9709/12 · May/June 2023

Find a curve from its derivative, a power of a linear bracket, and a point on it.

Binomial expansion: compare coefficients to find an unknown constant.

Complete the square, then use the discriminant for a quadratic with no real roots.

Solve an equation that is quadratic in a power of x.

Area under a curve with fractional powers, by integration.

Arc length and areas of sectors and segments in radians.

Prove a trigonometric identity and use it to solve an equation.

Inverse function: find it, sketch it and describe transformations of a sine graph.

Geometric progressions: first term from the second term and the sum to infinity.

Circle and tangent: find a constant, the normal and parallel tangents.

Differentiate a square-root function, find a stationary point and a normal.