Given f(x)=1/(a-x)^2, evaluate f(x/z) where a is a randomised constant, and z is a randomised letter.

Give f(x)=ax^2+b a simple function input (like 6x-3) and evaluate. Constants and variables, and the function input are all randomised.

evaluate a function with randomised alphanumeric expressions as inputs.

Evaluate a given, randomised, linear function at a given, randomised, value.

Student is shown a simple (randomised) function and asked to describe its behaviour. This is an information only question. Students need to view the advice to check their answer.

A difficult question that involves rearranging a complicated formula, then applying unit conversions to variable values, then evaluating the formula for the selected value. The variable values are randomised.

Rearrange a complex formula involving squares, square roots, fractions and additions. This is a fixed question with no randomisation.

Rearrange a linear function in x and y to make y the subject. Line variables are randomised.

Transpose PV=RT to make a random variable the subject.

Convert a random number of cubic metres into cubic centimetres

Convert a random value in square metres to square centimetres.

Evaluate J = (1/2)Ma^2 for random values of M and a.

convert a random length in m to centimetres

evaluate a function (4a)/(pi*b^2cd) given random values for a,b,c,d.

evaluate sqrt(x/z) where x and z are random positive decimals.

There are two parts: 

(3x)/4-x/5+x/3 and (3x/4)-(x/5+x/3).

The numbers are randomised to small, coprime, positive integers.

Simplify (qx+a)/(rx+b) +/- (sx+c)/(rx+b)^2

x is a randomised variable. a,b,c,d,q,r are randomised integers.

Simplify (qx+a)/(rx+b) +/- (sx+c)/(tx+d)

x is a randomised variable. a,b,c,d,q,r,s,t are randomised integers. a,b,c,d run from -5 to 5, including 0. q,r,s,t run from -3 to 3, and can be 0 if the constant term is nonzero, but are mostly 1.

Simplify ax/b +/- cx/d, where x is a randomised variable, and a,b,c,d are randomised integers.

Round random numbers to the closest whole number, 1, 2 or 3 decimals places.

This uses an embedded Geogebra graph of a sine curve $y=a\sin (bx+c)+d$  with random coefficients set by NUMBAS.

Simplify (a) a fully-factorised fraction with common factors, and (b) a fraction where the numerator is a product and the denominator a sum sharing the same variables (that cannot be simplified). The variables are randomised. Part of HELM book 1.4

Simplify, if possible,
(a) $\frac{2}{3}x^2 + \frac{x^2}{3}$, (b) $0.5x^2 + \frac{3}{4}x^2 - \frac{11}{2}x$, (c) $3x^3 - 11x + 3yx + 11$, and (d) $-4\alpha x^2 + \beta x^2$ where $\alpha$ and $\beta$ are constants.

The numbers and letters are all randomised.

Part of HELM Book 1.3

Given a randomly-generated list, the student must write code to return its first value.

There's an alternative to check if they get the second item, which they might do if they don't realise Python lists are zero-indexed.

It is estimated that 30% of all CIT students cycle to college. If a random sample of eight CIT students is chosen, calculate the probability that...

rebelmaths

Multiple choice question. Given a randomised polynomial select the possibe ways of writing the domain of the function.

Multiple choice question. Given a randomised polynomial select the possible ways of writing the domain of the function.

Given a randomised log function select the possible ways of writing the domain of the function.

Given a randomised rational function select the possible ways of writing the domain of the function.

Tests students' ability to apply the recursive form of the Extended Euclidean Algorithm.  Random four-digit inputs are chosen subject to the condition that the Euclidean Algorithm terminates in seven steps.