Surds and rationalising
Simplify before combining, and rationalise without changing the value.
Further Maths lessons
Read the explanation and worked examples, then try the questions yourself. Each lesson ends with a short check. The practice links follow your selected course.
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Quadratics: roots and turning points
Use factorised form to find roots and completed-square form to find the turning point.
Composite functions
Work out f(g(x)) and g(f(x)), keeping brackets around the function you substitute.
Inverse functions and domain restrictions
Find the inverse of a quadratic on each side of its turning point.
Arithmetic sequences and sums
Find the nth term and the sum of the first n terms of an arithmetic sequence.
Triangle area and side lengths
Match the known information to an area, cosine-rule or sine-rule calculation.
Equations of straight lines
Find gradients and recognise equivalent equations of a line.
Tangents and normals
Use the derivative for a gradient and the original curve for a point.
Matrix multiplication
Calculate AB and BA for two matrices and compare the results.
Multiplying and dividing complex numbers
Multiply using i² = −1 and divide with a conjugate.
Binomial probabilities
Check when a binomial model applies, then calculate the probability of a given number of successes.
Motion with constant acceleration
Use constant-acceleration equations with a consistent positive direction.