4MA1 Mathematics A: January 2022 Paper 1FRFoundation Tier Paper 1

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

(i)an even number

(ii)a multiple of 9

(iii)a prime number

[3]

Here are four cards. Each card has a number on it. The four cards are arranged to make the number 7358

(b)(i)Show how the four cards can be arranged to make the smallest number using all four cards.

(ii)Show how the four cards can be arranged to make a correct calculation below.

[2]

Here are three shapes.

Shape A is a triangle.

(a)Write down the mathematical name for this type of triangle.

[1]

Shape B is a rectangle.

(b)On shape B, draw its lines of symmetry.[1]

Shape C is a regular polygon.

(c)Write down the order of rotational symmetry of shape C.

[1]

(a)Change 6 metres into centimetres.

_centimetres[1]

(b)Change 4500 grams into kilograms.

_kilograms[1]

Lauren has 3 litres of fruit juice. She is going to use the fruit juice to make some drinks for a party. Each cup of drink will contain 225 millilitres of fruit juice.

Lauren is going to make as many cups of drink as possible.

(c)Work out how much fruit juice Lauren has left when she has made as many cups of drink as possible. Give your answer in millilitres.

_millilitres[4]

40 people were asked to name their favourite type of holiday. The pictogram gives information about the number of these people who said each of City Break or Beach or Walking.

City Break

Beach

Walking

(a)How many of these people said Beach?

[1]

4 people said Cruise. 9 people said Skiing.

(b)Show this information on the pictogram.[2]

One person from the 40 people asked is selected at random.

(c)Find the probability that this person said City Break.

[2]

Here are the first 4 terms of a number sequence.

(a)(i)Write down the next term of the sequence.

[1]

(ii)Explain how you worked out your answer.

[1]

(b)Is 256 a number in the sequence?

Tick one of the boxes below and give a reason for your answer.

Give a reason for your answer.

[1]

(a)Write these numbers in order of size. Start with the smallest number.

[1]

(b)Write 0.7 as a fraction.

[1]

(c)Write 30 as a fraction of 48 Give your fraction in its simplest form.

[2]

(d)Write 23% as a decimal.

[1]

Rita has some beads in a bag.

Of these beads, Rita gives

12 to Sheng

and 25 to Tusco

Rita now has 3 beads left in the bag.

(e)Work out how many beads Rita originally had in the bag.

[3]

(a)Simplify 3c + 5d – c + 2d

[2]

(b)Simplify 8e × 5f

[1]

(c)Solve 5r – 3 = 8

r = [2]

ABC is a straight line and BCD is a triangle.

(a)Work out the value of x

x = [2]

PO, RO, SO and TO are four straight lines.

(b)(i)Work out the value of y

y = [2]

(ii)Give a reason for your answer.

[1]

In November, Andre received a monthly salary of 2500 euros.

Of this he spent

40% on his rent 300 euros on leisure

The rest of Andre’s monthly salary was spent on household bills and on food where

the amount spent on household bills : the amount spent on food = 3 : 7

Work out how much of his November monthly salary Andre spent on food.

_euros[4]

50 students have lessons at a dance school. Two of the lessons are ballet lessons (B) and tap lessons (T).

Of the 50 students

31 have ballet lessons 27 have tap lessons 18 have ballet lessons and tap lessons

Complete the Venn diagram for this information.

[3]

The table shows information about the number of eggs laid by each of 36 hens in one week.

Work out the mean number of eggs laid.

[3]

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

[2]

(b)On the grid above, enlarge triangle A with scale factor 2 and centre O Label your triangle C[2]

(a)Factorise 6x – 15

[1]

There are 200 bolts in each box of bolts. Samira buys c boxes of bolts.

Samira uses the bolts she bought to fill packets of bolts. There are 50 bolts in each packet of bolts. Samira sells d packets of bolts.

The total number of bolts Samira has left is T

(b)Write down a formula for T in terms of c and d

[3]

Work out the value of 7.4 + 5.13

Write down all the figures on your calculator display.

[2]

n is an integer.

(a)Write down all the values of n such that –2  n < 3

[2]

(b)On the number line, represent the inequality y  1

[1]

Each time John plays a game, the probability that he wins the game is 0.65

John is going to play the game 300 times.

Work out an estimate for the number of games that John wins.

[2]

The shaded shape is made using three identical right-angled triangles and a square.

Work out the perimeter of the shaded shape.

_cm[4]

(a)Complete the table of values for y = x²– 4x + 3

[2]

(b)On the grid, draw the graph of y = x²– 4x + 3 for values of x from –2 to 4

[2]

Yusuf sat 8 examinations.

Here are his marks for 5 of the examinations.

For his results in all 8 examinations

the mode of his marks is 80 the median of his marks is 74 the range of his marks is 16

Find Yusuf’s marks for each of the other 3 examinations.

[4]

(a)Work out the lowest common multiple (LCM) of 36 and 120

[2]

A = 5 × 7 × 11^p B = 5^2/m × 7^4/n–5 × 11

m, n and p are integers such that m > 2 n > 10 p > 1

(b)Find the highest common factor (HCF) of A and B Give your answer as a product of powers of its prime factors.

[2]

Milly went on a car journey. She travelled from Anesey to Breigh to Clando and then to Duckbridge.

For Anesey to Breigh, Milly drove the 245 km in 2.5 hours. For Breigh to Clando, Milly drove the 220 km at an average speed of 80 km/h For Clando to Duckbridge, Milly drove at an average speed of 72 km/h in 50 minutes.

Work out Milly’s average speed, in km/h, for the journey from Anesey to Duckbridge. Give your answer correct to one decimal place.

_km/h[4]

(a)Write 5 × 10⁴ as an ordinary number.

[1]

(b)Write 0.000 06 in standard form.

[1]

(c)Work out (4 × 10⁵¹²) ÷ (1.6 × 10⁷⁰⁰) Give your answer in standard form.

[2]

(a)Simplify x⁴ × x⁵

[1]

(b)Simplify (4y²)³

[2]

(c)Factorise n²– 7n + 12

[2]

Jonty has a storage container in the shape of a cuboid, as shown in the diagram.

Jonty is going to paint the outside of his storage container, apart from the base which is shown shaded in the diagram. He needs enough paint to cover the four sides and the top.

Each tin of paint covers an area of 15 m²

The cost of each tin of paint recently increased by 10% After the increase, the cost of each tin of paint is £26.95

Jonty says

“Before the increase, I could have bought enough paint for less than £200”

Show that Jonty is correct. Show your working clearly.[6]