IGCSE Mathematics - Additional (0606) — May–June 2024, Paper 13

The diagram shows the graph of y = a sin bx + c, for −320° ≤ x ≤ 320°, where a, b and c are constants. The curve oscillates between a maximum of 6 and a minimum of −2 (y-axis from…

Solve the equation 3(2^(2x + 1)) − 11(2^x) + 3 = 0, giving your answers correct to 2 decimal places.

Find the coordinates of the stationary points on the curve y = (2x + 1)²(x − 3).

Find ∫₀¹ (1 + e^(2x))² dx, giving your answer in exact form.

When e^(2y) is plotted against x³, a straight line graph that passes through the points (2, 5) and (6.4, 7.2) is obtained. Find y in terms of x.

It is given that y = ln(2x² + 1)/(x + 2), x ≠ −2. Find dy/dx.

A 6-digit number is to be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The 6-digit number cannot start with 0. Each digit can be used at most once in any 6-digit number.…

The line L is the normal to the curve y = 3(5x + 6)^(1/2) at the point where x = 2. The point (−2, k), where k is a constant, lies on L. Find the exact value of k.

In this question, all lengths are in metres, and time, t, is in seconds. A particle P moves in a straight line such that, t seconds after leaving a fixed point O, its…

In an arithmetic progression, the first term is a and the common difference is d. The sum of the first three terms of this arithmetic progression is 42. The product of the first…

Solve the following simultaneous equations, giving your answers in exact form: 8 log₃ x + 12 log₈₁ y = 5 and 4 log₉ x + 3 log₃ y = 2.

Solve the equation sec(3θ − π/2) = 2 for −π/2 ≤ θ ≤ π/2. Give your answers in exact form.