IGCSE Mathematics (0580) — October–November 2024, Paper 22

These are the first eight terms of a sequence. c -3 -9 -15 -21 -27 -33 k Find the value of c and the value of k.

The diagram shows an isosceles triangle (NOT TO SCALE) with apex angle x° and a base angle of 43°. Find the value of x.

From the list 0.25, 3.142, sqrt(3), -3, 24, -0.4, 1.2, -1/4, complete each statement with a number from the list. ......... is a natural number. ......... is an irrational number.…

The scatter diagram shows the number of rooms and the number of people in each of eight buildings. One of the buildings has 67 rooms. Write down the number of people in this…

Convert 7.51 m^2 into cm^2.

The diagram shows a trapezium (NOT TO SCALE) with parallel sides x cm and 9.5 cm and base 6 cm. The area of the trapezium is 42 cm^2. Calculate the value of x.

Without using a calculator, work out 2/7 ÷ 6/11. You must show all your working and give your answer as a fraction in its simplest form.

The diagram shows a parallelogram (NOT TO SCALE) with two angles marked (132 - 2x)° and (15 + 5x)°. Work out the size of the smallest interior angle of the parallelogram.

Points A, B, C and D lie on a circle (NOT TO SCALE). ABCD is a square with area 72 cm^2. Calculate the area of the circle. Give your answer as a multiple of π.

Calculate cube root of (1 + 10.9 x 0.4^2).

Factorise fully. 24x^2 - 9xy

y is directly proportional to the square root of x + 1. y = 10.5 when x = 8. Find y when x = 1.56.

The region R satisfies these inequalities: -3 < y <= 2 y <= x - 1 By drawing suitable straight lines and shading unwanted regions, find and label the region R.

The diagram shows the speed-time graph for 17 seconds of a car journey (NOT TO SCALE). Speed rises from 0 to 20 m/s in the first 10 seconds, then is constant at 20 m/s to 17…

At the start of an experiment there are 40 000 bacteria. The number of bacteria increases at a rate of 15% per hour. Calculate the number of bacteria after 3 hours.

75 people are asked if they have a car, C, and if they have a job, J. The Venn diagram shows the results: C only 9, C∩J 51, J only 13, outside 2. A person is chosen at random from…

A, B and C are points on the circumference of a circle, centre O. DA and DC are tangents to the circle. Angle ABC = 64°. Work out the value of x (angle ADC at D).

Universal set = {8 x 10^-1, 0.8 (recurring), 8%, sqrt(0.08)}. A = {a: 0.08 < a <= 0.8}, B = {b: b = 0.8}. Complete the Venn diagram (two sets A and B).

A solid is made from a cylinder and a hemisphere, both of radius 4.3 cm (NOT TO SCALE). The cylinder has length 11.9 cm. Calculate the volume of the solid. [The volume, V, of a…

Find an expression for the nth term of this sequence. 1/7, 1, 7, 49, 343, 2401, ...

Expand and simplify. (x + 3)(x + 5)(2x + 1)

A is the point (17, 9) and B is the point (23, 39). Find the equation of the perpendicular bisector of line AB. Give your answer in the form y = mx + c.

The small box is mathematically similar to the large box (NOT TO SCALE). The volume of the large box is 72.8% greater than the volume of the small box. The small box has length…