AS & A Level Mathematics (9709) — October–November 2024, Paper 13

An arithmetic progression has fourth term 15 and eighth term 25. Find the 30th term of the progression.

Find the exact solution of the equation cos(1/6 π) + tan 2x + √3/2 = 0 for −1/4 π < x < 1/4 π.

Find the coefficients of x³ and x⁴ in the expansion of (3 − ax)⁵, where a is a constant. Give your answers in terms of a.

Solve the equation 4 sin⁴θ + 12 sin²θ − 7 = 0 for 0° ⩽ θ ⩽ 360°.

In the diagram, the graph with equation y = f(x) is shown with solid lines and the graph with equation y = g(x) is shown with broken lines. Describe fully a sequence of three…

The first term of a convergent geometric progression is 10. The sum of the first 4 terms of the progression is p and the sum of the first 8 terms of the progression is q. It is…

The diagram shows a metal plate ABCDEF consisting of five parts. The parts BCD and DEF are semicircles. The part BAFO is a sector of a circle with centre O and radius 20 cm, and D…

Express 3x² − 12x + 14 in the form 3(x + a)² + b, where a and b are constants to be found.

The diagram shows the curves with equations y = x³ − 3x + 3 and y = 2x³ − 4x² + 3. Find the x-coordinates of the points of intersection of the curves.

Points A and B have coordinates (4, 3) and (8, −5) respectively. A circle with radius 10 passes through the points A and B. Show that the centre of the circle lies on the line y =…

The equation of a curve is y = kx^(1/2) − 4x² + 2, where k is a constant. Find dy/dx and d²y/dx² in terms of k.