AS & A Level Mathematics (9709) — October–November 2024, Paper 12

The diagram shows the curve with equation y = a sin(bx) + c for 0 ≤ x ≤ 2π, where a, b and c are positive constants. State the values of a, b and c.

The first term of an arithmetic progression is −20 and the common difference is 5. Find the sum of the first 20 terms of the progression.

The equation of a curve is y = 2x² − 3. Two points A and B with x-coordinates 2 and (2 + h) respectively lie on the curve. Find and simplify an expression for the gradient of the…

Find the term independent of x in the expansion of the following: (x + 3/x²)⁶.

The function f is defined by f(x) = (2x + 1)/(2x − 1) for x < ½. State the value of f(−1).

The diagram shows a metal plate OABCDEF consisting of sectors of two circles, each with centre O. The radii of sectors AOB and EOF are r cm and the radius of sector COD is 2r cm.…

By expressing −2x² + 8x + 11 in the form −a(x − b)² + c, where a, b and c are positive integers, find the coordinates of the vertex of the graph with equation y = −2x² + 8x + 11.

The equation of a circle is x² + y² + px + 2y + q = 0, where p and q are constants. Express the equation in the form (x − a)² + (y − b)² = r², where a is to be given in terms of p…

The equation of a curve is y = ½k²x² − 2kx + 2 and the equation of a line is y = kx + p, where k and p are constants with 0 < k < 1. It is given that one of the points of…

A function f with domain x 0 is such that f′(x) = 8(2x − 3)^(1/3) − 10x^(2/3). It is given that the curve with equation y = f(x) passes through the point (1, 0). Find the equation…