Help with the Stack online test system

Overview

Stack is a computer system that assists in the teaching of some parts of University mathematics.

The basic idea is as follows. In Blackboard, you will see links to individual Stack quizzes or to pages containing a list of Stack quizzes. Lecturers will ask you to complete these quizzes by a certain deadline. The system will show you various problems, which you should go away and solve. You can then enter your answers, and they will be marked automatically.

Watch the video

For some quizzes, a video will be displayed when you first access the quiz. In those cases, you should start by viewing the video all the way through. You should treat the video like a lecture, taking notes as appropriate, thinking carefully through the material and trying to work through examples or recast it in your own words, and only then looking at the quiz.

Do the questions on paper

When you first access a quiz, you will see a number of questions, together with input boxes or checkboxes that you can use to enter your answers. We do not recommend that you jump in and start entering answers immediately. Instead you should print or copy out the questions, move away from your computer and work through the relevant calculations carefully on paper. Even though you will only enter the final result in the computer, it will be helpful for your learning if you write out the intermediate steps in a neat and well-organised manner.

Enter your answers

When you are ready, you can go back to the online test system to enter your answers. Quizzes will typically have a final deadline for submission, often a week after they are first made available, but no other kinds of time limits are imposed. Thus, you can take your time to do your working carefully and to check your answers. Some questions will just involve multiple choice, so you will be asked to tick one or more boxes. For some other questions, you will be asked to enter a number or a mathematical expression. The syntax used for mathematical expressions is similar to that used in spreadsheets or in programming languages and is explained below. For example, if you think that the answer is \(e^{-10x}\sin 11\pi x\), you will need to type e^(-10*x)*sin(11*pi*x).

Read the feedback and try again

Most questions will give no credit for partially correct answers. Instead, however, you can make multiple attempts. Most questions will have a button marked Check which you can click to mark your answer. The system will then tell you whether your answer is correct. If it is not, then the system may also give you some further information about what is wrong. You should read this information carefully, and think through your answer again taking into account what you have learned. You may want to move away from the computer again to do this. By default, you lose 0.1 marks for every incorrect attempt, so you will get 0.7 marks if you answer correctly on the fourth attempt, for example. However, for multiple choice questions the penalty is usually larger than 0.1 marks.

Finish up

When you have answered all questions correctly, or run out of attempts, you can click Finish attempt, and then Submit all and finish. It is not crucial to do this, as attempts will automatically be submitted when the deadline passes.

Solutions

After the submission deadline has passed, you can revisit the quiz to see the correct answers. Some questions will also have detailed solutions showing the intermediate working.

Syntax for mathematical expressions

You should type in your answers using the syntax described below. This is broadly similar to the syntax used for mathematical formulae in Python, MATLAB, R, Excel and similar systems, so you will find it useful to master it. Stack tries quite hard to give helpful information about syntax errors.
  • Numbers like \(1/4\) should be entered as 1/4, not as 0.25, which can cause some subtle problems.
  • Use a star for multiplication: for example, \(3x\) should be entered as 3*x. If you leave out a star, Stack will usually warn you as soon as you enter the offending expression.

  • Use a caret (^) for raising something to a power: for example, \(x^{2}\) should be entered as x^2. You can get a caret by holding down the SHIFT key and pressing the 6 key on most keyboards. Fractional powers need brackets: enter \(x^{1/3}\) as x^(1/3). Similarly, \(x^{i+j}\) should be entered as x^(i+j).

  • More generally, when in doubt, use brackets. For example, \[ \frac{a+b}{c+d} \] should be entered as (a+b)/(c+d). Note that in this context you should always use ordinary round bracket (like (a+b)), not square or curly ones (like [a+b] or {a+b}).
    If you type a+b/(c+d), then Stack will think that you mean \[ a + \frac{b}{c+d}. \] If you type (a+b)/c+d, then Stack will think that you mean \[ \frac{a+b}{c} + d. \] If you type a+b/c+d, then Stack will think that you mean \[ a + \frac{b}{c} + d. \]
    Some other examples:
    • \(2^{a+b}\) should be entered as 2^(a+b)
    • \(2 \cos 3x\) should be entered as 2*cos(3*x)
    • \(e^{ax}\sin(bx)\) should be entered as exp(a*x)*sin(b*x)
    • \((a x^{2} + b x + c)^{-1}\) should be entered as (a*x^2 + b*x + c)^(-1).


  • The syntax is case-sensitive. Do not enter X instead of x, or a instead of A, or Log(Z) instead of log(z).
  • The absolute value of \(x\), which is written as \(|x|\) in traditional notation, must be entered as abs(x).
  • The square root of \(x\) can be entered as sqrt(x). Similarly, type sqrt(x^2+y^2) for \(\sqrt{x^2+y^2}\).
  • Standard functions such as sin, cos, tan, exp, log and so on can be entered using their usual names. However, the argument must always be enclosed in brackets: \(\sin x\) should be entered as sin(x), \(\ln 3\) should be entered as ln(3) and so on. You can use either log(x) or ln(x) for the natural logarithm of x (note that both of these start with a lower case l as in lemon, not a capital I). Recall that \(\exp(x)\) and \(e^x\) mean the same thing; it can be entered as exp(x) or e^x.

  • The expression \(\sin^{2}x\) should be entered as sin(x)^2 (which is what it really means, after all). Similarly for \(\tan^{2}(x)\), \(\sinh^{2}(x)\) and so on.

  • Recall that \(\sin^{-1}(x)\) traditionally means the number \(t\) such that \(\sin(t) = x\), which is of course completely different from the number \(\sin(x)^{-1} = 1/\sin(x)\). This traditional notation is not used by any computer system. In Stack, \(\sin^{-1}(x)\) should be entered as asin(x), and \(\tan^{-1}(x)\) should be entered as atan(x) and so on.

  • Greek letters can be entered using their English names: for example, enter \(\alpha+\beta\) as alpha+beta, and \(2\theta\) as 2*theta.

  • Lists or vectors should be entered with square brackets, like [6,2,-8]. (Using round brackets will give a syntax error.) Matrices can be entered using nested square brackets, like [[10,11],[12,13]] for the matrix \(\begin{pmatrix}10 & 11 \\ 12 & 13\end{pmatrix}\).
  • Finite sets can be entered using curly brackets, such as {1,pi,pi^2} for the set \(\{1,\pi,\pi^2\}\), or {10,11,12}.