Evaluate a composition of functions for a randomised numerical input. The functions are 3t+2 and t+3. This is part of HELM Book 2.1.3.

Given f(x)=(x+a)/(x+b) and g(x) = 1/x, compute f(g(x)) and g(f(x)).

a and b are randomised integers.

Given 2 randomised functions f(x) (linear) and g(x) (quadratic), find one of f(f), f(g), g(f) or g(g) at a randomised integer x-value

Given 2 randomised functions f (linear) and g (quadratic), find one of f(f), f(g), g(f) or g(g)

Student is asked to find the distance from a given point, A, to a house, given the distance between A and another point B, and the angles at A and B. Requires use of the sine rule. Distance and angles are randomised.

Student is asked to find the distance from a given point, B, to a house, given the distance between B and another point A, and the angles at A and B. Requires use of the sine rule. Distance and angles are randomised.

Students need to solve a quadratic equation and recognise that only the positive root has physical significance. Roots are randomised with one always negative and one positive. Equation can be factorised fairly easily or the quadratic formula can be used to find the solution. Advice gives solution by factorisation.

Students are given lengths of 3 sides of a triangle (all randomised) and asked to find one of the angles in degrees. Requires use of the cosine rule.

Students are asked to solve two simulatineous linear equations in an application of mixing two liquids to arrive at a given final volume and concentration. Students are expected to write up working for their solution and upload it seperately. Final volume, final concentration and concentrations of each solution are randomised.

This question is an application of a quadratic equation. Student is given dimensions of a rectangular area, and an area of pavers that are available. They are asked to calculate the width of a border that can be paved around the given rectangle (assuming border is the same width on all 4 sides). The equation for the area of the border is given in terms of the unknown border width. Students need to recognise that only one solution of the quadratic gives a physically possible solution.

The dimensions of the rectangle, available area of tiles and type of space are randomised. Numeric variables are constructed so that resulting quadratic equation has one positive and one negative root.

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.

There's one question, which you have to get right 5 times in a row. If you get it wrong, you have to start again.

This makes more sense if the question is randomised!

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.

Two functions given in words. Write down the function definition. The numbers in the function definitions are randomised.

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

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.

Add (a/b).x +/- (c/d) where a,b,c,d are randomised positive integers, and x is a randomised letter.

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.

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

Written for the Western Sydney University MESH numeracy preparation workshop for the LANTITE test (Australia). Students must work backwards to work out what the original number was, or alternatively test out each supplied multiple choice option. There are 8 possible randomised numbers in this question.

This practice quiz contains 40 numeracy questions, for students preparing for the Australian LANTITE numeracy test. Each question is randomised.

There are 10 questions each from the Number and Algebra, Measurement and Geometry, Statistics and Probability, and non-Calculator strands.

Students are allowed 75 minutes to complete the test. The questions are multiple choice, true/false or fill the number in the box.

Twenty questions which can be used by Initial Teacher Education students preparing for the Australian LANTITE numeracy test. The questions are grouped in content strands and each question is randomised. Questions are either multiple choice, true/false or type the answer in a box. The questions are chosen from a menu and there is no time limit. They are different to the questions in Timed Practice Quiz v2.