AQA GCSE Maths Paper 3: Calculator Higher June 2018 question paper 8300/3H

Circle the decimal that is closest in value to

0.56 0.6 0.525 0.5

Circle the list of all the integers that satisfy –2 x 4

–2, –1, 0, 1, 2, 3 –1, 0, 1, 2, 3

–2, –1, 0, 1, 2, 3, 4 –1, 0, 1, 2, 3, 4

Circle the largest number.

What is the size of an exterior angle of a regular decagon? Circle your answer.

18° 36° 144° 162°

a is a common factor of 72 and 120 b is a common multiple of 6 and 9 Work out the highest possible value of

A and B are similar shapes. B is an enlargement of A with scale factor 1.5 Not drawn

Work out the values of x, h and w.

x = degrees h = cm w = cm

Investment A Save £150 per month for 2 years. 2.5% interest is added to the total amount saved. Investment B Invest £3500 Compound interest is added at 3% per year. After 2 years, how much more is investment B worth than investment A?

Show that the lines y = 3 x + 7 and 2 y – 6 x = 8 are parallel. Do not use a graphical method.

Is the point (–5, –6) above, below or on the line y = 3 x + 7 ? Tick one box.

You must show your working. Do not use a graphical method.

The cost of a ticket increases by 10% to £19.25 Work out the original cost.

The n th term of a sequence is 12 n – 5 Work out the numbers in the sequence that have two digits and are not prime.

6 –1 –4 11 a = b = c = –10 2 7

Work out a + b + c

Show that a + 2 c is parallel to b

A force of 40 Newtons is applied to an area of 3.2 square metres. Work out the pressure. Give the units of your answer.

Tick all the statements that are true for any rhombus.

Draw the graph of y = 0.8 for values of x from 0 to 6

Amy has x beads. Billy has three more beads than Amy. Carly has four times as many beads as Billy. Circle the expression for the number of beads that Carly has.

4 x + 3 3 x + 4 4(x + 3) x + 12

Two straight lines intersect at point A.

Circle the coordinates of A.

Here are two methods to make a 4-digit code. Codes can have repeated digits.

Method A For the first two digits use an odd number between 30 and 100 For the last two digits use a multiple of 11

Method B Use four digits in the order even odd even odd Do not use the digit zero

Which method gives the greater number of possible codes? You must show your working.

Show that, for x ≠ 0

can be written in the form where a, b and c are integers.

The equation of a straight line is 3 x + 2 y = 24 Circle the point where the line crosses the x-axis.

(0, 8) (12, 0) (0, 12) (8, 0)

All dimensions are in centimetres.

Use Pythagoras’ theorem to work out the exact value of

The mass of an ornament is m grams. The height of the ornament is h centimetres. m is directly proportional to the cube of h. m = 1600 when h = 8

Work out an equation connecting m and h.

Work out the mass of an ornament of height 12 centimetres.

A, B and C are points on a circle. DCB is a straight line. PAQ is a tangent to the circle.

Sam is trying to work out the size of angle m. Here is his working.

angle ACB = 56° angles in the same segment are equal m = 180° – 56° angles at a point on a straight line add up to 180° m = 124°

Make a criticism of his working.

A sequence of numbers is formed by the iterative process

Work out the values of u₂ and u₃

The speed-time graph shows 20 seconds of a car journey. Harry wants to estimate the distance the car travels in this time. He uses a triangle and a trapezium, as shown, to estimate the area under the graph.

Complete Harry’s method to estimate the distance the car travels.

For this journey, which of these is true for Harry’s method? Tick one box.

ABCDEF is a triangular prism which represents part of a hill. ABCF is the horizontal rectangular base. D is vertically above C.

Work out the height CD.

Jamil walks in a straight line from A to D.

Work out the size of angle DAC. You must show your working.

The histogram shows information about the speed of cars as they pass a checkpoint. The scale on the frequency density axis is missing.

The histogram shows information about 480 cars.

How many cars does the first bar represent?

Cars with a speed greater than 40 mph are over the speed limit. Use the histogram to estimate the number of cars that are over the speed limit.

A bag contains 30 discs. 10 are red and 20 are blue. One disc is taken out at random and replaced by two of the other colour. Another disc is then taken out at random and replaced by two of the other colour. Another disc is then taken out at random. Work out the probability that all three discs taken out are red.

P is a point on the circle with equation x² + y² = 80 P has x-coordinate 4 and is below the x-axis.

Work out the equation of the tangent to the circle at P.