IGCSE Mathematics - Additional (0606) — October–November 2024, Paper 11

The diagram shows the graph of y = f(x) , where f(x) is a cubic polynomial. The graph touches/crosses the x-axis at x = −4, x = 0.5 and x = 2, and the y-intercept of f(x) is 24.…

Given that 256^(x + y) × 16^(−2x) = 8^(−x + 3y), show that y = 3x.

The diagram shows part of the graph of f(x) = a cos bx + c, where a, b and c are constants. The curve has a maximum of 6 on the f(x)-axis and crosses the x-axis at x = ±320°.…

Given that ∫₀^(2a + 1) 8/(4x + 3) dx = ln 16, find the exact value of the constant a.

In the expansion of (1 + kx)¹⁵, where k is a constant, the coefficient of x³ is −29 120. Find the value of k.

The polynomial p is such that p(x) = ax³ + 11x² + bx + c, where a, b and c are integers. It is given that p′(0) = 12. It is also given that x + 3 is a factor of p. When p is…

When e^(5y) is plotted against x³, a straight line passing through the points (−2.56, 4.38) and (6.54, 9.84) is obtained. Find y in terms of x.

Given that f''(x) = (3x + 5)^(−2/3), f'(1) = 6, and f(1) = 20, find an expression for f(x).

The equation of a curve is y = e^(−3x + 2)/(x + 1) where x < −1. Show that dy/dx = e^(−3x + 2)/(x + 1)²·(Ax + B), where A and B are integers to be found.

The 3rd and 8th terms of a geometric progression are 6 and 1458 respectively. Find the common ratio and the first term of this progression.

The diagram shows part of the curve y = 4 + 2 sin 3x and the straight line AB. The points A and B lie on the curve. The x-coordinate of A is π/18 and the x-coordinate of B is π/3.…

Solve the equation 2 cosec²θ − 5 = 5 cot θ for −180° ≤ θ ≤ 180°.