4MA1 Mathematics A: January 2022 Paper 2FFoundation Tier Paper 2

The diagram shows a square and its diagonals.

(a)Shade 14 of the square.[1]

Here is a rhombus.

(b)What fraction of the rhombus is shaded?

[1]

(c)Write 0.9 as a fraction.

[1]

Here is a list of numbers.

(a)From the numbers in the list, write down

(i)a cube number

[1]

(ii)a factor of 70

[1]

(iii)a multiple of 6

[1]

(iv)a prime number.

[1]

Here is a number machine.

(b)Work out the input when the output is 108

[2]

The diagram shows a fair 8-sided spinner.

Hollie is going to spin the spinner once.

(a)Write down the word from the box above that best describes the likelihood that the spinner will land on

(i)yellow

[1]

(ii)red.

[1]

(b)On the probability scale below, mark with a cross (×) the probability that the spinner will land on blue.

[1]

The table below shows the maximum recorded temperature and the minimum recorded temperature on one day in each of four countries.

(a)Which country has the highest maximum recorded temperature?

[1]

(b)Work out the difference between the maximum recorded temperature in Finland and the minimum recorded temperature in Finland.

°C[1]

On the same day, the minimum recorded temperature in Japan is 15 °C lower than the minimum recorded temperature in Morocco.

(c)Work out the minimum recorded temperature in Japan.

°C[1]

The diagram shows points A and B marked on a grid of squares.

(a)On the grid, draw the line with equation y = −2[1]

M is the midpoint of AB

(b)Find the coordinates of M

( , )[2]

D is the point with coordinates (5, d ) where d > 0 The triangle ABD is an isosceles triangle.

(c)Find the value of d

d = [1]

Here are nine shapes drawn on a grid of squares.

Shape D is a quadrilateral.

(a)What is the mathematical name of this quadrilateral?

[1]

One of the shapes is congruent to shape G

(b)Write down the letter of this shape.

[1]

(c)Write down the order of rotational symmetry of shape H

[1]

(d)How many lines of symmetry has shape E?

[1]

38 of the members of a squash club are children.

56 of these children are right-handed.

What fraction of the members of the squash club are right-handed children? Give your answer as a fraction in its simplest form. Show your working clearly.

[3]

By writing each value correct to one significant figure, work out an estimate for the value of

Show your working clearly.

[3]

The diagram shows triangle ABD

ABC, BDE and ADF are straight lines.

angle CBD = 132° angle ADB = 58°

(a)(i)Write down the value of x

x =

(ii)Give a reason for your answer.

[2]

(b)Work out the value of y

y = [2]

In a library there are two trolleys of books.

On trolley 1 the subjects of the books are Buildings (B), Rivers (R) and Space (S). On trolley 2 the subjects of the books are Buildings (B), History (H) and Animals (A).

Tomos takes one book from trolley 1 and one book from trolley 2

Write down all the possible combinations of subjects that Tomos can take.

[2]

Here is a sequence of patterns made from counters.

(a)In the space below, draw Pattern number 4[1]

(b)Complete the table.

[1]

(c)Work out the number of counters in Pattern number 10

[1]

Sven has exactly 70 counters.

(d)Can Sven make Pattern number 25 using his 70 counters?

Tick the appropriate box below.

Yes No

Give a reason for your answer.

[1]

The diagram shows a box B and a carton C

The box B is in the shape of a cuboid. Each carton C is in the shape of an 8 cm cube.

Martha is going to put as many of the cartons as possible into the box. She has enough cartons to do this.

Martha will then fill the remaining space inside the box with packing material.

Work out the volume of the space inside the box that Martha will fill with packing material.

_cm³[5]

Here is a conversion graph to change between Canadian dollars and pounds (£)

(a)Use the graph to change

(i)46 Canadian dollars to pounds (£)

£

(ii)£10 to Canadian dollars.

_{Canadiandollars}[2]

Alana is on holiday in London and is going to Paris. She is going to book a hotel in Paris. She knows that

(b)Change 528 euros to Canadian dollars.

_{Canadiandollars}[3]

Iman walked for 3 hours 15 minutes. He walked a distance of 18.2 kilometres.

Work out Iman’s average speed for his walk. Give your answer in km/h

_km / h[3]

Here is a list of the ingredients needed to make 12 chocolate brownies.

Thalia buys exactly enough of these ingredients to make 120 of these brownies.

1.5 kg of flour costs £1.30 500 g of chocolate spread costs £2.60 6 eggs cost £1.10

Thalia sells all 120 brownies at £0.40 each.

Work out the profit that she makes.

£ [5]

(a)Expand and simplify x(2x − 3) + 7(2x + 1) − 5

[3]

(b)Expand and simplify ( y + 4)(2 − y)

[2]

(c)Factorise fully 15b⁵ c − 35b³ c⁹

[2]

Show that 6 34 ÷ 2 47 = 2 58[3]

Triangle ABC is similar to triangle PQR

(a)Calculate the length of BC

_cm[2]

(b)Write down an expression for y in terms of x

y = [1]

Each side of a regular octagon has a length of 18 mm, correct to the nearest 0.5 mm

(a)Write down the lower bound of the length of each side of the octagon.

_mm[1]

(b)Write down the upper bound of the length of each side of the octagon.

_mm[1]

The scale diagram shows the position on a map of a house, A

House C is on a bearing of 110° from A The distance from A to C is 700 m

(a)Mark the position of C on the diagram with a cross (×) Label your cross C[3]

(b)Write the scale of the map in the form 1 : n

1 : [1]

A bag contains only pink sweets, white sweets, green sweets and red sweets.

The table gives each of the probabilities that, when a sweet is taken at random from the bag, the sweet will be green or the sweet will be red.

number of pink sweets : number of white sweets = 2 : 1

There are 28 red sweets in the bag.

Work out the number of white sweets in the bag.

[5]

Find the lowest common multiple (LCM) of 28, 42 and 63 Show your working clearly.

[3]

The table gives information about the average house price in England in 2018 and in 2019

(a)Work out the percentage increase in the average house price from 2018 to 2019 Give your answer correct to one decimal place.

_%[2]

The average house price in 2019 was 7.7% greater than the average house price in 2017

(b)Work out the average house price in 2017 Give your answer correct to 3 significant figures.

£ [3]

The frequency table gives information about the number of points scored by a player.

The mean number of points scored is 2

Work out the value of x

x = [4]

Solve the simultaneous equations

Show clear algebraic working.

x =

y = [3]

The diagram shows a regular 10-sided polygon, ABCDEFGHIJ

Show that x = y[4]