Eduqas GCSE Maths Component 2H Higher June 2024 question paper

45 students took part in a 400 m race. Their times, in seconds, were recorded. The frequency diagram below shows the results. The groups used are as follows: 70 time < 80, 80 time 90, 90 time 100, 100 time 110 and 110 time 120.

Calculate an estimate for the mean time it took to complete the race.

Factorise x² − 5x − 24.

Represent the inequality –2 x 3 on the number line below.

ABC and BCD are right-angled triangles. AB = 5·4 cm, AC = 7·2 cm and CD = 4·9 cm.

Calculate the area of triangle BCD.

Area of triangle BCD is_{…………........ …………….} cm²

For her lunch, Gina sometimes eats a salad and sometimes drinks a coffee.

The probability she eats a salad for lunch on a given day is 0·4. The probability she drinks a coffee on a given day is 0·25. Eating a salad for lunch and drinking a coffee are independent.

Complete the following tree diagram.

Calculate the probability that, on a given day, Gina does not eat a salad for lunch but

does drink a coffee.

When a ball is dropped, the maximum height it reaches after each bounce decreases.

Maddox says,

The ball is dropped from a height of 4 m.

What height will the ball reach above the ground after its 7th bounce?

State any assumptions you have made in answering part (a).

What effect could your assumption have on your answer to part (a)?

There are 50 people in a sports club.

Two of the sports the people can take part in are rowing and cycling.

Of these 50 people: • 27 take part in rowing • 32 take part in cycling • 8 do not take part in rowing or cycling.

One person is chosen at random from the sports club.

Find the probability that they take part in rowing but not in cycling.

Abdul is travelling from the UK to Brazil for a holiday.

Abdul has £825 to exchange for Brazilian reals (R$). The exchange rate is £1 = 6.27R$. The bank Abdul uses to exchange his money only has 50R$ notes.

What is the maximum amount of Brazilian reals Abdul can buy and what will this cost him in pounds? Give your answer correct to the nearest penny.

You must show all your working.

In part (a) the identity symbol () has been used.

Explain why this has been used and not an equal sign.

The point D is equidistant from the lines AB and BC. Point D is also equidistant from the points B and C.

Using only a ruler and a pair of compasses, construct suitable arcs and lines to show the

position of point D.

The fish tank exerts a pressure of 0·97 N/cm² on the ground.

What force is exerted on the ground by the fish tank?

A solution to the equation 2x³ − 5x − 23 = 0 lies between 2 and 3.

Use the method of trial and improvement to find the solution correct to 1 decimal place.

You must show all your working.

A solid cone has a base radius of y cm.

The height of the cone is six times its radius. The cone is made from material which has a density of 7 g/cm³. Write an expression for the mass of the cone in grams.

Give your answer, in terms of y and π, in its simplest form.

A video game company investigated how long, in minutes, one group of 10-year-old students and one group of 14-year-old students spent playing video games last Wednesday evening.

Diagrams displaying the results for each age group are shown below.

Lewis says,

“14-year-olds spend longer, on average, playing video games than 10-year-olds.”

Is Lewis correct?

Yes No

Use information from the diagrams to justify your answer.

Complete the following sentences using information from the diagrams.

The percentage of 14-year-old students that spent less than 40 minutes playing

video games last Wednesday evening was_........ %.

The percentage of 10-year-old students that spent more than 120 minutes

playing video games last Wednesday evening was_........ %.

Compare the inter-quartile range of the times each age group spent playing video games last Wednesday evening. What conclusions can you draw about the length of time 10-year-olds and 14-year-olds

spent playing video games last Wednesday evening?

Noah and Jenny take it in turns to shoot an arrow at the target. In the game, Noah shoots the first arrow. When one of them hits the target the game ends and that person wins the game.

Calculate the probability that Jenny wins the game on her first shot.

Calculate the probability that Noah wins the game on his second shot.

Kian went for a run.

The route he runs is 3000 metres, correct to the nearest 100 metres. He ran the route in a time of 720 seconds, correct to the nearest 10 seconds.

Calculate Kian’s greatest possible average speed for this run. Give your answer in metres per second.

You must show all your working.

Kian’s greatest possible average speed is_{………………........ ……………….} metres per second.

Enlarge the shape shown on the grid below by a scale factor of –2.

Use (1, 2) as the centre of enlargement.

The diagram shows points R, S and T on the circumference of a circle with centre O.

The lines QR and QT are both tangents to the circle.

Show that RQT = 48°.

Give a reason for each step of your answer.

WXY is a straight line.

Calculate the length of YZ.

Hollie makes wooden horses that are mathematically similar.

Two of these horses are shown below.

The large horse has a total surface area of 640 cm².

Hollie uses spray paint to cover the total surface area of each horse. One can of spray paint covers an area of 9300 cm² and costs £8.45.

Calculate the cost of buying the least number of cans of spray paint required to cover 30 large

horses and 50 small horses.

The diagram shows:

• the circle with equation x² + y² = 32 • a tangent to the circle. The tangent passes through (a, 0) and (0, a).

Calculate the value of a.

Calculate, in kilometres per hour, the velocity of the roller coaster at time

t = 4 seconds.

Velocity is_{…………........ ………} kilometres per hour.

Calculate an estimate for the acceleration of the roller coaster at time t = 2 seconds.

Give your answer in m/s².

Describe the acceleration of the roller coaster between t = 4 and t = 10 seconds.

Use five vertical strips of equal width to calculate an estimate for the distance the roller coaster travelled between t = 4 and t = 14 seconds.

Give your answer in metres.

Find the coordinates of the points of intersection of the curve 3x² + 2y² =12 and

the line y = x − 3. Give your solutions correct to 1 decimal place.

You must show all your working.