WJEC GCSE Mathematics Unit 2: Calculator-allowed Higher June 2025 question paper 3300U60-1

The diagram below shows two towns, A and B, on a map.

The scale of the map is 1 cm represents 4·5 km.

On the map, shade the region containing all the points that are: • closer to town A than to town B, and

• less than 27 km from town B.

In this question you will be assessed on the quality of your organisation, communication and accuracy in writing.

A charity is organising a game using this fair spinner.

In the game, each player spins the spinner once.

100 players each pay £x to play the game once. Each player who gets an even number on the spinner wins £3.

The charity expects to make a profit of £130.

Find the value of x.

You must show all your working.

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.

Calculate the length of PQ.

Calculate the size of angle x.

Calculate the value of the smaller share.

You must show all your working.

In the diagram below, the triangles ABC and DBE are mathematically similar.

= 8 cm, = 7.5 cm, = 5 cm and = . CB DB BE ACB DEB

Calculate the length of AB.

A number has been decreased by 20% to give an answer of 84.

What was the original number?

A bag contains 5 red balls and 4 blue balls.

Megan chooses a ball from the bag at random. She replaces the ball in the bag. Then she chooses a second ball from the bag at random.

Complete the tree diagram below.

Find the probability that Megan chooses two balls of the same colour.

The total surface area of all 6 faces of the cuboid below is 240 cm².

Find the volume of the cuboid.

You must show all your working.

The points A, B and C lie on the circumference of a circle.

The straight line DCE is a tangent to the circle. AB = BC. ACB = x, where x is measured in degrees.

Find an expression for the size of ACD. Give your answer in terms of x.

You must give a reason for each step of your solution.

The table below shows the value of g and the value of h.

It also shows the degree of accuracy of each value.

Use the formula

to calculate the greatest possible value of f.

You must show all your working.

(i) y is inversely proportional to x³. y = 0·15 when x = 6.

Use this information to write an expression for y in terms of x.

Use the expression you found in part (i) to complete the following table.

c is directly proportional to the square root of d. What happens to c if d is multiplied by 4?

Circle the correct statement below.

c is c is c is c is c is multiplied by 16 divided by 16 multiplied by 2 divided by 2 squared

The diagram shows a sector of a circle with centre O and radius 29 cm.

The area of the sector is 756 cm². AOB = x°.

Calculate the value of x.

You must show all your working.

Rearrange the following to make w the subject.

Use the cosine rule to show that 3x² +10x − 35 = 0.

Solve the equation

You must use the quadratic formula and show all your working.

Give your answers correct to 2 decimal places.

Evaluate the length of PQ.

You must justify any decision that you make.

The lowest point of a curve is called a minimum point.

The diagram shows a sketch of the curve with equation y = f ()x. The minimum point of the curve has coordinates (6, –3).

For each of the following equations, write down the coordinates of the minimum point of the curve.

y = 4 f ()x

The coordinates of the minimum point are (_{……........ …..},_{……........ ….}).

y = f (x + 2)

The coordinates of the minimum point are (_{……........ ….},_{……........ ….}).

The curve with equation y = f ()x is reflected in the x-axis. Write down the equation of the transformed curve.

You should use function notation.

The diagram shows a quadrilateral EFGH.

Calculate the area of triangle FGH.

Carys says,

“It will never be possible for the volume of a cube of side length r to be equal to the volume of a hemisphere of radius r.”

Use algebraic expressions to show that Carys is correct.