# Question Authoring Cheat Sheet

## Part Types

 Information only Normally used in Steps; no student input. Gap-fill Place multiple inputs inside the prompt text. Mathematical expression Algebraic answer; instant rendering of input. Number entry Accept a number within a range; can require certain number of sig. fig.s or d.p. Matrix entry Answer is a matrix of numbers; individual cells marked like number entry. Match text pattern Free text input. Must match given regular expression. Choose one from a list Student picks one answer from a multiple choice list. Choose several from a list Student picks any number of answers from a list; can specify max. and min. choices. Match choices with answers 2D grid; match items from two lists. Can allow one answer per choice or many.

You can add additional Step parts to any part. These should provide extra hints, or break the question into smaller steps.

## Displaying Maths

LaTeX is only used to render maths, not for text or layout.

Variables and correct answers are defined using JME syntax, not LaTeX.

Inline maths is enclosed in dollar signs: $x^2 + 1$ produces $x^2 + 1$.

Display maths is enclosed in $ and $, and displayed on its own line. $x^2 + 1$ produces: $x^2 + 1$

### LaTeX commands

Command Output
x \lt y \gt z $x \lt y \gt z$
A_{x} A^{y} $A_{x} A^{y}$
a = b \neq c $a = b \neq c$
\frac{x}{y} $\frac{x}{y}$
x \times y \cdot z $x \times y \cdot z$
\alpha, \beta, \dots $\alpha, \beta, \dots$
\left( \sum_{x=1}^{\infty} x^2 \right) $\left( \sum_{x=1}^{\infty} x^2 \right)$

## Content

### To insert a video

Go to the YouTube / Vimeo page for the video. Copy the URL in the address bar. In the editor, click Insert video and paste in the URL.

### To insert an image

Click Insert image. Click Upload an image and select the image.

## Randomised content

To substitute text, wrap a variable name in curly braces: My name is {name} produces output like My name is Bob.

To substitute a simple number in maths, use the \var command in LaTeX: $x + \var{a}$ produces $x + 2$.

For randomised expressions which might need simplifying, use \simplify. Expressions inside curly braces are evaluated: $\simplify{ {a}x + {b}x + {c} }$ produces $2x - 3$ when $a=2,b=0,c=-3$.

### Variable annotations

Use annotations to display variable names differently inside a simplified expression. For example, $\simplify{ vector:x }$ produces $\boldsymbol{x}$.

Any LaTeX command can be used as an annotation for notation which is not built-in, e.g. $\simplify{ vec:x }$ produces $\vec{x}$.

Annotations can be chained together. For example, $\simplify{ unit:v:x }$ produces $\hat{\boldsymbol{x}}$.

Annotation Output Meaning
 verb:pi  $\pi$ Verbatim - overrides built-in constants $e, \pi, i$.
 op:x  $\operatorname{x}$ Operator name
 v:x  $\boldsymbol{x}$ Vector
 unit:x  $\hat{x}$ Unit vector
 dot:x  $\dot{x}$ Dot on top
 matrix:A  $\mathrm{A}$ Matrix

### Simplification rules

Usage: $\simplify[rule1,rule2,...]{ expression }$

  unitFactor  Cancel products of 1.  unitPower  Cancel exponents of 1.  unitDenominator  Cancel fractions with denominator 1.  zeroFactor  Cancel products of 0 to 0.  zeroTerm  Omit zero terms.  zeroPower  Cancel exponents of 0 to 1.  noLeadingMinus  Rearrange expressions so they don't start with a minus.  collectNumber  Collect together numerical products and sums.  simplifyFractions  Cancel fractions to lowest form.  zeroBase  Cancel any power of zero.  constantsFirst  Numbers go to the left of multiplications.  sqrtProduct  Collect products of square roots.  sqrtDivision  Collect fractions of square roots.  sqrtSquare  Cancel square roots of squares, and squares of square roots.  trig  Apply some trigonometric identities.  otherNumbers  Evaluate powers of numbers.  all  Apply all of the above rules, but not the two display rules below.  fractionNumbers  Numbers are displayed as fractions instead of decimals.  rowVector  Vectors are displayed as rows instead of columns.