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

Express $\displaystyle b+  \frac{dx+p}{x + q}$ as an algebraic single fraction. 

Express $\displaystyle \frac{ax+b}{x + c} \pm  \frac{dx+p}{x + q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{ax+b}{cx + d} \pm  \frac{rx+s}{px + q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$

Refresher questions on topics in algebra that students beginning a maths undergraduate course should be familiar with.

Solve a simple linear equation algebraically. The unknown appears on both sides of the equation.

Find the remainder when dividing two polynomials, by algebraic long division.

A fill-in-the-blank style question to test vocabulary within the topic of Algebra.

Questions on rearranging expressions, expanding brackets and collecting like terms.

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Several quadratics are given and students are asked to complete the square.

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

Instructions on inputting ratios of algebraic expressions.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

How to input x^2 and x*y.

Inputting ratios of algebraic expressions.

Entering numbers and algebraic symbols  in Numbas.

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

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

Factorising polynomials using the highest common factor.

Adapted from 'Factorisation' by Steve Kilgallon.

Factorising polynomials using the highest common factor.

Adapted from 'Factorisation' by Steve Kilgallon.

Refresher questions on topics in algebra that students beginning a maths undergraduate course should be familiar with.

A fill-in-the-blank style question to test vocabulary within the topic of Algebra.

Simplifying indices.

Simplifying indices.