4MA1 Mathematics A: May/June 2022 Paper 2HRHigher Tier Paper 2

(a)Describe fully the single transformation that maps triangle A onto triangle B

[3]

(b)On the grid above, translate triangle A by the vector −4  

Label your triangle C[1]

Write 1200 as a product of powers of its prime factors. Show your working clearly.

[3]

Alberto, Bill, Candela and Diana are four friends.

Here is some information about the height of each of these friends.

Alberto’s height is 158 cm. Bill’s height is 175 cm. Candela’s height is greater than Diana’s height.

The median height of these four friends is 160 cm. The range of the heights of these four friends is 21 cm.

Work out Candela’s height and Diana’s height.

Candela cm

Diana cm[3]

E = {9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} A = {multiples of 3} B = {odd numbers}

(a)List the members of the set

(i)A ∩ B

[1]

(ii)A ∪ B

[1]

(b)Is it true that 24 ∈ A?

Tick one of the boxes below.

Yes No

Give a reason for your answer.

[1]

Set C has 4 members such that C ∩ B¢ = {10, 18}

(c)List the members of one possible set C

[2]

The diagram shows a shape made from a square ABCD and 4 identical semicircles.

As shown in the diagram, the semicircles have AB, BC, CD and DA as diameters.

The area of the square is 36 cm²

Calculate the total area of the shape. Give your answer correct to one decimal place.

cm²[4]

(a)Solve p = 3 p − 510

Show clear algebraic working.

p = [3]

(b)Simplify a⁰ where a > 0

[1]

(c)Simplify fully

[2]

(d)Factorise fully 10c³ d²+ 15cd⁴

[2]

2^k_x

Find an expression for x in terms of k and n

x = [2]

A cinema increased the cost of an adult ticket by 12%

After the increase, the cost of an adult ticket was £18.20

Work out the cost of an adult ticket before the increase.

£ [3]

The table gives information about the population, correct to 2 significant figures, of each of five cities in 2018

(a)Write 8.8 × 10⁶ as an ordinary number.

[1]

(b)Which of these cities had the least population in 2018?

[1]

(c)Work out the difference between the population of Tokyo and the population of Ahmedabad in 2018 Give your answer in standard form correct to 2 significant figures.

[2]

The diagram shows triangle ABP inside the regular hexagon ABCDEF

Work out the size of angle PAF Give your answer correct to 3 significant figures.

[5]

The cumulative frequency table shows information about the ages of 60 people who went to a gym on Saturday.

(a)On the grid, draw a cumulative frequency graph for the information in the table.

[2]

(b)Use your graph to find an estimate for the median of the ages of these people.

_years[1]

(c)Use your graph to find an estimate for the interquartile range of the ages of these people.

_years[2]

(d)Use your graph to find an estimate for the number of these people who are older than 55 years.

[2]

ACE and BCD are straight lines. AB is parallel to DE

Work out the value of x

x = [3]

The diagram shows a sector AOB of a circle with centre O

Angle AOB = 67° OA = OB = 5.2 cm

Calculate the perimeter of the sector. Give your answer correct to 3 significant figures.

cm[3]

Ciara throws four fair six‑sided dice.

The faces of each dice are labelled with the numbers 1, 2, 3, 4, 5, 6

Work out the probability that at least one of the dice lands on an even number.

[3]

The diagram shows a kite ABCD

Calculate the area of the kite. Give your answer correct to 3 significant figures.

cm²[3]

Here are nine graphs.

Complete the table below with the letter of the graph that could represent each given equation. Write each answer on the dotted line.

[3]

Use algebra to show that 0.345 = 1955[2]

Kaidan and Sonja went on two different car journeys.

For Kaidan’s journey distance = 80 km correct to the nearest 5 km time = 2.7 hours correct to 1 decimal place

For Sonja’s journey distance = 33 km correct to 2 significant figures time = 1 hour correct to the nearest 0.1 hour

Kaidan says, “My average speed could have been greater than Sonja’s average speed.”

By considering bounds, show that Kaidan is correct. Show your working clearly.[4]

f(x) = x²– 4

g(x) = 2x + 1

Solve fg(x) > 0 Show clear algebraic working.

[4]

The centre O of a circle has coordinates (4, 7)

The point A, on the circle, has coordinates (6, 11) and AOP is a diameter of the circle.

Find an equation of the tangent to the circle at the point P

[4]

Solve the simultaneous equations

Show clear algebraic working.

[5]

The point A with coordinates (–3, 2) lies on the straight line with equation y = f(x)

(a)Find the coordinates of the image of the point A on the straight line with equation

(i)y = f(x) – 3

( , )[1]

(ii)y = f  x 2

( , )[1]

Here is a sketch of part of the curve with equation y = g(x)

The point B with coordinates ( p, q) lies on the curve.

(b)Find the coordinates of the image of the point B on the curve with equation

where c is a constant.

( , )[2]

Express  x 20− 36 − 2x − 6 14 − x as a single fraction in its simplest form. ₂  ×

[3]

The diagram shows a frustum of a cone, and a sphere.

The frustum, shown shaded in the diagram, is made by removing the small cone from the large cone. The small cone and the large cone are similar.

The height of the small cone is h cm and the radius of the base of the small cone is r cm. The height of the large cone is kh cm and the radius of the base of the large cone is kr cm. The radius of the sphere is r cm.

The sphere is divided into two hemispheres, each of radius r cm.

Solid A is formed by joining one of the hemispheres to the frustum. The plane face of the hemisphere coincides with the upper plane face of the frustum, as shown in the diagram below.

Solid B is formed by joining the other hemisphere to the small cone that was removed from the large cone. The plane face of the hemisphere coincides with the plane face of the base of the small cone, as shown in the diagram below.

The volume of solid A is 6 times the volume of solid B.

Given that k >³ 7

find an expression for h in terms of k and r

h = [6]

ABCD is a parallelogram and ADM is a straight line.

AB = a BC = b DM = 12 b

K is the point on AB such that AK : AB = λ : 1 L is the point on CD such that CL : CD = μ : 1 KLM is a straight line.

Given that λ : μ = 1 : 2

use a vector method to find the value of λ and the value of μ

λ =

μ = [5]