AQA GCSE Maths Paper 3: Calculator Higher November 2019 question paper 8300/3H

Circle the relative frequency that represents 13 successes out of 50 trials.

0.13 26 13: 50 0.26

The equation of a straight line is 2 y = 3 x + 5 Circle the gradient of the line.

(2 x – 4)(3 x + 5) is expanded and simplified. Circle the term which is part of the answer.

2 x – 2 x 22 x – 22 x

When rounded to 3 significant figures, x = 6.37 Circle the correct error interval.

Solve the simultaneous equations 7 x + 2 y = 36 3 x + 2 y = 16

Tom is tiling a wall. He needs to buy at least 100 tiles. The tiles are sold in large packs and small packs.

Large pack 40 tiles £18 Small pack 28 tiles £14 Special offer 25% reduction when you buy 3 or more large packs

Work out the cheapest cost for Tom to buy the packs of tiles he needs.

Tom is also tiling a floor. The floor is a rectangle with length 600 cm and width 240 cm Each tile is a square with side 40 cm Tom uses this method to work out the number of tiles he needs.

Number of tiles that will fit along the width = 240 ÷ 40 = 6 Total number of tiles needed = 15 + 6

Give a reason why Tom’s method is wrong.

An equilateral triangle has side length 16 metres. Using ruler and compasses only, construct a scale drawing of the triangle. Use the scale 1 centimetre represents 2 metres. Scale: 1 cm represents 2 m

In a choir there are 35 men and 48 women. The probability that a man chosen at random wears glasses is The probability that a woman chosen at random wears glasses is

Work out the number of people in the choir who wear glasses.

A person is chosen at random from the choir. Work out the probability that the person does not wear glasses.

The pie chart shows information about people at a theme park.

There were 450 more women than men. Work out the number of children.

10 Density =

The mass is divided by 2 and the volume is multiplied by 4 What happens to the density? Circle your answer.

× 2 ÷ 2 × 8 ÷ 8

Work out cube root of 512: reciprocal of 0.4 Give your answer in the form n: 1

The graph shows how much Molly is paid for working for up to 40 hours. She receives a basic rate of pay for the first 35 hours worked a higher rate of pay for the next 5 hours worked.

Work out the difference between the higher rate of pay and the basic rate of pay. Give your answer in £ per hour.

Naga states a hypothesis. “Most people read more than 100 books a year.” She asks a sample of five people in a book club how many books they read last month. The table shows the results.

Show how Naga could use the data to support her hypothesis.

Give two reasons why this sample should not be used to support her hypothesis.

A graph has equation y = x³ + a where a is an integer. The graph passes through the point (3, 29) Draw the graph for values of x from – 3 to 3

When you earn money you pay income tax. The amount you pay depends on how much you earn that year. You pay 0% on the first £12 500 you earn 20% on the next £37 500 you earn 40% on the next £112 500 you earn. One year, Kim paid £9260 income tax. Work out how much she earned that year.

A building company employs 2 labourers 14 joiners 9 electricians 8 plumbers. For a job, the company needs one of each type of worker.

In how many ways can the company choose the four workers?

One labourer and two plumbers are on holiday. In how many ways can the company now choose the four workers?

f(x) = 3x² – 4x + 8 for all values of x Jenny says, “f(10) must equal 2 × f(5), because 10 is 2 × 5” Is Jenny correct? Show working to support your answer.

Work out the two roots of (7 x + 1)(2 x – 3) = 0 Circle both roots.

Here is a cuboid. DH = 8 cm DB = 13 cm

Work out the size of angle DBH.

Using your answer to part (a), work out the size of angle ECG.

P (– 1, 1) is a point on the circle, centre O, radius r.

Work out the value of r. Circle your answer.

Juice is sold in small bottles and large bottles. The volume of the large bottle is 1125 ml.

volume of small bottle: volume of large bottle = 2: 5 A café has small glasses and large glasses. volume of small glass: volume of large glass = 4: 7 A small bottle fills 6 small glasses with no juice left over. How many large glasses can be filled by a large bottle? You must show your working.

The only solution to x² + bx + c = 0 is x = 5 Work out the values of b and c.

What is x as a fraction of y ? Circle your answer.

Shape A and shape B are shown on the grid.

Describe the single transformation that maps shape A to shape B.

Here is a sketch of a speed-time graph for the first part of a journey.

The total distance for the journey is 130 kilometres. How far is left to travel?

Here is a triangular sail.

Vicky needs to buy waterproofing liquid for the sail. She will put 3 coats of liquid on each side of the sail. A litre of liquid covers 8.5 square metres of sail. How many 1-litre bottles of liquid does Vicky need?

Another sail is joined to the first sail as shown.

x is an acute angle. Work out the size of angle x.

Here is quadrilateral PQRS.

X is a point on PS where PX: XS = 1: 2 Y is a point on RQ where RY: YQ = 2: 1

Is XY parallel to PQ ? Show working to support your answer.

f(x) = 2x – 3 and g(x) = x²