4MA1 Mathematics A: Oct/Nov 2024 Paper 1FFoundation Tier Paper 1

The table gives the lengths, in metres, of five road tunnels.

(a)Which of these five tunnels has the greatest length?

[1]

(b)Write down the value of the 9 in the number 13 972

[1]

The length of one of the tunnels, when rounded to the nearest thousand, is 17 000 metres.

(c)Write down the name of this tunnel.

[1]

(d)Write the number 12 940 in words.

[1]

(e)Work out the total length of the Arlberg tunnel and the Jinpingshan tunnel.

metres[1]

Here are two shapes.

(a)Write down the mathematical name of the

(i)triangle,

[1]

(ii)quadrilateral.

[1]

(b)On the triangle, draw the line of symmetry.[1]

(c)Write down the order of rotational symmetry of the quadrilateral.

[1]

The pictogram gives information about the number of kilometres Thomas travelled on Monday, on Tuesday, on Wednesday and on Thursday.

(a)Write down the number of kilometres Thomas travelled on Tuesday.

kilometres[1]

On Wednesday, Thomas travelled further than he did on Thursday.

(b)How much further?

kilometres[2]

On Friday, Thomas travelled 13 kilometres.

(c)Show this information on the pictogram.[1]

The table shows information about the temperatures at different heights above sea level.

(a)Work out the difference in temperature between a height of 0 m and a height of 12 000 m

°C[1]

(b)Work out the difference in temperature between a height of 4000 m and a height of 6000 m

°C[1]

(c)At what height is the temperature 10°C warmer than the temperature at a height of 9000 m?

m[1]

(a)Simplify 8d  4d  7d

[1]

(b)Simplify m × 10 p

[1]

(c)Solve x  5  19

x = [1]

(d)Solve y8 = 6

y = [1]

(e)Simplify a × a × a × a

[1]

k = 8 and n = 12

(f)Work out the value of 9k − 4n

[2]

Pierre used 2358 units of water last year.

Each unit of water cost 0.28 euros.

Pierre has already paid for some of the water he used. He paid 42 euros each month last year.

Work out how much more Pierre has to pay for the water he used last year.

euros[4]

ABCD is a quadrilateral.

ADE is a straight line.

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

[4]

There are 80 cars in a car park.

27 of the cars are red 10 of the cars are blue the rest of the cars are white

One of the cars in the car park is chosen at random.

(a)Write down the probability that this car is red.

[1]

(b)Find the probability that this car is white.

[2]

15 identical pencil cases cost 41.25 Swiss francs.

Work out the cost of 52 of these pencil cases.

Swiss francs[2]

The scale diagram shows the positions of a castle and a tower.

Angela walks from the castle to the tower along a straight path.

She takes 18 minutes to walk each km.

Work out how many minutes Angela takes to walk from the castle to the tower.

minutes[3]

Make d the subject of the formula c  8d  5

[2]

On the grid below, draw the graph of y  12 x  1 for values of x from −2 to 3

[3]

The diagram shows a rectangular wall and a square tile.

Hamish wants to cover all the wall with tiles.

The tiles are sold in boxes. There are 6 tiles in each box. Each box of tiles costs £17.50

Work out the total cost of the tiles Hamish needs.

£ [4]

Kate has a fair triangular spinner and a fair square spinner.

The triangular spinner can land on 2 or 4 or 6 The square spinner can land on 1 or 2 or 3 or 4

Kate spins each spinner once. She adds the number the triangular spinner lands on to the number the square spinner lands on to get her score.

(a)Complete the table to show all possible scores. Four of the scores have been done for you.

[2]

Kate spins each spinner once.

(b)Find the probability that her score is 9 or less.

[2]

Rema buys 140 plants.

35% of the 140 plants cost $6 each.

14 of the 140 plants cost $8 each.

The rest of the 140 plants cost $10 each.

Work out the total cost of the 140 plants.

$ [4]

By rounding each number to one significant figure, work out an estimate for

Show your working clearly.

[2]

Reflect shape P in the line x = 1[2]

The table shows some information about the hourly rates of pay of 60 workers.

10 < p  15 18

15 < p  20 16

20 < p  25 14

25 < p  30 8

30 < p  35 4

(a)Write down the modal class.

[1]

(b)Work out an estimate for the mean hourly rate of pay of the 60 workers.

dollars[4]

Use ruler and compasses only to construct the bisector of angle ABC You must show all your construction lines.

[2]

(a)Simplify p³

[1]

(b)Expand and simplify 2n4n  3  nn  4

[2]

(c)Solve 2x  53  4  x

Show clear algebraic working.

x = [3]

Here is a Venn diagram.

(a)List the members of the set B

[1]

(b)List the members of the set A ∩ B

[1]

(c)List the members of the set A′

[1]

The diagram shows a cylinder.

The radius of the cylinder is 70 cm The height of the cylinder is 18 cm

Work out the volume of the cylinder. Give your answer in litres correct to the nearest litre.

litres[4]

A  2³  5⁴  7  11

B  2²  5²  7² C  2²  5³  7⁴

Find the highest common factor (HCF) of A, B and C Write your answer as a product of prime factors.

[2]

Shop A and Shop B have offers for buying the same type of laptop.

The normal price of the laptop in Shop A is different to the normal price of the laptop in Shop B

Which shop gives more money off their normal price? Show your working clearly.[4]

(a)(i)Factorise x²  5x  24

[2]

(ii)Hence, solve x²  5x  24  0

[1]

(b)Solve the inequality 3y  5  7 y  10

Show clear algebraic working.

[3]

(a)Write 8.4  10 ⁵ as an ordinary number.

[1]

(b)Work out 6.5  10⁴⁰   8  10¹⁸⁵  Give your answer in standard form.

[2]

Here are two similar triangles.

Work out the value of x Show your working clearly.

x = [5]