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.

Add, subtract, multiply and divide algebraic fractions.

Add, subtract, multiply and divide algebraic fractions.

Graphs are given with areas underneath them shaded. The area of the shaded regions are given and from this the value of various integrals are to be deduced.

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.

Some quadratics are to be solved by factorising

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

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Find $\displaystyle \int\frac{ax^3+ax+b}{1+x^2}\;dx$. Enter the constant of integration as $C$.

Inputting algebraic expressions into Numbas.

Inputting ratios of algebraic expressions.

Entering numbers and algebraic symbols  in Numbas.

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 $\displaystyle ax+b+  \frac{dx+p}{x + q}$ 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.