IGCSE Mathematics - Additional (0606) — October–November 2023, Paper 11

The diagram shows part of the graph of y = a cos(x/b) + c, where a, b and c are integers. The graph is drawn over −720° ≤ x ≤ 720°, oscillating between a maximum of −1 and a…

The polynomial P(x) is such that P(x) = ax³ − 11x² + bx + c, where a, b and c are integers. P(x) is divisible by x and has a remainder of 3/2 when divided by 2x + 1. It is also…

The point A has position vector (2, −6) and the point B has position vector (−3, 6). Find, in vector form, the displacement of B from A.

The table shows values of the variables x and y, which are related by the equation y = Ax^b, where A and b are constants. x 1 2 3 4 5 --- --- --- --- --- --- y 20 57 104 160 224…

A 4-digit code is to be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. No digit may be used more than once in any code. A code may start with 0. Find how many codes can…

Write 3 lg x − (1/2) lg 4 + 2 as a single logarithm to base 10.

A curve has equation y = f(x), where f(x) = (2x + 1)(3x − 2)². Show that f′(x) can be written in the form 2(3x − 2)(px + q), where p and q are integers.

The diagram shows the line y = 1 − 4x meeting the curve y = 4x² − 6x − 5 at the points A and B. The tangent to the curve at B meets the horizontal line through A at the point C.…

The first three terms of an arithmetic progression are −3 tan(θ/2), −tan(θ/2), tan(θ/2), where 0 < θ < π/2. Given that the 12th term of this progression is equal to 19√3/3, find…

Given that y = (3x² − 2)/(x − 4), show that dy/dx can be written in the form (Ax + B)/((x − 4)²√(3x² − 2)), where A and B are integers to be found.