IGCSE Mathematics - Additional (0606) — May–June 2024, Paper 11

On the axes provided, sketch the graph of y = −(1/5)(x + 2)(2x − 1)(x + 5), stating the intercepts with the axes.

DO NOT USE A CALCULATOR IN THIS QUESTION. The polynomial p is such that p(x) = 6x³ − 35x² + 34x + 45. Find p(x) in the form (2x − 5)q(x) + r, where q(x) is a polynomial and r is a…

Write 1 + lg(x² − 1) − 2 lg(x − 1), where x 1, as a single logarithm to base 10. Give your answer in its simplest form.

The first three terms, in ascending powers of x, in the expansion of (3 + px)ⁿ are 243 + 810x + qx², where n, p and q are constants. Find the values of n, p and q.

The diagram shows the graph of y = a cos bx + c, for −360° ≤ x ≤ 360°, where a, b and c are constants. The curve oscillates between a maximum of 1 and a minimum of −9. Find the…

Find ∫₂^4 (2/(2x − 3) − 3/(3x − 5)²) dx, giving your answer in exact form.

Given that 2 + cot θ = 3x and sin θ = y, find y in terms of x.

Solve the equation 4 sin²(2α − π/3) = 1 for −π/2 ≤ α ≤ π/2. Give your answers in terms of π.

Solve the following simultaneous equations: e^(x + y) × e^(3x − 2y) = 1 and x²y = 256.

In this question, all distances are in metres and time, t, is in seconds. A particle P is at a fixed point O at time t = 0. The velocity, v, of P is given by v = 3 sin 2t for t ≥…

The tangent to the curve y = (3x − 1)^(1/3) at the point where x = 3 meets the coordinate axes at the points A and B. The point with coordinates (a, a) lies on the perpendicular…

It is given that y = ln(3x)/x² for x 0. Find dy/dx. Give your answer in the form (A + B ln 3x)/x³, where A and B are integers.