AQA GCSE Maths Paper 2: Calculator Higher June 2018 question paper 8300/2H

Here is a circle.

Circle the word that describes the shaded part.

segment chord sector arc

Circle the number that is in standard form.

Circle the ratio that is equivalent to y: x

2: 5 5: 2 3: 2 2: 3

Work out 40 as a percentage of 10 Circle your answer.

4% 25% 300% 400%

Match each sequence to its description. One has been done for you.

The table shows information about the population of a city.

Liam claims, “From 2011 to 2021 the population of the city will increase by the same percentage as from 2001 to 2011” He works out, population increase from 2001 to 2011 = 480 000 – 420 000 = 60 000 population in 2021 = 480 000 + 60 000 = 540 000 Does the population of 540 000 match his claim? You must show your working.

On three days, Ali throws darts at a target. Here are his results.

Work out two different estimates for the probability of Ali hitting the target.

Which of your two answers is the better estimate for the probability of Ali hitting the target? Give a reason for your answer.

Theo starts with savings of £18 James starts with no savings. Each week from now, Theo will save £4.50 and James will save £4 In how many weeks will Theo and James have savings in the ratio 15: 8 ?

The length of each side of a regular pentagon is 8.4 cm to 1 decimal place.

Complete the error interval for the length of one side.

Complete the error interval for the perimeter.

A container is a hemisphere of radius 30 cm

Sand fills the container at a rate of 4000 cm³ per minute. Does it take less than a quarter of an hour to fill the container? You must show your working.

Two ordinary fair dice are rolled.

Complete the tree diagram.

Work out the probability that both dice land on a number less than 3

Work out the probability that exactly one of the dice lands on a number less than 3

A straight line is drawn on the centimetre grid.

Fay assumes that the scale is 1 cm represents 1 unit.

Use her assumption to work out the gradient of the line.

In fact, the scale is 1 cm represents 2 units. Which statement is correct? Tick one box.

Show that, for x ≠ –1 13 simplifies to the form ax + b where a and b are integers.

The scale drawing represents a garden. Water from a sprinkler at P reaches up to 20 metres from P. Water from a sprinkler at Q reaches up to 25 metres from Q. Scale: 1 cm represents 5 m

Using a pair of compasses, show the region that water from both sprinklers reaches.

100 men and 100 women took a test.

Using this data, which statement must be true? Tick one box.

Some concrete has volume 3.8 m³

The density of the concrete is 2400 kg/m³ Work out the mass of the concrete.

The 3.8 m³ of concrete is made into the shape of a cylinder. The base has radius 0.5 metres.

Work out the height of the cylinder.

A ball is thrown vertically upwards. The graph shows the height of the ball above the ground after it is thrown.

For how many seconds is the ball at a height of more than 2 metres?

After how many seconds is the ball at instantaneous rest when it is in the air?

Work out the average speed of the ball when it is moving downwards.

The solution of 3^x = 300 lies between two consecutive integers. Work out the two integers.

A pentagon is made from a square and an isosceles triangle.

Work out the perimeter of the pentagon.

Here is an inflated swimming ring with dimensions in centimetres.

The volume of the ring, V cm³, is given by

Work out the volume when a = 20 and b = 30 Give your answer to 3 significant figures.

Liz and Tia are walking towards a shop along different straight paths. The diagram shows their positions at 2 pm

Assume they walk at the same speed. Who will arrive at the shop first? You must show your working.

In fact, Liz walks at a faster speed than Tia. How does this affect the answer to part (a)?

A circle, centre O, passes through (5, 0).

What is the equation of the circle? Circle your answer.

Solids X and Y are similar.

Work out the surface area of Y.

A tank is a cuboid measuring 50 cm by 35 cm by 20 cm All lengths are to the nearest centimetre. A container has a capacity of exactly 34 litres.

Which has the greater capacity? Tick one box.

Show working to support your answer.

The Venn diagram shows some information about 150 students. ξ = 150 students C = students who study Chemistry P = students who study Physics

The probability that a Physics student, chosen at random, also studies Chemistry is One of the 150 students is chosen at random. Work out the probability that the student does not study either Chemistry or Physics.

A curve has equation y = 4x² + 5x + 3 A line has equation y = x + 2 Show that the curve and the line have exactly one point of intersection. Do not use a graphical method.

Prove algebraically that 2.75 converts to the fraction

f(x) = 5 – x and g(x) = 3 x + 7

Simplify f(2 x) + g(x – 1)

Solve g^–1(x) = 2x

x =