4MA1 Mathematics A: January 2021 Paper 1FFoundation Tier Paper 1

The table shows the height, in metres, of each of seven volcanoes.

Ojos del Salado 6893

Semeru 3676

(a)Which of these volcanoes has the greatest height?

[1]

(b)Write down the value of the 8 in the number 4585

[1]

(c)Write the number 6046 in words.

[1]

(d)Write the number 5137 correct to the nearest hundred.

[1]

(e)Work out the difference in the height of the Acamarachi volcano and the height of the Semeru volcano.

_metres[1]

Sandeep is designing some 3‑sided spinners.

He is going to spin each spinner once.

(a)(i)Write a different number on each dotted line so that when the spinner is spun it is impossible that the spinner will land on a number greater than 9

[1]

(ii)Write a different number on each dotted line so that when the spinner is spun it is certain that the spinner will land on a multiple of 10

[1]

The likelihood of an outcome is evens.

(b)On the probability scale, mark with a cross (X) the probability of this outcome.

[1]

Amir is going on holiday.

He weighs his suitcase on the weighing scales at the airport. The reading on the scale gives the weight of Amir’s suitcase.

An excess luggage charge has to be paid when the weight of a suitcase is greater than 25 kg. This charge is 7.45 euros for each kilogram over the 25 kg limit.

Work out the excess luggage charge that Amir has to pay.

_euros[3]

(a)Write 0.57 as a fraction.

[1]

(b)Write 0.02 as a percentage.

%[1]

(c)Write 7284 as a fraction in its simplest form.

[1]

(d)Write 225 as a mixed number.

[1]

(e)Work out 18 of 624

[1]

A sequence of shapes is made by shading squares on a square grid.

(a)On the grid, draw Shape number 4[1]

(b)Complete the table.

[1]

(c)Find the number of shaded squares in Shape number 8

[1]

(d)Explain why no shape in the sequence is made by shading exactly 50 squares.

[1]

Nav makes bracelets using cord.

Nav has a 6 metre length of cord. Each bracelet needs 17.5 cm of cord.

Work out the greatest number of bracelets that Nav can make.

[3]

(a)Simplify 10x + 4y + 3x – 6y

[2]

(b)Solve 2n + 5 = 16

n = [2]

The two‑way table shows some information about the 60 noodle meals eaten in a noodle bar by each of 60 people last Friday.

(a)Complete the two‑way table.[3]

One of the 60 people is selected at random.

(b)Write down the probability that this person ate Fried Udon noodles.

[1]

The diagram shows quadrilateral ABCD and isosceles triangle ADE, where AE = AD.

EDC is a straight line.

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

x = [4]

In Koko’s shop

5 chocolate bars cost $5.75

2 chocolate bars and 3 packets of sweets cost $7.85

Work out the cost of one packet of sweets.

$ [3]

Akiko travelled from London to Tokyo by plane.

The plane left London at 18 40 on Friday. The plane arrived in Tokyo the next day, at 06 25 London time.

How long did the flight take? Give your answer in hours and minutes.

_{hours minutes}[2]

(a)Expand x(4 – x)

[1]

t = ab – c

a = 1.5 b = 2.4 c = –5.6

(b)Work out the value of t.

t = [2]

(c)Make d the subject of y = dx – e

[2]

(a)Express 180 as a percentage of 750

%[2]

Zaina has booked a singer for a show. The singer will get 94% of the total money from the ticket sales.

The cost of each ticket for the show is 32.50 dirhams. Zaina sells 180 tickets.

(b)Work out the amount of money the singer will get.

_dirhams[3]

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

[2]

(b)Describe fully the single transformation that maps shape B onto shape C.

[3]

A bag contains 30 coloured counters. The table gives the number of counters of each colour.

One of the counters is taken at random from the bag.

(a)Write down the probability that this counter is green.

[1]

(b)Write down the probability that this counter is not red.

[2]

Show that 56 − 38 = 1124[2]

Pieter owns a currency conversion shop.

Last Monday, Pieter changed a total of 20 160 rand into a number of different currencies.

He changed 310 of the 20 160 rand into euros.

He changed the rest of the rands into dollars, rupees and francs in the ratios 9 : 5 : 2

Pieter changed more rands into dollars than he changed into francs.

Work out how many more.

_rand[4]

The table gives information about the speeds, in kilometres per hour, of 80 motorbikes as each pass under a bridge.

Speed Frequency

(a)Write down the modal class.

[1]

(b)Work out an estimate for the mean speed of the motorbikes as they pass under the bridge. Give your answer correct to 3 significant figures.

_{kilometresperhour}[4]

The diagram shows a container for water in the shape of a prism.

The rectangular base of the prism, shown shaded in the diagram, is horizontal. The container is completely full of water.

Tuah is going to use a pump to empty the water from the container so that the volume of water in the container decreases at a constant rate.

The pump starts to empty water from the container at 10 30 and at 12 00 the water level in the container has dropped by 20 cm.

Find the time at which all the water has been pumped out of the container.

[4]

E = {20, 21, 22, 23, 24, 25, 26, 27, 28, 29}

A = {odd numbers} B = {multiples of 3}

List the members of the set

(i)A ∩ B

[1]

(ii)A ∪ B

[1]

(a)Factorise fully 15y⁴+ 20uy³

[2]

(b)Solve 4 – 3x = 5 − 8x4

Show clear algebraic working.

x = [3]

(a)Write 2 840 000 000 in standard form.

[1]

(b)Write 2.5 × 10^–4 as an ordinary number.

[1]

Chen invests 40 000 yuan in a fixed‑term bond for 3 years.

The fixed‑term bond pays compound interest at a rate of 3.5% each year.

(a)Work out the value of Chen’s investment at the end of 3 years. Give your answer to the nearest yuan.

_yuan[3]

Wang invested P yuan. The value of his investment decreased by 6.5% each year.

At the end of the first year, the value of Wang’s investment was 30 481 yuan.

(b)Work out the value of P.

P = [3]

The region, shown shaded in the diagram, is a path.

The boundary of the path is formed by two semicircles, with the same centre O, and two straight lines.

The inner semicircle has a radius of 7 metres. The path has a width of 2 metres.

Work out the perimeter of the path. Give your answer correct to one decimal place.

_m[3]

(a)Simplify (2x³ y⁵)⁴

[2]

(b)(i)Factorise x²+ 5x – 36

[2]

(ii)Hence, solve x²+ 5x – 36 = 0

[1]

Here is isosceles triangle ABC.

A

D is the midpoint of AC and DB = 16 cm.

Angle DAB = 65°

Work out the perimeter of triangle ABC. Give your answer correct to one decimal place.

cm[4]