A-Level Maths: Pure Mathematics Practice

Solve x² - 6x + 2 = 0, giving your answers in the form a ± √b.

Express (3x + 5)/(x² + 3x + 2) in partial fractions.

Find the set of values of x for which |2x - 3| > 5.

Find the equation of the perpendicular bisector of the line segment joining (2, 5) and (6, 1).

A circle has equation x² + y² - 6x + 4y - 12 = 0. Find its centre and radius.

A curve has parametric equations x = 2t², y = 4t. Find dy/dx in terms of t.

Prove that (sinθ + cosθ)² = 1 + sin2θ for all θ.

Solve 2cos²x - cosx - 1 = 0 for 0 ≤ x ≤ 2π.

Express 3sinx + 4cosx in the form Rsin(x + α) where R > 0 and 0 < α < π/2, and state the maximum value.

Find dy/dx when y = (2x + 1)⁵(3x - 1)³ using the product rule.

Find the coordinates of the stationary point of y = x³ - 6x² + 9x + 1 and determine its nature.

Given y = x²eˣ, find d²y/dx².

Evaluate ∫₀² (4x³ - 6x + 1) dx.

Find the area enclosed by the curve y = x² - 4x + 3 and the x-axis.

Use the trapezium rule with 4 strips to estimate ∫₁³ 1/(x²+1) dx.

The 3rd term of an arithmetic sequence is 14 and the 7th term is 38. Find the first term and common difference.

Find the sum to infinity of the geometric series 8 + 4 + 2 + 1 + ...

Find the coefficient of x³ in the binomial expansion of (2 - 3x)⁵.