9709/12 · May/June 2022

Match binomial coefficients to find a positive constant.

Sum to infinity of a geometric progression from two of its terms.

Integrate a derivative and use a point to find the curve.

Arithmetic progression: find a constant, then the sum of 30 terms.

Where a parabola meets a line, and the condition for a tangent.

Exact area between a square-root curve and a line.

Arc length to find an angle, then the area of a triangle.

Circle through two points: find the centre, then a tangent.

Differentiate and find and classify a stationary point.

Inverse and composite functions, when no inverse exists, and a tangent triangle area.

Trigonometric equation as a quadratic, and the discriminant to show no solutions.