AS & A Level Mathematics (9709) — October–November 2024, Paper 11

In the expansion of (kx + 2/x)⁴, where k is a positive constant, the term independent of x is equal to 150. Find the value of k and hence determine the coefficient of x² in the…

The curve y = x² − a/x has a stationary point at (−3, b). Find the values of the constants a and b.

The diagram shows a sector of a circle, centre O, where OB = OC = 15 cm. The size of angle BOC is (2/5)π radians. Points A and D on the lines OB and OC respectively are joined by…

Show that the curve with equation x² − 3xy − 40 = 0 and the line with equation 3x + y + k = 0 meet for all values of the constant k.

The equation of a curve is such that dy/dx = 4x − 3√x + 1. Find the x-coordinate of the point on the curve at which the gradient is 11/2.

Circles C₁ and C₂ have equations x² + y² + 6x − 10y + 18 = 0 and (x − 9)² + (y + 4)² − 64 = 0 respectively. Find the distance between the centres of the circles.

The diagram shows part of the curve with equation y = 12/∛(2x + 1). The point A on the curve has coordinates (7/2, 6). Find the equation of the tangent to the curve at A. Give…

It is given that β is an angle between 90° and 180° such that sin β = a. Express tan²β − 3 sin β cos β in terms of a.

The equation of a curve is y = 4 + 5x + 6x² − 3x³. Find the set of values of x for which y decreases as x increases.

An arithmetic progression has first term 5 and common difference d, where d 0. The second, fifth and eleventh terms of the arithmetic progression, in that order, are the first…

The function f is defined by f(x) = 3 + 6x − 2x² for x ∈ ℝ. Express f(x) in the form a − b(x − c)², where a, b and c are constants, and state the range of f.