AQA GCSE Maths Paper 3: Calculator Higher June 2024 question paper 8300/3H

Here are the first three Patterns in a sequence made up of small squares.

On the grid, draw Pattern 4

The expression for the number of small squares in Pattern n is n² + 4

Work out the least value of n for which the number of small squares is greater than 500

n =

Use Pythagoras’ theorem to work out the value of x. Give your answer as a decimal.

Rick claims most of the flats in his 8-floor building are energy efficient. He samples 45 flats from floors 1 to 5

Give a reason why this sample may not be useful in testing Rick’s claim.

4 3(x – 1) 3x – 3 is an identity. Tick one box.

The front elevation of a cuboid is shown on this centimetre grid.

Draw the side elevation on this centimetre grid.

On Monday, Larrs swims 50 metres in 40 seconds at a constant speed. On Tuesday, Larrs swims 1.5 kilometres.

Assume he swims at the same constant speed as on Monday.

How many minutes does he swim for on Tuesday?

In fact, on Tuesday Larrs swims at a slower constant speed than on Monday.

What does this mean about the number of minutes he swims for on Tuesday? Tick the correct box.

Four people are taking part in a television talent show.

Here are Amy’s marks from the 6 judges.

The pie chart represents the phone vote.

Amy’s total score is found by

4 × the mean of her marks

her percentage of the phone vote

Work out Amy’s total score.

Town A has a population of 84 000 an area of 7 square miles.

Town B has a population density of 4695 people per square kilometre.

Which town has the greater population density?

Use 1 square mile = 2.6 square kilometres Tick a box.

Show working to support your answer.

On a biased dice, P(lands on 6) = 0.38

This dice is rolled 150 times.

How many times would you expect the dice not to land on 6 ?

Write a number in each box to make the calculations correct.

Cards are either gold or not gold. P(gold) = 0.05 Harim chooses a card at random and replaces it. He then chooses a second card.

Complete the tree diagram.

What is the probability that at least one of Harim’s cards is gold?

Here is a quadratic graph with equation y = f(x)

Write down the roots of the equation f(x) = 0

b = 45 ° and a: b = 7: 3 and x: y = 4: 1

Show that a: y = 5: 2

A straight line passes through points A (– 5, 9), B and C (3, – 7).

AB: BC = 1: 3

Work out the coordinates of point B.

Work out the equation of the line perpendicular to AC that passes through C.

Jing rolls a fair six-sided dice 72 times.

Is the relative frequency of rolling a 5 greater than the theoretical probability? Tick a box.

Give a reason for your answer.

a and b are different prime numbers.

Work out the value of a⁴ × b

c and d are different prime numbers.

Circle the equation for which c⁴ × d² × e is a cube number.

Here is triangle A.

Use the sine rule to show that x = 64 ° to the nearest degree.

Here is triangle B.

Anna thinks that w must be 64 ° to the nearest degree. She says, “This is because t riangle B has two sides and one angle the same as triangle A.”

Without further calculation, is she correct? Tick a box.

Give a reason for your answer.

f(x) = x – 3 g(x) = 4 x – 7

Work out the value of fg(6)

Solve (f(x))² = g(x)

P, Q, and R have positive values. P is directly proportional to Q When P = 8, Q = 2

When R = 10, Q = 3

Work out the value of R when P = 0.5

A cylinder, C, and a sphere, S, each have radius r C has height h

volume of C = volume of S

Work out the ratio r: h You must show your working.

A different cylinder has radius 3 r and height 2 h.

How many times bigger is the volume of this cylinder than the volume of C?

Fatima is choosing a 4-digit code. Each digit is a whole number from 0 to 9 She decides all her digits will be odd numbers no digits will be repeated.

How many different codes can she make?

Quadrilateral ABCD is reflected in edge BC.

How many of the vertices are invariant? Circle your answer.

1 2 0 4

Write 2 x 2 – 12 x + 7 in the form d (x + e) 2 + f where d, e and f are integers.