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

No description given

Simplifying indices.

Simplifying indices.

Simplifying indices.

Expansion of two brackets

rebelmaths

A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.

A quadratic equation (equivalent to $(x+a)^2-b$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

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

Practice with adding, subtracting and dividing basic algebraic fractions

A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.

No description given

No description given

No description given

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.

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.

No description given

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.