AQA GCSE Maths Paper 2: Calculator Higher November 2023 question paper 8300/2H

Expand 5x(x² + 3)

Write 1.52 as an improper fraction in its simplest form.

Work out 60 as a percentage of 20

Use Pythagoras’ theorem to work out the value of x.

A, B and C are three points.

Work out the bearing of C from A.

Three shops sell the same type and size of lip balm stick.

Which shop is the best value for 8 sticks and what is the total cost in that shop? Show working to support your answer.

Round 1 of voting for Head Student is taking place in a school.

To reach round 2, a student must receive at least of the votes. What is the largest possible number of students that can reach round 2? Circle your answer.

15 11 3 4

There are 900 votes in round 1 Sean receives 180 votes.

Amy draws a pie chart to represent the results. Here is her method to work out the angle needed for Sean.

Is Amy’s method correct? Tick a box.

Give a reason for your answer.

Here is a prism drawn on an isometric grid.

Work out the volume of the prism.

Tasha drove 198 miles. Her average speed for the first 3 hours was 45 miles per hour. Her average speed for the rest of the journey was 31.5 miles per hour.

Work out her average speed for the whole journey.

miles per hour

Here is the term-to-term rule for a sequence.

The first three terms of the sequence are a + 1 2 a + 5 4 a + 13

Show that the sum of the first four terms is a multiple of 3

Which of these represents the shaded region? Circle your answer.

B A' U B A' ∩ B A'

A fair coin is thrown a number of times. The probability that every throw results in Heads is How many times is the coin thrown?

Here is some information about the members of a basketball club.

Work out the mean height of all 50 members of the club. Give your answer as a decimal.

A straight line passes through (3, 14) and (12, 32)

Work out the equation of the line. Give your answer in the form y = mx + c

Use a ruler and compasses in this question.

The scale diagram shows port P and lighthouse Q.

Scale: 1 cm represents 2 km

A ship is less than 14 km from P and closer to Q than to P.

Label the region, R, where the ship could be. Show all your construction lines.

A bag contains discs.

Trial A disc is chosen at random from the bag. The colour of the disc is noted. The disc is put back into the bag.

The trial is carried out 100 times. The table shows the relative frequency of a blue disc after every 25 trials.

For the trials from the 26th to the 50th, how many times was a blue disc chosen?

There is a total of 1000 discs in the bag.

Work out the best estimate of the number of blue discs in the bag.

a 0 and b 0

Circle the correct statement.

190 people were asked how much they spent on takeaways one month. The table shows information about the results.

Amount, x (£)	Cumulative frequency
0 x 10	16
0 x 20	64
0 x 30	140
0 x 40	184
0 x 50	190

How many people spent more than £20 ?

Farah draws this cumulative frequency curve to represent the results.

Give two criticisms of her graph.

By completing the square, prove that x² + 6x + 13 is always positive.

A is directly proportional to B⁴ The value of B is doubled.

Pete thinks that the value of A will be 8 times bigger because 4 × 2 is 8

Is he correct? Tick a box.

Give a reason for your answer.

Jack is loading a van. The van can safely carry 1375 kg of furniture. Jack has already loaded 1200 kg of furniture to the nearest 50 kg A table has mass 140 kg to the nearest 10 kg

Can the table safely be added to the furniture in the van? You must show your working.

Factorise 25a² – b²

Here is the velocity-time graph of a cyclist for 40 seconds.

By dividing the area under the graph into four sections of equal widths, estimate the distance travelled during the 40 seconds.

Work out the average acceleration of the cyclist during the 40 seconds. State the units of your answer.

You must show your working.

Here are two square-based paving stones. The stones are similar solids.

The price per cm³ is the same for both stones. The price of the larger stone is £17.50

Work out the price of the smaller stone.

Rick borrows £1500 from a bank. He pays back £100 each month.

This iterative formula works out the amount he still owes at the end of each month.

Work out the amount he still owes at the end of the 2nd month.

g(x) = a × b where a and b are constants. g(0) = 8 and g(3) = 343

Work out the value of g(1)

VABCD is a pyramid with a horizontal square base. X is the centre of the base. V is vertically above X. BD = 18 cm Angle VBX = 72 °

Work out the length of VB.

A code is three letters, each of which is in the word LOGIC Vinny assumes that letters in the code may be used more than once. He works out how many possible codes there are. In fact, the first two letters are the same and the third is different.

How many of Vinny’s codes are not possible?