AQA GCSE Maths Paper 1: Non-calculator Higher June 2018 question paper 8300/1H

Circle your answer.

40 80 400 4000

Circle the vector that translates B to A.

Circle the expression that is equivalent to 3 a – a × 4 a + 2 a

5 50 500 5000

Solve 5(x + 3) < 60

The height of Zak is 1.86 metres. The height of Fred is 1.6 metres. Write the height of Zak as a fraction of the height of Fred. Give your answer in its simplest form.

A (0, 2) and B (6, 5) are points on the straight line ABCD.

AB = BC = CD Work out the coordinates of D.

A coin is thrown 50 times. It lands on heads 31 times.

Write down the relative frequency it lands on heads.

Raj says, “The coin is biased towards heads.” Use the data to give a reason why he might be correct.

Work out the largest number.

y is inversely proportional to x. Complete the table.

A large rectangle is made by joining three identical small rectangles as shown.

The perimeter of one small rectangle is 15 cm Work out the perimeter of the large rectangle.

Put these numbers in order from smallest to largest.

Circle the volume that is the same as 15 cm³

Patterns are made using straight lines and arcs.

More rows are added to Pattern B so that number of straight lines: number of arcs = 10: 9 How many rows are added?

A different pattern is made using 20 straight lines and 16 arcs. The straight lines and arcs are made from metal. 20 straight lines cost £12 cost of one straight line: cost of one arc = 2: 3 Work out the total cost of the metal in the pattern.

A biased dice is thrown. Here are the probabilities of each score.

The dice is thrown 200 times. Work out the expected number of times the score will be odd.

The value of y is 20% more than the value of x. Circle the ratio x: y

5: 6 6: 5 4: 5 5: 4

Here is a triangle.

Circle the correct equation.

Here is a tunnel for a toy train.

The diagram below shows the cross section of the tunnel.

AD is a semicircular arc of radius 10 cm BC is a semicircular arc of radius 7 cm The length of the tunnel is 30 cm Work out the total area of all six faces of the tunnel. Give your answer in terms of π.

Type A batteries and type B batteries were tested. The cumulative frequency diagram shows information about the battery life of type A.

Estimate the interquartile range for type A.

Estimate the number of type A batteries that had a battery life of more than 1600 hours.

The box plot shows information about the battery life of type B.

On average, which type had the greater battery life? Tick a box.

Using data from both diagrams, state how you chose your answer.

A linear sequence starts a + 2 b a + 6 b a + 10 b …….. …….. The 2nd term has value 8 The 5th term has value 44 Work out the values of a and b.

a =

b =

Enlarge triangle ABC by scale factor –2, centre (4, 1)

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

A shopkeeper compares the income from sales of a laptop in March and April.

By what fraction does the income from these sales decrease in April?

Work out the value of 2¹⁴ ÷ 2⁹² Give your answer as a fraction in its simplest form.

Work out the value of 25

Here is a sketch of the graph of y = cos x for values of x from 0° to 360°

cos x = cos 60° Work out the value of x when 90° x 360°

cos x = – cos 60° Work out the value of x when 180° ≤ x ≤ 360°

b is two thirds of c. 5 a = 4 c Work out the ratio a: b: c Give your answer in its simplest form where a, b and c are integers.

Jo wants to work out the solutions of x² + 3x – 5 = 0 She says, ‘‘The solutions cannot be worked out because x² + 3x – 5 does not factorise to (x + a)(x + b) where a and b are integers.’’ Is Jo correct? Tick a box.

Give a reason for your answer.

Without expanding any brackets, show how to work out the exact solutions of 9(x + 3)² = 4 Give the solutions.

Here are sketches of two graphs.

The graph of y = x² – 1 is translated 3 units to the left to give graph A.

The equation of graph A can be written in the form y = x² + bx + c Work out the values of b and c.

b =

The graph of y = x² – 1 is reflected in the x-axis to give graph B. Work out the equation of graph B.

Show that the value of cos 30° × tan 60° + sin 30° is an integer.