CONF {"raw":[100,100]}

00:14:54.320 --> 00:14:58.340
<v Speaker 1>Not is that in the case when the correct answer

NOTE CONF {"raw":[99,100,100,99,100,100,100,100,100,100]}

00:14:58.340 --> 00:14:59.610
<v Speaker 1>is only one out.

NOTE CONF {"raw":[100,97,100,83]}

00:14:59.690 --> 00:15:04.340
<v Speaker 1>Full list of options, actually, if I was to click

NOTE CONF {"raw":[75,100,100,100,100,100,100,99,100,100]}

00:15:04.340 --> 00:15:07.550
<v Speaker 1>on another option after having chosen five, for example, on

NOTE CONF {"raw":[100,100,100,100,100,100,95,100,100,100]}

00:15:07.550 --> 00:15:11.910
<v Speaker 1>the option to then my answer automatically is no longer

NOTE CONF {"raw":[100,100,100,100,97,85,100,100,100,100]}

00:15:11.930 --> 00:15:14.360
<v Speaker 1>five, but just the option to and once I submit

NOTE CONF {"raw":[100,100,99,100,100,100,56,55,100,100]}

00:15:14.660 --> 00:15:17.780
<v Speaker 1>part, I get zero because this is the correct answer.

NOTE CONF {"raw":[70,100,100,100,100,100,100,100,100,100]}

00:15:18.080 --> 00:15:20.810
<v Speaker 1>But if I click on five again and submit part,

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,48]}

00:15:21.320 --> 00:15:25.190
<v Speaker 0>I receiving the feedback that the answer is correct in

NOTE CONF {"raw":[100,100,100,100,100,99,100,100,99,100]}

00:15:25.190 --> 00:15:30.410
<v Speaker 0>another type of multiple choice question with only one answer,

NOTE CONF {"raw":[100,100,100,100,100,99,100,100,100,100]}

00:15:30.410 --> 00:15:34.190
<v Speaker 1>it could be that the correct answer, again, is only

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,90,99]}

00:15:34.190 --> 00:15:34.770
<v Speaker 1>one option.

NOTE CONF {"raw":[100,100]}

00:15:34.790 --> 00:15:39.340
<v Speaker 1>However, the options are given not through radio boxes he

NOTE CONF {"raw":[100,100,100,88,63,100,94,96,58,28]}

00:15:39.470 --> 00:15:44.190
<v Speaker 1>here, but the inner scroll down sort of menu.

NOTE CONF {"raw":[100,97,44,44,100,100,100,100,100]}

00:15:44.780 --> 00:15:46.850
<v Speaker 1>So for example, suppose that the correct answer to the

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:15:46.850 --> 00:15:48.200
<v Speaker 1>following question is straight.

NOTE CONF {"raw":[100,100,100,64]}

00:15:48.470 --> 00:15:52.100
<v Speaker 1>In order to choose the correct answer, I click on

NOTE CONF {"raw":[100,100,100,100,78,100,100,100,100,100]}

00:15:53.030 --> 00:15:55.280
<v Speaker 1>the menu and I click on the correct option three

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,77,74]}

00:15:55.340 --> 00:15:56.510
<v Speaker 1>and then submit part.

NOTE CONF {"raw":[100,100,100,92]}

00:15:57.410 --> 00:16:00.330
<v Speaker 1>And this turns out again to be the correct answer.

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:16:01.130 --> 00:16:04.310
<v Speaker 1>Now, in another variety of multiple choice questions, there could

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,97,100]}

00:16:04.310 --> 00:16:08.750
<v Speaker 1>be a number of correct answers to a list, to

NOTE CONF {"raw":[100,100,100,100,100,100,100,92,92,97]}

00:16:08.750 --> 00:16:09.290
<v Speaker 0>a question.

NOTE CONF {"raw":[100,100]}

00:16:09.290 --> 00:16:11.440
<v Speaker 1>And they are all given in the list of options.

NOTE CONF {"raw":[100,100,100,99,100,96,100,100,100,100]}

00:16:11.450 --> 00:16:16.850
<v Speaker 1>For example, consider the question, choose all the colours and

NOTE CONF {"raw":[100,100,99,100,100,99,99,100,52,100]}

00:16:16.850 --> 00:16:20.180
<v Speaker 1>the options are economics blue, red and apple.

NOTE CONF {"raw":[100,100,100,100,100,54,99,60]}

00:16:20.600 --> 00:16:23.330
<v Speaker 1>Now, amongst all these four options, there are two colours,

NOTE CONF {"raw":[100,88,79,100,100,100,99,100,100,100]}

00:16:23.330 --> 00:16:24.910
<v Speaker 1>blue and red.

NOTE CONF {"raw":[100,100,96]}

00:16:25.340 --> 00:16:29.180
<v Speaker 1>Now notice that the like the previous type of menu

NOTE CONF {"raw":[100,87,94,78,79,100,100,100,100,100]}

00:16:29.180 --> 00:16:32.700
<v Speaker 1>where there is only one correct answer, where the answers

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:16:32.810 --> 00:16:36.020
<v Speaker 1>are in radio boxes, the options are given in radio

NOTE CONF {"raw":[56,100,100,100,100,100,100,95,62,97]}

00:16:36.020 --> 00:16:39.800
<v Speaker 1>boxes here when multiple correct answers are possible.

NOTE CONF {"raw":[100,100,100,100,100,77,100,100]}

00:16:40.760 --> 00:16:44.240
<v Speaker 0>There are in fact squares, tick boxes that I have

NOTE CONF {"raw":[100,100,100,100,100,49,100,100,100,100]}

00:16:44.240 --> 00:16:44.720
<v Speaker 0>to take.

NOTE CONF {"raw":[100,79]}

00:16:45.170 --> 00:16:47.660
<v Speaker 0>Now, the two correct answers are blue and red and

NOTE CONF {"raw":[99,66,85,100,100,99,97,97,100,100]}

00:16:47.660 --> 00:16:50.330
<v Speaker 1>once I click on Submit McBath, I get one marked

NOTE CONF {"raw":[100,100,100,100,58,42,100,100,100,78]}

00:16:50.330 --> 00:16:51.220
<v Speaker 1>for this question.

NOTE CONF {"raw":[100,100,100]}

00:16:51.560 --> 00:16:54.020
<v Speaker 1>Now, if I was to only have selected one of

NOTE CONF {"raw":[100,100,100,95,100,100,100,100,100,100]}

00:16:54.020 --> 00:16:57.740
<v Speaker 1>the correct answers, this would be incorrect.

NOTE CONF {"raw":[100,100,100,100,97,100,100]}

00:16:58.280 --> 00:17:02.360
<v Speaker 1>Now let's turn attention to a slightly more interesting type

NOTE CONF {"raw":[100,100,100,67,100,93,100,100,100,100]}

00:17:02.360 --> 00:17:05.439
<v Speaker 1>of questions, which is questions where the correct answer is

NOTE CONF {"raw":[100,97,98,98,100,100,100,100,100,99]}

00:17:05.520 --> 00:17:05.990
<v Speaker 1>no.

NOTE CONF {"raw":[100]}

00:17:06.350 --> 00:17:08.870
<v Speaker 1>Such a question can come out of a situation such

NOTE CONF {"raw":[100,97,98,97,100,100,100,100,100,100]}

00:17:08.870 --> 00:17:11.900
<v Speaker 1>as the type of question asked in question one Yakir.

NOTE CONF {"raw":[100,95,100,100,79,75,96,100,100,89]}

00:17:11.900 --> 00:17:13.370
<v Speaker 1>The correct answer was no.

NOTE CONF {"raw":[100,100,100,100,91]}

00:17:15.319 --> 00:17:17.510
<v Speaker 0>Now, let's scroll down again.

NOTE CONF {"raw":[88,100,100,100,100]}

00:17:18.650 --> 00:17:21.959
<v Speaker 1>Now, suppose that the correct answer to a question is

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:17:21.959 --> 00:17:23.120
<v Speaker 1>the particular integer.

NOTE CONF {"raw":[62,100,100]}

00:17:24.319 --> 00:17:26.329
<v Speaker 1>So I suppose that the correct answer to the question

NOTE CONF {"raw":[99,67,100,100,100,100,100,100,100,100]}

00:17:26.329 --> 00:17:28.280
<v Speaker 1>is how to type in the correct answer.

NOTE CONF {"raw":[100,97,100,99,96,100,100,100]}

00:17:28.300 --> 00:17:31.040
<v Speaker 1>Well, in the answer box, I click on the answer

NOTE CONF {"raw":[49,91,100,100,100,100,100,100,100,100]}

00:17:31.040 --> 00:17:32.330
<v Speaker 1>box and I type five.

NOTE CONF {"raw":[100,99,100,98,70]}

00:17:33.560 --> 00:17:38.960
<v Speaker 0>If I click submit part, I identified that the answer

NOTE CONF {"raw":[100,100,100,33,93,99,99,100,100,100]}

00:17:38.960 --> 00:17:39.540
<v Speaker 1>is correct.

NOTE CONF {"raw":[100,100]}

00:17:40.010 --> 00:17:42.730
<v Speaker 1>Now, it could be similarly that the correct answer is

NOTE CONF {"raw":[100,100,100,100,79,100,100,100,100,99]}

00:17:42.740 --> 00:17:43.820
<v Speaker 1>a negative integer.

NOTE CONF {"raw":[88,100,100]}

00:17:44.030 --> 00:17:47.000
<v Speaker 1>If this is the case, I simply type in the

NOTE CONF {"raw":[100,100,100,100,100,100,100,98,98,100]}

00:17:47.000 --> 00:17:48.790
<v Speaker 1>negative integer from my keyboard.

NOTE CONF {"raw":[100,100,100,100,100]}

00:17:48.800 --> 00:17:50.660
<v Speaker 1>So if the correct answer is minus seven, when I

NOTE CONF {"raw":[100,95,100,100,100,100,100,35,51,100]}

00:17:50.660 --> 00:17:54.260
<v Speaker 1>type in minus seven and when I click on submit

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:17:54.260 --> 00:17:57.580
<v Speaker 0>part, my answer is evaluate.

NOTE CONF {"raw":[72,100,100,100,60]}

00:17:57.600 --> 00:17:58.160
<v Speaker 1>That's correct.

NOTE CONF {"raw":[98,100]}

00:17:58.160 --> 00:18:01.490
<v Speaker 1>If I had typed only seven, of course this would

NOTE CONF {"raw":[100,100,100,100,100,100,100,71,100,79]}

00:18:01.490 --> 00:18:02.660
<v Speaker 1>have been incorrect.

NOTE CONF {"raw":[100,100,100]}

00:18:02.660 --> 00:18:05.240
<v Speaker 1>So minus seven is the correct answer.

NOTE CONF {"raw":[100,100,100,100,100,100,100]}

00:18:07.700 --> 00:18:10.190
<v Speaker 1>Now in another type of question, the correct answer may

NOTE CONF {"raw":[100,97,100,100,100,95,100,100,100,78]}

00:18:10.200 --> 00:18:11.930
<v Speaker 1>be a number, which is a fraction.

NOTE CONF {"raw":[100,100,100,100,100,92,100]}

00:18:12.470 --> 00:18:15.170
<v Speaker 1>So suppose that the correct answer to a question is

NOTE CONF {"raw":[99,100,98,100,100,100,100,91,100,100]}

00:18:15.170 --> 00:18:17.240
<v Speaker 1>the fraction one over three, for example.

NOTE CONF {"raw":[100,100,100,100,100,100,100]}

00:18:17.240 --> 00:18:20.060
<v Speaker 0>This could be you may want to type such an

NOTE CONF {"raw":[100,100,100,100,64,100,100,99,100,100]}

00:18:20.060 --> 00:18:23.960
<v Speaker 1>answer to a question that says solve the linear equation

NOTE CONF {"raw":[100,100,97,100,100,99,98,99,100,100]}

00:18:23.960 --> 00:18:25.570
<v Speaker 1>three times X is equal to one.

NOTE CONF {"raw":[100,100,75,100,100,100,100]}

00:18:25.820 --> 00:18:26.810
<v Speaker 1>What is the answer for?

NOTE CONF {"raw":[100,100,100,100,51]}

00:18:27.140 --> 00:18:29.280
<v Speaker 1>Well, the answer is one over three.

NOTE CONF {"raw":[100,100,100,100,100,100,100]}

00:18:29.690 --> 00:18:34.010
<v Speaker 1>Well, the white type, the fraction, one over three is

NOTE CONF {"raw":[100,100,70,98,100,100,96,100,100,98]}

00:18:34.010 --> 00:18:40.270
<v Speaker 0>by one slash three where slash corresponds to divided.

NOTE CONF {"raw":[100,100,98,100,58,100,100,100,73]}

00:18:40.760 --> 00:18:45.230
<v Speaker 1>Notice that now next to the answer box, the rendering

NOTE CONF {"raw":[100,100,100,100,79,37,100,98,100,100]}

00:18:45.230 --> 00:18:52.070
<v Speaker 1>of the expression reveals an expression typed in, in fact

NOTE CONF {"raw":[100,100,100,100,100,100,94,97,100,100]}

00:18:52.070 --> 00:18:57.800
<v Speaker 1>in Lubbock, which is sort of prettier than one three.

NOTE CONF {"raw":[100,71,100,100,96,100,100,100,100,97]}

00:18:58.280 --> 00:19:02.720
<v Speaker 1>And if I submit part, I am going to reveal

NOTE CONF {"raw":[100,100,100,100,57,90,89,100,100,93]}

00:19:02.720 --> 00:19:07.580
<v Speaker 1>that the answer is correct so I can enter fractions

NOTE CONF {"raw":[100,100,100,100,98,100,100,99,90,100]}

00:19:07.850 --> 00:19:09.210
<v Speaker 1>in the answer boxes as well.

NOTE CONF {"raw":[100,100,100,100,100,100]}

00:19:09.230 --> 00:19:11.970
<v Speaker 1>And this is useful in many cases.

NOTE CONF {"raw":[79,100,100,100,100,100,100]}

00:19:12.380 --> 00:19:17.390
<v Speaker 0>Now notice that if a correct answer to a question

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,99,100]}

00:19:17.390 --> 00:19:20.510
<v Speaker 1>turns out to be a rational number, a fraction, then

NOTE CONF {"raw":[100,100,100,100,95,95,99,89,100,100]}

00:19:20.510 --> 00:19:24.530
<v Speaker 1>as best practise, you should indeed choose to type this

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:19:24.530 --> 00:19:25.370
<v Speaker 0>rational number.

NOTE CONF {"raw":[96,100]}

00:19:27.650 --> 00:19:32.420
<v Speaker 0>Now, in some cases, when the answer is a rational

NOTE CONF {"raw":[99,100,100,100,100,100,100,100,96,100]}

00:19:32.420 --> 00:19:35.300
<v Speaker 1>number, which could be expressed as a fraction, the quiz

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,96]}

00:19:35.300 --> 00:19:39.320
<v Speaker 1>may also allow you to type the answer in decimal

NOTE CONF {"raw":[99,100,100,100,100,100,100,100,100,100]}

00:19:39.320 --> 00:19:44.630
<v Speaker 1>form, subject to a certain specified precision.

NOTE CONF {"raw":[92,100,100,100,100,99,100]}

00:19:45.140 --> 00:19:48.920
<v Speaker 1>For example, this particular question is set to allow decimal

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:19:48.920 --> 00:19:54.740
<v Speaker 1>representation as long yes, we use at least two decimal

NOTE CONF {"raw":[100,95,100,57,100,99,100,100,100,100]}

00:19:54.740 --> 00:19:55.650
<v Speaker 1>points of precision.

NOTE CONF {"raw":[100,100,100]}

00:19:55.670 --> 00:19:57.680
<v Speaker 1>For example, if I was to type zero point three,

NOTE CONF {"raw":[100,100,100,100,99,68,93,100,100,99]}

00:19:57.680 --> 00:19:59.430
<v Speaker 1>three, three and four McPartlin.

NOTE CONF {"raw":[100,100,100,49,60]}

00:19:59.540 --> 00:20:02.390
<v Speaker 1>Will again be considered correct, or in fact, zero point

NOTE CONF {"raw":[93,100,100,100,100,97,100,100,100,100]}

00:20:02.690 --> 00:20:05.360
<v Speaker 1>three three will again be considered correct.

NOTE CONF {"raw":[94,100,88,100,100,100,100]}

00:20:05.390 --> 00:20:07.610
<v Speaker 1>However, if I was the only type zero point three,

NOTE CONF {"raw":[100,100,100,100,55,97,58,100,100,100]}

00:20:08.030 --> 00:20:14.930
<v Speaker 1>this would be considered incorrect, even if decimal four is

NOTE CONF {"raw":[100,90,100,100,100,100,100,100,48,100]}

00:20:14.930 --> 00:20:15.410
<v Speaker 1>allowed.

NOTE CONF {"raw":[100]}

00:20:15.560 --> 00:20:19.160
<v Speaker 1>However, as best practise, I would advise that if the

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:20:19.160 --> 00:20:21.410
<v Speaker 1>correct answer is a fraction, yes, you should use the

NOTE CONF {"raw":[100,100,100,100,100,45,100,100,98,100]}

00:20:21.410 --> 00:20:23.760
<v Speaker 1>capability of the quiz to type a fraction.

NOTE CONF {"raw":[100,100,100,90,90,98,99,99]}

00:20:24.080 --> 00:20:26.600
<v Speaker 1>And this also allows you not to use.

NOTE CONF {"raw":[100,100,100,100,100,100,100,100]}

00:20:27.200 --> 00:20:30.470
<v Speaker 0>There is basically this one reason when why using a

NOTE CONF {"raw":[62,91,98,100,100,100,100,75,100,99]}

00:20:30.470 --> 00:20:34.790
<v Speaker 1>calculator will not be necessary in many of the cases,

NOTE CONF {"raw":[100,100,100,100,100,92,100,100,100,100]}

00:20:34.790 --> 00:20:38.450
<v Speaker 1>because you can type your answers as fractions in this

NOTE CONF {"raw":[100,100,99,100,100,78,83,100,100,100]}

00:20:38.450 --> 00:20:41.420
<v Speaker 1>case and there is no need to evaluate the fraction

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:20:41.420 --> 00:20:43.040
<v Speaker 1>in terms of decimal representation.

NOTE CONF {"raw":[100,100,100,100,100]}

00:20:44.810 --> 00:20:53.290
<v Speaker 0>Now, another type of question may have May ELT's.

NOTE CONF {"raw":[97,100,100,100,100,98,100,78,34]}

00:20:53.330 --> 00:20:55.220
<v Speaker 1>It may be that the correct answer to a question

NOTE CONF {"raw":[100,99,99,100,100,100,100,100,100,100]}

00:20:55.220 --> 00:20:59.450
<v Speaker 1>is the number which is naturally represented in power for

NOTE CONF {"raw":[100,88,99,100,100,100,98,87,100,96]}

00:21:00.650 --> 00:21:03.050
<v Speaker 0>for example, it could be that the correct answer to

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:21:03.050 --> 00:21:03.470
<v Speaker 1>a question.

NOTE CONF {"raw":[96,100]}

00:21:03.470 --> 00:21:06.020
<v Speaker 1>You have obtained this 12 to the power of three,

NOTE CONF {"raw":[97,83,83,64,70,100,100,100,100,100]}

00:21:06.140 --> 00:21:09.780
<v Speaker 1>which of course also equals two one seven to eight.

NOTE CONF {"raw":[100,100,100,100,100,68,100,100,100,100]}

00:21:11.180 --> 00:21:15.230
<v Speaker 0>Now we can if the correct answer is in this

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:21:15.230 --> 00:21:17.840
<v Speaker 1>form, we can choose to type our answer either as

NOTE CONF {"raw":[100,88,100,100,100,100,100,100,100,100]}

00:21:17.870 --> 00:21:20.870
<v Speaker 1>one seven to eight, which is correct.

NOTE CONF {"raw":[99,100,99,98,100,100,100]}

00:21:21.680 --> 00:21:25.580
<v Speaker 1>But alternatively, we can simply type 12 to the power

NOTE CONF {"raw":[100,100,100,99,98,96,83,100,100,100]}

00:21:25.580 --> 00:21:26.120
<v Speaker 1>of three.

NOTE CONF {"raw":[100,100]}

00:21:27.170 --> 00:21:30.700
<v Speaker 0>So if in the context of your calculations, you arrive

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,90]}

00:21:31.370 --> 00:21:33.590
<v Speaker 1>to the situation where you know that the answer to

NOTE CONF {"raw":[100,100,100,100,100,99,100,100,100,100]}

00:21:33.590 --> 00:21:35.780
<v Speaker 1>a particular question is the number twelve to the power

NOTE CONF {"raw":[84,100,100,100,100,100,63,100,100,100]}

00:21:35.780 --> 00:21:37.970
<v Speaker 1>of three, there is no need to take out your

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,99]}

00:21:37.970 --> 00:21:41.240
<v Speaker 1>calculator and evaluate what to have the power of threes

NOTE CONF {"raw":[100,100,100,60,70,58,100,100,100,82]}

00:21:41.240 --> 00:21:44.390
<v Speaker 1>because you can simply type 12 to the power of

NOTE CONF {"raw":[100,100,100,100,100,78,100,100,100,100]}

00:21:44.390 --> 00:21:44.690
<v Speaker 0>three.

NOTE CONF {"raw":[100]}

00:21:45.200 --> 00:21:51.410
<v Speaker 0>Note that we use the symbol hat in order to

NOTE CONF {"raw":[61,100,99,100,100,58,90,100,100,100]}

00:21:53.750 --> 00:21:57.380
<v Speaker 1>in order to denote raising a number to a power

NOTE CONF {"raw":[100,100,100,100,100,62,98,100,96,100]}

00:21:57.380 --> 00:22:01.610
<v Speaker 1>in general in order to type the number eight to

NOTE CONF {"raw":[100,100,99,99,97,100,100,100,99,96]}

00:22:01.610 --> 00:22:02.510
<v Speaker 1>the power of B..

NOTE CONF {"raw":[100,100,100,83]}

00:22:02.780 --> 00:22:07.970
<v Speaker 1>We can type A, this symbol B, and this is

NOTE CONF {"raw":[100,100,98,78,100,100,70,100,100,100]}

00:22:07.970 --> 00:22:09.860
<v Speaker 1>going to hold the number eight to the power of

NOTE CONF {"raw":[100,100,51,94,98,95,100,100,100,100]}

00:22:09.860 --> 00:22:10.070
<v Speaker 0>B.

NOTE CONF {"raw":[63]}

00:22:10.760 --> 00:22:15.140
<v Speaker 1>Note is that the correct answer is rendered here.

NOTE CONF {"raw":[62,96,100,100,100,100,98,96,100]}

00:22:15.140 --> 00:22:15.770
<v Speaker 1>Exactly.

NOTE CONF {"raw":[100]}

00:22:15.770 --> 00:22:16.240
<v Speaker 1>On the right.

NOTE CONF {"raw":[100,100,100]}

00:22:16.250 --> 00:22:20.390
<v Speaker 1>You can see in the verification box that exactly what

NOTE CONF {"raw":[100,99,100,100,100,100,80,90,100,100]}

00:22:20.390 --> 00:22:22.820
<v Speaker 1>you typed is interpreted as 12th to the power of

NOTE CONF {"raw":[100,99,100,100,100,34,100,100,100,100]}

00:22:22.820 --> 00:22:23.230
<v Speaker 1>three.

NOTE CONF {"raw":[98]}

00:22:23.480 --> 00:22:24.680
<v Speaker 1>And this is useful.

NOTE CONF {"raw":[100,100,100,100]}

00:22:26.240 --> 00:22:30.400
<v Speaker 1>While you are getting used to the syntax of numbers,

NOTE CONF {"raw":[99,100,100,100,92,100,100,100,100,100]}

00:22:30.800 --> 00:22:32.810
<v Speaker 1>this is just so in order to verify that what

NOTE CONF {"raw":[100,100,71,74,100,100,100,100,100,100]}

00:22:32.810 --> 00:22:35.510
<v Speaker 1>you are typing is interpreted in the way that you

NOTE CONF {"raw":[51,51,100,100,98,99,100,100,100,99]}

00:22:35.510 --> 00:22:37.460
<v Speaker 1>would like it to be interpreted.

NOTE CONF {"raw":[99,100,99,100,100,100]}

00:22:38.180 --> 00:22:43.040
<v Speaker 0>Now, this use of power and notation is especially useful

NOTE CONF {"raw":[100,100,100,100,100,60,88,100,100,100]}

00:22:44.150 --> 00:22:48.560
<v Speaker 0>when the correct answer, for example, involves special numbers such

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,65,100]}

00:22:48.560 --> 00:22:52.280
<v Speaker 1>as Euler's constant e Euler's number.

NOTE CONF {"raw":[100,99,100,77,68,67]}

00:22:52.380 --> 00:22:56.420
<v Speaker 1>So suppose that the correct answer to a particular question

NOTE CONF {"raw":[100,100,91,100,100,100,100,99,100,100]}

00:22:56.420 --> 00:23:00.320
<v Speaker 1>is C to the power of five, where it is

NOTE CONF {"raw":[100,81,100,100,99,100,99,99,95,100]}

00:23:00.320 --> 00:23:03.380
<v Speaker 1>our last number, which is remember a number, approximately two

NOTE CONF {"raw":[100,93,100,100,100,100,100,100,100,100]}

00:23:03.380 --> 00:23:06.860
<v Speaker 1>point seven one eight two, etc..

NOTE CONF {"raw":[100,100,100,68,100,98]}

00:23:07.370 --> 00:23:11.060
<v Speaker 1>This is important council, which you often encounter in your

NOTE CONF {"raw":[100,100,100,79,100,85,100,100,100,100]}

00:23:11.060 --> 00:23:14.480
<v Speaker 1>study of both mathematics and economics.

NOTE CONF {"raw":[100,100,82,100,100,100]}

00:23:15.020 --> 00:23:19.070
<v Speaker 1>It turns out that for some special number, such as

NOTE CONF {"raw":[100,100,100,100,100,100,100,86,100,100]}

00:23:19.070 --> 00:23:23.960
<v Speaker 1>the number three numbers and in fact JMT, the programming

NOTE CONF {"raw":[100,92,84,100,100,100,100,24,99,100]}

00:23:23.960 --> 00:23:30.770
<v Speaker 1>language behind numbers actually N understands E yeah, it understands

NOTE CONF {"raw":[100,100,98,100,58,98,61,91,98,100]}

00:23:30.770 --> 00:23:33.170
<v Speaker 1>the number and you can type E to the power

NOTE CONF {"raw":[100,88,100,100,100,99,86,100,100,100]}

00:23:33.170 --> 00:23:36.860
<v Speaker 1>of five rather than taking your calculator and evaluating quality

NOTE CONF {"raw":[100,55,100,100,96,92,100,67,100,82]}

00:23:36.860 --> 00:23:37.750
<v Speaker 1>to the power of five.

NOTE CONF {"raw":[99,100,100,100,93]}

00:23:38.540 --> 00:23:42.680
<v Speaker 1>And once you submit part, your answer will be considered

NOTE CONF {"raw":[100,77,100,78,64,100,100,100,100,100]}

00:23:42.860 --> 00:23:43.430
<v Speaker 0>correct.

NOTE CONF {"raw":[100]}

00:23:44.930 --> 00:23:49.730
<v Speaker 1>Now this fact, the fact that you can type a

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:23:49.730 --> 00:23:55.280
<v Speaker 0>number mpower form is useful in the case when an

NOTE CONF {"raw":[96,52,81,99,100,100,100,100,100,100]}

00:23:55.280 --> 00:23:59.080
<v Speaker 1>answer to a question is some rules.

NOTE CONF {"raw":[100,100,100,100,93,100,40]}

00:23:59.900 --> 00:24:03.350
<v Speaker 0>For example, suppose that the answer to a particular question

NOTE CONF {"raw":[100,100,100,100,100,100,100,99,100,100]}

00:24:03.350 --> 00:24:06.990
<v Speaker 1>is the square root of two, which remember is equivalent

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,98,100]}

00:24:06.990 --> 00:24:09.280
<v Speaker 1>to to race to the power of one half.

NOTE CONF {"raw":[94,58,60,99,100,100,94,100,94]}

00:24:10.610 --> 00:24:13.340
<v Speaker 1>Then one way to type this answer is to pick

NOTE CONF {"raw":[99,100,99,100,99,100,100,100,100,100]}

00:24:13.340 --> 00:24:16.670
<v Speaker 1>your calculator, to calculate what the square root of two

NOTE CONF {"raw":[100,100,100,100,72,100,100,100,100,100]}

00:24:16.670 --> 00:24:18.740
<v Speaker 1>is, and you will see that it's something like one

NOTE CONF {"raw":[98,98,100,100,100,100,100,100,100,100]}

00:24:18.740 --> 00:24:22.340
<v Speaker 1>point four, one four, etc. and you can indeed type

NOTE CONF {"raw":[100,80,100,97,89,100,98,98,44,100]}

00:24:22.640 --> 00:24:24.910
<v Speaker 0>one point for one four.

NOTE CONF {"raw":[100,100,67,100,60]}

00:24:24.920 --> 00:24:30.470
<v Speaker 0>And if the answer if the question allows three decimal

NOTE CONF {"raw":[100,100,100,100,99,100,100,100,100,100]}

00:24:30.470 --> 00:24:33.080
<v Speaker 1>places of precision, this will be considered correct.

NOTE CONF {"raw":[100,100,100,98,92,100,100,100]}

00:24:33.110 --> 00:24:36.440
<v Speaker 1>In fact, this one allows even two decimal places of

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,94]}

00:24:36.440 --> 00:24:39.950
<v Speaker 1>precision, but one decimal places precision is not correct.

NOTE CONF {"raw":[100,100,100,100,100,100,99,100,100]}

00:24:40.970 --> 00:24:45.140
<v Speaker 0>However, a much more elegant way of typing a question

NOTE CONF {"raw":[100,98,100,100,100,100,100,68,99,100]}

00:24:45.140 --> 00:24:47.480
<v Speaker 1>like this is by using power notation.

NOTE CONF {"raw":[100,100,100,100,100,100,52]}

00:24:47.960 --> 00:24:50.450
<v Speaker 1>So, for example, if I was to type two to

NOTE CONF {"raw":[100,100,100,100,100,97,99,100,100,100]}

00:24:50.450 --> 00:24:57.980
<v Speaker 0>the power of one cuff type like this and interpret

NOTE CONF {"raw":[100,100,100,100,68,67,100,100,100,99]}

00:24:57.980 --> 00:24:58.730
<v Speaker 1>it like this.

NOTE CONF {"raw":[97,100,100]}

00:24:59.560 --> 00:25:02.650
<v Speaker 1>And if you submit part, you're going to see that

NOTE CONF {"raw":[100,62,99,100,56,64,100,100,100,100]}

00:25:02.650 --> 00:25:04.480
<v Speaker 1>the answer is accepted as correct.

NOTE CONF {"raw":[96,96,100,86,95,100]}

00:25:06.070 --> 00:25:10.750
<v Speaker 1>Now notice that I am using brackets around one over

NOTE CONF {"raw":[100,83,100,100,100,100,99,100,99,94]}

00:25:10.750 --> 00:25:15.510
<v Speaker 0>to here in order to tell the interpreter, the numbers

NOTE CONF {"raw":[88,95,100,100,100,100,100,100,100,100]}

00:25:15.520 --> 00:25:20.890
<v Speaker 1>interpreter that one over two is the fraction to which

NOTE CONF {"raw":[96,100,100,98,90,100,57,98,95,100]}

00:25:20.890 --> 00:25:22.510
<v Speaker 1>I raise the number two.

NOTE CONF {"raw":[94,50,100,100,91]}

00:25:22.930 --> 00:25:25.720
<v Speaker 1>Now, what would be true if I don't use brackets?

NOTE CONF {"raw":[100,100,100,100,70,100,100,100,100,100]}

00:25:26.770 --> 00:25:30.160
<v Speaker 1>If I don't use brackets because of the are there

NOTE CONF {"raw":[100,100,100,100,100,100,84,71,60,58]}

00:25:30.370 --> 00:25:33.880
<v Speaker 1>in the order of operation rising to power has precedence

NOTE CONF {"raw":[100,100,100,100,93,62,91,95,74,98]}

00:25:33.880 --> 00:25:38.110
<v Speaker 1>over division numbers, is going to interpret this expression I

NOTE CONF {"raw":[99,100,77,93,100,100,100,100,100,58]}

00:25:38.200 --> 00:25:41.430
<v Speaker 1>due to the power of one divided by two.

NOTE CONF {"raw":[45,99,100,100,100,100,100,100,100]}

00:25:41.650 --> 00:25:43.720
<v Speaker 1>And this would of course be an error.

NOTE CONF {"raw":[100,100,97,100,100,100,100,100]}

00:25:44.500 --> 00:25:52.120
<v Speaker 0>Therefore, I should be careful when using fractions and in

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:25:52.120 --> 00:25:58.450
<v Speaker 1>many other cases to respect the order of operations.

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100]}

00:25:58.720 --> 00:26:02.440
<v Speaker 1>And whenever there is a scope for interpretation, I should

NOTE CONF {"raw":[100,100,100,100,91,100,100,100,100,100]}

00:26:02.440 --> 00:26:05.040
<v Speaker 1>be careful to include brackets.

NOTE CONF {"raw":[100,100,100,100,100]}

00:26:05.320 --> 00:26:07.690
<v Speaker 1>So in order to type two to the power of

NOTE CONF {"raw":[100,99,85,80,79,92,100,100,100,98]}

00:26:07.690 --> 00:26:11.410
<v Speaker 0>one half, I type two to the power and then

NOTE CONF {"raw":[100,87,100,65,100,100,100,100,100,100]}

00:26:11.410 --> 00:26:15.220
<v Speaker 0>one half in brackets, this is the best way.

NOTE CONF {"raw":[99,84,100,100,100,100,100,100,100]}

00:26:15.790 --> 00:26:20.220
<v Speaker 0>Now notice that damn the programming language behind numbers.

NOTE CONF {"raw":[100,100,100,36,100,100,100,100,100]}

00:26:20.230 --> 00:26:23.140
<v Speaker 1>Also, he has an inbuilt function obscurity.

NOTE CONF {"raw":[100,72,100,100,100,100,74]}

00:26:25.510 --> 00:26:27.850
<v Speaker 1>And if you type obscurity and then in brackets a

NOTE CONF {"raw":[99,96,96,94,99,99,98,100,100,56]}

00:26:27.850 --> 00:26:31.150
<v Speaker 1>number, this is interpreted as the square root of the

NOTE CONF {"raw":[52,100,100,100,95,100,100,100,100,100]}

00:26:31.150 --> 00:26:34.000
<v Speaker 1>particular number and this is also the correct answer.

NOTE CONF {"raw":[100,100,100,42,95,100,100,100,100]}

00:26:34.870 --> 00:26:38.440
<v Speaker 1>However, as you can imagine, in many cases when there

NOTE CONF {"raw":[100,98,100,100,100,100,100,100,100,100]}

00:26:38.470 --> 00:26:41.200
<v Speaker 1>are rules, for example, if there are roots to other

NOTE CONF {"raw":[100,75,100,100,99,100,100,77,99,100]}

00:26:41.710 --> 00:26:46.570
<v Speaker 0>power other than two, there is no specific inbuilt function.

NOTE CONF {"raw":[100,100,100,55,100,100,100,100,85,100]}

00:26:46.570 --> 00:26:50.080
<v Speaker 1>And therefore something that will always work is to raise

NOTE CONF {"raw":[99,100,100,100,92,100,100,100,100,93]}

00:26:50.530 --> 00:26:53.980
<v Speaker 0>the number to the power that you would like it

NOTE CONF {"raw":[100,90,91,100,100,100,100,90,100,100]}

00:26:53.980 --> 00:26:54.780
<v Speaker 1>to be raised.

NOTE CONF {"raw":[100,100,98]}

00:26:55.270 --> 00:26:58.330
<v Speaker 0>And in this representation, you can type the correct answer

NOTE CONF {"raw":[99,100,100,100,100,99,96,100,100,100]}

00:26:58.330 --> 00:27:00.860
<v Speaker 0>to if the correct answer is square root.

NOTE CONF {"raw":[68,100,100,100,100,100,100,100]}

00:27:00.870 --> 00:27:03.910
<v Speaker 1>Two, not as an example of this.

NOTE CONF {"raw":[45,55,100,100,100,100,100]}

00:27:03.910 --> 00:27:06.760
<v Speaker 1>Suppose that the correct answer to a question is the

NOTE CONF {"raw":[99,100,100,100,100,100,77,100,100,100]}

00:27:06.760 --> 00:27:08.540
<v Speaker 0>cubic root of five.

NOTE CONF {"raw":[100,100,94,100]}

00:27:09.460 --> 00:27:14.620
<v Speaker 1>Now it turns out that there is an inbuilt function

NOTE CONF {"raw":[98,100,100,100,100,100,100,100,100,100]}

00:27:14.620 --> 00:27:18.010
<v Speaker 1>for a cubic root in numbers in Jammey, but I

NOTE CONF {"raw":[100,100,100,97,100,100,78,57,100,100]}

00:27:18.010 --> 00:27:18.820
<v Speaker 0>don't know it.

NOTE CONF {"raw":[100,100,100]}

00:27:19.810 --> 00:27:23.740
<v Speaker 1>Therefore, one way to type this number is to recognise

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,77]}

00:27:23.740 --> 00:27:27.040
<v Speaker 1>that the cubic root, the five is simply five race

NOTE CONF {"raw":[100,100,100,100,100,100,100,99,99,86]}

00:27:27.040 --> 00:27:29.090
<v Speaker 1>to the power of one over three.

NOTE CONF {"raw":[82,100,100,100,100,100,100]}

00:27:30.640 --> 00:27:34.480
<v Speaker 1>And if I submit this, this will evaluate the correct

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:27:34.480 --> 00:27:39.400
<v Speaker 1>answer because the given group, the five is just five

NOTE CONF {"raw":[100,100,100,92,97,83,77,99,100,98]}

00:27:39.400 --> 00:27:41.140
<v Speaker 1>raised to the power of one over three.

NOTE CONF {"raw":[55,100,100,100,98,99,98,99]}

00:27:42.730 --> 00:27:45.100
<v Speaker 1>Now, not is that in principle the correct group of

NOTE CONF {"raw":[100,76,64,100,100,99,99,91,99,68]}

00:27:45.100 --> 00:27:45.480
<v Speaker 1>five.

NOTE CONF {"raw":[96]}

00:27:45.480 --> 00:27:48.910
<v Speaker 1>This can be approximated as one point seven zero nine

NOTE CONF {"raw":[46,100,100,100,85,100,100,100,100,100]}

00:27:48.910 --> 00:27:52.300
<v Speaker 1>nine seven five nine, etc. But it turns out that

NOTE CONF {"raw":[100,100,100,100,77,100,100,100,100,100]}

00:27:52.300 --> 00:27:56.710
<v Speaker 1>this particular question is set not to allow decimal representation

NOTE CONF {"raw":[100,100,100,100,73,100,100,100,100,98]}

00:27:56.710 --> 00:27:57.480
<v Speaker 1>to any precision.

NOTE CONF {"raw":[93,100,100]}

00:27:57.490 --> 00:28:03.040
<v Speaker 1>So if I was to type the decimal representation to

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:28:03.040 --> 00:28:04.330
<v Speaker 1>a very high precision.

NOTE CONF {"raw":[100,100,100,100]}

00:28:08.010 --> 00:28:12.600
<v Speaker 0>Like this, it would still be none us is going

NOTE CONF {"raw":[100,100,100,93,100,100,42,44,99,100]}

00:28:12.600 --> 00:28:15.130
<v Speaker 1>to recognise that my answer is numerically correct.

NOTE CONF {"raw":[100,95,100,100,100,100,100,100]}

00:28:15.150 --> 00:28:18.930
<v Speaker 1>However, one mark is taken away because I should not

NOTE CONF {"raw":[100,88,92,97,99,100,100,100,100,100]}

00:28:19.170 --> 00:28:20.260
<v Speaker 0>use decimals.

NOTE CONF {"raw":[100,100]}

00:28:20.910 --> 00:28:25.890
<v Speaker 1>Now, if something like this happens in a question, usually

NOTE CONF {"raw":[100,100,100,100,100,100,100,97,100,100]}

00:28:25.890 --> 00:28:29.450
<v Speaker 1>most questions will be set to accept decimal representations.

NOTE CONF {"raw":[100,100,100,100,95,100,100,100,96]}

00:28:29.460 --> 00:28:32.190
<v Speaker 1>But if something like this happens in a question, then

NOTE CONF {"raw":[100,96,100,100,100,100,77,87,100,100]}

00:28:32.190 --> 00:28:35.280
<v Speaker 1>the feedback is going to allow you to understand that

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:28:35.280 --> 00:28:37.560
<v Speaker 1>in order to get the full score, you should you

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,97,100]}

00:28:37.560 --> 00:28:41.070
<v Speaker 1>are requested to type your answer not in a decimal,

NOTE CONF {"raw":[100,96,100,100,100,100,100,100,94,100]}

00:28:41.070 --> 00:28:44.460
<v Speaker 1>but in some other form where you give the correct

NOTE CONF {"raw":[100,99,100,100,97,100,100,100,100,100]}

00:28:45.210 --> 00:28:47.540
<v Speaker 1>number, which is five to the power of one over

NOTE CONF {"raw":[100,100,100,62,95,100,100,100,91,89]}

00:28:47.550 --> 00:28:47.800
<v Speaker 0>three.

NOTE CONF {"raw":[82]}

00:28:48.930 --> 00:28:52.170
<v Speaker 1>Now, in either case, where the answer could be a

NOTE CONF {"raw":[94,77,77,100,100,99,100,100,100,96]}

00:28:52.170 --> 00:28:55.740
<v Speaker 1>number, is that the answer could in fact be a

NOTE CONF {"raw":[96,100,100,95,95,100,100,100,100,100]}

00:28:55.740 --> 00:28:59.820
<v Speaker 0>logarithm and the logarithm of to a given base of

NOTE CONF {"raw":[100,100,98,100,93,100,83,84,100,100]}

00:28:59.820 --> 00:29:01.050
<v Speaker 1>some number is a number.

NOTE CONF {"raw":[100,100,99,91,100]}

00:29:01.080 --> 00:29:04.110
<v Speaker 1>So, for example, suppose that the correct answer to a

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:29:04.110 --> 00:29:08.160
<v Speaker 1>question is log to the base three of five, for

NOTE CONF {"raw":[100,100,41,100,100,98,100,70,100,100]}

00:29:08.160 --> 00:29:08.670
<v Speaker 0>example.

NOTE CONF {"raw":[100]}

00:29:08.850 --> 00:29:12.540
<v Speaker 0>A question that could have this as an answer is

NOTE CONF {"raw":[100,100,100,100,100,99,100,100,100,100]}

00:29:12.750 --> 00:29:13.980
<v Speaker 1>solve the equation.

NOTE CONF {"raw":[69,98,100]}

00:29:14.310 --> 00:29:16.510
<v Speaker 1>Three to the power of X is equal to five.

NOTE CONF {"raw":[100,91,100,100,100,100,100,100,100,100]}

00:29:17.000 --> 00:29:18.780
<v Speaker 0>Yeah, find X.

NOTE CONF {"raw":[85,100,72]}

00:29:19.020 --> 00:29:21.390
<v Speaker 1>The answer to this question will be exactly equal to

NOTE CONF {"raw":[100,100,100,99,100,98,100,100,100,100]}

00:29:21.750 --> 00:29:23.820
<v Speaker 1>lock to the base three of five.

NOTE CONF {"raw":[55,89,100,100,94,30,96]}

00:29:24.570 --> 00:29:29.130
<v Speaker 0>Now it turns out that and now this is a

NOTE CONF {"raw":[100,100,100,100,100,83,100,100,100,94]}

00:29:29.130 --> 00:29:33.450
<v Speaker 1>slightly more special syntax that you don't need to remember

NOTE CONF {"raw":[100,100,100,99,100,100,100,100,100,100]}

00:29:33.450 --> 00:29:38.040
<v Speaker 1>in general, because if you are expected to type a

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,96,100]}

00:29:38.040 --> 00:29:41.130
<v Speaker 1>longer answer in logarithm form in some of your questions,

NOTE CONF {"raw":[99,98,98,100,83,78,100,100,100,100]}

00:29:41.130 --> 00:29:44.790
<v Speaker 1>there will be a reminder in a hint button next

NOTE CONF {"raw":[96,100,100,100,100,100,92,100,83,100]}

00:29:44.790 --> 00:29:45.230
<v Speaker 0>to it.

NOTE CONF {"raw":[100,100]}

00:29:46.050 --> 00:29:51.330
<v Speaker 0>But in general, JMB allows that a logarithm of a

NOTE CONF {"raw":[100,100,100,52,100,100,97,99,100,93]}

00:29:51.330 --> 00:29:54.990
<v Speaker 0>number can be typed, in particular in the logarithm to

NOTE CONF {"raw":[93,100,100,81,95,95,91,100,100,100]}

00:29:54.990 --> 00:29:58.440
<v Speaker 1>the base rate of B for two constants, and B

NOTE CONF {"raw":[100,100,91,100,84,70,46,89,99,96]}

00:29:58.800 --> 00:30:00.480
<v Speaker 1>this can be typed as luck.

NOTE CONF {"raw":[100,100,100,86,73,37]}

00:30:01.110 --> 00:30:07.150
<v Speaker 0>B, comma, a song in particular type the number LOC

NOTE CONF {"raw":[90,99,100,80,51,99,100,100,98,33]}

00:30:07.170 --> 00:30:09.510
<v Speaker 1>to the base three of five I can type block

NOTE CONF {"raw":[69,100,98,100,51,100,100,98,100,66]}

00:30:10.740 --> 00:30:14.700
<v Speaker 0>of five to the base three and you can see

NOTE CONF {"raw":[52,100,100,100,99,71,100,100,100,100]}

00:30:15.330 --> 00:30:18.810
<v Speaker 0>in the next to the answer box in the rendering

NOTE CONF {"raw":[100,100,100,51,97,100,100,100,99,100]}

00:30:18.810 --> 00:30:21.740
<v Speaker 1>of the answer that this is exactly interpreted correctly as

NOTE CONF {"raw":[100,100,100,100,97,100,100,100,100,80]}

00:30:21.750 --> 00:30:23.110
<v Speaker 1>look to the base three of five.

NOTE CONF {"raw":[55,62,100,100,100,90,100]}

00:30:24.000 --> 00:30:28.140
<v Speaker 0>Now if you use your calculator you can find that

NOTE CONF {"raw":[100,100,100,100,93,100,100,100,100,100]}

00:30:28.140 --> 00:30:28.830
<v Speaker 1>lock to the base.

NOTE CONF {"raw":[35,100,100,100]}

00:30:28.830 --> 00:30:32.130
<v Speaker 1>Three of five is approximately one point four six four

NOTE CONF {"raw":[100,81,100,99,100,100,100,100,100,100]}

00:30:32.130 --> 00:30:32.960
<v Speaker 1>nine seven.

NOTE CONF {"raw":[100,100]}

00:30:33.150 --> 00:30:37.890
<v Speaker 1>And this particular question allows typing in decimal representation as

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:30:38.370 --> 00:30:40.590
<v Speaker 1>long as you use at least two decimal point.

NOTE CONF {"raw":[100,100,100,100,100,100,98,100,99]}

00:30:40.590 --> 00:30:43.200
<v Speaker 1>So I can type one point four six if I

NOTE CONF {"raw":[100,100,100,99,100,100,71,100,100,100]}

00:30:43.200 --> 00:30:45.740
<v Speaker 1>have used my calculator and found what the answer is.

NOTE CONF {"raw":[100,61,100,100,100,99,83,100,100,100]}

00:30:46.110 --> 00:30:50.070
<v Speaker 1>However, as best practise, if you're the answer to the

NOTE CONF {"raw":[100,100,100,100,100,73,100,100,100,55]}

00:30:50.070 --> 00:30:51.750
<v Speaker 1>question is up to the base three or five, I

NOTE CONF {"raw":[100,52,72,99,100,100,100,71,100,100]}

00:30:51.750 --> 00:30:55.740
<v Speaker 1>would encourage you to actually type it in its correct

NOTE CONF {"raw":[100,100,100,100,100,100,83,100,83,100]}

00:30:56.640 --> 00:30:57.240
<v Speaker 0>form.

NOTE CONF {"raw":[97]}

00:30:57.780 --> 00:31:00.960
<v Speaker 0>And there is this, again, one example that you don't

NOTE CONF {"raw":[100,94,93,100,78,100,100,100,100,100]}

00:31:00.960 --> 00:31:06.510
<v Speaker 1>need to use a calculator in many contexts because your

NOTE CONF {"raw":[100,100,100,97,100,100,100,99,100,100]}

00:31:06.510 --> 00:31:09.300
<v Speaker 1>computer is in fact a very powerful calculator.

NOTE CONF {"raw":[100,100,100,100,100,100,100,100]}

00:31:09.300 --> 00:31:14.400
<v Speaker 1>And the quizzes that you are using understand what looked

NOTE CONF {"raw":[95,100,100,100,97,97,100,100,100,66]}

00:31:14.460 --> 00:31:14.790
<v Speaker 1>at the base.

NOTE CONF {"raw":[66,100,84]}

00:31:14.790 --> 00:31:15.810
<v Speaker 1>Three of five is.

NOTE CONF {"raw":[83,86,91,99]}

00:31:17.400 --> 00:31:21.150
<v Speaker 1>Now, this is these are a number of situations where

NOTE CONF {"raw":[100,98,98,99,100,100,100,100,100,100]}

00:31:21.150 --> 00:31:23.340
<v Speaker 1>the correct answer to a question could be a number.

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,98]}

00:31:23.340 --> 00:31:29.210
<v Speaker 1>And I hope that this guidance hopefully allows we will

NOTE CONF {"raw":[100,100,100,100,99,100,100,100,62,84]}

00:31:29.210 --> 00:31:34.020
<v Speaker 1>allow you to type your answers correctly in pretty much

NOTE CONF {"raw":[100,100,100,100,100,97,100,98,100,100]}

00:31:34.020 --> 00:31:36.430
<v Speaker 1>every context where the correct answer is no.

NOTE CONF {"raw":[100,100,100,100,100,100,100,100]}

00:31:37.350 --> 00:31:44.880
<v Speaker 0>Now, a slightly more interesting case is questions where the

NOTE CONF {"raw":[99,91,100,100,100,100,100,100,95,100]}

00:31:44.880 --> 00:31:45.990
<v Speaker 1>correct answer is a..

NOTE CONF {"raw":[100,100,99,54]}

00:31:45.990 --> 00:31:47.160
<v Speaker 1>Jailbreak expression.

NOTE CONF {"raw":[77,100]}

00:31:47.160 --> 00:31:50.520
<v Speaker 1>That is an expression involving variables.

NOTE CONF {"raw":[100,100,100,100,92,100]}

00:31:51.510 --> 00:31:55.320
<v Speaker 1>Such type of questions can arise naturally in many contexts.

NOTE CONF {"raw":[100,98,100,100,100,100,100,100,100,100]}

00:31:55.330 --> 00:31:58.530
<v Speaker 1>For example, if you are given a particular function, the

NOTE CONF {"raw":[100,100,100,97,97,99,100,100,100,100]}

00:31:58.530 --> 00:32:00.180
<v Speaker 1>question could be right.

NOTE CONF {"raw":[100,100,100,71]}

00:32:00.180 --> 00:32:04.770
<v Speaker 0>The derivative of this function and then this derivative itself

NOTE CONF {"raw":[96,100,100,100,100,100,62,98,100,97]}

00:32:04.770 --> 00:32:07.710
<v Speaker 1>be a function which is going to involve some variables.

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,95]}

00:32:07.710 --> 00:32:11.490
<v Speaker 1>So the expression for the derivative will be a mathematical

NOTE CONF {"raw":[100,100,100,98,100,100,100,100,100,100]}

00:32:11.640 --> 00:32:12.310
<v Speaker 0>expression.

NOTE CONF {"raw":[100]}

00:32:13.080 --> 00:32:15.810
<v Speaker 1>So, for example, suppose that the correct answer to S

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,81]}

00:32:15.810 --> 00:32:18.110
<v Speaker 1>question is three X plus five.

NOTE CONF {"raw":[100,100,100,100,100,100]}

00:32:19.500 --> 00:32:21.750
<v Speaker 0>How do we type a correct answer?

NOTE CONF {"raw":[100,100,100,100,100,100,100]}

00:32:22.830 --> 00:32:25.000
<v Speaker 1>The correct answer if this is the correct answer.

NOTE CONF {"raw":[100,100,100,94,100,100,100,100,100]}

00:32:25.740 --> 00:32:32.970
<v Speaker 0>Now the way to type algebraic expressions in numbers is

NOTE CONF {"raw":[99,100,100,100,100,100,97,99,99,100]}

00:32:33.000 --> 00:32:35.120
<v Speaker 1>effectively the same approach.

NOTE CONF {"raw":[100,100,100,98]}

00:32:35.120 --> 00:32:37.260
<v Speaker 1>You should use the same syntax as you used to

NOTE CONF {"raw":[62,84,87,100,100,100,72,71,37,100]}

00:32:37.260 --> 00:32:43.620
<v Speaker 1>some graphical calculator, sorry, most programming languages or numerical packages

NOTE CONF {"raw":[71,100,95,86,100,100,100,100,100,99]}

00:32:43.620 --> 00:32:44.180
<v Speaker 1>out there.

NOTE CONF {"raw":[100,100]}

00:32:44.790 --> 00:32:49.220
<v Speaker 1>So pretty much the best practise to type three X

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,97]}

00:32:49.230 --> 00:32:55.530
<v Speaker 1>plus five is to type three times X plus five

NOTE CONF {"raw":[100,100,100,100,99,100,100,100,100,100]}

00:32:56.460 --> 00:32:57.960
<v Speaker 0>plus five.

NOTE CONF {"raw":[100,100]}

00:32:58.500 --> 00:33:00.960
<v Speaker 0>If I type this on the right, I see that

NOTE CONF {"raw":[100,100,76,100,100,100,100,100,100,100]}

00:33:00.960 --> 00:33:04.440
<v Speaker 1>my correct answer is interpreted as three X plus five

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:33:04.860 --> 00:33:06.090
<v Speaker 0>and if I submit BA.

NOTE CONF {"raw":[100,100,100,100,28]}

00:33:08.600 --> 00:33:12.670
<v Speaker 0>You can see that, indeed, my answer is found that

NOTE CONF {"raw":[100,100,96,100,100,100,100,100,100,61]}

00:33:12.680 --> 00:33:16.460
<v Speaker 1>to be numerically correct note is that in cases when

NOTE CONF {"raw":[100,100,99,100,49,60,100,100,98,97]}

00:33:16.460 --> 00:33:22.580
<v Speaker 1>the answer is algebraic expression, something that we can do

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:33:23.060 --> 00:33:25.220
<v Speaker 0>is equally correct.

NOTE CONF {"raw":[100,92,100]}

00:33:25.220 --> 00:33:28.940
<v Speaker 1>Answer would be an algebraic expression, which is basically equivalent

NOTE CONF {"raw":[100,89,100,100,100,100,100,100,21,100]}

00:33:28.940 --> 00:33:31.670
<v Speaker 1>to the given expression, for example, rather than three X

NOTE CONF {"raw":[100,98,93,100,100,100,100,100,100,100]}

00:33:31.670 --> 00:33:35.920
<v Speaker 1>plus five, we could have typed five plus three times

NOTE CONF {"raw":[100,100,100,100,99,80,100,100,100,77]}

00:33:36.560 --> 00:33:38.960
<v Speaker 1>and this would still be the correct answer.

NOTE CONF {"raw":[100,99,100,100,100,100,100,100]}

00:33:41.200 --> 00:33:44.620
<v Speaker 1>Or, in fact, five plus X times three, and this

NOTE CONF {"raw":[98,100,100,100,100,80,91,90,100,100]}

00:33:44.620 --> 00:33:48.070
<v Speaker 1>would still be the correct answer because this expressions are

NOTE CONF {"raw":[99,100,100,100,100,100,100,100,83,99]}

00:33:48.220 --> 00:33:48.880
<v Speaker 1>equivalent.

NOTE CONF {"raw":[100]}

00:33:49.630 --> 00:33:54.610
<v Speaker 0>Now notice that even though I recommend that you always

NOTE CONF {"raw":[100,93,100,100,100,100,100,100,100,100]}

00:33:54.610 --> 00:33:59.770
<v Speaker 1>are explicit in typing the multiplication sign in algebraic expressions,

NOTE CONF {"raw":[100,100,100,100,100,100,100,89,100,100]}

00:34:01.120 --> 00:34:05.860
<v Speaker 0>actually, in some cases, numbers will understand if you are

NOTE CONF {"raw":[100,100,100,100,100,91,100,100,100,94]}

00:34:05.860 --> 00:34:08.260
<v Speaker 0>mkt the multiplication sign.

NOTE CONF {"raw":[36,100,100,100]}

00:34:08.290 --> 00:34:11.889
<v Speaker 1>So if you just typed three X plus five, which

NOTE CONF {"raw":[100,100,100,100,67,100,100,100,100,100]}

00:34:12.159 --> 00:34:19.149
<v Speaker 1>I guess comes naturally in that context, the answer will

NOTE CONF {"raw":[100,100,100,100,88,69,100,100,100,100]}

00:34:19.149 --> 00:34:24.429
<v Speaker 1>be found to be numerically correct, because Jemmy understands that

NOTE CONF {"raw":[100,100,100,100,100,100,100,43,100,100]}

00:34:25.330 --> 00:34:27.909
<v Speaker 0>three x X is a variable and three X is

NOTE CONF {"raw":[100,95,100,96,98,100,100,100,100,100]}

00:34:27.909 --> 00:34:31.720
<v Speaker 1>not a very, very strict times the variable X because

NOTE CONF {"raw":[100,100,70,79,73,91,100,100,99,100]}

00:34:32.080 --> 00:34:35.040
<v Speaker 0>the name of a variable cannot start with the number

NOTE CONF {"raw":[100,100,100,100,100,98,100,100,94,98]}

00:34:35.050 --> 00:34:35.560
<v Speaker 1>pretty much.

NOTE CONF {"raw":[100,100]}

00:34:35.590 --> 00:34:38.620
<v Speaker 1>However, if I was to type X three plus five,

NOTE CONF {"raw":[100,100,100,100,55,100,100,100,100,100]}

00:34:38.830 --> 00:34:41.850
<v Speaker 1>this would be incorrectly interpreted.

NOTE CONF {"raw":[100,100,100,100,100]}

00:34:41.860 --> 00:34:44.290
<v Speaker 1>And that's why Y you are getting used to the

NOTE CONF {"raw":[100,100,100,93,99,100,100,96,100,100]}

00:34:44.290 --> 00:34:47.800
<v Speaker 1>precise rules for the syntax dialled visu to always be

NOTE CONF {"raw":[100,88,100,100,100,30,60,100,100,100]}

00:34:47.800 --> 00:34:52.720
<v Speaker 1>explicit and use the multiplication sign whenever there is a

NOTE CONF {"raw":[100,100,100,100,100,95,99,100,100,100]}

00:34:52.720 --> 00:34:53.500
<v Speaker 0>multiplication.

NOTE CONF {"raw":[100]}

00:34:54.190 --> 00:34:57.320
<v Speaker 1>Now let's consider something slightly more difficult.

NOTE CONF {"raw":[100,99,100,100,100,100,100]}

00:34:57.940 --> 00:35:00.490
<v Speaker 1>So suppose that the correct answer to a question is

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:35:00.640 --> 00:35:03.850
<v Speaker 1>the expression for X squared plus three X to the

NOTE CONF {"raw":[100,100,96,100,100,100,100,100,100,100]}

00:35:03.850 --> 00:35:06.850
<v Speaker 1>power of a half plus two over X.

NOTE CONF {"raw":[100,100,97,100,100,85,100,91]}

00:35:07.850 --> 00:35:10.080
<v Speaker 1>Now in order to type the correct answer to this,

NOTE CONF {"raw":[100,100,100,100,99,100,100,100,99,100]}

00:35:10.090 --> 00:35:15.160
<v Speaker 1>we followed the same rules as we follow for multiplication,

NOTE CONF {"raw":[100,63,100,100,100,100,100,100,90,100]}

00:35:15.160 --> 00:35:16.750
<v Speaker 1>raising to power and so forth.

NOTE CONF {"raw":[81,73,85,100,100,100]}

00:35:16.750 --> 00:35:20.020
<v Speaker 1>And in particular we type four times X to the

NOTE CONF {"raw":[100,100,100,92,96,100,100,100,99,100]}

00:35:20.020 --> 00:35:23.170
<v Speaker 0>power of two four four X squared and then we

NOTE CONF {"raw":[100,100,100,78,80,99,100,100,100,100]}

00:35:23.170 --> 00:35:27.940
<v Speaker 0>have plus three times X and we want to raise

NOTE CONF {"raw":[100,100,100,100,95,100,100,100,100,100]}

00:35:27.940 --> 00:35:29.820
<v Speaker 1>X to the power of one half.

NOTE CONF {"raw":[100,100,100,100,100,100,87]}

00:35:30.100 --> 00:35:35.230
<v Speaker 1>But remember that because if we do not include brackets

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:35:35.230 --> 00:35:40.540
<v Speaker 1>here, because racing to power, he has precedence over division

NOTE CONF {"raw":[100,100,65,92,99,60,69,73,73,100]}

00:35:40.540 --> 00:35:44.200
<v Speaker 1>in the order of operation, our answer is interpreted incorrectly.

NOTE CONF {"raw":[100,100,99,100,96,100,100,100,100,99]}

00:35:44.410 --> 00:35:46.360
<v Speaker 1>And in order to account for this, we would like

NOTE CONF {"raw":[73,100,100,100,100,100,100,100,100,100]}

00:35:46.360 --> 00:35:49.410
<v Speaker 1>to enclose the one over two in brackets.

NOTE CONF {"raw":[100,100,100,100,100,96,100,100]}

00:35:49.960 --> 00:35:53.770
<v Speaker 1>And then finally we have plus two divided by X

NOTE CONF {"raw":[100,100,100,92,100,100,100,100,100,92]}

00:35:53.770 --> 00:35:55.680
<v Speaker 1>in order to get to our X.

NOTE CONF {"raw":[100,100,100,100,100,56,69]}

00:35:56.200 --> 00:36:00.220
<v Speaker 0>Now, if we submit part, you can see that our

NOTE CONF {"raw":[100,100,100,100,63,100,100,100,100,100]}

00:36:00.220 --> 00:36:02.280
<v Speaker 1>answer is considered valid.

NOTE CONF {"raw":[100,100,100,100]}

00:36:02.710 --> 00:36:06.160
<v Speaker 1>Not is that if we had changed the order in

NOTE CONF {"raw":[77,77,100,100,100,82,100,100,100,100]}

00:36:06.160 --> 00:36:09.120
<v Speaker 1>which we entered the numbers, the expressions here.

NOTE CONF {"raw":[100,100,89,100,100,100,97,100]}

00:36:09.130 --> 00:36:11.500
<v Speaker 1>So if we had typed instead for X squared plus

NOTE CONF {"raw":[100,100,100,100,100,60,38,100,100,100]}

00:36:11.500 --> 00:36:13.510
<v Speaker 1>two over X plus three X to the power of

NOTE CONF {"raw":[100,79,100,100,100,100,100,100,100,100]}

00:36:13.510 --> 00:36:17.770
<v Speaker 1>one half, since this is an equivalent algebraically equivalent expression

NOTE CONF {"raw":[91,83,100,100,100,100,100,55,100,100]}

00:36:17.770 --> 00:36:20.740
<v Speaker 1>to the answer, if we submit that this would still

NOTE CONF {"raw":[100,99,100,100,100,98,61,100,100,100]}

00:36:20.740 --> 00:36:22.840
<v Speaker 1>be considered correct.

NOTE CONF {"raw":[100,100,100]}

00:36:24.590 --> 00:36:29.420
<v Speaker 0>Yeah, and again, the what we discussed before is still

NOTE CONF {"raw":[99,100,68,49,100,98,99,100,98,100]}

00:36:29.420 --> 00:36:32.570
<v Speaker 1>true, that, in fact, this multiplication science here are not,

NOTE CONF {"raw":[99,100,100,100,98,74,52,99,99,100]}

00:36:32.870 --> 00:36:35.330
<v Speaker 1>strictly speaking, necessary in this context.

NOTE CONF {"raw":[100,100,99,100,100,100]}

00:36:36.230 --> 00:36:41.910
<v Speaker 1>However, sometimes if we don't include the syntax, the multiplication

NOTE CONF {"raw":[100,100,100,100,93,99,100,51,100,100]}

00:36:41.910 --> 00:36:47.000
<v Speaker 1>in the syntax correctly, there could be a mis interpretation

NOTE CONF {"raw":[74,100,100,100,96,100,100,100,100,100]}

00:36:47.000 --> 00:36:48.440
<v Speaker 1>of what we are typing from numbers.

NOTE CONF {"raw":[100,100,100,100,100,100,100]}

00:36:48.470 --> 00:36:50.960
<v Speaker 1>That's why I would suggest that while you are getting

NOTE CONF {"raw":[92,100,100,100,100,100,71,73,100,100]}

00:36:50.960 --> 00:36:55.070
<v Speaker 1>used to typing your answers, you are explicit in typing

NOTE CONF {"raw":[100,100,99,85,88,100,100,100,100,100]}

00:36:55.190 --> 00:36:56.600
<v Speaker 1>the multiplication signs.

NOTE CONF {"raw":[100,100,84]}

00:36:57.860 --> 00:37:02.190
<v Speaker 1>Now let's consider something slightly more difficult.

NOTE CONF {"raw":[100,100,100,100,100,100,99]}

00:37:02.210 --> 00:37:07.760
<v Speaker 1>Now we have three times, six times in brackets, one

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:37:07.760 --> 00:37:10.550
<v Speaker 0>over two times six minus X over two.

NOTE CONF {"raw":[100,100,96,95,100,98,99,70]}

00:37:12.110 --> 00:37:14.100
<v Speaker 0>All rise to the power of a half.

NOTE CONF {"raw":[75,44,99,100,100,100,96,60]}

00:37:14.630 --> 00:37:16.910
<v Speaker 1>So in order to type this expression, we can type

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,96,100]}

00:37:16.910 --> 00:37:18.830
<v Speaker 1>three times, six times.

NOTE CONF {"raw":[100,99,100,100]}

00:37:19.310 --> 00:37:24.440
<v Speaker 0>Now, in brackets, what we have is one over two

NOTE CONF {"raw":[100,100,100,100,100,100,100,99,100,100]}

00:37:25.400 --> 00:37:27.800
<v Speaker 0>multiplied by X, and I would like to enclose the

NOTE CONF {"raw":[100,100,90,98,100,100,100,100,100,100]}

00:37:27.800 --> 00:37:32.180
<v Speaker 1>one over two in brackets in order to be certain

NOTE CONF {"raw":[100,100,98,100,100,100,100,100,100,100]}

00:37:33.080 --> 00:37:36.080
<v Speaker 0>that the one over to multiply sex and I have

NOTE CONF {"raw":[100,100,100,98,100,100,88,100,87,100]}

00:37:36.080 --> 00:37:38.000
<v Speaker 1>minus X to the power of two.

NOTE CONF {"raw":[100,100,100,100,100,100,100]}

00:37:38.420 --> 00:37:39.740
<v Speaker 1>This is inside the brackets.

NOTE CONF {"raw":[100,100,100,100,100]}

00:37:39.950 --> 00:37:42.980
<v Speaker 1>And now finally, I would like to race the whole

NOTE CONF {"raw":[100,100,100,100,100,100,100,49,100,86]}

00:37:42.980 --> 00:37:46.060
<v Speaker 1>term in brackets to the power of one over two.

NOTE CONF {"raw":[86,99,100,100,100,100,100,100,80,92]}

00:37:46.310 --> 00:37:50.300
<v Speaker 1>And this is one way to type the correct answer.

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:37:50.340 --> 00:37:53.540
<v Speaker 0>As you can see, you can go through the quiz

NOTE CONF {"raw":[100,100,100,100,100,99,100,100,100,71]}

00:37:53.540 --> 00:37:56.150
<v Speaker 1>on your own and you are going to notice a

NOTE CONF {"raw":[100,100,98,100,100,100,100,100,100,100]}

00:37:56.150 --> 00:38:01.730
<v Speaker 1>number of suggestions about how to type and what things

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,96]}

00:38:01.730 --> 00:38:02.660
<v Speaker 1>might not.

NOTE CONF {"raw":[100,100]}

00:38:03.810 --> 00:38:12.090
<v Speaker 0>Work and what will work, and you can try to

NOTE CONF {"raw":[100,100,100,99,100,100,100,100,100,60]}

00:38:12.090 --> 00:38:13.170
<v Speaker 1>squeeze this on your own.

NOTE CONF {"raw":[56,39,100,100,100]}

00:38:14.130 --> 00:38:16.410
<v Speaker 1>Now suppose that the correct answer is there would be

NOTE CONF {"raw":[100,100,100,100,100,100,100,91,52,50]}

00:38:16.440 --> 00:38:17.440
<v Speaker 1>a break fraction.

NOTE CONF {"raw":[77,91,94]}

00:38:18.030 --> 00:38:20.250
<v Speaker 1>Why do the power of two plus to a minus

NOTE CONF {"raw":[96,78,100,99,100,100,100,52,62,100]}

00:38:20.250 --> 00:38:25.500
<v Speaker 1>one in the numerator over Y plus two alter the

NOTE CONF {"raw":[100,100,100,100,100,83,100,85,86,100]}

00:38:25.500 --> 00:38:27.750
<v Speaker 1>power of two in the denominator?

NOTE CONF {"raw":[100,98,97,100,100,100]}

00:38:28.290 --> 00:38:31.940
<v Speaker 1>Now, this is slightly more exciting expression to type.

NOTE CONF {"raw":[100,100,100,100,100,100,100,96,100]}

00:38:31.950 --> 00:38:36.240
<v Speaker 0>So one way to go open brackets and type the

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,98,99]}

00:38:36.240 --> 00:38:39.960
<v Speaker 1>numerator y to the power of two plus two times

NOTE CONF {"raw":[100,97,99,100,100,100,100,100,100,100]}

00:38:39.960 --> 00:38:45.210
<v Speaker 1>Y minus one and now divide by the numerator.

NOTE CONF {"raw":[100,100,100,100,100,99,100,100,100]}

00:38:45.480 --> 00:38:49.800
<v Speaker 1>The denominator and the denominator is Y plus two to

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:38:49.800 --> 00:38:50.610
<v Speaker 0>the power of two.

NOTE CONF {"raw":[100,100,100,100]}

00:38:51.240 --> 00:38:54.690
<v Speaker 0>And you can see next to the Starbucks that this

NOTE CONF {"raw":[100,100,99,85,100,100,99,75,100,100]}

00:38:54.690 --> 00:38:56.360
<v Speaker 1>is indeed why they wanted to type.

NOTE CONF {"raw":[100,100,68,94,97,100,98]}

00:38:56.370 --> 00:38:59.430
<v Speaker 1>If I submit Barcia, you can see that this answer

NOTE CONF {"raw":[99,99,100,35,100,100,99,100,98,100]}

00:38:59.430 --> 00:39:01.610
<v Speaker 1>is incorrect.

NOTE CONF {"raw":[100,40]}

00:39:02.130 --> 00:39:04.470
<v Speaker 1>Now it turns out that this out there that I

NOTE CONF {"raw":[100,100,100,100,100,100,66,58,37,98]}

00:39:04.470 --> 00:39:09.540
<v Speaker 1>typed here are probably not necessary because raising to the

NOTE CONF {"raw":[98,100,100,100,100,100,100,71,62,100]}

00:39:09.540 --> 00:39:13.530
<v Speaker 1>bar has precedence over division in the order the operations,

NOTE CONF {"raw":[73,99,97,99,100,100,100,46,49,99]}

00:39:13.530 --> 00:39:16.950
<v Speaker 1>and therefore, even if I type without the lower brackets

NOTE CONF {"raw":[100,100,100,100,100,87,100,100,100,100]}

00:39:17.220 --> 00:39:20.580
<v Speaker 1>numbers, is going to correctly interpret the answer.

NOTE CONF {"raw":[99,99,100,100,100,99,100,100]}

00:39:20.940 --> 00:39:26.340
<v Speaker 1>However, if there is any scope for interpretation or misinterpretation,

NOTE CONF {"raw":[100,100,100,100,99,100,100,100,100,100]}

00:39:26.490 --> 00:39:29.670
<v Speaker 1>I would advise you if you have any doubts, be

NOTE CONF {"raw":[100,100,93,100,100,100,100,100,100,100]}

00:39:29.670 --> 00:39:33.510
<v Speaker 1>explicit and use brackets wherever you think that an issue

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:39:33.930 --> 00:39:34.890
<v Speaker 0>may arise.

NOTE CONF {"raw":[100,100]}

00:39:36.660 --> 00:39:39.720
<v Speaker 1>Now suppose that the correct answer is an algebraic expression,

NOTE CONF {"raw":[100,100,100,100,100,100,98,95,100,100]}

00:39:39.720 --> 00:39:43.770
<v Speaker 1>which in fact involves two variables X and Y.

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100]}

00:39:44.430 --> 00:39:46.920
<v Speaker 1>So in this case, the correct answer is X to

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:39:46.920 --> 00:39:49.770
<v Speaker 1>the power of two plus two times X, Y plus

NOTE CONF {"raw":[100,100,99,100,100,100,100,100,100,100]}

00:39:49.770 --> 00:39:50.850
<v Speaker 1>Y to the power of two.

NOTE CONF {"raw":[100,100,100,100,100,98]}

00:39:51.510 --> 00:39:54.810
<v Speaker 0>Now the correct answer, the correct way to type is

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:39:54.810 --> 00:39:59.040
<v Speaker 1>X to the power of two plus two times X

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:39:59.040 --> 00:40:03.020
<v Speaker 0>times Y plus Y to the power of two.

NOTE CONF {"raw":[100,100,100,100,100,100,100,99,99]}

00:40:04.470 --> 00:40:08.730
<v Speaker 0>If we submit the Bartons, surprisingly, our answer is correct.

NOTE CONF {"raw":[100,100,100,98,43,98,100,100,100,100]}

00:40:09.360 --> 00:40:12.840
<v Speaker 1>Now notice that if we had missed the first multiplication

NOTE CONF {"raw":[100,74,100,100,100,100,99,100,100,100]}

00:40:12.840 --> 00:40:17.190
<v Speaker 1>sign in two times, six times Y, and if we

NOTE CONF {"raw":[99,100,97,99,100,100,93,100,100,100]}

00:40:17.190 --> 00:40:20.790
<v Speaker 0>submitted the part, the answer would still be considered correct.

NOTE CONF {"raw":[100,100,93,100,100,100,100,100,100,100]}

00:40:20.820 --> 00:40:24.060
<v Speaker 1>Therefore, numbers would correctly understand that there is a multiplication

NOTE CONF {"raw":[99,100,99,100,89,100,100,99,93,100]}

00:40:24.060 --> 00:40:24.760
<v Speaker 1>sign here.

NOTE CONF {"raw":[95,100]}

00:40:25.170 --> 00:40:28.800
<v Speaker 1>However, if we had missed the second multiplication sign between

NOTE CONF {"raw":[100,100,100,100,100,100,95,100,98,100]}

00:40:28.800 --> 00:40:33.690
<v Speaker 1>X times Y, what is rendered here looks approximately more

NOTE CONF {"raw":[100,100,98,93,87,93,100,99,100,100]}

00:40:33.690 --> 00:40:36.240
<v Speaker 1>or less looks like what we want to hear.

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,70]}

00:40:36.510 --> 00:40:39.570
<v Speaker 1>However, if we submit that, we are going to find

NOTE CONF {"raw":[100,100,100,100,69,49,97,100,100,100]}

00:40:39.570 --> 00:40:41.010
<v Speaker 1>that your answer is incorrect.

NOTE CONF {"raw":[100,100,100,99,97]}

00:40:41.340 --> 00:40:43.920
<v Speaker 1>And the reason for this is that now numbers things

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,75,55]}

00:40:43.920 --> 00:40:48.870
<v Speaker 1>that X Y is a variable on its own, and

NOTE CONF {"raw":[100,100,100,100,100,100,100,98,99,100]}

00:40:48.870 --> 00:40:52.280
<v Speaker 0>this is one way in which a mistake could arise.

NOTE CONF {"raw":[94,100,100,100,100,100,94,100,100,100]}

00:40:52.290 --> 00:40:55.440
<v Speaker 1>And that's why this is yet another reason why when

NOTE CONF {"raw":[99,92,100,100,100,100,100,100,100,100]}

00:40:55.440 --> 00:40:58.890
<v Speaker 1>typing your answers, I would encourage you to be explicit

NOTE CONF {"raw":[99,100,98,100,100,100,100,100,100,100]}

00:40:59.460 --> 00:41:04.490
<v Speaker 0>in the use of multiplication signs and always type your

NOTE CONF {"raw":[100,100,100,100,100,55,100,100,93,99]}

00:41:04.500 --> 00:41:09.040
<v Speaker 1>answers in the way that you would find them in

NOTE CONF {"raw":[92,99,100,100,100,100,100,76,100,92]}

00:41:09.060 --> 00:41:11.100
<v Speaker 0>a graphical calculator.

NOTE CONF {"raw":[92,100,100]}

00:41:12.870 --> 00:41:16.560
<v Speaker 1>Now, there are a number of other examples here that

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:41:16.560 --> 00:41:19.360
<v Speaker 1>you can go over it on your own.

NOTE CONF {"raw":[100,100,100,100,86,100,100,100]}

00:41:19.380 --> 00:41:22.320
<v Speaker 1>Now, I want to turn attention to a few final

NOTE CONF {"raw":[98,100,100,100,100,100,100,100,100,100]}

00:41:22.350 --> 00:41:23.100
<v Speaker 1>remarks.

NOTE CONF {"raw":[100]}

00:41:23.760 --> 00:41:26.580
<v Speaker 1>In some situations, the correct answer could be an expression,

NOTE CONF {"raw":[100,99,100,100,100,100,99,100,100,100]}

00:41:26.580 --> 00:41:28.470
<v Speaker 1>which is in fact an equation.

NOTE CONF {"raw":[100,100,100,100,100,100]}

00:41:30.210 --> 00:41:33.960
<v Speaker 1>For example, in the context of optimising the function, you

NOTE CONF {"raw":[100,100,100,100,100,100,92,100,100,100]}

00:41:33.960 --> 00:41:36.600
<v Speaker 1>might be asked to write the first order condition for

NOTE CONF {"raw":[100,100,100,100,100,100,100,46,94,100]}

00:41:36.630 --> 00:41:37.580
<v Speaker 1>optimisation.

NOTE CONF {"raw":[90]}

00:41:38.010 --> 00:41:41.140
<v Speaker 1>The first order condition for optimisation will be an equation

NOTE CONF {"raw":[100,100,31,98,100,91,100,100,90,93]}

00:41:41.160 --> 00:41:43.790
<v Speaker 1>setting the first derivative of the function equal to zero.

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:41:44.490 --> 00:41:46.770
<v Speaker 0>And this is how a correct answer, which is an

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:41:46.770 --> 00:41:47.820
<v Speaker 1>equation, could arise.

NOTE CONF {"raw":[100,100,100]}

00:41:48.270 --> 00:41:50.850
<v Speaker 1>Now suppose that the correct answer is in fact an

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:41:50.850 --> 00:41:53.250
<v Speaker 1>equation X squared minus X minus two is equal to

NOTE CONF {"raw":[100,99,100,100,100,100,80,100,100,100]}

00:41:53.250 --> 00:41:53.610
<v Speaker 1>zero.

NOTE CONF {"raw":[100]}

00:41:53.620 --> 00:41:56.040
<v Speaker 0>Then the way we are going to type it is

NOTE CONF {"raw":[100,100,100,75,75,100,100,93,78,60]}

00:41:56.040 --> 00:41:59.940
<v Speaker 1>exactly as an expression equal to zero.

NOTE CONF {"raw":[100,91,100,100,100,100,100]}

00:42:01.140 --> 00:42:02.640
<v Speaker 1>And this would be the correct answer.

NOTE CONF {"raw":[100,100,60,100,100,100,100]}

00:42:02.670 --> 00:42:06.240
<v Speaker 1>However, what is important is to realise that the objects

NOTE CONF {"raw":[100,100,100,100,100,100,77,100,67,70]}

00:42:06.240 --> 00:42:09.240
<v Speaker 1>in question, if we had made the mistake and all

NOTE CONF {"raw":[86,86,100,99,73,78,99,100,100,94]}

00:42:09.240 --> 00:42:12.360
<v Speaker 1>included the left hand side without setting equal to zero,

NOTE CONF {"raw":[97,100,100,100,100,100,65,100,100,100]}

00:42:12.600 --> 00:42:14.280
<v Speaker 0>this would be incorrect.

NOTE CONF {"raw":[100,99,100,100]}

00:42:15.600 --> 00:42:19.230
<v Speaker 0>So we need to have equal to zero now.

NOTE CONF {"raw":[100,100,100,100,93,100,100,100,100]}

00:42:19.740 --> 00:42:25.440
<v Speaker 1>Similarly, the correct answer might involve inequalities, just like it

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:42:25.440 --> 00:42:29.460
<v Speaker 0>could involve equalities, it could involve inequalities.

NOTE CONF {"raw":[93,100,50,85,99,100,94]}

00:42:29.460 --> 00:42:35.670
<v Speaker 0>Now, in general, we use the type, the simple greater

NOTE CONF {"raw":[99,100,100,93,78,74,97,100,55,100]}

00:42:35.700 --> 00:42:39.780
<v Speaker 1>for greater than the simple less therefore less then and

NOTE CONF {"raw":[94,100,99,100,89,98,94,99,68,100]}

00:42:39.780 --> 00:42:41.580
<v Speaker 1>therefore greater than are equal.

NOTE CONF {"raw":[99,100,100,65,100]}

00:42:41.580 --> 00:42:45.840
<v Speaker 1>We should use that in sequence, the simple greater followed

NOTE CONF {"raw":[100,100,100,79,100,100,100,83,99,100]}

00:42:45.840 --> 00:42:48.750
<v Speaker 1>by an equality sine and for less than our equal.

NOTE CONF {"raw":[100,76,77,72,100,100,100,100,100,100]}

00:42:49.230 --> 00:42:52.650
<v Speaker 1>We are the symbol less then followed by inequality sine

NOTE CONF {"raw":[100,83,95,58,62,69,100,100,98,56]}

00:42:53.700 --> 00:42:57.510
<v Speaker 0>another rule with inequalities.

NOTE CONF {"raw":[100,74,99,100]}

00:42:58.080 --> 00:42:59.440
<v Speaker 1>I'm going to discuss in a bit.

NOTE CONF {"raw":[100,100,100,100,100,100,100]}

00:42:59.460 --> 00:43:02.520
<v Speaker 1>So suppose that the correct answer is to a question

NOTE CONF {"raw":[97,99,100,100,100,100,100,100,93,100]}

00:43:02.790 --> 00:43:03.150
<v Speaker 1>on any.

NOTE CONF {"raw":[86,28]}

00:43:03.280 --> 00:43:06.710
<v Speaker 1>Authority is greater than five, then the correct answer is

NOTE CONF {"raw":[29,41,100,100,100,72,100,100,100,100]}

00:43:06.710 --> 00:43:08.720
<v Speaker 1>type the six, greater than five.

NOTE CONF {"raw":[77,58,34,100,100,100]}

00:43:10.190 --> 00:43:13.340
<v Speaker 1>Now, if I had typed in correctly, X is greater

NOTE CONF {"raw":[100,100,100,97,100,61,61,100,100,100]}

00:43:13.340 --> 00:43:15.320
<v Speaker 1>than or equal to five, this would be incorrect.

NOTE CONF {"raw":[100,100,100,100,100,100,98,100,98]}

00:43:15.320 --> 00:43:17.510
<v Speaker 1>Or if I had typed let X is less than

NOTE CONF {"raw":[99,100,100,100,100,82,100,96,100,100]}

00:43:17.510 --> 00:43:17.940
<v Speaker 1>five.

NOTE CONF {"raw":[100]}

00:43:17.990 --> 00:43:20.900
<v Speaker 1>This would be incorrect if I had typed incorrectly.

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,70]}

00:43:21.140 --> 00:43:22.580
<v Speaker 1>X is greater than six.

NOTE CONF {"raw":[100,100,100,100,100]}

00:43:22.820 --> 00:43:24.470
<v Speaker 1>This would still be incorrect.

NOTE CONF {"raw":[100,98,100,100,100]}

00:43:24.480 --> 00:43:27.890
<v Speaker 1>So the correct answer is X is greater than five.

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:43:28.580 --> 00:43:30.830
<v Speaker 1>Now suppose that the correct answer is X is less

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:43:30.830 --> 00:43:33.080
<v Speaker 1>than or equal to minus three in order to type

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,70]}

00:43:33.080 --> 00:43:37.670
<v Speaker 1>this with type X less than equal minus three.

NOTE CONF {"raw":[100,83,92,98,100,79,100,100,100]}

00:43:38.190 --> 00:43:40.680
<v Speaker 1>And you can see that this is rendered.

NOTE CONF {"raw":[100,100,100,100,100,100,100,60]}

00:43:40.730 --> 00:43:41.270
<v Speaker 1>Exactly.

NOTE CONF {"raw":[100]}

00:43:41.270 --> 00:43:41.660
<v Speaker 0>Yes.

NOTE CONF {"raw":[71]}

00:43:41.960 --> 00:43:44.930
<v Speaker 0>Then we can equality that we want to have.

NOTE CONF {"raw":[86,86,86,94,100,100,100,100,100]}

00:43:45.920 --> 00:43:47.810
<v Speaker 0>And if we submit parts, we can see that the

NOTE CONF {"raw":[91,100,100,100,68,100,100,92,100,100]}

00:43:47.810 --> 00:43:48.480
<v Speaker 1>answer is correct.

NOTE CONF {"raw":[100,100,100]}

00:43:48.500 --> 00:43:51.410
<v Speaker 1>Now, if we had forgotten to add the equality sine

NOTE CONF {"raw":[100,100,100,94,100,90,86,100,75,69]}

00:43:51.420 --> 00:43:53.900
<v Speaker 1>then we had just type X is less than minus

NOTE CONF {"raw":[52,100,100,70,97,100,100,100,100,100]}

00:43:53.900 --> 00:43:54.190
<v Speaker 1>three.

NOTE CONF {"raw":[99]}

00:43:54.320 --> 00:43:55.830
<v Speaker 1>This would be incorrect.

NOTE CONF {"raw":[100,100,100,100]}

00:43:58.730 --> 00:44:01.690
<v Speaker 1>Now, in some occasions, an answer could be a set

NOTE CONF {"raw":[100,100,100,100,89,93,100,100,100,100]}

00:44:01.700 --> 00:44:04.150
<v Speaker 1>of values specified by inequalities.

NOTE CONF {"raw":[88,85,100,100,63]}

00:44:04.160 --> 00:44:07.790
<v Speaker 1>For example, suppose that the correct answer is all the

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:44:07.790 --> 00:44:10.880
<v Speaker 1>various effects between minus one and one.

NOTE CONF {"raw":[85,89,100,100,100,100,100]}

00:44:12.350 --> 00:44:12.980
<v Speaker 1>For example.

NOTE CONF {"raw":[100,100]}

00:44:12.980 --> 00:44:14.900
<v Speaker 1>This could be the answer to a question for what

NOTE CONF {"raw":[100,99,100,100,100,100,100,100,100,100]}

00:44:14.900 --> 00:44:18.800
<v Speaker 1>values effects is X minus one times X plus one

NOTE CONF {"raw":[98,54,100,100,100,100,100,100,100,95]}

00:44:18.800 --> 00:44:19.750
<v Speaker 1>less than zero.

NOTE CONF {"raw":[100,100,100]}

00:44:20.240 --> 00:44:22.760
<v Speaker 0>The answer to this is for values effects between minus

NOTE CONF {"raw":[100,100,91,96,100,82,52,60,100,100]}

00:44:22.760 --> 00:44:23.790
<v Speaker 1>one and one.

NOTE CONF {"raw":[100,100,100]}

00:44:24.260 --> 00:44:28.490
<v Speaker 0>So one way to type this is through the change.

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,58]}

00:44:28.520 --> 00:44:30.800
<v Speaker 1>Inequality, just like it appears minus one is less than

NOTE CONF {"raw":[52,100,100,100,99,100,100,95,100,100]}

00:44:30.800 --> 00:44:32.150
<v Speaker 1>X is less than one.

NOTE CONF {"raw":[100,100,100,100,100]}

00:44:35.570 --> 00:44:42.050
<v Speaker 1>And another way to type is as a logical union

NOTE CONF {"raw":[100,100,100,100,100,55,81,71,100,100]}

00:44:42.590 --> 00:44:46.280
<v Speaker 1>of two inequalities, so X is greater than minus one

NOTE CONF {"raw":[95,63,98,100,100,100,100,99,100,100]}

00:44:47.040 --> 00:44:51.080
<v Speaker 0>and at the same time X is less than one.

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:44:52.760 --> 00:44:55.440
<v Speaker 1>This is a correct representation.

NOTE CONF {"raw":[99,100,100,100,100]}

00:44:55.990 --> 00:45:01.010
<v Speaker 1>Not is that whenever there are sequences, sort of sex

NOTE CONF {"raw":[52,54,100,100,100,100,96,66,100,73]}

00:45:01.010 --> 00:45:03.980
<v Speaker 1>specified inequalities like this, we can make use of the

NOTE CONF {"raw":[87,73,100,100,100,95,100,100,100,100]}

00:45:03.980 --> 00:45:10.520
<v Speaker 1>logic cooperation operators and Antaria where and is the logical

NOTE CONF {"raw":[91,72,98,100,51,99,93,100,100,57]}

00:45:10.520 --> 00:45:12.680
<v Speaker 1>operation of our intersection of sets.

NOTE CONF {"raw":[68,61,42,100,100,61]}

00:45:12.950 --> 00:45:17.930
<v Speaker 1>And DA is the logical operator for a union of

NOTE CONF {"raw":[100,75,100,100,98,100,100,100,100,87]}

00:45:17.960 --> 00:45:18.410
<v Speaker 0>sets.

NOTE CONF {"raw":[85]}

00:45:18.800 --> 00:45:22.970
<v Speaker 0>And in this case we the set minus one to

NOTE CONF {"raw":[100,100,100,100,100,99,99,100,100,95]}

00:45:22.970 --> 00:45:30.110
<v Speaker 0>one can be understood as the the intersection of X

NOTE CONF {"raw":[100,86,100,100,100,100,100,100,100,100]}

00:45:30.110 --> 00:45:32.180
<v Speaker 1>greater than minus one and X less than one.

NOTE CONF {"raw":[100,100,100,100,100,87,100,100,100]}

00:45:32.180 --> 00:45:33.320
<v Speaker 1>And that's why we use the term.

NOTE CONF {"raw":[95,98,100,100,89,52,58]}

00:45:33.360 --> 00:45:37.190
<v Speaker 1>And but now suppose that the correct answer is X

NOTE CONF {"raw":[69,100,100,100,100,100,100,100,100,100]}

00:45:37.190 --> 00:45:41.420
<v Speaker 1>is less than minus one R, X is greater than

NOTE CONF {"raw":[100,100,96,100,100,71,100,100,100,100]}

00:45:41.420 --> 00:45:42.200
<v Speaker 1>one, for example.

NOTE CONF {"raw":[80,100,100]}

00:45:42.350 --> 00:45:44.690
<v Speaker 1>It's an answer to the question for what values the

NOTE CONF {"raw":[89,100,100,100,100,100,100,100,58,46]}

00:45:44.690 --> 00:45:48.020
<v Speaker 1>FXE X minus one times X plus one in fact

NOTE CONF {"raw":[78,100,100,100,100,100,100,100,100,100]}

00:45:48.020 --> 00:45:51.170
<v Speaker 1>greater than zero where it would be greater than zero

NOTE CONF {"raw":[100,100,100,69,99,65,100,100,100,100]}

00:45:51.170 --> 00:45:54.500
<v Speaker 1>if X is minus one are effects is greater than

NOTE CONF {"raw":[95,100,51,100,100,56,98,100,100,100]}

00:45:54.500 --> 00:45:57.590
<v Speaker 1>one, but not if it is between minus one and

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:45:57.590 --> 00:45:57.860
<v Speaker 1>one.

NOTE CONF {"raw":[100]}

00:45:58.400 --> 00:46:02.930
<v Speaker 0>And hear the correct way to type such an inequality

NOTE CONF {"raw":[100,51,100,100,100,100,100,100,93,100]}

00:46:02.930 --> 00:46:08.720
<v Speaker 1>will be X is less than minus one or X

NOTE CONF {"raw":[72,100,100,100,100,100,100,100,99,100]}

00:46:08.720 --> 00:46:10.170
<v Speaker 0>is greater than one.

NOTE CONF {"raw":[100,100,100,100]}

00:46:11.000 --> 00:46:15.920
<v Speaker 1>Notice the special word R which corresponds to a union

NOTE CONF {"raw":[99,100,100,90,63,100,100,100,100,100]}

00:46:16.280 --> 00:46:17.000
<v Speaker 0>affects.

NOTE CONF {"raw":[52]}

00:46:19.250 --> 00:46:23.780
<v Speaker 1>Now, usually for questions where the correct answer is inequality,

NOTE CONF {"raw":[100,100,52,100,98,100,100,100,99,63]}

00:46:23.840 --> 00:46:26.390
<v Speaker 1>our sense of inequality, so when there is more special

NOTE CONF {"raw":[93,91,100,84,60,100,99,100,100,98]}

00:46:26.410 --> 00:46:29.720
<v Speaker 1>syntax involved, there will be hints, buttons that are going

NOTE CONF {"raw":[89,100,90,100,100,34,72,100,100,100]}

00:46:29.720 --> 00:46:31.970
<v Speaker 1>to remind you about the special use of are.

NOTE CONF {"raw":[100,100,100,100,100,99,100,91,30]}

00:46:31.970 --> 00:46:35.900
<v Speaker 1>And then there therefore is not something you have to

NOTE CONF {"raw":[40,46,96,100,36,100,100,100,100,100]}

00:46:35.900 --> 00:46:37.820
<v Speaker 1>remember off the top of your head.

NOTE CONF {"raw":[100,79,100,100,100,100,98]}

00:46:38.180 --> 00:46:42.440
<v Speaker 0>But it could be that the answer some some questions

NOTE CONF {"raw":[100,100,100,100,100,100,100,87,100,100]}

00:46:42.440 --> 00:46:46.760
<v Speaker 1>will involve ants and thoughts now as the final thing

NOTE CONF {"raw":[100,100,87,99,50,100,100,74,100,100]}

00:46:46.760 --> 00:46:47.540
<v Speaker 1>to focus on.

NOTE CONF {"raw":[100,100,100]}

00:46:47.960 --> 00:46:51.680
<v Speaker 1>In some situations, there will be questions where the correct

NOTE CONF {"raw":[100,100,100,100,100,100,100,99,100,100]}

00:46:51.680 --> 00:46:53.360
<v Speaker 1>answer will be a matrix.

NOTE CONF {"raw":[100,100,100,100,100]}

00:46:54.050 --> 00:46:57.890
<v Speaker 0>For example, suppose that the correct answer is in particular

NOTE CONF {"raw":[100,100,100,100,100,100,78,60,100,100]}

00:46:57.890 --> 00:47:00.230
<v Speaker 1>in the topic of linear algebra.

NOTE CONF {"raw":[85,78,100,100,100,100]}

00:47:00.290 --> 00:47:02.240
<v Speaker 1>Naturally, the answer could be a matrix.

NOTE CONF {"raw":[100,100,100,100,100,100,98]}

00:47:02.240 --> 00:47:06.130
<v Speaker 1>I suppose that we need to input the Matrix with

NOTE CONF {"raw":[89,100,100,100,100,97,49,100,100,100]}

00:47:06.140 --> 00:47:08.600
<v Speaker 1>first row one, two and three and next row four

NOTE CONF {"raw":[99,55,100,100,100,100,100,100,82,91]}

00:47:08.600 --> 00:47:10.670
<v Speaker 1>or five and six, a two by three matrix.

NOTE CONF {"raw":[88,100,100,100,28,100,100,100,100]}

00:47:11.240 --> 00:47:15.380
<v Speaker 0>Then very intuitively, the our box could be a matrix

NOTE CONF {"raw":[100,100,100,27,45,89,100,100,100,100]}

00:47:15.380 --> 00:47:18.980
<v Speaker 1>itself of the correct order, the correct dimension.

NOTE CONF {"raw":[100,100,98,100,82,100,100,93]}

00:47:18.980 --> 00:47:21.680
<v Speaker 1>And we can type in our answer by filling in

NOTE CONF {"raw":[99,100,100,98,98,100,100,100,100,100]}

00:47:22.760 --> 00:47:26.090
<v Speaker 0>the boxes inside the Matrix, the elements of the Matrix.

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:47:28.520 --> 00:47:32.210
<v Speaker 0>However, it could be in some cases, the answer is

NOTE CONF {"raw":[99,100,100,100,100,100,100,100,100,97]}

00:47:32.210 --> 00:47:35.390
<v Speaker 1>not going to reveal what is that is going to

NOTE CONF {"raw":[100,100,100,93,92,96,80,99,100,100]}

00:47:35.390 --> 00:47:37.430
<v Speaker 1>reveal that the correct answer is the matrix, but not

NOTE CONF {"raw":[99,100,100,100,100,100,100,100,100,100]}

00:47:37.430 --> 00:47:39.040
<v Speaker 1>what is the dimension of the matrix.

NOTE CONF {"raw":[100,100,100,100,100,100,100]}

00:47:39.050 --> 00:47:41.960
<v Speaker 1>And in this case, the answer will be specified in

NOTE CONF {"raw":[93,100,100,100,100,100,98,100,100,100]}

00:47:41.960 --> 00:47:44.420
<v Speaker 1>the form of something like this, where you need to

NOTE CONF {"raw":[100,100,100,100,100,100,60,64,64,100]}

00:47:44.420 --> 00:47:47.690
<v Speaker 0>choose what is the number of rows and to set

NOTE CONF {"raw":[100,99,100,100,100,98,30,100,100,100]}

00:47:47.690 --> 00:47:51.170
<v Speaker 1>the number of columns in order to fill in the

NOTE CONF {"raw":[100,100,100,100,100,100,100,97,94,100]}

00:47:51.170 --> 00:47:51.860
<v Speaker 1>correct answer.

NOTE CONF {"raw":[100,55]}

00:47:51.920 --> 00:47:57.500
<v Speaker 1>So in this particular case, we have one, two, three,

NOTE CONF {"raw":[63,100,100,100,100,100,99,100,100,100]}

00:47:57.710 --> 00:47:59.240
<v Speaker 0>four, five, six.

NOTE CONF {"raw":[100,100,100]}

00:47:59.690 --> 00:48:02.280
<v Speaker 1>And once we submit parts, we are done.

NOTE CONF {"raw":[100,100,100,100,65,100,100,100]}

00:48:03.110 --> 00:48:05.280
<v Speaker 1>So this is our question two.

NOTE CONF {"raw":[100,100,100,41,99,41]}

00:48:05.300 --> 00:48:08.210
<v Speaker 1>Now, I notice that somewhere I have left an incorrectly

NOTE CONF {"raw":[100,100,56,100,100,100,100,100,45,100]}

00:48:09.410 --> 00:48:11.060
<v Speaker 1>answered question.

NOTE CONF {"raw":[90,97]}

00:48:11.060 --> 00:48:12.260
<v Speaker 0>So let's do this.

NOTE CONF {"raw":[100,99,98,100]}

00:48:24.020 --> 00:48:30.740
<v Speaker 0>And pretty much this is how you input answers for

NOTE CONF {"raw":[100,100,100,100,100,100,95,99,100,100]}

00:48:31.130 --> 00:48:33.770
<v Speaker 1>many different types of questions into numbers.

NOTE CONF {"raw":[100,100,100,100,100,73,96]}

00:48:34.340 --> 00:48:39.260
<v Speaker 0>Now, if you at some point you have issues with

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:48:39.260 --> 00:48:42.830
<v Speaker 1>inputting your answers to numbers, I suggest at any point

NOTE CONF {"raw":[87,100,100,100,100,90,99,84,100,100]}

00:48:42.830 --> 00:48:45.920
<v Speaker 1>you can return back to this question and look through

NOTE CONF {"raw":[100,99,100,100,100,99,52,100,100,99]}

00:48:45.920 --> 00:48:49.670
<v Speaker 0>the rules that are discussed throughout the quiz about how

NOTE CONF {"raw":[100,99,100,100,100,100,100,92,100,100]}

00:48:49.670 --> 00:48:50.650
<v Speaker 1>to improve your answer.

NOTE CONF {"raw":[100,100,100,98]}

00:48:50.710 --> 00:48:53.510
<v Speaker 1>So alternatively, you can take a look at the cheat

NOTE CONF {"raw":[51,100,100,100,100,100,100,100,100,100]}

00:48:53.510 --> 00:48:57.530
<v Speaker 1>sheet available on the model page at the same point

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:48:58.580 --> 00:49:04.640
<v Speaker 1>where the quizzes, which has a number of suggested syntaxes

NOTE CONF {"raw":[100,100,99,100,100,98,100,100,93,99]}

00:49:05.000 --> 00:49:07.550
<v Speaker 1>for possible answers that you might want to get.

NOTE CONF {"raw":[84,100,100,100,100,100,100,100,61]}

00:49:08.510 --> 00:49:12.200
<v Speaker 1>Now, a final point I would like to raise is

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,99,100]}

00:49:12.200 --> 00:49:16.670
<v Speaker 0>that some questions that you encountered during this course could

NOTE CONF {"raw":[100,100,100,100,100,87,100,100,82,100]}

00:49:16.670 --> 00:49:19.670
<v Speaker 1>be like question three in this video.

NOTE CONF {"raw":[100,100,94,97,88,100,100]}

00:49:20.120 --> 00:49:20.830
<v Speaker 1>In this quiz.

NOTE CONF {"raw":[100,100,100]}

00:49:20.840 --> 00:49:24.350
<v Speaker 1>That is a multipart question question to ask.

NOTE CONF {"raw":[100,100,100,100,100,100,57,33]}

00:49:24.380 --> 00:49:25.760
<v Speaker 1>Also a multipart question.

NOTE CONF {"raw":[100,95,100,100]}

00:49:25.770 --> 00:49:26.750
<v Speaker 1>There are many parts.

NOTE CONF {"raw":[100,100,100,93]}

00:49:27.050 --> 00:49:30.470
<v Speaker 1>However, it could be a multipart question where some of

NOTE CONF {"raw":[100,100,100,100,100,100,100,97,99,100]}

00:49:30.470 --> 00:49:34.040
<v Speaker 1>the parts are hidden and only become hidden once you

NOTE CONF {"raw":[100,100,100,100,100,100,99,52,100,100]}

00:49:34.040 --> 00:49:35.610
<v Speaker 0>do the first part.

NOTE CONF {"raw":[100,100,100,100]}

00:49:35.630 --> 00:49:39.750
<v Speaker 0>For example, consider the following question.

NOTE CONF {"raw":[100,100,100,100,100,92]}

00:49:39.770 --> 00:49:46.070
<v Speaker 1>So suppose that consider the set apple orange, blue and

NOTE CONF {"raw":[100,100,100,84,100,63,96,100,98,100]}

00:49:46.070 --> 00:49:47.900
<v Speaker 0>to offset the farthings.

NOTE CONF {"raw":[98,100,100,36]}

00:49:48.590 --> 00:49:50.720
<v Speaker 1>And the question is how many of the elements in

NOTE CONF {"raw":[100,100,100,100,100,100,100,99,100,100]}

00:49:50.720 --> 00:49:53.080
<v Speaker 1>this set corresponds to a colour?

NOTE CONF {"raw":[100,100,61,100,99,80]}

00:49:53.660 --> 00:49:56.690
<v Speaker 1>Now, within this set there are two colour Sorrenti and

NOTE CONF {"raw":[100,100,58,100,100,100,99,60,58,99]}

00:49:56.990 --> 00:49:59.300
<v Speaker 1>therefore the correct answer to this part of the question

NOTE CONF {"raw":[100,100,100,100,100,87,84,100,100,100]}

00:49:59.300 --> 00:50:03.710
<v Speaker 1>is to once I submit the part, you will notice

NOTE CONF {"raw":[100,69,100,100,99,100,96,98,98,99]}

00:50:03.710 --> 00:50:08.150
<v Speaker 0>that I have only answered correctly two out of two

NOTE CONF {"raw":[100,100,99,96,100,100,100,100,100,100]}

00:50:08.150 --> 00:50:10.070
<v Speaker 1>points for the first part of the question, but we

NOTE CONF {"raw":[100,60,100,100,100,100,100,100,100,62]}

00:50:10.070 --> 00:50:12.170
<v Speaker 1>have not gotten the full score for the question.

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,99]}

00:50:12.170 --> 00:50:14.270
<v Speaker 1>In order to get the full score, I need to

NOTE CONF {"raw":[100,100,100,100,100,99,100,100,100,100]}

00:50:14.270 --> 00:50:16.790
<v Speaker 0>click under what to do next.

NOTE CONF {"raw":[100,65,100,100,100,100]}

00:50:16.790 --> 00:50:19.260
<v Speaker 1>I need to click on part two and once I

NOTE CONF {"raw":[100,100,100,100,100,70,86,98,100,88]}

00:50:19.260 --> 00:50:23.990
<v Speaker 1>am at part two, this is where I am asked

NOTE CONF {"raw":[72,41,97,92,100,100,100,100,75,100]}

00:50:24.200 --> 00:50:26.690
<v Speaker 0>our next part of the question for the full marks.

NOTE CONF {"raw":[94,100,100,100,100,100,100,100,100,100]}

00:50:26.930 --> 00:50:30.800
<v Speaker 1>For example, here, choose all the colours and the correct

NOTE CONF {"raw":[100,100,100,99,98,100,97,100,100,100]}

00:50:31.070 --> 00:50:35.090
<v Speaker 1>answers are blue and orange in this amongst these four

NOTE CONF {"raw":[99,99,100,100,84,42,100,84,95,100]}

00:50:35.090 --> 00:50:35.510
<v Speaker 1>elements.

NOTE CONF {"raw":[100]}

00:50:35.510 --> 00:50:40.340
<v Speaker 1>And once I submit part now, I have completed the

NOTE CONF {"raw":[99,80,100,100,52,100,100,100,100,100]}

00:50:40.670 --> 00:50:44.720
<v Speaker 0>question three in total, I have received all the marks

NOTE CONF {"raw":[100,100,100,94,100,100,100,100,100,100]}

00:50:45.500 --> 00:50:49.280
<v Speaker 0>and as you can see, I have received twenty nine

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:50:49.280 --> 00:50:52.030
<v Speaker 1>out of twenty nine on this quiz.

NOTE CONF {"raw":[100,100,100,100,100,100,97]}

00:50:52.940 --> 00:50:57.470
<v Speaker 1>Now, once you are finished with the quiz you should

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:50:57.470 --> 00:50:59.000
<v Speaker 1>click on and exam.

NOTE CONF {"raw":[100,100,90,98]}

00:51:02.380 --> 00:51:04.630
<v Speaker 1>And following this, you are going to get to a

NOTE CONF {"raw":[100,100,100,84,91,100,100,100,97,97]}

00:51:04.630 --> 00:51:09.100
<v Speaker 1>place like this where you have the option to print

NOTE CONF {"raw":[52,100,100,100,100,100,100,100,100,100]}

00:51:09.820 --> 00:51:13.240
<v Speaker 1>the results, for example, into a PDF file of your

NOTE CONF {"raw":[100,100,100,100,96,100,100,100,99,100]}

00:51:13.240 --> 00:51:18.340
<v Speaker 0>attempt in a PDF, in a PDF file for your

NOTE CONF {"raw":[90,100,100,100,100,100,100,100,100,100]}

00:51:18.340 --> 00:51:22.210
<v Speaker 1>later records, for example, when this way you can save

NOTE CONF {"raw":[100,100,100,100,56,100,100,100,100,94]}

00:51:22.420 --> 00:51:23.140
<v Speaker 0>your answer.

NOTE CONF {"raw":[100,100]}

00:51:25.990 --> 00:51:29.140
<v Speaker 0>Now, notice that if the quiz that you are doing

NOTE CONF {"raw":[100,89,100,100,100,23,100,100,100,100]}

00:51:29.140 --> 00:51:35.620
<v Speaker 1>is a diagnostic quiz, then your score will be recorded

NOTE CONF {"raw":[94,99,100,100,100,100,98,100,100,100]}

00:51:35.620 --> 00:51:36.620
<v Speaker 1>on the model page.

NOTE CONF {"raw":[98,100,100,100]}

00:51:38.350 --> 00:51:41.740
<v Speaker 0>However, for all the other quizzes, there will be no

NOTE CONF {"raw":[100,100,100,100,100,99,100,100,100,100]}

00:51:41.740 --> 00:51:43.000
<v Speaker 1>record on the model page.

NOTE CONF {"raw":[69,93,100,90,81]}

00:51:43.000 --> 00:51:45.520
<v Speaker 1>And after you are finished with the quiz, you won't

NOTE CONF {"raw":[87,100,99,99,100,100,100,100,100,100]}

00:51:45.520 --> 00:51:49.660
<v Speaker 1>be able to come back to, you know, where where

NOTE CONF {"raw":[100,100,100,100,100,100,86,86,97,81]}

00:51:49.660 --> 00:51:52.060
<v Speaker 1>the quizzes and to find what your progress was.

NOTE CONF {"raw":[100,100,100,100,100,95,100,100,100]}

00:51:52.060 --> 00:51:55.780
<v Speaker 1>Therefore, if you want to keep some records of your

NOTE CONF {"raw":[96,100,100,100,100,100,100,100,100,100]}

00:51:56.830 --> 00:52:01.030
<v Speaker 0>performance, one way to go to print the results summary

NOTE CONF {"raw":[100,91,100,100,100,80,99,100,96,99]}

00:52:01.030 --> 00:52:02.330
<v Speaker 1>as demonstrated here.

NOTE CONF {"raw":[100,100,100]}

00:52:03.520 --> 00:52:09.320
<v Speaker 0>So this completes this actually turned out fairly long video.

NOTE CONF {"raw":[100,100,100,100,100,84,100,100,100,82]}

00:52:10.420 --> 00:52:14.290
<v Speaker 0>I hope that you don't have to watch it more

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:52:14.290 --> 00:52:19.660
<v Speaker 1>than once and that it clarified many questions that you

NOTE CONF {"raw":[100,100,100,100,99,100,100,100,100,100]}

00:52:19.660 --> 00:52:22.780
<v Speaker 1>had in mind and that if you need to return

NOTE CONF {"raw":[100,100,100,47,100,100,100,95,96,100]}

00:52:22.780 --> 00:52:26.800
<v Speaker 1>to these issues once more, you will be able to

NOTE CONF {"raw":[100,65,84,100,100,100,99,100,100,100]}

00:52:26.800 --> 00:52:29.410
<v Speaker 1>navigate your way to the correct answer, to the answer

NOTE CONF {"raw":[100,100,100,100,100,100,88,97,98,100]}

00:52:29.410 --> 00:52:33.100
<v Speaker 1>to our questions by just playing around with the practise

NOTE CONF {"raw":[100,58,100,100,100,100,100,100,97,100]}

00:52:33.100 --> 00:52:39.250
<v Speaker 1>quiz that you can obtain on the model page, together

NOTE CONF {"raw":[100,100,100,100,100,100,100,99,100,100]}

00:52:39.250 --> 00:52:41.680
<v Speaker 1>with the further resources about how to improve the answer

NOTE CONF {"raw":[100,64,100,72,100,100,100,88,100,100]}

00:52:41.680 --> 00:52:44.300
<v Speaker 1>to our question of how to use the numbers quiz.

NOTE CONF {"raw":[100,97,100,100,100,100,100,100,100,91]}

00:52:44.770 --> 00:52:47.830
<v Speaker 1>So thanks for watching and see you again for the

NOTE CONF {"raw":[100,100,100,100,100,100,100,100,100,100]}

00:52:47.830 --> 00:52:49.510
<v Speaker 1>next videos.

NOTE CONF {"raw":[100,98]}