AQA GCSE Maths Paper 1: Non-calculator Higher June 2019 question paper 8300/1H

Here are two right-angled triangles.

Circle the value of y.

11 7.5 9 4

Circle your answer.

Work out the arc length, in metres, of a semicircle of radius 6 metres. Circle your answer.

3 π 6 π 12 π 18 π

Circle the fraction that is equivalent to 4.625

Write 0.000 97 in standard form.

Give your answer as an ordinary number.

Anna plays a game with an ordinary, fair dice. If she rolls 1 she wins. If she rolls 2 or 3 she loses. If she rolls 4, 5 or 6 she rolls again. When she has to roll again, if she rolls an odd number she wins if she rolls an even number she loses.

Complete the tree diagram with the four missing probabilities.

Is Anna more likely to win or to lose? You must work out the probability that she wins.

Three friends arrive at a party. Their arrival increases the number of people at the party by 20% In total, how many people are now at the party?

Work out the value of (3¹² ÷ 3⁵) ÷ (3² × 3)

A shaded semicircle is inside a circle as shown.

The radius of the circle is 10 cm The diameter of the semicircle is 8 cm How many times bigger is the unshaded area than the shaded area?

t is the time in minutes the machine takes to make one item. The value of t changes for different types of item.

On the grid below, draw the graph of n = for values of t from 1 to 4

The machine takes 3 minutes 30 seconds to make one item. Use your graph to estimate the value of n.

Ed and Fay shared £330 in the ratio 7: 4 Ed gives Fay some of his money. Fay now has the same amount as Ed. How much does Ed give Fay?

The next term of a sequence is made by adding the previous two terms. Which of these sequences follows this rule? Circle your answer.

–9 2 –7 –5 –12 –3 5 –2 3 1

0 –3 –3 0 –3 –1 –1 –2 –3 1

The triangular cross section of a prism is an isosceles right-angled triangle.

Use approximations to estimate the value of x. You must show your working.

Here is a quadrilateral.

a = 90° and a: b = 5: 3 x: y = 1: 3 Show that b = x

Here is some information about the test marks of 120 students.

Mark, m	0 m 10	10 m 20	20 m 30	30 m 40	40 m 50
Frequency	20	28	40	20	12

Complete the cumulative frequency table.

Mark, m	m 10	m 20	m 30	m 40	m 50
Cumulative frequency	20	48

Draw a cumulative frequency graph.

Students who scored 15 marks or fewer take another test. Use your graph to estimate how many students take another test.

Toby is forming and solving equations.

The product of half of a number and three more than the number is the same as the square of the number Toby uses y to represent the number. Write an equation that Toby could form.

Toby forms another equation.

He wants to work out the values of x. Here is his working.

What error has he made in his working?

Here is an identity.

Use the identity to work out the value of 193² – 7² You must show your working.

Factorise 100a² – 81b²

Circle the fraction that is equivalent to 0 1.

A, B and C are points on a circle. CD is a tangent.

Assume that triangle ABC is isosceles with AC = BC Prove that AB is parallel to DC.

In fact, triangle ABC is equilateral. Tick the two boxes for the statements that must be correct.

Solve the simultaneous equations 2 x + 3 y = 5 p y = 2 x + p where p is a constant. Give your answers in terms of p in their simplest form.

ABC and ACD are triangles. k is a constant.

Show that CD = 6a + 4.5b

BCD is a straight line. Work out the value of k. You must show your working.

Give your answer in the form 2^m where m is an integer.

f(x) = sin(x – 90°) Circle the value of f(0°)

P (4, 8) is a point on a circle, centre O. The tangent at P intersects the axes at points A and B.

Show that the gradient of the tangent is –

Work out the length AB.

You must show your working.

The turning point of the graph y = (x + a)² + b has x-coordinate –2 (3, 1) is another point on the graph. Work out the y-coordinate of the turning point.

Angle x is acute. cos x = sin 60° × tan 30° Work out the size of angle x. You must show your working.