AQA GCSE Maths Paper 3: Calculator Higher June 2022 question paper 8300/3H

Circle the smallest number.

Circle your answer.

Here are four scatter graphs.

For which graph is a straight line of best fit appropriate? Circle your answer.

A B C D

Which graph has one outlier? Circle your answer.

A B C D

Use trigonometry to work out the size of angle x.

x = °

Laura works in a shop. The table shows the number of hours she works on two weekends.

Work out the percentage increase in her total hours from Weekend 1 to Weekend 2

Here is a sketch of the curve y = x² – 4x – 5

Write down the two roots of x² – 4x – 5 = 0

Work out the coordinates of T, the turning point of the curve.

A is an arithmetic progression. Here are the first four terms. 13 16 19 22

G is a geometric progression. Here are the first four terms. 2 4 8 16

Work out the value of n.

n =

Information about two fridge-freezers, A and B, is shown.

Grace buys one of these fridge-freezers. She buys the one with the greater freezer capacity. Which one does she buy? You must show your working.

Tom and Adil are the two runners in a 200-metre race. Tom completes the race in 24 seconds. Adil completes the race at an average speed of 28.8 kilometres per hour. Who wins the race? You must show your working.

The mass of a baby is 3.6 kilograms to 1 decimal place. What is the error interval for the mass in kilograms? Tick one box.

A quadrilateral has angles 70 °, 110 °, 130 ° and 50 ° Circle the possible type of quadrilateral.

kite parallelogram rhombus trapezium

B is 6 km due South of A and 6 km due West of C.

Work out the bearing of A from C.

Here is a scale drawing.

A ship is going to sail from D to E. Mia works out that the ship needs to sail on a bearing of 068 ° Why must Mia be wrong?

Circle your answer.

Students in two classes, A and B, raised money for charity. The box plot for class A is shown on the grid.

For class B,

• the lowest amount was £3 and the highest amount was £26

• the lower quartile was £11

• the median was £2 greater than the class A median

• the interquartile range was 1 times greater than the class A interquartile range.

Draw the box plot for class B on the grid.

A town has a population density of 278 people per km² and a population of 158 460

The population increases to 168 720 Work out the population density after the increase.

Here is a scale drawing of a reservoir. Scale: 1 cm represents 500 m

Virat wants to estimate the volume of water in the reservoir. He draws on the scale drawing a circle with radius 3 cm

Virat estimates the volume of the reservoir by assuming that

• the reservoir is a cylinder whose cross section is the circle

• the depth of the reservoir is 17 metres.

Work out Virat’s estimate in cubic metres.

In fact,

• the depth of the reservoir is 13.8 metres

• the reservoir is not a cylinder (see diagram).

Which statement about the actual volume of the reservoir is correct? Tick one box.

Give a reason for your answer.

In a video game, players make their own character. They choose one of each from 8 faces 4 bodies 5 hairstyles.

How many different characters can be made?

Two characters are made at random. What is the probability that they are exactly the same?

A, B and C are points on a circle, centre O. DC is a tangent to the circle.

Show that angle ABO: angle ACO = 3: 1

Here is the plan of the floor of an L-shaped room. All lengths are in metres.

The area of the floor is 75 m²

By factorising x² + x – 90 work out the value of x. You must show your working

£2448 is invested in an account at a rate of compound interest. One year after the investment there is £2496.96 in the account. How much is in the account four years after the investment?

Use the sine rule to work out the size of angle x.

x = °

f(x) = 3x and g(x) = x² Circle the expression for fg(x)

Here are two simultaneous equations.

and y = 3 x + d There is a solution when x = 5 Work out the value of c + d

Here is a sketch of the graphs of y = k^x and y = x² + c^box k and c are positive constants.

Work out the value of r.

r =

A company makes tubes of toothpaste. The masses of 80 tubes are checked. A histogram is drawn to represent the data.

The company makes 28 000 tubes each day. Estimate how many tubes each day have a mass less than 122 grams.

Q and R are two numbers. As a product of prime factors,

The highest common factor (HCF) of Q and R is 4056 Work out the value of a.

Work out the lowest common multiple (LCM) of Q and R.

Expand and simplify fully (x – 3)(x – 4)(x + 8)