4MA1 Mathematics A: January 2023 Paper 1FRFoundation Tier Paper 1

Here is a list of numbers.

From this list, write down

(a)the odd number

[1]

(b)the multiple of 6

[1]

(c)the square number

[1]

(d)the prime number

[1]

(e)two numbers with a sum of 26

[1]

Here are 6 counters. Each counter has a number on it.

Finn takes at random one of these counters.

(i)Select with a tick ( ) the word that best describes the likelihood that Finn takes a

counter with the number 2 on it.

(ii)Select with a tick ( ) the word that best describes the likelihood that Finn takes a

counter with the number 3 on it.

(iii)Select with a tick ( ) the word that best describes the likelihood that Finn takes a

counter with a number greater than 4 on it.

[3]

(a)Write down the mathematical name of this 3‑D shape.

[1]

(b)(i)How many faces does this shape have?

[1]

(ii)How many vertices does this shape have?

[1]

Here is a different 3‑D shape.

Marie makes a model of the shape. She uses a length of wire to make each edge of the model. Each edge of the model is 5 cm long.

Marie has 70 cm of wire.

(c)What length of wire does she have left after making the model?

cm[2]

(a)Simplify 10y – y

[1]

(b)Simplify 3p × 4p

[1]

(c)Solve 7x = 42

x = [1]

(d)Solve n + 6 = 5

n = [1]

(e)Simplify 8c + 5d – 2c – 3d

[2]

Zoya buys a book and some pencils.

The book costs £6.90 Each pencil costs £0.55

Zoya has a total of £15 to spend on the book and the pencils. She buys as many pencils as she can.

Work out how many pencils she buys.

[3]

(a)Write down all the factors of 10

[1]

(b)Find the lowest common multiple (LCM) of 18 and 60

[2]

(a)Write these decimals in order of size. Start with the smallest decimal.

[1]

(b)Write 0.08 as a percentage.

%[1]

(c)Write 319 as a mixed number.

[1]

(d)Find the number that is exactly halfway between 725 and 0.88

[2]

The two‑way table shows some information about the desserts chosen at lunch yesterday by the 80 students from Year 5 and Year 6. Each student chose one dessert from apple pie or fruit or ice cream.

(a)Complete the two‑way table.[3]

(b)What fraction of these 80 students were in Year 5 and chose apple pie? Give your answer in its simplest form.

[2]

BCD is an isosceles triangle with BD = CD ABC is a straight line. ABDE is a quadrilateral.

Work out the value of x Give a reason for each stage of your working.

x = [4]

The graph below can be used to change between dollars and Danish krone.

(a)Change 40 dollars to Danish krone.

_Danishkrone[1]

(b)Change 350 Danish krone to dollars.

_dollars[1]

Robert needs 950 Danish krone to pay for a hotel stay. He has 170 dollars.

(c)Show that Robert has enough money to pay for his hotel stay.[2]

(a)Work out the value of 2.5 + 3.612 .7 + 8.25 × 3.6

Give your answer as a decimal. Write down all the figures on your calculator display.

[2]

(b)Write your answer to part (a) correct to 3 significant figures.

[1]

Aarav uses this rule to estimate the time, in minutes, that a bus journey takes.

Time = 2.5 × length of journey in kilometres + 1.5 × number of bus stops

Aarav’s bus journey to work has a length of 12 kilometres. There are 5 bus stops on the route.

(a)Use Aarav’s rule to work out an estimate for the time this bus journey takes.

_minutes[2]

A different bus journey takes 55 minutes. There are 8 bus stops on the route.

(b)Use Aarav’s rule to work out an estimate for the distance of this bus journey.

km[3]

Tom puts boxes into a shipping container.

The container is a cuboid 10 metres by 2.4 metres by 2.4 metres. Each box is a cube of side 40 centimetres.

Work out the greatest number of these boxes that Tom can put into the container.

[3]

The accurate scale drawing shows the positions of two lighthouses, S and T

(a)Find, by measuring, the bearing of lighthouse T from lighthouse S

°[1]

A boat is on a bearing of 084° from S The boat is 13 km from T

(b)On the diagram, mark with a cross (X) the position of the boat. Label the cross B[3]

The table shows information about the frame size, in cm, of 60 bicycles sold in a shop.

(a)Write down the modal class.

[1]

(b)Work out an estimate for the mean frame size.

cm[4]

The diagram shows a solid triangular prism.

6 cm

Work out the total surface area of the triangular prism. Give your answer correct to 3 significant figures.

cm²[3]

Here is a list of six numbers written in order of size.

Find the value of x, the value of y and the value of z

x =

y =

z = [3]

(a)Simplify w¹² ÷ w³

[1]

(b)Simplify 5m⁴ p² × 2m³ p

[2]

Divya and Yuan each pay for a holiday at a special offer price.

The amount that Divya pays is the same as the amount that Yuan pays.

Work out the value of k

k = [4]

C grams of chocolate is shared in the ratios 2 : 5 : 8 The difference between the largest share and the smallest share is 390 grams.

Work out the value of C

C = [3]

Solve the simultaneous equations

Show clear algebraic working.

x =

y = [3]

(a)Write 9.32 × 10^–5 as an ordinary number.

[1]

(b)Work out 3 × 10⁵– 6 × 10⁴ Give your answer in standard form.

[2]

(c)Work out (3 × 10⁵⁵) × (6 × 10⁶⁵) Give your answer in standard form.

[2]

(a)Factorise fully 18c³ d²– 21c²

[2]

(b)(i)Factorise y²– 3y – 18

[2]

(ii)Hence, solve y²– 3y – 18 = 0

[1]

The diagram shows an isosceles triangle ABC

AB = 7 cm AC = BC = ycm

The area of the triangle is 42 cm²

Work out the value of y

y = [4]

R and T are points on a circle, centre O

RT = 12 cm M is the midpoint of RT Angle ROM = 52°

Work out the area of the circle. Give your answer correct to 3 significant figures.

cm²[4]