AQA GCSE Maths Paper 3: Calculator Higher November 2021 question paper 8300/3H

b is 3 more than the square root of a. Circle the correct equation.

Circle the largest number.

A line has equation 3 y = 3 x – 2 Circle the coordinates of the intercept of the line with the y-axis.

Factorise x² – 64 Circle your answer.

(x + 8)² (x – 8)² (x + 8)(x – 8) x(x – 64)

Six positive numbers have a mean of 10 a range of 19 Four of the numbers are 12 7 15 3 Work out the other two numbers.

At a country park there is a house, a museum and a garden. The table shows the prices per person to visit the park.

One day, 480 people visit the park. 67 visit the garden only. 40% visit the house and the museum. visit the house only. The rest visit the museum only. In total, how much do the 480 people pay to visit the park? You may use the Venn diagram to help you.

Jeff and Kaz share £270 in the ratio Jeff: Kaz = 2.6: 1 How much more than Kaz does Jeff get?

The heel of a shoe exerts a pressure of 198 pounds per square inch. Convert this pressure into kilograms per square centimetre. Use 1 pound = 0.45 kilograms 1 square inch = 6.25 square centimetres

Rectangle ABCD is split into four smaller rectangles. Two of the smaller rectangles are shaded.

4: x = 1: 2 For rectangle ABCD, work out the ratio shaded area: unshaded area Give your answer in its simplest form.

A solid shape is drawn on isometric paper.

On the centimetre grid, draw the elevation of the shape from A.

On the centimetre grid, draw a plan of the shape.

Erik thinks of a prime number between 20 and 30 His number is x % of 125 Work out one possible value of x.

Part of a regular polygon with 15 sides is shown.

Work out the size of an interior angle.

A box is the shape of half a cylinder on top of a cuboid.

Work out the volume of the box.

Phil sells ties. He increases the original price of each tie by 10% to £13.20 A month later he announces a sale.

Phil says, “The ties will be back to their original price, because each change was by 10%” Is he correct? Tick a box.

Show working to support your answer.

A biased spinner can land on A, B or C. The table shows the probabilities, in terms of k, of A, B and C.

Work out the probability of B.

P is the point (2, 14) Q is the point (6, 8) R is the point (2, 5) Use gradients to show that angle PQR is not a right angle.

m² 9 Circle the possible value of m.

Simplify w¹ × w⁰ Circle your answer.

The equation of a circle is x² + y² = 11 Work out the length of the diameter. Circle your answer.

= 3c

Work out the value of a when c = 8

Here is some information about the ages of babies at a clinic.

Draw a histogram to represent the information.

A sequence of patterns is made using horizontal sticks and vertical sticks.

The table shows the number of horizontal sticks and vertical sticks in each pattern.

What fraction of the total number of sticks in Pattern n are horizontal? Give your answer in terms of n.

The equation of a curve is y = 16

Circle the point that lies on the curve.

(2, 32) (32, 2) (2, 256) (256, 2)

A different point on the curve has y-coordinate Work out the x-coordinate.

a^b = 3 where a is an integer and b is a proper fraction. Work out one possible pair of values of a and b.

Expand and simplify fully (x – 3)(x + 2)(x + 5)

Here are two similar cones.

The surface area of cone A is 2 m² The surface area of cone B is 4.5 m² Work out the ratio radius of cone A: radius of cone B Give your answer in the form 1: n

In the diagram

EX: XH = 3: 1 EF: FG = 1: 3

Is DXF a straight line? Show working to support your answer.

a = 4.72 to 3 significant figures. b = 158 to 3 significant figures. Work out the upper bound of You must show your working.

A, B and C are three points on the circumference of a circle, centre O. BD and CD are tangents to the circle. ABDC is a kite.

Prove that angle ABO is 45° –

A sphere has radius r cm An approximate value of r can be found using the iterative formula

The starting value is r₁ = 7

Work out the values of r₂ and r₃

Continue the iteration to work out the radius to 1 decimal place.