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,
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
 What is the difference between the diagnostic quizzes, mini quizzes, economic application quizzes and advanced quizzes?
The only quizzes that you are required to pass are the diagnostic quizzes. If you can pass these, we believe you should be ready for the mathematics you'll see in your course. All of the quizzes can be used to provide extra practise and provide feedback and solutions to help you learn. diagnostic quizzes:
The diagnostic quizzes cover question from all of the subtopics from the tutorials in that topic (e.g. in topic 2.3 Rules of differentiation, they will cover subtopics 2.3.1  2.3.7). This is the level we expect you to be comfortable with. The length of the diagnostic quizzes will vary across topics but typically you should expect them to take around 2030 minutes.  mini quizzes:
These are typically short quizzes of 12 questions similar to those in the diagnostic quizzes but only covering material from the particular subtopic mentioned in the tutorial.  economic application quizzes:
These are typically short quizzes of a few questions that tackle an economic application of the mathematics covered in the particular subtopic and relate to the corresponding economic application video.  advanced quizzes:
These quizzes cover somewhat more difficult problems than the ones in the diagnostic quiz and can be used as further exercise in case you want to dig deeper into the topic. While they may be a good source of additional exercises for topics in which you feel comfortable with the diagnostic quizzes, we believe that their level exceeds what is required to kick start your degree.
 diagnostic quizzes:
 What is the pass mark for the diagnostic quizzes?
The pass mark for the diagnostic quizzes is 80%. However, the best way to use these quizzes is as a way to identify topics where you can benefit from further revision. In addition, upon submitting an answer you will receive immediate feedback as to whether your answer was correct or not. If incorrect you can click on "Reveal answer" to see a worked solution and then on "Try another question like this one" to attempt a similar question. There is no penalty from doing this and we would strongly encourage you to make use of this option. Hence, even though the pass mark is 80%, we believe that you should aim for 100% on the diagnostic quizzes.  How is my score calculated?
When you open a quiz, next to each answer box you can see the maximum score that can be awarded for this question, together with your current score. Your mark for any given quiz is calculated as the ratio of the sum of your scores across all questions to the sum of the maximum scores of all questions and is expressed in percentage terms.  How long is each quiz?
The length of quizzes varies in length across topics but you should typically find that diagnostic quizzes take no longer than 2030 minutes to complete.  Should I use a calculator?
While you are free to use a calculator we think that the best ways to use the quizzes is to avoid using one, except in very rare cases where you are asked to evaluate some arithmetic expression to a given precision.  How many times can I take each quiz?
You can take each quiz as many times as you like. Each time you take the quiz, new questions will be generated.  What happens to my quiz scores?
The quizzes are rendered in your browser and no record remains (even for yourself) after you exit the quiz. If you would like to keep a record on your performance on such a quiz for your own purposes we suggest that after ending the quiz (by clicking on "End Exam") you print a summary of your attempt into a pdf file (by clicking on "Print the results summary").  How can I get extra questions for practice?
Each time you take the quiz, new questions will be generated so you can keep practising until you feel comfortable with the material. If you want questions on just one subtopic then try the miniquizzes in the "tutorials" section of each topic page. And if you want more advanced quizzes with harder questions, these are available near the bottom of each topic page. The "further resources" links also often contain more questions from external websites.  What happens if I click "Reveal answer"?
Your browser will display a warning window instructing that your current answers will be locked. Once you click "OK" your browser will reveal the correct answers and will display a worked solution at the bottom of the question. Note that even though you will not be able to answer the same question again, you will have the option "Try another question like this one" and when you click on it you will get a different randomized version of the same question, which you can attempt anew. Notice that there is no penalty for revealing the answer, but in order to receive marks you will need to answer the new randomly generated question. As a whole, using the option to reveal an answer and then trying another similar question should prove a valuable way to learn and we would encourage you to use it if you have any doubts even if you answered a question correctly.  What happens if I click "Try another question like this one"?
Your browser will display a warning window and upon clicking "OK" you will receive a new randomized version of the same question. Your score from the previous attempt on the same question will be lost but you can answer the new question. There is no penalty from requestion a new similar question in this way and doing so can be a valuable way to learn. As a whole, this could be one way of getting more exercises on the topic and we would encourage you to use the option if you have any doubts even if you answered the original question correctly.  How do I input my answers into the quizzes?
Please see the video at the begining of this section, the dedicated practice quiz and the cheat sheet.
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).
 For example, in order to enter \(x(2x+3)(x1)\) you should as best practice type
x*(2*x+3)*(x1)
in the answer box (see further examples below).  Note that, typically and unless further specified, an expression will be evaluated as correct as long as it is algebraically equivalent to the correct expression. For example, equally valid ways to enter \(x(2x+3)(x1)\) are to type
x*(3+x*2)*(x1)
or(2*x^2+3*x)*(x1)
or2*x^3 + x^2  3*x
and all of these will evaluate to a correct answer.  Note that in some circumstances a more simplified syntax is also allowed where
*
is not needed for multiplication provided that there is no ambiguity for interpretation. For example, \(7x+1\) can be entered as7*x+1
but also as7x+1
, however, not asx7+1
(which could be wrongly interpreted as the sum of the variablex7
and1
). Note that \(xy\) should be always entered asx*y
ory*x
but not asxy
(which is interpreted as a variable called xy) oryx
. Over time you will get used to using the simplified syntax but in the meantime you are encouraged to be explicit.  As a general rule, you should make sure that the answers are entered in a way that respects the order of operations. If at any point you suspect that there may be any ambiguity, you can always self insure yourself by using brackets. For example,
to enter \(\frac{x^2+1}{x^2}\) you can type
(x^2+1)/x^2
because raising to a power has precedence over division in the order of operations. However, you can also insure yourself by being slightly more explicit and type(x^2+1)/(x^2)
which is also correct.
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 
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) 
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  \(x^2\) \(x^{3}\) \(x^{1/3}\) \(3x^2+2x^{5}\frac{1}{3}x^{1/3}\) \(x^2+2xy+y^2\) \((x^2+3x2)^{1/3}\) \(2^{x^2+3}\) \(\left(3\right)^{x^2+1}\) 
x^2 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)
(3)^(x^2+1) (Note:
3^(x^2+1) will not work) 
algebraic fractions  \(\frac{y^2+7y3}{(2y+1)^3}\) \(\frac{x^2+1}{y1}\) 
(y^2+7*y3)/((2*y+1)^3) 
exponentials and logarithms  \(e^x\) \(e^{x^2+3x1}\) \(\ln x\) \(\ln(3x^21)\) \(\log_2 (x^33)\) 
e^x or exp(x) e^(x^2+3*x1) or exp(x^2+3*x1)
log(x^33,2) or ln(x^33)/ln(2) 
Equations and inequalities  
equations  \(x^23x+2=0\) \(e^{x^2+3}=1\) 
x^23*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 