Shows how to define variables to stop degenerate examples.

A simultaneous equations question with integers only

5 questions which introduce the student to the Numbas system:

1. Input 1

2. Input 2

3. Input 3         

4. Input 4       

5. Input 5                                                                                  

Solving quadratic equations using the formula

Selection of Quadratic Equations to Solve

Selection of Quadratic Equations to Solve

Finding equation of a straight line graph and a parallel line through a given point.

This task is part of a set of three assessment tasks for 7.RP.2.

7.RP.2 Robot Races asks students to "explain what a point (x,y) on the graph of a proportional relationship means in terms of the situation" and to "compute unit rates associated with ratios of fractions." Students also need to compare the speeds of the robots.

Given two ordered sets of vectors $S,\;T$ in $\mathbb{R^5}$ find the reduced echelon form of the matrices given by $S$ and $T$ and hence determine whether or not they span the same subspace.

r digits are picked at random (with replacement) from the set $\{0,\;1,\;2,\ldots,\;n\}$. Probabilities that 1) all $\lt k$, 2) largest is $k$?

This exercise will help you solve equations of type ax-b = c.

Solving linear equations to find the value of x.

Calculate the expression $\frac{12}{4}a+\frac{3}{5}a$. One of the following is not correct, which one?

Basic solving of linear equations.

A 3-digit number multiplied by a 2-digit number.

A 2-digit number multplied by a 1-digit number.

Basic calculation exercise using distance, mpg and cost per litre (with the conversion factor for gallons to litres given).

Based on a generic test QTS question.

Add/subtract fractions and reduce to lowest form.

Given value of x^(1/n), x^(-1/n) find x.

Given amounts of ingredients for n cakes, given list of ingredients for m.

Finding speeds and impulses 

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multiple choice testing sin, cos, tan of  random(0,90,120,135,150,180,210,225,240,270,300,315,330) degrees

Seven standard elementary limits of sequences. 

These 5 questions will introduce the student to the Numbas system-

1. Input 1          

2. Input 2

3. Input 3

4. Input 4     

5. Input 5                                           

Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.

Solve a first order algebraic equation

This question allows you to practice identifying the coordinates of points on graphs.

Factorising polynomials using the highest common factor.

Adapted from 'Factorisation' by Steve Kilgallon.

Applying trigonometry to find heughts and lengths.