Inputting ratios of algebraic expressions.

Solve for $x$: $\displaystyle \frac{px+s}{ax+b} = \frac{qx+t}{cx+d}$ with $pc=qa$.

A few simple functions are provided of the form ax, x+b and cx+d. Values of the functions, inverses and compositions are asked for. Most are numerical but the last few questions are algebraic.

A quadratic is given and sketched. Based on the sketch, task is to determine the number of solutions to the equation $f(x)=0$.

Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by substitution 3 with parts' by Joshua Boddy.

Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by elimination 1 with parts' by Joshua Boddy.

These basic questions will help you expand one set of brackets for linear variables

Factorising polynomials using the highest common factor.

Adapted from 'Factorisation' by Steve Kilgallon.

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A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

A detailed look at how algebraic fractions can be manipulated and simplified.

Add, subtract, multiply and divide numerical fractions.

Adapted from 'Algebraic fractions: operations involving algebraic fractions' by Ben Brawn.

Some practice collecting like terms of algebraic expressions, with detailed advice.

Adapted from 'Collecting like terms' by Ben Brawn.

A (quadratic) function is skethed sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

A graph of an (invertible) cubic is given. The question is to determine values of $f$ from graph.

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

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Simplifying algebraic expressions

Tests Algebra, Graphing Straight Lines, Probability, Statistics

Practice with adding, subtracting and dividing basic algebraic fractions

A quadratic is given and sketched. Based on the sketch, task is to determine the number of solutions to the equation $f(x)=0$.

Fourth part of the Core Foundation Maths pre-arrival self-assessment material:

Question 1:  Algebra IV: Properties of indices (1) - Multiplication/Division                                 

Question 2: Algebra IV: Properties of indices (2) - Fractions                                 

Question 3: Algebra IV - Properties of Indices (4) - Further

Question 4: Numbers V: standard index form (conversions and operations)                                 

Practice with adding, subtracting and dividing basic algebraic fractions

Tests the ability to find the gradient and intercept of a straight line graph.

A graph of a straight line $f$ is given. Questions include determining values of $f$, of $f$ inverse, and determing the equation of the line.

Putting algebraic fractions into their simplest forms

Three graphs are given with areas underneath them shaded. Student is asked to determine the minimum and maximum $x$-values of the regions. This will involve solving a linear equation and two trigonmetric equations.

Several quadratics are given and students are asked to factorise them.

A few simple functions are provided of the form ax, x+b and cx+d. Values of the functions, inverses and compositions are asked for. Most are numerical but the last few questions are algebraic.

A graph of a straight line $f$ is given. Questions include determining values of $f$, of $f$ inverse, and determining the equation of the line.