IGCSE Mathematics - Additional (0606) — October–November 2023, Paper 12

The diagram shows the graph of the cubic polynomial y = f(x). The curve crosses the x-axis at x = −1/3, x = 1 and x = 5/2, and the y-intercept is −15. Find an expression for f(x)…

The function g is defined by g(x) = 5 sin(3x/4) − 2 for all values of x. Write down the amplitude of g.

When ln(y + 2) is plotted against x² a straight line graph is obtained. The line passes through the points (2.25, 9.37) and (4.75, 3.92). Find y in terms of x.

It is given that the first four terms, in ascending powers of x, in the expansion of (1 − x/2)ⁿ can be written in the form 1 − 8x + px² + qx³, where n, p and q are integers. Find…

Solve the equation 3 sec²(2θ + π/6) = 4 for −π/2 < θ < π/2, giving your answers in terms of π.

The polynomial p(x) is such that p(x) = ax³ + bx² + cx − 5, where a, b and c are integers. It is given that p′(0) = 12. It is also given that p(x) has a factor of 3x − 1 and a…

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

It is given that f : x ↦ (3x + 1)² − 4 for x ≥ a, and that f⁻¹ exists. Find the least possible value of a.

Solve the equation 12x^(2/3) − 5x^(1/3) − 11 = 0 for x 0. Give your answer correct to one decimal place.

In this question all lengths are in centimetres and all angles are in radians. The diagram shows a badge which consists of a minor sector OAB of the circle with centre O and…

In the triangle OAB, OA = a and OB = b. The mid-point of the line OB is X, and the mid-point of the line AB is Y. The lines OY and AX intersect at the point Z. It is given that AZ…

A curve has equation y = √(5x − 2)/(x − 3). Explain why the curve does not exist when x < 2/5.