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 How to use the NUMBAS quizzes

The first few minutes of the video explains where the quizzes are, and then the video continues to run through how to input your answers by going through the practice quiz linked below which is designed to show you how to input your answers. The "cheat sheet" gives examples of how to input various answers as in the table at the bottom of this page,

NUMBAS Cheat sheet Practice quiz

The quizzes for the mathematics refresher course were created by a team of students as part of a Warwick Internship Scheme for Economics (WISE) project funded by the Royal Economic Society. If a problem with a diagnostic quiz means you are unable to pass the quiz, please try again a different version of the question (as it may be that it will work properly). Failing this, please do not worry about passing the associated quiz.

 Frequently asked questions

 How to input your answers

Depending on the context the answer to a quiz question could be an element (or several elements) from a list (for multiple choice questions), a number or an arithmetic expression, an algebraic expression, or a matrix, among others. In most cases the format of the input box will make it clear which of the above apply and in cases where this might not be obvious you will find hints in dedicated "Show steps" boxes. Where the correct answer is a number or an algebraic expression, when typing you will see a rendering of your answer in mathematical notation beside the input box which will help you judge if what you are typing is interpreted in the way you want.

Inputting numbers and algebraic expressions

Where the answer to a question is a number, you will typically be able to enter it either in decimal form up to a specified precision or by entering the correct number in the form of a fraction, a power, a logarithm, etc. While in most cases decimal represenation will not be explicitly forbidden we would like to encourage you to avoid it. For example, if the correct answer is \(1/3\) as best practice you should type it as 1/3 rather than as 0.33 or 0.333, etc; if a correct answer is \(3\sqrt{2}\) as best practice type 3*sqrt(2) or 3*2^(1/2) rather than 4.243 ; if a correct answer is \(\log_3 2\) as best practice type log(3,2) rather than 0.631; etc.

When the answer is an algebraic expression the syntax you should use for inputting the answer is broadly similar to the syntax used in graphical calculators, numerical packages (such as Mathematica, R, Stata) and general programming languages, with some particularities specific to JME (the programming language behind the quizzes).

While typing your answers in this way might feel awkward at first, by getting used to a few basic rules you will not only be able to extract the most from the quizzes but also build up some background in technical computing which will be useful in further studying numerical packages such as Stata and R further in your degree. The table below lists some examples of numbers and expressions you might be required to enter together with corresponding ways in which they can be correctly typed in the answer box.

Useful syntax


Example Suggested syntax
Numbers
fractions \(\frac{3}{7}\)

\(-\frac{1}{4}\)

\(\frac{13}{3}\)
3/7

-1/4

13/3
powers and surds \(2^4\)

\(2^{-3}\)

\(\left(\frac{2}{3}\right)^3\)

\(3^{1/5}\)

\(\sqrt{5}\)

\(\sqrt[3]{5}\)
2^4 or 16

2^(-3) or 1/(2^3) or 1/8

(2/3)^3 or 8/27 or (2^3)/(3^3)

3^(1/5) or root(3,5)

sqrt(5) or 5^(1/2)

5^(1/3) or root(5,3)
logarithms \(\log_3 5\)

\(\log_5 3\)

\(\ln 6\)
log(5,3)

log(3,5)

ln(6)
Algebraic expressions
addition and multiplication \(5x\)

\(x+y\)

\(5x+3\)

\(x(2x+3)\)
5*x or x*5 (Note: 5x will also work, but x5 will not)

x+y or y+x

5*x+3 or 3+5*x or 3+x*5

x*(2*x+3) (Note: x*(2x+3) will also work but x(2x+3) will not)
powers \(x^2\)

\(x^{-3}\)

\(x^{1/3}\)

\(3x^2+2x^{-5}-\frac{1}{3}x^{1/3}\)

\(x^2+2xy+y^2\)

\((x^2+3x-2)^{1/3}\)

\(2^{x^2+3}\)

\(\left(-3\right)^{x^2+1}\)
x^2

x^(-3)
or 1/(x^3) (Note: x^-3 will not work)

x^(1/3) (Note: x^1/3 will not work)

3*x^2+2*x^(-5)-(1/3)*x^(1/3) (Note: 3x^2+2x^(-5)-(1/3)x^(1/3) will also work)

x^2+2*x*y+y^2 (Note: x^2+2x*y+y^2 will also work but x^2+2xy+y^2 will not)

(x^2+3*x-2)^(1/3)

2^(x^2+3)

(-3)^(x^2+1) (Note: -3^(x^2+1) will not work)
algebraic fractions \(\frac{y^2+7y-3}{(2y+1)^3}\)

\(\frac{x^2+1}{y-1}\)
(y^2+7*y-3)/((2*y+1)^3)

(x^2+1)/(y-1)
exponentials and logarithms \(e^x\)

\(e^{x^2+3x-1}\)

\(\ln x\)

\(\ln(3x^2-1)\)

\(\log_2 (x^3-3)\)
e^x or exp(x)

e^(x^2+3*x-1) or exp(x^2+3*x-1)

ln(x)

ln(3x^2-1)

log(x^3-3,2) or ln(x^3-3)/ln(2)
 Equations and inequalities
equations \(x^2-3x+2=0\)

\(e^{x^2+3}=1\)
x^2-3*x+2=0

e^(x^2+3)=1 or exp(x^2+3)=1
inequalities \(x>5\)

\(x\leq13\)

\(3x+5\geq0\)
x>5

x<=13

3*x+5>=0
sets specified with inequalities \(5>x>1\) or \(x\in(1,5)\)

\(2\leq x <7\) or \(x\in[2,7)\)

\(x\in(-\infty,3]\cup(7,\infty)\)
5>x>1 or 1<x<5 or x<5 and x>1

2<=x<7 or 7>x>=2 or 2<=x and x<7

x<=-3 or x>7
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