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

1 2^x = 32 Circle the value of x.

4 5 6 7

What is 1.8 × 10^–4 as an ordinary number? Circle your answer.

– 180 000
– 18 000
0.000 18
0.000 018

Expand 6x²(x³ + 2) Circle your answer.

4 30 x 300 x is 200% of y

Circle the correct inequality.

ABCDE is a pentagon.

Work out the area of the pentagon.

Joe, Kim and Lisa each have an amount of money. Joe has £72 Joe’s amount: Kim’s amount = 6: 5 Lisa’s amount is times Joe’s amount.

Show that, in total, they have less than £250

Here is the rule for a sequence.

After the first two terms, each term is the sum of the previous two terms

The 1st term is 33 The 2nd term is x The 4th term is 73

Work out the value of x.

An expression for the nth term of a different sequence is n – n² Ruth says, ‘‘All the terms will be negative because n² is always greater than n.’’

Is she correct?

Give a reason for your answer.

Here is some information about the members of clubs A and B.

Give your answer as a decimal.

P and Q are points. The x-coordinate of Q is 4 more than the x-coordinate of P. The y-coordinate of Q is 5 less than the y-coordinate of P.

Work out the gradient of the straight line through P and Q.

Here are the results after 250 spins of a coin.

The coin is spun an extra 50 times. After all 300 spins, the relative frequency of Heads is 0.49

For the extra 50 spins, work out number of Heads: number of Tails

Part of a running track is the arc of a semicircle joined to a straight line. The semicircle has diameter 45 metres. The straight line has length 75 metres.

Abby runs once along this part of the track in 18 seconds.

Work out her average speed. Give your answer to 2 significant figures.

Triangles ABC and DEF are shown on a grid.

Describe a single transformation that shows the triangles are congruent.

A fair, ordinary dice is rolled and a counter is taken at random from a bag. The tree diagram shows the probabilities.

How do the probabilities show that all the counters in the bag are red, blue or green?

Circle the probability that the counter is red or blue.

0.0009 0.8 0.03 0.4

Circle the probability that the dice lands on an even number and the counter is blue.

0.15 0.3 0.35 0.8

Here are two solid cubes, X and Y. The mass of X is 10.976 kg The area of each face of X is 784 cm²

Zayan wants to know the density of Y. He assumes that Y is identical to X.

What density should he get for Y? Give your answer in grams per cubic centimetre.

In fact, the mass of Y is less than the mass of X the area of each face of Y is greater than the area of each face of X.

What does this mean about the actual density of Y? Tick one box.

A mobile phone takes 2 hours to charge from empty. When the phone is being charged, the current flow into the phone

• starts at full current flow (100%)

• continues at full current flow for a period of time

• gradually decreases until the phone is fully charged.

This is shown on Graph A below.

Graph B shows the percentage charge in the phone when charging from empty.

Megan’s phone is empty of charge. She starts to charge her phone at 10.00 am

Using Graph A, estimate the time when the current flow starts to decrease.

Using Graph A and Graph B, estimate the percentage charge in the phone when the current flow is 40%

Using Graph B, estimate the rate of increase in the percentage charge when the phone has 90% charge.

percent per minute

H is inversely proportional to the cube root of L. H = 7 when L = 64

Work out an equation connecting H and L.

Work out the value of H when L = 2744

A, B and C are points on a circle, centre O. BD is a tangent to the circle. OCD is a straight line.

Work out the size of angle x.

Rearrange 9m + 4(2m – 1) = p² + pm to make m the subject.

A circle has centre (0, 0) and passes through (0, 11)

Write down the equation of the circle.

There should be a train leaving a station every hour from 7 am No trains leave early.

P(the first train leaves on time) = 0.9 For all the other trains, if the previous train did leave on time, P(this train leaves on time) = 0.8 if the previous train did not leave on time, P(this train leaves on time) = 0.65

Work out P(the first three trains leave on time)

The 2 pm train does not leave on time.

Work out P(exactly one of the next two trains does not leave on time)

Shape A is enlarged to shape B.

Circle the scale factor of the enlargement.

Write down the coordinates of the centre of enlargement.

Give your answer as a single fraction.

Alec makes a bowl for dog food from a solid wooden cone. The sketches show how the bowl is made.

The cone has radius 9 cm and perpendicular height 30 cm A smaller cone, with radius 6 cm, is removed.

A hemisphere with radius 6 cm is then removed.

Volume of a hemisphere = πr³ where r is the radius

Work out the volume of the remaining wood that forms the bowl.

On the same day, Kate buys a car for £14 000 and a painting for £5000

The value of the car decreases by 35% in the first year, and then by 10% each year. The value of the painting increases by 4% each year.

Show that the painting becomes worth more than the car during the fifth year.

Two sides of a triangle are measured to 1 decimal place. The angle between the sides is measured to the nearest degree.

Work out the upper bound for the area of the triangle.

You must show your working.

On the axes below, sketch the graph of y = –5^x