Speaker 0: Hi, everyone, and welcome to this demonstration video on how
Speaker 1: to use the quizes in this.
Speaker 1: Central to the philosophy of this module is the view
Speaker 1: that the best way to learn Mazzara to revise maths
Speaker 0: is through exercise.
Speaker 1: And in order to enable you to get as much
Speaker 1: exercise as you want in the context of your revision.
Speaker 1: This module is to a very large degree structured around
Speaker 0: quizzes, in particular for every section of this class.
Speaker 1: Whenever you open a particular section, you will see that
Speaker 1: the model pages structured in a way around a number
Speaker 1: of different types of quizzes.
Speaker 0: For example, this is the page of the model page
Speaker 1: on topic two point three univariate calculus.
Speaker 1: And as you can see, as you scroll down the
Speaker 0: page, one of the first resources that you'll see here
Speaker 1: is a diagnostic quiz that I will be a diagnostic
Speaker 1: quiz on every topic.
Speaker 1: Then further to this, there are a sequence of tutorial
Speaker 1: videos on topics related to the rules of differentiation.
Speaker 1: And together with every with each one of these videos,
Speaker 1: there is an associated many ways that look specifically at
Speaker 1: the number of exercises related to the topic of the
Speaker 1: video.
Speaker 1: Further down, typically, for most topics, there is an economic
Speaker 1: application of discussion of some economic example of the mathematical
Speaker 0: concepts studied in this topic.
Speaker 1: Together with there an associated economic application.
Speaker 1: Squiz, which goes over, allows you to practise through some
Speaker 0: examples, the contents discussed in The View.
Speaker 1: And finally, there is an advanced quiz of consisting of
Speaker 1: somewhat more difficult questions that you are able to look
Speaker 0: at if you have done the diagnostic quiz already and
Speaker 1: you want some further exercise.
Speaker 0: So it is our intention that this quizzes are fairly
Speaker 0: easy to use.
Speaker 1: It should be fairly self-explanatory how to use the quizzes
Speaker 1: and there should be no technical difficulty in accessing and
Speaker 1: playing around with the quizzes.
Speaker 1: However, since the quizzes are made in a platform known
Speaker 0: as numbers, which allows for a relatively versatile type of
Speaker 1: question types rather than just the usual and secure types,
Speaker 1: it is also understood that you might on occasions find
Speaker 1: it a little bit challenging how to improve your answers
Speaker 1: to these quizzes.
Speaker 1: And there might be a scope for explaining further what
Speaker 1: is the best way to use this quiz.
Speaker 1: So the purpose of this short video will be to
Speaker 0: walk you over one practise quiz and through this question
Speaker 1: to demonstrate the possibilities of numbers and how and advice
Speaker 1: on how best to use these quizzes in order to,
Speaker 1: you know, support your learning.
Speaker 1: Now, in order to get there, I am going to
Speaker 0: open the page on how to use quizzes on the
Speaker 1: model page.
Speaker 1: And as you can see here on this page, there
Speaker 1: is a practise quiz, which I am now going to
Speaker 1: open in a new top.
Speaker 1: And once you open a quiz, you are going to
Speaker 1: see a page that looks something like this.
Speaker 1: There will be a statement on the number of questions
Speaker 1: and the number of marks that are distributed.
Speaker 1: There will be a statement on the bus percentage.
Speaker 1: In this case, it's set to be 80 percent and
Speaker 1: some introductory statement.
Speaker 0: Once you have this page open, if you click on
Speaker 0: start, you are opening the quiz.
Speaker 0: And now the way in which the quiz is structured
Speaker 1: is through a sequence of questions that you can see
Speaker 0: on the left.
Speaker 1: In this particular example, in this particular quiz, there are
Speaker 1: only three questions.
Speaker 1: And at that point, by clicking on different questions on
Speaker 1: the left hand side, you can jump between questions and
Speaker 1: other things you can observe.
Speaker 1: Is that associated with each question?
Speaker 1: There is a score, for example, question why?
Speaker 1: Yes, a maximum score of one.
Speaker 1: Currently my score is zero because I have not yet
Speaker 1: attempted, let alone correctly, answer the question.
Speaker 1: So similarly in question three, in fact, there are twenty
Speaker 1: four marks currently my score.
Speaker 1: Zero altogether and question three, yes, far marks and that
Speaker 1: far in Tokyo, there are 29 marks that can be
Speaker 1: obtained from the case.
Speaker 1: The total scar that one obtains from the case consists
Speaker 1: of the scars that you get divided by the total
Speaker 1: scar available, expressed in percentage terms.
Speaker 0: Now, let's start by taking a look at the first
Speaker 1: question on the quiz, which is indeed one very basic
Speaker 1: question whose purpose is simply to allow us to explore
Speaker 0: the what is possible within the case and how best
Speaker 1: to use this resource in order to support learning.
Speaker 1: So I'll consider the question.
Speaker 1: I eat nine apples per day and then the question
Speaker 1: is how many apples Dwight Burwick associated with the question?
Speaker 1: There is an answer box here and inside the centre
Speaker 1: answer box.
Speaker 1: I can type stuff in this particular example.
Speaker 1: The question is, if I eat nine apples per day,
Speaker 1: how many apples?
Speaker 1: Right, Burwick?
Speaker 1: Well, since there are seven days in one week, if
Speaker 1: I eat nine apples per day, then the total number
Speaker 1: of apples eight Burwick is nine times seven equals to
Speaker 0: sixty three.
Speaker 1: If I type in my answer here.
Speaker 1: Note is that to the right of the answer box,
Speaker 1: a new box appears which renders the answer that I've
Speaker 1: typed into mathematical notation.
Speaker 1: In this particular case, there is nothing unusual in the
Speaker 0: rendering of the number.
Speaker 0: Once I have typed my answer, I can click on
Speaker 1: submit answer and page immediately tells me that this answer
Speaker 1: is correct or not.
Speaker 1: It turns out that sixth tracing the correct answer to
Speaker 1: this question.
Speaker 1: Surprisingly, and therefore I also predict one mark for my
Speaker 1: answer.
Speaker 1: As you can see my scar on the left for
Speaker 0: question one change from zero out of one to one
Speaker 1: out of one on account of me correctly answering this
Speaker 0: question.
Speaker 0: Now, of course, this question is fairly easy and it
Speaker 1: is unlikely that in practise I'm going to make a
Speaker 1: mistake in answering the question.
Speaker 1: But suppose that I get that an incorrect answer.
Speaker 1: For example, 50, this is still something I can do
Speaker 1: if I now click on submit answer, I receive immediately
Speaker 1: the feedback that my answer is incorrect.
Speaker 1: Now, there is no problem with this because once I
Speaker 1: have entered it and come back to the answer box
Speaker 1: and as long as I haven't submitted the quiz, I
Speaker 0: can try another answer.
Speaker 1: For example, the correct answer 63.
Speaker 1: And once I click on Submit Answer, this is immediately
Speaker 0: seen as numerically correct.
Speaker 1: Now something I can do inside the question.
Speaker 1: So I suppose that I made a mistake in answering
Speaker 0: fifty and I don't actually know how to tackle this
Speaker 1: question.
Speaker 1: Something I can do is click on a button at
Speaker 0: the bottom right called to reveal answers.
Speaker 1: If I click on this button, I receive this notification
Speaker 0: rate through it.
Speaker 1: Then once I click on OK here in a box
Speaker 1: near the answer box, I get another box known as
Speaker 1: which says expected answer.
Speaker 1: That is what is the correct answer to that question?
Speaker 1: And in fact tells me that the correct answer was
Speaker 1: six to three.
Speaker 1: Further down the page, I receive feedback or advice that
Speaker 1: is typically a work solution to the problem.
Speaker 1: And in this case, the work solution tells me that
Speaker 1: since there are seven days per week, if I eat
Speaker 1: nine apples every day, then I will wait seven times
Speaker 1: ninety six to sixty three apples.
Speaker 1: Now notice that whilst I have clicked on review answers,
Speaker 1: my car is locked to zero.
Speaker 1: For this question.
Speaker 1: However, I receive the option to try another question like
Speaker 1: this.
Speaker 1: And if I click on this question, the on this
Speaker 1: option and if I click OK, I am back at
Speaker 1: the beginning where I am given a slightly different but
Speaker 1: in fact similar type of question where I am now,
Speaker 1: I suppose that I ate for apples birthday.
Speaker 1: Remember that previously I had nine apples per day.
Speaker 1: Now suppose that I eat four apples per day.
Speaker 1: How many apples die per week?
Speaker 1: And now the correct answer is twenty eight.
Speaker 1: I can submit this answer and notice that my score
Speaker 1: becomes one out of one.
Speaker 1: Therefore, one possibility of this quiz is if you get
Speaker 0: the question that you don't know how to answer something
Speaker 1: that is revealed the answers.
Speaker 1: This is going to give you some feedback, including countless
Speaker 1: other questions like this.
Speaker 1: And then you have the option to try another question
Speaker 1: like this one now, of course.
Speaker 1: You have the option to try another question like this
Speaker 1: one, even if you do not reveal the answer.
Speaker 1: So, for example, I'm going to click on try another
Speaker 1: question like this again.
Speaker 1: And now I receive yet another question.
Speaker 1: My car is reverted back to zero, and now I
Speaker 1: have to answer the question again.
Speaker 1: Now, the correct answer to this variety of the question,
Speaker 1: if I ate apples per day, then within a week
Speaker 1: I'm going to eat eight times seven fifty six apples.
Speaker 0: And now if I submit the answer, I get the
Speaker 0: score of one out of one note is that there
Speaker 1: is no penalty from tranqs.
Speaker 1: And other questions like this are revealing the answers to
Speaker 1: the question.
Speaker 1: And the only difference is that if you click on
Speaker 1: one of these options, rather than answering the question, your
Speaker 1: original score will be reverted to zero yet.
Speaker 0: So, for example, it was one out of one zero
Speaker 1: out of one.
Speaker 1: And now the question is eight five apples per day.
Speaker 1: How many like Burwick?
Speaker 1: Well, the answer is thirty five.
Speaker 1: Notice that in some cases there will be the option
Speaker 1: of shelf steps.
Speaker 1: Usually clicking on shelf steps is going to reveal some
Speaker 1: reveal, some sort of hint.
Speaker 1: In this case, the hint is that there are seven
Speaker 1: days in a week.
Speaker 1: Notice that again, there is no penalty from revealing the
Speaker 1: steps, which I can again hide after I have revealed
Speaker 0: once and in some cases you might want to click
Speaker 1: on this shelf steps button in order to review a
Speaker 1: potentially useful hint about how to answer a question.
Speaker 0: Now, this is the basic structure of a quiz question,
Speaker 0: and one of the good things about the squillace is
Speaker 1: that you can use them to learn by clicking on
Speaker 0: if you feel and even if you know what the
Speaker 1: correct answer is, if you feel that you can benefit
Speaker 1: from more exercise, you can get this exercise simply by
Speaker 1: clicking on.
Speaker 1: Try another question like this as many times as you
Speaker 1: like.
Speaker 1: And in this way you can recreate a particular type
Speaker 1: of exercise menotti's.
Speaker 1: For example, if there is a question on the power
Speaker 1: rule and you answer the first draught of the question,
Speaker 0: well, but you want to exercise more on the power
Speaker 1: than by clicking on try another question like this.
Speaker 1: You are going to get more and more dros of
Speaker 1: a similar question.
Speaker 1: And in this way you can you can, you know,
Speaker 1: get as much exercise as you like.
Speaker 0: Now I'm going to move to question two from the
Speaker 1: quiz, which is a helper on how to input your
Speaker 1: answers to this question.
Speaker 1: Now, given the versatility of numbers as a system for
Speaker 0: quizzes, the types of questions that could be asked spend
Speaker 1: not only the usual multiple type questions, where the answers
Speaker 1: are to be picked from a list of alternatives by
Speaker 1: clicking.
Speaker 1: But in addition to this, there are the possibilities that
Speaker 1: the answer to a question will be a number, just
Speaker 1: like was the case in question, one that we discussed
Speaker 0: just now, or in fact, it could be an algebraic
Speaker 1: expression that is some sort of expression involving variables or
Speaker 1: an equation.
Speaker 1: And inequality are in fact, the matrix.
Speaker 1: And even though the syntax of how these types of
Speaker 1: expressions are input into numbers is generally quite user-friendly, there
Speaker 1: is some sense in which certain rules have to be
Speaker 1: followed.
Speaker 1: And the purpose of this part of the value will
Speaker 1: be to walk you through the different types of questions
Speaker 1: that could happen on a number of squares.
Speaker 1: And how are the answers to these questions given?
Speaker 1: So we're going to go over a sequence of possible
Speaker 1: questions, starting with the simplest case.
Speaker 1: That is, suppose that a question that is being cast
Speaker 1: on equity, some multiple choice question.
Speaker 1: So it could be that in some cases you are
Speaker 1: asked multiple choice question and suppose that, you know, there
Speaker 1: is a multiple choice question with exactly one answer.
Speaker 1: For example, suppose that your question such that the correct
Speaker 1: answer to this question is five and then you are
Speaker 1: asked to choose the correct answer.
Speaker 1: And there is a list of options, one of which
Speaker 1: is the correct option.
Speaker 1: So in this case, we know that the correct option
Speaker 1: is five.
Speaker 1: And how do we choose this option is simply by
Speaker 1: clicking on the correct option five.
Speaker 1: And once you click on submit part, you see that
Speaker 1: you are getting the feedback that we have chosen a
Speaker 1: correct answer.
Speaker 1: Not is that in the case when the correct answer
Speaker 1: is only one out.
Speaker 1: Full list of options, actually, if I was to click
Speaker 1: on another option after having chosen five, for example, on
Speaker 1: the option to then my answer automatically is no longer
Speaker 1: five, but just the option to and once I submit
Speaker 1: part, I get zero because this is the correct answer.
Speaker 1: But if I click on five again and submit part,
Speaker 0: I receiving the feedback that the answer is correct in
Speaker 0: another type of multiple choice question with only one answer,
Speaker 1: it could be that the correct answer, again, is only
Speaker 1: one option.
Speaker 1: However, the options are given not through radio boxes he
Speaker 1: here, but the inner scroll down sort of menu.
Speaker 1: So for example, suppose that the correct answer to the
Speaker 1: following question is straight.
Speaker 1: In order to choose the correct answer, I click on
Speaker 1: the menu and I click on the correct option three
Speaker 1: and then submit part.
Speaker 1: And this turns out again to be the correct answer.
Speaker 1: Now, in another variety of multiple choice questions, there could
Speaker 1: be a number of correct answers to a list, to
Speaker 0: a question.
Speaker 1: And they are all given in the list of options.
Speaker 1: For example, consider the question, choose all the colours and
Speaker 1: the options are economics blue, red and apple.
Speaker 1: Now, amongst all these four options, there are two colours,
Speaker 1: blue and red.
Speaker 1: Now notice that the like the previous type of menu
Speaker 1: where there is only one correct answer, where the answers
Speaker 1: are in radio boxes, the options are given in radio
Speaker 1: boxes here when multiple correct answers are possible.
Speaker 0: There are in fact squares, tick boxes that I have
Speaker 0: to take.
Speaker 0: Now, the two correct answers are blue and red and
Speaker 1: once I click on Submit McBath, I get one marked
Speaker 1: for this question.
Speaker 1: Now, if I was to only have selected one of
Speaker 1: the correct answers, this would be incorrect.
Speaker 1: Now let's turn attention to a slightly more interesting type
Speaker 1: of questions, which is questions where the correct answer is
Speaker 1: no.
Speaker 1: Such a question can come out of a situation such
Speaker 1: as the type of question asked in question one Yakir.
Speaker 1: The correct answer was no.
Speaker 0: Now, let's scroll down again.
Speaker 1: Now, suppose that the correct answer to a question is
Speaker 1: the particular integer.
Speaker 1: So I suppose that the correct answer to the question
Speaker 1: is how to type in the correct answer.
Speaker 1: Well, in the answer box, I click on the answer
Speaker 1: box and I type five.
Speaker 0: If I click submit part, I identified that the answer
Speaker 1: is correct.
Speaker 1: Now, it could be similarly that the correct answer is
Speaker 1: a negative integer.
Speaker 1: If this is the case, I simply type in the
Speaker 1: negative integer from my keyboard.
Speaker 1: So if the correct answer is minus seven, when I
Speaker 1: type in minus seven and when I click on submit
Speaker 0: part, my answer is evaluate.
Speaker 1: That's correct.
Speaker 1: If I had typed only seven, of course this would
Speaker 1: have been incorrect.
Speaker 1: So minus seven is the correct answer.
Speaker 1: Now in another type of question, the correct answer may
Speaker 1: be a number, which is a fraction.
Speaker 1: So suppose that the correct answer to a question is
Speaker 1: the fraction one over three, for example.
Speaker 0: This could be you may want to type such an
Speaker 1: answer to a question that says solve the linear equation
Speaker 1: three times X is equal to one.
Speaker 1: What is the answer for?
Speaker 1: Well, the answer is one over three.
Speaker 1: Well, the white type, the fraction, one over three is
Speaker 0: by one slash three where slash corresponds to divided.
Speaker 1: Notice that now next to the answer box, the rendering
Speaker 1: of the expression reveals an expression typed in, in fact
Speaker 1: in Lubbock, which is sort of prettier than one three.
Speaker 1: And if I submit part, I am going to reveal
Speaker 1: that the answer is correct so I can enter fractions
Speaker 1: in the answer boxes as well.
Speaker 1: And this is useful in many cases.
Speaker 0: Now notice that if a correct answer to a question
Speaker 1: turns out to be a rational number, a fraction, then
Speaker 1: as best practise, you should indeed choose to type this
Speaker 0: rational number.
Speaker 0: Now, in some cases, when the answer is a rational
Speaker 1: number, which could be expressed as a fraction, the quiz
Speaker 1: may also allow you to type the answer in decimal
Speaker 1: form, subject to a certain specified precision.
Speaker 1: For example, this particular question is set to allow decimal
Speaker 1: representation as long yes, we use at least two decimal
Speaker 1: points of precision.
Speaker 1: For example, if I was to type zero point three,
Speaker 1: three, three and four McPartlin.
Speaker 1: Will again be considered correct, or in fact, zero point
Speaker 1: three three will again be considered correct.
Speaker 1: However, if I was the only type zero point three,
Speaker 1: this would be considered incorrect, even if decimal four is
Speaker 1: allowed.
Speaker 1: However, as best practise, I would advise that if the
Speaker 1: correct answer is a fraction, yes, you should use the
Speaker 1: capability of the quiz to type a fraction.
Speaker 1: And this also allows you not to use.
Speaker 0: There is basically this one reason when why using a
Speaker 1: calculator will not be necessary in many of the cases,
Speaker 1: because you can type your answers as fractions in this
Speaker 1: case and there is no need to evaluate the fraction
Speaker 1: in terms of decimal representation.
Speaker 0: Now, another type of question may have May ELT's.
Speaker 1: It may be that the correct answer to a question
Speaker 1: is the number which is naturally represented in power for
Speaker 0: for example, it could be that the correct answer to
Speaker 1: a question.
Speaker 1: You have obtained this 12 to the power of three,
Speaker 1: which of course also equals two one seven to eight.
Speaker 0: Now we can if the correct answer is in this
Speaker 1: form, we can choose to type our answer either as
Speaker 1: one seven to eight, which is correct.
Speaker 1: But alternatively, we can simply type 12 to the power
Speaker 1: of three.
Speaker 0: So if in the context of your calculations, you arrive
Speaker 1: to the situation where you know that the answer to
Speaker 1: a particular question is the number twelve to the power
Speaker 1: of three, there is no need to take out your
Speaker 1: calculator and evaluate what to have the power of threes
Speaker 1: because you can simply type 12 to the power of
Speaker 0: three.
Speaker 0: Note that we use the symbol hat in order to
Speaker 1: in order to denote raising a number to a power
Speaker 1: in general in order to type the number eight to
Speaker 1: the power of B..
Speaker 1: We can type A, this symbol B, and this is
Speaker 1: going to hold the number eight to the power of
Speaker 0: B.
Speaker 1: Note is that the correct answer is rendered here.
Speaker 1: Exactly.
Speaker 1: On the right.
Speaker 1: You can see in the verification box that exactly what
Speaker 1: you typed is interpreted as 12th to the power of
Speaker 1: three.
Speaker 1: And this is useful.
Speaker 1: While you are getting used to the syntax of numbers,
Speaker 1: this is just so in order to verify that what
Speaker 1: you are typing is interpreted in the way that you
Speaker 1: would like it to be interpreted.
Speaker 0: Now, this use of power and notation is especially useful
Speaker 0: when the correct answer, for example, involves special numbers such
Speaker 1: as Euler's constant e Euler's number.
Speaker 1: So suppose that the correct answer to a particular question
Speaker 1: is C to the power of five, where it is
Speaker 1: our last number, which is remember a number, approximately two
Speaker 1: point seven one eight two, etc..
Speaker 1: This is important council, which you often encounter in your
Speaker 1: study of both mathematics and economics.
Speaker 1: It turns out that for some special number, such as
Speaker 1: the number three numbers and in fact JMT, the programming
Speaker 1: language behind numbers actually N understands E yeah, it understands
Speaker 1: the number and you can type E to the power
Speaker 1: of five rather than taking your calculator and evaluating quality
Speaker 1: to the power of five.
Speaker 1: And once you submit part, your answer will be considered
Speaker 0: correct.
Speaker 1: Now this fact, the fact that you can type a
Speaker 0: number mpower form is useful in the case when an
Speaker 1: answer to a question is some rules.
Speaker 0: For example, suppose that the answer to a particular question
Speaker 1: is the square root of two, which remember is equivalent
Speaker 1: to to race to the power of one half.
Speaker 1: Then one way to type this answer is to pick
Speaker 1: your calculator, to calculate what the square root of two
Speaker 1: is, and you will see that it's something like one
Speaker 1: point four, one four, etc. and you can indeed type
Speaker 0: one point for one four.
Speaker 0: And if the answer if the question allows three decimal
Speaker 1: places of precision, this will be considered correct.
Speaker 1: In fact, this one allows even two decimal places of
Speaker 1: precision, but one decimal places precision is not correct.
Speaker 0: However, a much more elegant way of typing a question
Speaker 1: like this is by using power notation.
Speaker 1: So, for example, if I was to type two to
Speaker 0: the power of one cuff type like this and interpret
Speaker 1: it like this.
Speaker 1: And if you submit part, you're going to see that
Speaker 1: the answer is accepted as correct.
Speaker 1: Now notice that I am using brackets around one over
Speaker 0: to here in order to tell the interpreter, the numbers
Speaker 1: interpreter that one over two is the fraction to which
Speaker 1: I raise the number two.
Speaker 1: Now, what would be true if I don't use brackets?
Speaker 1: If I don't use brackets because of the are there
Speaker 1: in the order of operation rising to power has precedence
Speaker 1: over division numbers, is going to interpret this expression I
Speaker 1: due to the power of one divided by two.
Speaker 1: And this would of course be an error.
Speaker 0: Therefore, I should be careful when using fractions and in
Speaker 1: many other cases to respect the order of operations.
Speaker 1: And whenever there is a scope for interpretation, I should
Speaker 1: be careful to include brackets.
Speaker 1: So in order to type two to the power of
Speaker 0: one half, I type two to the power and then
Speaker 0: one half in brackets, this is the best way.
Speaker 0: Now notice that damn the programming language behind numbers.
Speaker 1: Also, he has an inbuilt function obscurity.
Speaker 1: And if you type obscurity and then in brackets a
Speaker 1: number, this is interpreted as the square root of the
Speaker 1: particular number and this is also the correct answer.
Speaker 1: However, as you can imagine, in many cases when there
Speaker 1: are rules, for example, if there are roots to other
Speaker 0: power other than two, there is no specific inbuilt function.
Speaker 1: And therefore something that will always work is to raise
Speaker 0: the number to the power that you would like it
Speaker 1: to be raised.
Speaker 0: And in this representation, you can type the correct answer
Speaker 0: to if the correct answer is square root.
Speaker 1: Two, not as an example of this.
Speaker 1: Suppose that the correct answer to a question is the
Speaker 0: cubic root of five.
Speaker 1: Now it turns out that there is an inbuilt function
Speaker 1: for a cubic root in numbers in Jammey, but I
Speaker 0: don't know it.
Speaker 1: Therefore, one way to type this number is to recognise
Speaker 1: that the cubic root, the five is simply five race
Speaker 1: to the power of one over three.
Speaker 1: And if I submit this, this will evaluate the correct
Speaker 1: answer because the given group, the five is just five
Speaker 1: raised to the power of one over three.
Speaker 1: Now, not is that in principle the correct group of
Speaker 1: five.
Speaker 1: This can be approximated as one point seven zero nine
Speaker 1: nine seven five nine, etc. But it turns out that
Speaker 1: this particular question is set not to allow decimal representation
Speaker 1: to any precision.
Speaker 1: So if I was to type the decimal representation to
Speaker 1: a very high precision.
Speaker 0: Like this, it would still be none us is going
Speaker 1: to recognise that my answer is numerically correct.
Speaker 1: However, one mark is taken away because I should not
Speaker 0: use decimals.
Speaker 1: Now, if something like this happens in a question, usually
Speaker 1: most questions will be set to accept decimal representations.
Speaker 1: But if something like this happens in a question, then
Speaker 1: the feedback is going to allow you to understand that
Speaker 1: in order to get the full score, you should you
Speaker 1: are requested to type your answer not in a decimal,
Speaker 1: but in some other form where you give the correct
Speaker 1: number, which is five to the power of one over
Speaker 0: three.
Speaker 1: Now, in either case, where the answer could be a
Speaker 1: number, is that the answer could in fact be a
Speaker 0: logarithm and the logarithm of to a given base of
Speaker 1: some number is a number.
Speaker 1: So, for example, suppose that the correct answer to a
Speaker 1: question is log to the base three of five, for
Speaker 0: example.
Speaker 0: A question that could have this as an answer is
Speaker 1: solve the equation.
Speaker 1: Three to the power of X is equal to five.
Speaker 0: Yeah, find X.
Speaker 1: The answer to this question will be exactly equal to
Speaker 1: lock to the base three of five.
Speaker 0: Now it turns out that and now this is a
Speaker 1: slightly more special syntax that you don't need to remember
Speaker 1: in general, because if you are expected to type a
Speaker 1: longer answer in logarithm form in some of your questions,
Speaker 1: there will be a reminder in a hint button next
Speaker 0: to it.
Speaker 0: But in general, JMB allows that a logarithm of a
Speaker 0: number can be typed, in particular in the logarithm to
Speaker 1: the base rate of B for two constants, and B
Speaker 1: this can be typed as luck.
Speaker 0: B, comma, a song in particular type the number LOC
Speaker 1: to the base three of five I can type block
Speaker 0: of five to the base three and you can see
Speaker 0: in the next to the answer box in the rendering
Speaker 1: of the answer that this is exactly interpreted correctly as
Speaker 1: look to the base three of five.
Speaker 0: Now if you use your calculator you can find that
Speaker 1: lock to the base.
Speaker 1: Three of five is approximately one point four six four
Speaker 1: nine seven.
Speaker 1: And this particular question allows typing in decimal representation as
Speaker 1: long as you use at least two decimal point.
Speaker 1: So I can type one point four six if I
Speaker 1: have used my calculator and found what the answer is.
Speaker 1: However, as best practise, if you're the answer to the
Speaker 1: question is up to the base three or five, I
Speaker 1: would encourage you to actually type it in its correct
Speaker 0: form.
Speaker 0: And there is this, again, one example that you don't
Speaker 1: need to use a calculator in many contexts because your
Speaker 1: computer is in fact a very powerful calculator.
Speaker 1: And the quizzes that you are using understand what looked
Speaker 1: at the base.
Speaker 1: Three of five is.
Speaker 1: Now, this is these are a number of situations where
Speaker 1: the correct answer to a question could be a number.
Speaker 1: And I hope that this guidance hopefully allows we will
Speaker 1: allow you to type your answers correctly in pretty much
Speaker 1: every context where the correct answer is no.
Speaker 0: Now, a slightly more interesting case is questions where the
Speaker 1: correct answer is a..
Speaker 1: Jailbreak expression.
Speaker 1: That is an expression involving variables.
Speaker 1: Such type of questions can arise naturally in many contexts.
Speaker 1: For example, if you are given a particular function, the
Speaker 1: question could be right.
Speaker 0: The derivative of this function and then this derivative itself
Speaker 1: be a function which is going to involve some variables.
Speaker 1: So the expression for the derivative will be a mathematical
Speaker 0: expression.
Speaker 1: So, for example, suppose that the correct answer to S
Speaker 1: question is three X plus five.
Speaker 0: How do we type a correct answer?
Speaker 1: The correct answer if this is the correct answer.
Speaker 0: Now the way to type algebraic expressions in numbers is
Speaker 1: effectively the same approach.
Speaker 1: You should use the same syntax as you used to
Speaker 1: some graphical calculator, sorry, most programming languages or numerical packages
Speaker 1: out there.
Speaker 1: So pretty much the best practise to type three X
Speaker 1: plus five is to type three times X plus five
Speaker 0: plus five.
Speaker 0: If I type this on the right, I see that
Speaker 1: my correct answer is interpreted as three X plus five
Speaker 0: and if I submit BA.
Speaker 0: You can see that, indeed, my answer is found that
Speaker 1: to be numerically correct note is that in cases when
Speaker 1: the answer is algebraic expression, something that we can do
Speaker 0: is equally correct.
Speaker 1: Answer would be an algebraic expression, which is basically equivalent
Speaker 1: to the given expression, for example, rather than three X
Speaker 1: plus five, we could have typed five plus three times
Speaker 1: and this would still be the correct answer.
Speaker 1: Or, in fact, five plus X times three, and this
Speaker 1: would still be the correct answer because this expressions are
Speaker 1: equivalent.
Speaker 0: Now notice that even though I recommend that you always
Speaker 1: are explicit in typing the multiplication sign in algebraic expressions,
Speaker 0: actually, in some cases, numbers will understand if you are
Speaker 0: mkt the multiplication sign.
Speaker 1: So if you just typed three X plus five, which
Speaker 1: I guess comes naturally in that context, the answer will
Speaker 1: be found to be numerically correct, because Jemmy understands that
Speaker 0: three x X is a variable and three X is
Speaker 1: not a very, very strict times the variable X because
Speaker 0: the name of a variable cannot start with the number
Speaker 1: pretty much.
Speaker 1: However, if I was to type X three plus five,
Speaker 1: this would be incorrectly interpreted.
Speaker 1: And that's why Y you are getting used to the
Speaker 1: precise rules for the syntax dialled visu to always be
Speaker 1: explicit and use the multiplication sign whenever there is a
Speaker 0: multiplication.
Speaker 1: Now let's consider something slightly more difficult.
Speaker 1: So suppose that the correct answer to a question is
Speaker 1: the expression for X squared plus three X to the
Speaker 1: power of a half plus two over X.
Speaker 1: Now in order to type the correct answer to this,
Speaker 1: we followed the same rules as we follow for multiplication,
Speaker 1: raising to power and so forth.
Speaker 1: And in particular we type four times X to the
Speaker 0: power of two four four X squared and then we
Speaker 0: have plus three times X and we want to raise
Speaker 1: X to the power of one half.
Speaker 1: But remember that because if we do not include brackets
Speaker 1: here, because racing to power, he has precedence over division
Speaker 1: in the order of operation, our answer is interpreted incorrectly.
Speaker 1: And in order to account for this, we would like
Speaker 1: to enclose the one over two in brackets.
Speaker 1: And then finally we have plus two divided by X
Speaker 1: in order to get to our X.
Speaker 0: Now, if we submit part, you can see that our
Speaker 1: answer is considered valid.
Speaker 1: Not is that if we had changed the order in
Speaker 1: which we entered the numbers, the expressions here.
Speaker 1: So if we had typed instead for X squared plus
Speaker 1: two over X plus three X to the power of
Speaker 1: one half, since this is an equivalent algebraically equivalent expression
Speaker 1: to the answer, if we submit that this would still
Speaker 1: be considered correct.
Speaker 0: Yeah, and again, the what we discussed before is still
Speaker 1: true, that, in fact, this multiplication science here are not,
Speaker 1: strictly speaking, necessary in this context.
Speaker 1: However, sometimes if we don't include the syntax, the multiplication
Speaker 1: in the syntax correctly, there could be a mis interpretation
Speaker 1: of what we are typing from numbers.
Speaker 1: That's why I would suggest that while you are getting
Speaker 1: used to typing your answers, you are explicit in typing
Speaker 1: the multiplication signs.
Speaker 1: Now let's consider something slightly more difficult.
Speaker 1: Now we have three times, six times in brackets, one
Speaker 0: over two times six minus X over two.
Speaker 0: All rise to the power of a half.
Speaker 1: So in order to type this expression, we can type
Speaker 1: three times, six times.
Speaker 0: Now, in brackets, what we have is one over two
Speaker 0: multiplied by X, and I would like to enclose the
Speaker 1: one over two in brackets in order to be certain
Speaker 0: that the one over to multiply sex and I have
Speaker 1: minus X to the power of two.
Speaker 1: This is inside the brackets.
Speaker 1: And now finally, I would like to race the whole
Speaker 1: term in brackets to the power of one over two.
Speaker 1: And this is one way to type the correct answer.
Speaker 0: As you can see, you can go through the quiz
Speaker 1: on your own and you are going to notice a
Speaker 1: number of suggestions about how to type and what things
Speaker 1: might not.
Speaker 0: Work and what will work, and you can try to
Speaker 1: squeeze this on your own.
Speaker 1: Now suppose that the correct answer is there would be
Speaker 1: a break fraction.
Speaker 1: Why do the power of two plus to a minus
Speaker 1: one in the numerator over Y plus two alter the
Speaker 1: power of two in the denominator?
Speaker 1: Now, this is slightly more exciting expression to type.
Speaker 0: So one way to go open brackets and type the
Speaker 1: numerator y to the power of two plus two times
Speaker 1: Y minus one and now divide by the numerator.
Speaker 1: The denominator and the denominator is Y plus two to
Speaker 0: the power of two.
Speaker 0: And you can see next to the Starbucks that this
Speaker 1: is indeed why they wanted to type.
Speaker 1: If I submit Barcia, you can see that this answer
Speaker 1: is incorrect.
Speaker 1: Now it turns out that this out there that I
Speaker 1: typed here are probably not necessary because raising to the
Speaker 1: bar has precedence over division in the order the operations,
Speaker 1: and therefore, even if I type without the lower brackets
Speaker 1: numbers, is going to correctly interpret the answer.
Speaker 1: However, if there is any scope for interpretation or misinterpretation,
Speaker 1: I would advise you if you have any doubts, be
Speaker 1: explicit and use brackets wherever you think that an issue
Speaker 0: may arise.
Speaker 1: Now suppose that the correct answer is an algebraic expression,
Speaker 1: which in fact involves two variables X and Y.
Speaker 1: So in this case, the correct answer is X to
Speaker 1: the power of two plus two times X, Y plus
Speaker 1: Y to the power of two.
Speaker 0: Now the correct answer, the correct way to type is
Speaker 1: X to the power of two plus two times X
Speaker 0: times Y plus Y to the power of two.
Speaker 0: If we submit the Bartons, surprisingly, our answer is correct.
Speaker 1: Now notice that if we had missed the first multiplication
Speaker 1: sign in two times, six times Y, and if we
Speaker 0: submitted the part, the answer would still be considered correct.
Speaker 1: Therefore, numbers would correctly understand that there is a multiplication
Speaker 1: sign here.
Speaker 1: However, if we had missed the second multiplication sign between
Speaker 1: X times Y, what is rendered here looks approximately more
Speaker 1: or less looks like what we want to hear.
Speaker 1: However, if we submit that, we are going to find
Speaker 1: that your answer is incorrect.
Speaker 1: And the reason for this is that now numbers things
Speaker 1: that X Y is a variable on its own, and
Speaker 0: this is one way in which a mistake could arise.
Speaker 1: And that's why this is yet another reason why when
Speaker 1: typing your answers, I would encourage you to be explicit
Speaker 0: in the use of multiplication signs and always type your
Speaker 1: answers in the way that you would find them in
Speaker 0: a graphical calculator.
Speaker 1: Now, there are a number of other examples here that
Speaker 1: you can go over it on your own.
Speaker 1: Now, I want to turn attention to a few final
Speaker 1: remarks.
Speaker 1: In some situations, the correct answer could be an expression,
Speaker 1: which is in fact an equation.
Speaker 1: For example, in the context of optimising the function, you
Speaker 1: might be asked to write the first order condition for
Speaker 1: optimisation.
Speaker 1: The first order condition for optimisation will be an equation
Speaker 1: setting the first derivative of the function equal to zero.
Speaker 0: And this is how a correct answer, which is an
Speaker 1: equation, could arise.
Speaker 1: Now suppose that the correct answer is in fact an
Speaker 1: equation X squared minus X minus two is equal to
Speaker 1: zero.
Speaker 0: Then the way we are going to type it is
Speaker 1: exactly as an expression equal to zero.
Speaker 1: And this would be the correct answer.
Speaker 1: However, what is important is to realise that the objects
Speaker 1: in question, if we had made the mistake and all
Speaker 1: included the left hand side without setting equal to zero,
Speaker 0: this would be incorrect.
Speaker 0: So we need to have equal to zero now.
Speaker 1: Similarly, the correct answer might involve inequalities, just like it
Speaker 0: could involve equalities, it could involve inequalities.
Speaker 0: Now, in general, we use the type, the simple greater
Speaker 1: for greater than the simple less therefore less then and
Speaker 1: therefore greater than are equal.
Speaker 1: We should use that in sequence, the simple greater followed
Speaker 1: by an equality sine and for less than our equal.
Speaker 1: We are the symbol less then followed by inequality sine
Speaker 0: another rule with inequalities.
Speaker 1: I'm going to discuss in a bit.
Speaker 1: So suppose that the correct answer is to a question
Speaker 1: on any.
Speaker 1: Authority is greater than five, then the correct answer is
Speaker 1: type the six, greater than five.
Speaker 1: Now, if I had typed in correctly, X is greater
Speaker 1: than or equal to five, this would be incorrect.
Speaker 1: Or if I had typed let X is less than
Speaker 1: five.
Speaker 1: This would be incorrect if I had typed incorrectly.
Speaker 1: X is greater than six.
Speaker 1: This would still be incorrect.
Speaker 1: So the correct answer is X is greater than five.
Speaker 1: Now suppose that the correct answer is X is less
Speaker 1: than or equal to minus three in order to type
Speaker 1: this with type X less than equal minus three.
Speaker 1: And you can see that this is rendered.
Speaker 1: Exactly.
Speaker 0: Yes.
Speaker 0: Then we can equality that we want to have.
Speaker 0: And if we submit parts, we can see that the
Speaker 1: answer is correct.
Speaker 1: Now, if we had forgotten to add the equality sine
Speaker 1: then we had just type X is less than minus
Speaker 1: three.
Speaker 1: This would be incorrect.
Speaker 1: Now, in some occasions, an answer could be a set
Speaker 1: of values specified by inequalities.
Speaker 1: For example, suppose that the correct answer is all the
Speaker 1: various effects between minus one and one.
Speaker 1: For example.
Speaker 1: This could be the answer to a question for what
Speaker 1: values effects is X minus one times X plus one
Speaker 1: less than zero.
Speaker 0: The answer to this is for values effects between minus
Speaker 1: one and one.
Speaker 0: So one way to type this is through the change.
Speaker 1: Inequality, just like it appears minus one is less than
Speaker 1: X is less than one.
Speaker 1: And another way to type is as a logical union
Speaker 1: of two inequalities, so X is greater than minus one
Speaker 0: and at the same time X is less than one.
Speaker 1: This is a correct representation.
Speaker 1: Not is that whenever there are sequences, sort of sex
Speaker 1: specified inequalities like this, we can make use of the
Speaker 1: logic cooperation operators and Antaria where and is the logical
Speaker 1: operation of our intersection of sets.
Speaker 1: And DA is the logical operator for a union of
Speaker 0: sets.
Speaker 0: And in this case we the set minus one to
Speaker 0: one can be understood as the the intersection of X
Speaker 1: greater than minus one and X less than one.
Speaker 1: And that's why we use the term.
Speaker 1: And but now suppose that the correct answer is X
Speaker 1: is less than minus one R, X is greater than
Speaker 1: one, for example.
Speaker 1: It's an answer to the question for what values the
Speaker 1: FXE X minus one times X plus one in fact
Speaker 1: greater than zero where it would be greater than zero
Speaker 1: if X is minus one are effects is greater than
Speaker 1: one, but not if it is between minus one and
Speaker 1: one.
Speaker 0: And hear the correct way to type such an inequality
Speaker 1: will be X is less than minus one or X
Speaker 0: is greater than one.
Speaker 1: Notice the special word R which corresponds to a union
Speaker 0: affects.
Speaker 1: Now, usually for questions where the correct answer is inequality,
Speaker 1: our sense of inequality, so when there is more special
Speaker 1: syntax involved, there will be hints, buttons that are going
Speaker 1: to remind you about the special use of are.
Speaker 1: And then there therefore is not something you have to
Speaker 1: remember off the top of your head.
Speaker 0: But it could be that the answer some some questions
Speaker 1: will involve ants and thoughts now as the final thing
Speaker 1: to focus on.
Speaker 1: In some situations, there will be questions where the correct
Speaker 1: answer will be a matrix.
Speaker 0: For example, suppose that the correct answer is in particular
Speaker 1: in the topic of linear algebra.
Speaker 1: Naturally, the answer could be a matrix.
Speaker 1: I suppose that we need to input the Matrix with
Speaker 1: first row one, two and three and next row four
Speaker 1: or five and six, a two by three matrix.
Speaker 0: Then very intuitively, the our box could be a matrix
Speaker 1: itself of the correct order, the correct dimension.
Speaker 1: And we can type in our answer by filling in
Speaker 0: the boxes inside the Matrix, the elements of the Matrix.
Speaker 0: However, it could be in some cases, the answer is
Speaker 1: not going to reveal what is that is going to
Speaker 1: reveal that the correct answer is the matrix, but not
Speaker 1: what is the dimension of the matrix.
Speaker 1: And in this case, the answer will be specified in
Speaker 1: the form of something like this, where you need to
Speaker 0: choose what is the number of rows and to set
Speaker 1: the number of columns in order to fill in the
Speaker 1: correct answer.
Speaker 1: So in this particular case, we have one, two, three,
Speaker 0: four, five, six.
Speaker 1: And once we submit parts, we are done.
Speaker 1: So this is our question two.
Speaker 1: Now, I notice that somewhere I have left an incorrectly
Speaker 1: answered question.
Speaker 0: So let's do this.
Speaker 0: And pretty much this is how you input answers for
Speaker 1: many different types of questions into numbers.
Speaker 0: Now, if you at some point you have issues with
Speaker 1: inputting your answers to numbers, I suggest at any point
Speaker 1: you can return back to this question and look through
Speaker 0: the rules that are discussed throughout the quiz about how
Speaker 1: to improve your answer.
Speaker 1: So alternatively, you can take a look at the cheat
Speaker 1: sheet available on the model page at the same point
Speaker 1: where the quizzes, which has a number of suggested syntaxes
Speaker 1: for possible answers that you might want to get.
Speaker 1: Now, a final point I would like to raise is
Speaker 0: that some questions that you encountered during this course could
Speaker 1: be like question three in this video.
Speaker 1: In this quiz.
Speaker 1: That is a multipart question question to ask.
Speaker 1: Also a multipart question.
Speaker 1: There are many parts.
Speaker 1: However, it could be a multipart question where some of
Speaker 1: the parts are hidden and only become hidden once you
Speaker 0: do the first part.
Speaker 0: For example, consider the following question.
Speaker 1: So suppose that consider the set apple orange, blue and
Speaker 0: to offset the farthings.
Speaker 1: And the question is how many of the elements in
Speaker 1: this set corresponds to a colour?
Speaker 1: Now, within this set there are two colour Sorrenti and
Speaker 1: therefore the correct answer to this part of the question
Speaker 1: is to once I submit the part, you will notice
Speaker 0: that I have only answered correctly two out of two
Speaker 1: points for the first part of the question, but we
Speaker 1: have not gotten the full score for the question.
Speaker 1: In order to get the full score, I need to
Speaker 0: click under what to do next.
Speaker 1: I need to click on part two and once I
Speaker 1: am at part two, this is where I am asked
Speaker 0: our next part of the question for the full marks.
Speaker 1: For example, here, choose all the colours and the correct
Speaker 1: answers are blue and orange in this amongst these four
Speaker 1: elements.
Speaker 1: And once I submit part now, I have completed the
Speaker 0: question three in total, I have received all the marks
Speaker 0: and as you can see, I have received twenty nine
Speaker 1: out of twenty nine on this quiz.
Speaker 1: Now, once you are finished with the quiz you should
Speaker 1: click on and exam.
Speaker 1: And following this, you are going to get to a
Speaker 1: place like this where you have the option to print
Speaker 1: the results, for example, into a PDF file of your
Speaker 0: attempt in a PDF, in a PDF file for your
Speaker 1: later records, for example, when this way you can save
Speaker 0: your answer.
Speaker 0: Now, notice that if the quiz that you are doing
Speaker 1: is a diagnostic quiz, then your score will be recorded
Speaker 1: on the model page.
Speaker 0: However, for all the other quizzes, there will be no
Speaker 1: record on the model page.
Speaker 1: And after you are finished with the quiz, you won't
Speaker 1: be able to come back to, you know, where where
Speaker 1: the quizzes and to find what your progress was.
Speaker 1: Therefore, if you want to keep some records of your
Speaker 0: performance, one way to go to print the results summary
Speaker 1: as demonstrated here.
Speaker 0: So this completes this actually turned out fairly long video.
Speaker 0: I hope that you don't have to watch it more
Speaker 1: than once and that it clarified many questions that you
Speaker 1: had in mind and that if you need to return
Speaker 1: to these issues once more, you will be able to
Speaker 1: navigate your way to the correct answer, to the answer
Speaker 1: to our questions by just playing around with the practise
Speaker 1: quiz that you can obtain on the model page, together
Speaker 1: with the further resources about how to improve the answer
Speaker 1: to our question of how to use the numbers quiz.
Speaker 1: So thanks for watching and see you again for the
Speaker 1: next videos.