WJEC GCSE Mathematics Unit 2: Calculator-allowed Higher June 2024 question paper 3300U60-1

What is the greatest integer value of n if 2n < 17?

What is the least integer value of n if 2ⁿ > 125?

The table below shows some of the values of y = 2x² + 5x − 3 for values of x from −4 to 2.

Complete the table above.

On the graph paper opposite, draw the graph of y = 2x² + 5x − 3 for values of x from

− 4 to 2.

At lunchtime on Wednesday, a café had 19 customers.

• 7 of these customers bought a meal and a drink. • 2 of these customers did not buy a meal or a drink. • The total number of customers who bought a meal was twice the total number of customers who bought a drink.

One of these customers is chosen at random.

What is the probability that this customer bought a meal?

The equation of a straight line is y = −3 x + 7.

What is the gradient of the line?

Circle the correct answer.

What are the coordinates of the point where the line intersects the y-axis?

Circle the correct answer.

(− 3, 7) (0, − 3) (0, 3)
(0, − 7) (0, 7)

In the diagram below, A B D and B C D are both right-angled triangles.

A B = 7·3 cm, A D = 13·8 cm and C D = 5·5 cm.

Calculate the value of y.

The triangles shown below are similar.

Calculate the value of x.

Four rectangles labelled A, B, C and D are shown below.

Which two rectangles are similar?

Give a reason for your choice.

The two rectangles which are similar are rectangles_........ and_........

Factorise x² + 3x − 40, and hence solve x² + 3x − 40 = 0.

a and b are two numbers, where b > a.

The mean of the two numbers is equal to the range of the two numbers.

Show that 3a = b.

Aled and Berwyn share £ x in the ratio 2: 3.

Aled’s share of the money is £0.4x.

What is Berwyn’s share of the money in terms of x?

Carys and Delyth share the same amount, £x, in the ratio 3: 7.

Show that one of these four people receives the same amount as the combined total of

two of the other people.

The pyramid below has a horizontal rectangular base A B C D.

The point O is the top of the pyramid. It is vertically above the point A. O C = 113 cm, A B = 72 cm and C B = 84 cm.

Calculate the length of O A, the vertical height of the pyramid.

Calculate the volume of this pyramid.

Triangle A B C has sides A B = 24·1 cm and A C = 17·9 cm, as shown below.

B A C = 37°.

Calculate the area of the triangle A B C.

The values e = 7·1, f = 73·9 and g = 65·7 are each given correct to 1 decimal place.

The value of h is found using the formula.h Calculate the greatest value of h. Give your answer correct to four decimal places.

You must show all your working.

Sketch the curve y cosx on the axes below, for values of x from 0° to 360°.

You must indicate any important values on both axes.

Solve the equation.2cosx 1

Give all answers in the range x = 0° to x = 360°.

Zoltan rolls three unbiased 6-sided dice.

Calculate the probability that the sum of the values shown on the dice is 17.

Two similar prisms have volumes of 569 cm³ and 3821 cm³, as shown below.

The uniform cross-sectional area of the smaller prism is 29 cm².

Calculate the uniform cross-sectional area of the larger prism.

Solve the equation 7 x (x + 3) + 1 = x (x + 2).

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

Give your answers correct to 2 decimal places.

In the diagram below, AB = 13 cm, AD = 17 cm, BC = 19 cm and DC = 11 cm.

Calculate the size of angle x.

You must show all your working.