9709/12 · Oct/Nov 2025

Complete the square, the condition for no real roots, and an exact solution.

Constant term in a binomial expansion.

Describe combined transformations and write the equation after a stretch and reflection.

Find a constant from a gradient condition, then integrate to find the curve.

Locate a maximum point, then the exact area under the curve.

Sketch a trigonometric graph with a linear term, count solutions and solve an equation.

Circle from a diameter, the tangent at a point and where two tangents meet.

Linked geometric and arithmetic progressions, a sum to infinity and a partial sum.

Show a function is increasing, decide if its inverse exists, and a composite function.

Circle geometry to show a length ratio, then the exact area of a shaded region.