Eduqas GCSE Maths Component 2H Higher November 2024 question paper

A right-angled triangle and a square are shown below.

The perimeter of the triangle is equal to the perimeter of the square.

Calculate the area of the square.

You must show all your working.

Elijah has a large cylinder of wax.

It has a radius of 7 cm and a height of 21 cm.

He melts down the large cylinder of wax to make small wax cylinders each with a volume of 102 cm³.

How many complete small wax cylinders can Elijah make?

The density of copper is 8·96 g / cm³.

A solid copper statue has a volume of 1540 cm³. Calculate its mass in kilograms.

Give your answer correct to two significant figures.

Simplify 4x³y⁵ × 7x²y.

n is an integer.

What is the least possible value of n?

Make x the subject of the formula.

Represent the inequality –3 < x 1 on the number line below.

1 micrometre = 1 × 10^–4 centimetres. Which of the answers below represents 2·4 micrometres in metres?

Circle your answer.

A new supermarket is about to open in a town with 8000 houses.

For the first four weeks, £10 vouchers will be sent out to encourage people to visit the supermarket.

At the start of the first week, 30% of the houses in the town will each be sent a voucher. At the start of each of the next three weeks, a voucher will be sent to 30% of the houses that have not yet received a voucher. The vouchers need to be used in the supermarket by the end of the four weeks.

John, the supermarket manager, says

“By the end of the four weeks, 6079 of the vouchers will have been used.”

Show that John could be correct.

State an assumption that John has made in part (a).

If John’s assumption was not correct, what effect would this have on the number

of vouchers used by the end of the four weeks?

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

Complete the table by finding the value of y for x = –1 and for x = 3.

On the graph paper below, draw the graph of y = 2x² – 3x – 4 for values of x

from –2 to 3.

What is the equation of the straight line that intersects the curve y = 2x² – 3x – 4 to give

the solutions to the equation 2x² – 3x – 7 = 0?

Tiana and Kamal work at a bank. Their hourly pay rates are different.

On Thursday, Tiana worked for six hours and Kamal worked for seven hours. Their combined income on Thursday was £185.75.

On Friday, Tiana worked for five hours and Kamal worked for four hours. Their combined income on Friday was £130.50.

Use an algebraic method (not trial and improvement) to calculate Tiana and Kamal’s hourly pay rates.

You must show all your working.

Tiana’s hourly pay rate is_........ Kamal’s hourly pay rate is_........

Fran also works at the bank part-time. She earns 35% less than the full-time salary at her pay rate. Fran’s annual part-time salary is £24 570.

What would Fran’s annual salary be if she worked full time?

There are 1800 eels in a lake.

On Saturday morning, Sadia captured a random sample of x eels from the lake and tagged them. She then released them back into the lake.

On Sunday morning, Sadia captured a second random sample of 150 eels from the lake. Seven of the eels in this sample were already tagged.

Use these values to calculate an estimate for x, the number of eels tagged in Sadia’s first

sample.

A ship sails 11 km due south from port A. It then travels 17 km due east and arrives at port B.

Calculate the bearing of port B from port A.

The bearing of port B from port A is_........

Enrico and Hugo are both boxers.

At the start of a six-week training block: • Enrico weighs exactly 170 pounds. • Hugo weighs exactly 175 pounds.

After the six-week training block: • Enrico has lost 9 pounds, correct to the nearest pound. • Hugo has lost 12 pounds, correct to the nearest two pounds.

What is the greatest possible difference between Enrico’s percentage weight loss and

Hugo’s percentage weight loss?

The greatest possible difference between Enrico’s percentage weight loss and Hugo’s percentage

Marcus has the cards shown below.

He places these cards in a bag.

Marcus selects two of the cards at random from the bag. The letters are recorded and the two cards are replaced in the bag. He repeats this process 275 times.

How many times would you expect Marcus to select the two cards with the letter A?

Kiera took part in a race. She ran at an average speed of (1·8x + 7) kilometres per hour for (5x + 0·5) kilometres. It took her 1 hour and 15 minutes to complete the race.

How far, in kilometres, did Kiera run? You must use an algebraic method (not trial and improvement).

You must show all your working.

A town council wishes to trial traffic-calming measures along a particular road in the town where the speed limit is 30 mph (miles per hour).

For the first trial, additional 30 mph signs were put in place. Irene surveyed the average speed at which cars travelled along the road. The results are shown in the histogram below.

Use the histogram to calculate an estimate for the median speed, in mph, of the cars Irene surveyed.

You must show all your working.

In the second trial, speed bumps were put in place. Irene surveyed the average speed of 150 cars. The results are shown in the histogram below.

Irene says,

“84% of cars travel at 30 mph or less when speed bumps are in place.”

Show that Irene could be correct.

Explain why Irene could be incorrect.

The diagram shows a shape made from a cone and a hemisphere. The cone has height 5 cm and base radius (x + 1) cm.

The volume of the shape is 24π cm³.

Show that 2x³ + 11x² + 16x = 65.

A solution to the equation 2x³ + 11x² + 16x = 65 lies between 1·6 and 1·7. Use the method of trial and improvement to find the solution correct to two decimal

places.

There are 143 Year 6 pupils going on a school trip to an adventure centre. They can choose to take part in up to three activities.

• All the pupils took part in at least one activity. • 8 pupils took part in all three activities. • 23 pupils took part in rock climbing and coasteering. • 29 pupils took part in rock climbing and gorge walking. • 22 pupils took part in coasteering and gorge walking. • 65 pupils took part in coasteering. • 76 pupils took part in rock climbing.

A Year 6 pupil is chosen at random.

Find the probability that this pupil takes part in gorge walking and coasteering only.

Given that a randomly chosen pupil from Year 6 took part in gorge walking, find the

probability they also took part in rock climbing.

The circle below is split into sectors, segments and triangles. A, B, C and D are points on the circumference of the circle with centre O. The lines AC and BD are diameters of the circle.

The area of sector AOB is 12 cm². Find the perimeter of the shaded segment.

You must show all your working.

The perimeter of the shaded segment is_........ cm

The diagram shows a sketch of y = cosx for the values of x from 0° to 360°.

Solve the equation cosx = –0·731 for all values of x from 0° to 360°.

Draw a sketch of y = cosx – 1 for the values of x from 0° to 360°.

You must indicate any important values on the axes.

Bert and Rehan use six-digit codes to lock their phones. They must use these digits to create their code:

Each digit can only be used once in a code.

Bert’s code must meet the following conditions: • The first digit is a multiple of four. • The second and third digits are both prime numbers. • There are no conditions for the remaining digits.

Rehan does not have any conditions for his code.

How many more code combinations can Rehan choose from than Bert?

y is inversely proportional to w³. w is directly proportional to the square root of x.

Find a formula for y in terms of x in the form y = mxⁿ, where m and n are fractions in their

simplest form.

By first completing the square, draw a sketch of y = 4x² – 16x – 6. You must clearly indicate the coordinates of any stationary points and the intercept with

the y-axis.