WJEC GCSE Mathematics Unit 2: Calculator-allowed Higher June 2022 question paper 3300U60-1

Rotate the shape below through 90° clockwise about the point (–1, 1).

Make m the subject of the formula w 8m 3.

Expand and simplify y 5y 4.

The height of a cylinder is 24·8 cm. The ratio of the diameter of the cylinder to the height of the cylinder is 3: 2.

Find the volume of the cylinder. Give your answer correct to 2 significant figures.

You must show all your working.

Factorise 8x² + 6xy.

Factorise x² + 13x + 40.

Explain how you can check that your answer to part (i) is correct.

Calculate 5·7 × 10⁵ × 6·4 × 10^–2.

Circle the correct answer.

The diagram below shows a right-angled triangle.

Calculate the value of x.

The diagram below shows a different right-angled triangle.

Calculate the value of y.

Show that 5x³ 15x 132.

A solution of the equation

lies between 2 and 3. Use the method of trial and improvement to find this solution correct to 1 decimal place.

You must show all your working.

Hence, find the height of the cuboid.

Calculate the total surface area of a solid hemisphere with a radius of 34 cm.

The diagram shows a triangle ABC and a circle with centre A.

The points B and D lie on the circumference of the circle.

The length of the line AC is 27 cm. The area of triangle ABC is 112 cm².

Calculate the area of the shaded region.

Express the following as a single fraction in its simplest form.

Three fair spinners are shown in the diagram below.

The three spinners are spun.

Calculate the probability that all the spinners will land on an even number.

The graph of y = 12 + x – x², for values of x from x = 0 to x = 4, is drawn below.

Use the trapezium rule, with the ordinates x = 0, x = 1, x = 2, x = 3 and x = 4, to estimate the

area of the region bounded by the curve, the positive x-axis and the positive y-axis.

Shape A is a square and Shape B is a rectangle, as shown below.

The area of square A is equal to the area of rectangle B.

Form an equation in x and hence calculate the value of x. Give your answer correct to 1 decimal place.

You must show all your working.

Solid A and Solid B are similar.

Solid A has a volume of 8000 cm³ and a height of 30 cm. Solid B has a volume of 4913 cm³.

Calculate the height of Solid B.