4MA1 Mathematics A: January 2021 Paper 2FRFoundation Tier Paper 2

Here are five discs. Each disc has a number on it.

These five discs are arranged to make the number 41283

(a)Show how all five discs can be arranged to make the smallest number.[1]

(b)Show how all five discs can be arranged to make the largest even number.[1]

(c)Which of the five numbers on the discs are factors of 21?

[2]

(d)Which of the five numbers on the discs are prime numbers?

[2]

The pictogram shows information about the number of emails Sophie received on each of four days.

Monday

Tuesday

(a)On which of Monday, Tuesday, Wednesday or Thursday did Sophie receive the least number of emails?

[1]

(b)Find the ratio of the number of emails Sophie received on Monday to the number of emails Sophie received on Tuesday. Give your ratio in its simplest form.

[2]

On Friday, Sophie received 14 emails.

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

On Friday, 6 of the 14 emails Sophie received were from Kamil.

(d)Write 6 as a fraction of 14 Write your fraction in its simplest form.

[2]

On Friday, Sophie received 14 emails, on Saturday she received 11 emails and on Sunday she received 6 emails.

(e)Draw a bar chart to show the number of emails Sophie received on each of Friday, Saturday and Sunday. Complete the frequency axis.

Frequency

[2]

(a)Complete the following estimates by writing a suitable metric unit on each of the dotted lines.

(i)The distance from Paris to Berlin is about 1000

(ii)A bucket holds about 5 of water.

(iii)The area of the screen of a mobile phone is about 90 [3]

(b)Write down an estimate for the height of a bedroom door in a house. Use a suitable metric unit.

[2]

Here are three 3D shapes, A, B and C.

(a)Write down the mathematical name for each of these 3D shapes.

(i) (ii) (iii) [3]

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

(ii)How many vertices does shape C have?

[2]

Here is a solid prism made from bricks. The bricks are identical triangular prisms.

The volume of the prism is 54 cm³

(c)Work out the volume of each brick.

cm³[2]

The table shows the temperature recorded in Amsterdam at 6 am on each of five days.

(a)What is the range of the temperatures in the table?

°C[2]

(b)What is the median of the temperatures in the table?

°C[2]

(c)What percentage of the temperatures in the table are lower than 0 °C?

%[2]

On Saturday of the same week, the temperature recorded in Amsterdam at 6 am was 8 °C higher than the temperature recorded at 6 am on Friday.

(d)What was the temperature recorded in Amsterdam at 6 am on Saturday?

°C[2]

Mikhal has 1200 grams of cake mixture.

He is going to make 3 cakes, cake A, cake B and cake C.

415 of the weight of the cake mixture will be used to make cake A.

The rest of the cake mixture will be used to make cake B and cake C.

The weight of the cake mixture used to make cake B and the weight of the cake mixture used to make cake C will be in the ratio 3 : 8

Work out the weight of the cake mixture used to make each of cake A, cake B and cake C.

Cake A _grams

Cake B _grams

Cake C _grams[4]

Here are five times, in a single day, using the 24‑hour clock.

(a)Write down the letter of the time nearest to 6 pm

[1]

(b)Work out the difference, in hours and minutes, between time A and time E.

_{hours minutes}[2]

Francesco uses the rule below to find the time, in minutes, to cook a chicken in his oven.

The clock on Francesco’s oven shows time B. Francesco starts cooking a chicken at this time. He stops cooking the chicken when the clock on his oven shows time E.

(c)Work out the weight of the chicken.

_kg[3]

(d)Use Francesco’s rule to write down a formula for the time, T minutes, to cook a chicken of weight k kilograms.

[2]

In Berlin, a watch costs 120 euros. In Dubai, the same model of watch costs 600 dirhams.

The currency exchange rates are

Calculate the difference between the cost of the watch in Berlin and the cost of the same model of watch in Dubai. Give your answer in pounds (£) correct to 2 decimal places.

£ [4]

The scale diagram shows the positions of a post office (A) and a police station (B) in a town.

(a)Measure the bearing of B from A.

[1]

The town hall is at a position C. The bearing of A from C is 045°

(b)Calculate the bearing of C from A.

[2]

Here is a list of ingredients needed to make 24 currant buns.

Gina wants to make 60 currant buns.

(a)Work out the weight of butter Gina needs.

_grams[2]

Hans wants to make 30 currant buns.

(b)Find the percentage increase in the weight of butter needed to make 30 currant buns rather than 24 currant buns.

%[2]

w = 5y²– y³

(a)Work out the value of w when y = –2

w = [2]

(b)Factorise fully 8p²– 2p

[2]

(c)Expand 4t(3t – 2)

[2]

(d)Expand and simplify (5x – 2)(x + 4)

[2]

The diagram shows a rectangle ABCD and a semicircle with diameter AB where AB = 12 cm. The point E lies on DC and also on the semicircle.

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

cm²[3]

Solve 5(2x – 3) = 20 Show clear algebraic working.

x = [3]

E = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30} A = {22, 24, 26, 28, 30} B = {21, 24, 27, 30}

(a)List the members of the set

(i)A ∩ B

(ii)Aʹ

[2]

C = {23, 25, 29}

(b)Using set notation, find an expression for C in terms of A and B.

[1]

(a)Simplify (3k²)⁴

[2]

(b)Simplify (21m⁴ n) ÷ (3n^–5)

[2]

Here is a shape P drawn on a grid of squares.

(a)On the grid, rotate shape P 180° about the point (–3, 2) Label the new shape Q.[2]

(b)On the grid, translate shape P by the vector 10 8 

Label the new shape R.[1]

Here are triangle T and triangle U drawn on a grid of squares.

(c)Describe fully the single transformation that maps triangle T onto triangle U.

[3]

On Wednesday, the price of 1 litre of petrol was £1.26 The price of petrol on Wednesday was 5% more than the price of petrol on the previous Monday.

Calculate the price of 30 litres of petrol on the previous Monday.

£ [3]

The shaded region R, shown in the diagram below, is bounded by the straight line with equation y = 3x – 2 and by two other straight lines.

Write down the three inequalities that define region R.

[3]

The table gives the length of the coastline, in kilometres, of each of five oceans.

Ocean Length of coastline (km)

(a)Which ocean has the greatest length of coastline?

[1]

(b)Calculate the difference between the length of the Atlantic Ocean’s coastline and the length of the Southern Ocean’s coastline. Give your answer in standard form.

km[2]

Solve x²– 21x + 20 = 0 Show your working clearly.

[3]

A mathematics teacher at a school asked a group of students how far, in kilometres, each student had travelled to get to school that day.

The table gives information about their answers.

The teacher calculated that an estimate for the mean distance travelled by the whole group of students was 4.25 km.

Work out the value of x. Show your working clearly.

x = [4]