4MA1 Mathematics A: January 2023 Paper 2FFoundation Tier Paper 2

Here are four cards. Each card has a number on it.

These four cards are arranged to make the number 5763

(a)Arrange the four cards to make the smallest possible number.[1]

(b)Arrange the four cards to make the largest possible even number.[1]

(c)Arrange two of the cards to make a prime number.[1]

(d)Arrange two of the cards to make a multiple of 8[1]

The pictogram shows information about the total weight of potatoes grown last year in each of five countries.

The pictogram shows one country where the total weight of potatoes grown last year was 20 million tonnes.

(a)Which country?

[1]

Last year, the weight of potatoes grown in The Netherlands was 6 million tonnes.

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

(c)Work out the total weight of potatoes grown in Germany and in France last year.

_{milliontonnes}[2]

Here is a number scale.

(a)On the scale, mark with an arrow ( ) the number 554[1]

Here is a different number scale.

(b)Write down the number shown marked by the arrow.

[1]

(a)In the space below, draw a line of length 6.5 cm[1]

The diagram shows the straight lines QP and QR

(b)Measure the size of angle PQR

[1]

The table gives information about the costs of sending parcels of different weights.

Peony has one parcel of weight 1.3 kg and another parcel of weight 8 kg to send to two different places.

(a)Work out the total cost of sending these two parcels.

£ [2]

Gryffyn sends 3 parcels each to a different place. One of the parcels has a weight of 1.5 kg and another of the parcels has a weight of 2.8 kg The total cost of sending the 3 parcels is £33.89

(b)Work out the greatest possible weight of the third parcel.

_kg[3]

(a)Write 5 15 pm using the 24-hour clock.

[1]

Roberta goes out for a walk. She leaves home at 16 35 She arrives back home at 20 15 on the same day.

(b)Work out for how much time Roberta is out for her walk.

_{hours minutes}[2]

(a)Simplify c × c × c × c × c

[1]

(b)Solve 5 + x = 12

x = [1]

(c)Solve y6= 3

y = [1]

(d)Expand 5(2 + 3h)

[1]

(e)Factorise g²+ 7g

[1]

Here is a number machine.

(a)Work out the output when the input is 9

[1]

Here is a different number machine.

When the input is 30 the output is 18

(b)Find a suitable way to complete the number machine.[1]

The following rule is used to work out the total cost, in euros, of hiring a cement mixer.

James hires a cement mixer for 3 days.

(c)Work out the cost to James of hiring the cement mixer.

_euros[1]

The cost to Sophia of hiring a cement mixer is 61 euros.

(d)For how many days does Sophia hire the cement mixer?

_days[2]

There are 120 cyclists in a cycling club. There are 67 professional cyclists and the rest are amateur cyclists. Each of these cyclists was asked to name their favourite type of bike.

The two-way table shows some information about their answers.

(a)Complete the table.[3]

(b)Work out the percentage of the cyclists who answered Mountain bike.

%[2]

Jacob is going to draw a pie chart for the age groups of the 120 cyclists. There are 41 people in the ‘over 60’ age group.

(c)Work out the size of the angle for the sector representing the ‘over 60’ age group.

[2]

The frequency table shows information about the number of cookies made by each of the 21 people in a cookery class.

(a)Write down the mode of the number of cookies made.

[1]

(b)Find the median number of cookies made.

[2]

(c)Find the total number of cookies made by the 21 people in the cookery class.

[2]

(a)Work out the value of (4 + 3 + 6)²

[1]

64 = 4ⁿ

(b)Write down the value of n

n = [1]

(c)Work out the value of 9.3 + 2.83.2 × 1.2

Write down all the figures on your calculator display.

[2]

Last season, Alisha and Jaya scored goals for their team in the ratio 4 : 7 Jaya scored 39 more goals than Alisha.

Work out the number of goals Alisha scored.

[3]

There are 380 students in a Sixth Form. The students are either in the Upper Sixth or in the Lower Sixth.

The number of students in the Upper Sixth is 20 fewer than the number of students in the Lower Sixth.

25 of the Upper Sixth students study mathematics.

32% of the Lower Sixth students study mathematics.

Work out the total number of students in the Sixth Form who study mathematics.

[4]

The diagram shows a solid prism.

The cross section of the prism is shown shaded.

The volume of the prism is 924 cm³

Work out the value of x

x = [4]

The diagram shows two parallel lines AB and DEF

BEG is a straight line.

Work out the value of w Give reasons for each stage of your working.

w = [4]

Show that 3 57 ÷ 1 58 = 2 27[3]

Change a speed of 90 kilometres per hour to a speed in metres per second. Show your working clearly.

_m/s[3]

ℰ = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

A = {even numbers} A ∩ B = {12, 16, 20} (A ∪ B)ʹ = {17, 19}

Complete the Venn diagram for the sets ℰ, A and B

[3]

The diagram shows rectangle ABCD

Work out the perimeter of the rectangle. Show your working clearly.

_cm[4]

The weight of a cake is 2.75 kg, correct to 2 decimal places.

(a)Write down the lower bound of the weight of the cake.

_kg[1]

(b)Write down the upper bound of the weight of the cake.

_kg[1]

Penny has worked out 81 .3 × 59 .21.9₂ on her calculator.

Her answer is 13 332.299 17

Penny’s answer is not sensible.

(c)By rounding each number to one significant figure, work out a suitable estimate to show that her answer is not sensible. Show your working clearly.[2]

The points A and B are on a coordinate grid.

The coordinates of A are (6, 4) The coordinates of B are (17, j) where j is a constant.

The midpoint of AB has coordinates (k, 15) where k is a constant.

Find the value of j and the value of k

j =

k = [3]

Solve the simultaneous equations

Show clear algebraic working.

x =

y = [3]

Matteo is going to invest 5000 Swiss francs for two years.

He can invest his money in Bank G or in Bank H.

The total amount of interest Matteo would receive at the end of two years from Bank G is more than the amount of interest Matteo would receive at the end of two years from Bank H.

How much more?

_Swissfrancs[4]

(a)Write down the value of (m + 2)⁰ where m is a positive integer.

[1]

(b)Simplify (3a² b⁴)³

[2]

(c)Factorise fully 14x² y⁴+ 21x³ y²

[2]

The diagram shows a straight line drawn on a grid.

(d)Write down an equation of the line.

[2]

The diagram shows an isosceles triangle, with base length 24 cm.

The perimeter of the triangle is 54 cm.

Work out the area of the triangle.

_cm²[5]