IGCSE Mathematics - Additional (0606) — May–June 2024, Paper 12

The diagram shows the graph of y = a sin bx + c for −360° ≤ x ≤ 360°, where a, b and c are constants. The curve oscillates between a maximum of 0 and a minimum of −8 (y-axis from…

Given that log₃ r + 2 log₉ s = 8, find the value of rs.

Given that y = tan(x/2), find the exact value of dy/dx when x = π/3.

A team of 8 people is to be formed from 6 teachers, 5 doctors and 4 police officers. Find the number of teams that can be formed.

DO NOT USE A CALCULATOR IN THIS QUESTION. In this question, all lengths are in centimetres. The diagram shows the trapezium ABCD. The lengths of AB, BC and CD are 8√7 − 7, √7 + 2…

In this question, all lengths are in metres and all angles are in radians. The diagram shows a circle with centre O and radius 5. The points A, B, C and D lie on the circumference…

The line y = 3x − 2 intersects the curve 2x² − xy + y² = 2 at the points A and B. The point C with coordinates (k, 7/8) lies on the perpendicular bisector of the line AB. Find the…

A curve has equation y = (3x² − 5)^(1/3)/(x + 4). Show that dy/dx can be written in the form (Ax² + Bx + C)/((3x² − 5)^(2/3)(x + 4)²), where A, B and C are integers.

In this question, all distances are in metres and time, t, is in seconds. A particle P moves with a speed of 14.5 parallel to the vector (−20, 21). Find the velocity vector of P.

The first 3 terms of an arithmetic progression are 3 sin 2x, 5 sin 2x, 7 sin 2x. Show that the sum to n terms of this arithmetic progression can be written in the form n(n + a)…

Given that y = x² ln x, find dy/dx.