Drills

Zetamac-style rapid-fire addition, subtraction, multiplication and division.

Instant recall of squares, cubes, square roots and cube roots.

Fraction arithmetic, converting between fractions, decimals and percentages, and percentages of amounts.

Write surds in simplest form, e.g. √50 = 5√2, including products and sums.

Rationalise a/√b and a/(b ± √c), giving the answer with an integer denominator.

Evaluate negative, zero and fractional powers and combine indices without a calculator.

Evaluate logs exactly, e.g. log₂ 32, log₃ (1/9), log₄ 8, ln e³ and log laws.

Solve equations such as 2ˣ = 32, 3ˣ⁺¹ = 81, 4ˣ = 8, log₂ x = 5 and logₓ 64 = 3.

Multiply out products of linear brackets and squares, e.g. (2x + 1)(x − 3).

Factorise monic and simple non-monic quadratics and differences of two squares.

Rewrite x² + bx + c as (x + p)² + q, optionally with odd b or a leading coefficient.

Solve quadratics with integer or half-integer roots by factorising; give both roots.

Factorise and cancel common factors, e.g. (x² − 9)/(x − 3) = x + 3.

Differentiate polynomials, including negative and fractional powers of x.

Find indefinite integrals of polynomials (the + c is optional).

Differentiate f(x) and evaluate f'(a) at a small integer a.

Recall exact values of sin, cos and tan at multiples of 30° and 45°, in degrees or radians.

Evaluate nCr and find coefficients in expansions such as (1 + 2x)ⁿ.