4MA1 Mathematics A: May/June 2022 Paper 2FRFoundation Tier Paper 2

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

[1]

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

[1]

(c)Write in figures the number five thousand two hundred and three.

[1]

(d)Write down the value of the 6 in the number 2468

[1]

The bar chart gives information about the total number, in millions, of cars produced in 2017 and 2018 for each of five countries.

The total number of cars produced in 2017 and 2018 in Mexico was 8 million.

(a)Draw a bar on the bar chart to show this information.[1]

(b)Which of these six countries produced the greatest total number of cars?

[1]

(c)Which country produced half as many cars as India?

[1]

(d)Work out the difference between the total number of cars produced in Japan and the total number of cars produced in Spain.

_million[1]

(a)Write down the number marked with the arrow on the scale above.

[1]

(b)Mark with an arrow ( ) the number 0.04 on the scale below.

[1]

(c)Write the number 5.68 correct to one decimal place.

[1]

Here are two sides of a parallelogram.

(a)On the grid above, complete the parallelogram.[1]

The diagram shows a 3‑D shape.

(b)(i)What is the mathematical name of this 3‑D shape?

[1]

(ii)How many faces has this shape?

[1]

Brigid recorded the distance she ran on each of three days.

The table shows her results.

Brigid set herself the target of running a total of at least 30 km on these three days.

Show that Brigid did not achieve her target.[3]

(a)Find the value of

(i)31 . 36

[1]

(ii)14³

[1]

(b)Write a number on each dotted line to make the calculation correct.

(i)10 – × 2 = 4[1]

(ii)(5 + ) × 3 = 36[1]

Here are the first five 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)Explain why 188 cannot be a number in the sequence.

[1]

Jordan buys 256 notebooks.

He buys the notebooks in packs of 8 notebooks. Each pack of 8 notebooks costs £2.48

Work out how much the 256 notebooks cost Jordan.

£ [3]

(a)Simplify a × a × a × a × a

[1]

(b)Simplify 8b × 3c

[1]

(c)Expand 3(x + 4)

[1]

Q = 5v²– w

(d)Work out the value of Q when v = 12 and w = 14

Q = [2]

It takes a machine 8 seconds to produce a bolt.

Each day, the machine starts producing bolts at 09 30 The machine produces bolts continuously every 8 seconds until it stops at 16 10 on the same day.

Work out how many bolts the machine produces each day.

[4]

Triangle ABC is an equilateral triangle of side 6 cm.

Using a ruler and compasses only, construct triangle ABC You must show all your construction lines.

Side AB has been drawn for you.

[2]

Mario is going to play two games on Saturday. He will play one game on Saturday morning and one game on Saturday afternoon.

The following table shows the games from which he is going to choose.

(a)Write down all the possible combinations of games that Mario can play on Saturday.

[2]

Mario asked 100 students in his school to name their favourite card game.

His results are shown in the two‑way table below.

One of the students Mario asked is picked at random.

(b)Write down the probability that this student is in Year 11

[1]

One of the Year 10 students is picked at random.

(c)Work out the probability that this student did not answer Whist.

[2]

The diagram shows a trapezium.

Work out the area of the trapezium.

m²[2]

On the grid, draw the graph of y = 2x – 1 for values of x from –1 to 4

[3]

Kim spends $N

Of this, she spends

40% on food

14 on clothes

and the rest on petrol

Kim spends $P on petrol.

Work out the ratio P : N in the form a : b where a and b are integers. Give your answer in its simplest form.

[4]

The table shows information about the number of mobile phones owned by each of 40 families.

For the information in the table,

(a)write down the mode,

[1]

(b)work out the mean.

[3]

Molly uses this number machine to work out the amount of tax that she has to pay on the money she earns.

Number of Amount of tax

hours worked to be paid in £

When Molly works n hours the amount of tax she has to pay is £T

Find a formula for T in terms of n

[3]

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

[3]

(b)On the grid above, translate triangle A by the vector −4  

Label your triangle C[1]

Write 1200 as a product of powers of its prime factors. Show your working clearly.

[3]

Alberto, Bill, Candela and Diana are four friends.

Here is some information about the height of each of these friends.

Alberto’s height is 158 cm. Bill’s height is 175 cm. Candela’s height is greater than Diana’s height.

The median height of these four friends is 160 cm. The range of the heights of these four friends is 21 cm.

Work out Candela’s height and Diana’s height.

Candela cm

Diana cm[3]

E = {9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} A = {multiples of 3} B = {odd numbers}

(a)List the members of the set

(i)A ∩ B

[1]

(ii)A ∪ B

[1]

(b)Is it true that 24 ∈ A?

Tick one of the boxes below.

Yes No

Give a reason for your answer.

[1]

Set C has 4 members such that C ∩ B¢ = {10, 18}

(c)List the members of one possible set C

[2]

The diagram shows a shape made from a square ABCD and 4 identical semicircles.

As shown in the diagram, the semicircles have AB, BC, CD and DA as diameters.

The area of the square is 36 cm²

Calculate the total area of the shape. Give your answer correct to one decimal place.

cm²[4]

(a)Solve p = 3 p − 510

Show clear algebraic working.

p = [3]

(b)Simplify a⁰ where a > 0

[1]

(c)Simplify fully

[2]

(d)Factorise fully 10c³ d²+ 15cd⁴

[2]

2^k_x

Find an expression for x in terms of k and n

x = [2]

A cinema increased the cost of an adult ticket by 12%

After the increase, the cost of an adult ticket was £18.20

Work out the cost of an adult ticket before the increase.

£ [3]

The table gives information about the population, correct to 2 significant figures, of each of five cities in 2018

(a)Write 8.8 × 10⁶ as an ordinary number.

[1]

(b)Which of these cities had the least population in 2018?

[1]

(c)Work out the difference between the population of Tokyo and the population of Ahmedabad in 2018 Give your answer in standard form correct to 2 significant figures.

[2]

The diagram shows triangle ABP inside the regular hexagon ABCDEF

Work out the size of angle PAF Give your answer correct to 3 significant figures.

[5]