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

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

[1]

(b)Write in figures the number five thousand, one hundred and two.

[1]

(c)Write down the value of the 3 in the number 7439

[1]

(d)Write the number 651 correct to the nearest hundred.

[1]

The bar chart shows information about the weight of steel, in millions of tonnes, exported by each of five countries in 2019

Using the information in the bar chart,

(a)write down the weight of steel exported by Germany,

_{milliontonnes}[1]

(b)write down the country that exported 88 million tonnes of steel,

[1]

(c)work out the difference between the weight of steel exported by Japan and the weight of steel exported by Saudi Arabia.

_{milliontonnes}[1]

Italy exported 25 million tonnes of steel in 2019

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

(a)Write down the mathematical name for an 8-sided polygon.

[1]

(b)What type of angle is the angle marked x?

[1]

(c)On the diagram above, draw a chord of the circle.[1]

(d)Change 3.6 metres into centimetres.

_cm[1]

The diagram shows three points, A, B and C, and a line EF on a grid.

(a)Write down the coordinates of the point A

( , )[1]

The coordinates of the point D are (3, –2)

(b)On the grid, mark with a cross (×) the position of D Label the cross D[1]

(c)Find the coordinates of the midpoint of BC

( , )[2]

(d)Write down the equation of the line EF

[1]

Pat has 4 parcels A, B, C and D

The weight of parcel A is 400 grams.

The weight of parcel B is 350 grams more than the weight of parcel A The weight of parcel C is twice the weight of parcel A

The total weight of the 4 parcels is 2.5 kilograms.

Work out the weight, in grams, of parcel D

_grams[4]

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)Work out the 13th term of the sequence.

[1]

(c)Explain why 467 cannot be a number in the sequence.

[1]

In a field, there are 60 sheep and 24 cows.

(a)Find the ratio of the number of sheep to the number of cows. Give your ratio in its simplest form.

[2]

In a barn, there are only white ducks and brown ducks. In the barn, the ratio

(b)What fraction of the ducks in the barn are white?

[1]

Giles and Sarah share some bales of hay in the ratio 11 : 4

Sarah receives 20 bales of hay.

(c)Work out how many bales of hay are shared in total.

[3]

Linford is going to take part in an athletics competition. He can choose one event from List A and one event from List B

Write down all the possible combinations Linford can choose.

[2]

(a)Write the time 8 30 pm using the 24-hour clock.

[1]

Ella started watching television at 10 50 am.

Ella watched

a comedy programme lasting 45 minutes a sports programme lasting 1 hour 10 minutes a history programme

There were no breaks and no advertisements between the programmes. Ella finished watching television at 2 20 pm.

(b)How long did the history programme last? Give your answer in minutes.

_minutes[3]

Hermann changed £500 into euros. The exchange rate was £1 = 1.18 euros.

(a)Work out how much money, in euros, Hermann received.

_euros[2]

Anita changed $350 into pounds (£) The exchange rate was £1 = $1.40

(b)Work out how much money, in pounds (£), Anita received.

£ [2]

Asif has 200 beads.

Asif gives 14 of the 200 beads to Bernadette.

Asif gives 25 of the 200 beads to Claudio.

Asif gives 43 beads to Derek.

What fraction of the 200 beads does Asif have left?

[4]

30 children were asked whether they have a cat (C ) or a dog (D)

Of the 30 children

13 have a dog 11 have only a cat

(a)Complete the Venn diagram.

[3]

One of the children is picked at random.

(b)Find the probability that this child

(i)has a dog,

[1]

(ii)does not have a dog and does not have a cat.

[1]

The diagram shows the plan of a floor.

Indira is going to paint the floor. She needs to buy enough tins of paint to cover the floor with one coat of paint.

Each tin of paint covers an area of 7 m² Each tin of paint costs £23.90

Indira buys the least possible number of tins of paint.

Work out the total cost of the tins of paint that Indira buys. Show your working clearly.

£ [5]

(a)Expand x(10 – x)

[1]

(b)Factorise 6y + 27

[1]

(c)Make m the subject of the formula h = m2+ 4

[2]

(d)Solve 7g + 3 = 2g – 5 Show clear algebraic working.

g = [3]

Show that 4 23 ÷ 1 56 = 2 611[3]

(a)On the grid, rotate triangle A 180° about (1, –1) Label the new triangle B[2]

(b)On the grid, translate triangle A by the vector  −7

Label the new triangle C[1]

–8 < 2y  2

y is an integer.

(a)Find all the possible values of y

[2]

(b)Write down the inequality shown on the number line.

[1]

Using ruler and compasses only, construct the bisector of angle BAC You must show all your construction lines.

[2]

On the grid, draw the graph of 5x + 2y = 10 for values of x from –2 to 4

[3]

In a bag, there are only red counters, blue counters, green counters and yellow counters.

The total number of counters in the bag is 80

In the bag

the number of red counters is x + 7 the number of blue counters is x – 11 the number of green counters is 3x

Jude takes at random a counter from the bag.

The probability that he takes a red counter is 14

Work out the probability that Jude takes a yellow counter.

[4]

(a)Find the highest common factor (HCF) of 200 and 420

[2]

A = 2³ × 3 × 5 ×7² B = 2 × 3² × 7 C = 3 × 5² × 11

(b)Find the lowest common multiple (LCM) of A, B and C Write your answer as a product of powers of prime factors.

[2]

60 students sat a Mathematics exam.

The mean mark for the 32 students in Class A was 55 The mean mark for the 28 students in Class B was 52

Find the mean mark for all 60 students.

[3]

Teresa invests $2000 for 3 years in a savings account. She gets 4% each year compound interest.

(a)How much money will Teresa have in her savings account at the end of 3 years? Give your answer correct to the nearest dollar.

$ [3]

Sam invested $T The value of his investment decreased by 9% each year.

At the end of the first year, the value of Sam’s investment was $1365

(b)Work out the value of T

[3]

The diagram shows two solids, A and B, made from two different metals.

Solid A is in the shape of a cylinder with radius 3 cm and height 7 cm Solid A has a mass of 2000 g

Solid B has a mass of 3375 g Solid B has a volume of 450 cm³

All of the metal from Solid A and Solid B is melted down to make a uniform Solid C

Given that there is no change to mass or volume during this process

work out the density of Solid C Give your answer correct to one decimal place.

_g / cm³[3]

A

AB, BC, CD, DE and EF are five sides of a regular polygon.

RST, SCU and BCV are straight lines. RST is parallel to CD Angle RSC = 128° Angle UCV = 32°

Work out how many sides the polygon has. Show your working clearly.

[4]