Eduqas GCSE Maths Component 2H Higher June 2023 question paper

The base of a filing cabinet is a rectangle. It measures 45 cm by 60 cm. The whole of the base is in contact with the horizontal ground.

The empty filing cabinet exerts a force of 675 N on the ground.

What is the pressure exerted on the ground by the empty filing cabinet?

Give your answer in N/cm².

When the filing cabinet is full, the pressure it exerts on the ground is 0·75 N/cm².

What is the force that the full filing cabinet exerts on the ground?

Give your answer in newtons (N).

The diagram shows information about the percentage of households in Eduvale that owned a desktop computer for the even-numbered years from 2006 to 2018.

Complete this statement.

The percentage of households that owned a desktop computer decreased

the most between the even-numbered years_........ and_........

Jane says,

“The graph shows that 70% of people owned a desktop computer in 2009 because it passes through that point.”

Is Jane correct? Yes No

Explain how you decide.

The table shows information about the percentage of households in Eduvale that had an internet connection for the even-numbered years from 2006 to 2018.

On the diagram on page 4, plot the information for internet connection.

In which even-numbered year was the difference in the percentage of households in Eduvale owning a desktop computer and the percentage of households having

an internet connection the greatest?

Eduvale is a large town in a county.

Comment on how, in this county, the percentage of households owning a desktop computer and the percentage of households having an internet connection are

likely to have changed in this time period.

Eric is carrying out a survey for a company that makes energy drinks, Pop and Whizz.

He asks 200 randomly selected adults to complete his survey.

Pop costs £1 per bottle. As part of his survey, Eric wants to find out how much money each month adults spend on Pop.

In the box below, write a suitable question for his survey to collect this information.

You must include response boxes.

In another question, he asks the 200 adults how many bottles of Whizz they buy each month. The table shows the results for the 200 adults.

Find the probability that an adult chosen at random from these 200

does not buy Whizz,

is 26 to 35 years old and buys 5 or more bottles of Whizz each month.

The diagram shows a circle inside a square of side 8·2 cm.

The sides of the square are tangents to the circle.

Find the area of the shaded region.

You must show all your working.

The diagram shows a parallelogram. It is the cross-section of a prism.

The length of the prism is 16 cm.

Find the volume of the prism.

Solve 7x 5 2x 3.

Roza is buying bananas and apples.

She buys x bananas which cost 30 pence each. She buys 2 more apples than the number of bananas she buys. Her apples cost 25 pence each. She pays a total of £5.45.

Use an algebraic method to find the number of bananas Roza buys.

Factorise x² 5x 4.

Heath has £3000 to invest for five years.

No extra money will be paid in or withdrawn during these five years. He is going to choose one of these accounts.

Which account gives Heath the greater percentage increase in his money at the end of 5 years and by how much is it greater?

Show how you decide. State any assumption that you make.

Account_........ gives the greater percentage increase by_........ %

Comment on the effect that your assumption in part (a) has had on your decision.

The diagram shows a small park with gates at A, B, C and D. The scale is 1 cm represents 10 m.

A new outdoor gym is to be built in the park.

This should be: • at least 55 m from the gate at A • nearer to the gate at B than the gate at C.

Use a ruler and a pair of compasses to show accurately on the diagram the region of the park where the outdoor gym can be built.

Indicate clearly the region that is your answer.

Diagram not drawn to scale

An aircraft is making its final approach ready to land.

The aircraft is: • flying at 3° to the horizontal, • 2·5 km horizontally from the start of the runway, as shown on the diagram above.

Calculate the vertical height of the aircraft above the horizontal ground.

You must show all your working.

A factory makes loaves of bread which are wrapped in packaging.

Independently, for any loaf wrapped in packaging, chosen at random: • The probability that there is a fault with the bread is 0·02. • The probability that there is a fault with the packaging is 0·01.

Complete the tree diagram to show this information.

A loaf wrapped in packaging is chosen at random.

Calculate the probability that neither the bread nor the packaging has a fault.

Calculate the probability that either the bread or the packaging has a fault but they

do not both have a fault.

Rearrange this formula to make y the subject.

The box plot summarises the heights, in cm, of a class of students.

Use the box plot to complete the table.

Enya’s house is put up for sale at the start of April. It does not sell, so at the start of May, the sale price of the house is reduced by 20%. At the start of June, the sale price is reduced by 15% of the price at the start of May.

Enya says,

“My house has been reduced in price by a total of 35%.”

Explain why Enya is incorrect.

The house is then sold for £306 000.

What was the original sale price of the house at the beginning of April?

The area of country A is 1 078 000 km², correct to 4 significant figures. The area of country B is 249 300 km², correct to 4 significant figures. The two countries merge to form country C.

Calculate the upper bound of the area of country C.

The population density of a country is the number of people per km². Country C has a population of 82 000 000, correct to the nearest million. Calculate the least possible value of the population density for country C.

You must show all your working.

Solve x² – 36 0.

On the axes below, sketch the part of the graph y x² 36 that represents the solution to the inequality x² – 36 0.

Mark any intercepts with the x-axis on your sketch.

Show that where the line and curve intersect, x satisfies the equation

f x x³

Find f ¹x.

Calculate the length of BC.

Calculate the length of EF.

Sian has seven numbered cards as shown below.

She shuffles them and turns them face down. She then turns them over to make a 7-digit number.

How many different 7-digit numbers can Sian make?

How many of these 7-digit numbers are multiples of 5?

What proportion of these 7-digit numbers are not multiples of 5?

An inverted cone is held in a stand.

The radius of the cone is 20 cm and the height of the cone is 50 cm.

Jake pours some water into this cone. When he stops, the radius of the surface of the water is 6 cm. The surface of the water is parallel to the base of the cone.

Rhian then pours water into the cone until it is completely full. She pours the water at a rate of 1 litre per 10 seconds.

How many seconds does it take Rhian to fill the cone?

The first 5 terms of a sequence are shown below.

5 8 11 14 17

Complete the term-to-term rule for this sequence.

to find a solution of x³ 2x 5 0 correct to 1 decimal place.

Write down all your values of x_n1.

In this question, x and y are horizontal and vertical distances in metres.

An engineer designs a tunnel. He models the uniform cross-section of this tunnel using the graph shown in the diagram.

The tunnel is 50 metres long and will cost £250 per m³ to excavate.

Use the graph with four vertical strips of equal width to calculate an estimate of the cost of

excavating this tunnel.

Cost of excavating the tunnel will be £_........