IGCSE Mathematics - Additional (0606) — May–June 2024, Paper 21

On the axes provided, sketch the graph of y = 4x − 6 , showing the points where the graph meets the axes.

Write 3 + 4x − 2x² in the form a + b(x + c)², where a, b and c are integers.

Use algebra to show that the equation 5x(x − 3) = 5x − 26 has no real solutions.

DO NOT USE A CALCULATOR IN THIS QUESTION. Find the exact distance between the two points where the curve 9(x − 1)² + 4(y − 3)² = 36 cuts the y-axis.

There are 3 women, 2 men and 4 children in a choir. The choir stands in a single straight line. Find the number of possible arrangements if the first person and last person are…

Variables x and y are such that y = cos x sin²x. Use differentiation to find the approximate change in y as x increases from 3 to 3 + h, where h is small.

It is given that y = mx² + x/2 + n, where m and n are non-zero constants. It is also given that 3·(d²y/dx²) = x·(dy/dx) − y for all values of x. Find the values of m and n.

In an arithmetic progression, the sum of the first 30 terms is −1065. The sum of the next 20 terms is −2210. Find the first term and the common difference.

The functions f and g are defined by f(x) = 3x²/(4x − 1) for x < 0, and g(x) = 2/x for x < 0. Explain why the function fg does not exist.

Show that (tan x + sec x)² can be written as (1 + sin x)/(1 − sin x).

In this question all lengths are in centimetres. The diagram shows a rectangle ABCD with BC = x. The area of the rectangle is 400 cm². Two identical quarter-circles of radius x/2,…

The diagram shows a triangle OBC. OA : OB = 4 : 7 and OD : OC = 4 : 7. OB = b and OC = c. The point P is the point of intersection of AC and BD such that AP = m·AC and BP = n·BD…