4MA1 Mathematics A: January 2020 Paper 1FRFoundation Tier Paper 1

(a)Write down the largest possible four digit number using all the digits that are in the box.

[1]

From the numbers in the circle, write down

(b)a multiple of 6

[1]

(c)a prime number

[1]

At 6 pm, the temperature in Victoria’s garden was 5 °C. By midnight, the temperature in Victoria’s garden had fallen by 9 °C.

(a)Work out the temperature in Victoria’s garden at midnight.

°C[2]

Here is a list of 7 temperatures.

(b)For the 7 temperatures in the list,

(i)write down the mode,

°C[1]

(ii)find the median.

°C[2]

(a)On the grid below, draw a kite.[1]

(b)Write down the mathematical name of an 8-sided polygon.

[1]

Here is a solid prism.

(c)(i)Write down the mathematical name of this prism.

(ii)How many vertices does the prism have?

[2]

Mike is going to buy

1 hammer at £6 2 boxes of nails at £3.50 for each box 4 pieces of wood at £4.20 for each piece some pairs of gloves at £1.80 for each pair

Mike has £40 to spend in total on these items. He wants to buy as many pairs of gloves as he can.

Work out the greatest number of pairs of gloves that Mike can buy.

[4]

The bar chart gives information about the number of points scored by each of four teachers in a quiz.

Joseph starts to draw a pictogram, shown below, for this information. The pictogram shows the number of points scored by Mr Causey and the number of points scored by Mrs Ramirez.

represents points

Complete the pictogram, including the key.[4]

(a)Simplify 3r × 5t

[1]

(b)Solve 4x + 5 = 27

x = [2]

P = 7w – 5y

(c)Find the value of P when w = 2 and y = 4

P = [2]

Q = 2u² − 5

(d)Find the value of Q when u = −3

Q = [2]

Mohsen is going to a party. He will choose at random one shirt from the three shirts and one pair of trousers from the three pairs of trousers in the list below.

(a)Write down all the possible combinations that Mohsen can choose.

[2]

(b)Find the probability that Mohsen chooses the red shirt to wear to the party.

[1]

There are 20 counters in a bag.

4 of the counters are pink. 9 of the counters are white. The rest of the counters are black.

Jean takes at random one counter from the bag.

(c)Work out the probability that Jean takes a black counter.

[2]

Here is a rectangle.

4 cm 28 cm²

The area of the rectangle is 28 cm²

Three of these rectangles are used to make the shape below.

Work out the perimeter of the shape.

_cm[4]

(a)Write 24.8635 correct to 3 significant figures.

[1]

(b)Find the value of 50. 41

[1]

(c)Change 78 to a percentage.

_%[2]

The accurate scale drawing shows the positions of two mobile phone masts, A and B.

The scale is 1 cm to 2.5 km.

(a)Find the bearing of A from B.

[1]

(b)Work out the actual distance, in km, between A and B.

_km[2]

A third mobile phone mast, C, is put up. C will be on a bearing of 115° from A. C will be 20 km from B.

(c)Find the position of C. Mark this point with a cross ( ) and label it C.[3]

On the grid, draw the graph of y = 3x + 2 for values of x from −2 to 4

[3]

Greg bought 36 oranges. He paid 50p for each orange.

Greg sold 12 of the oranges for 60p each.

He sold 13 of the oranges for 40p each.

He sold the remainder of the oranges for 25p each.

Work out Greg’s percentage loss.

%[5]

(a)Describe fully the single transformation that maps shape P onto shape Q.

[3]

(b)On the grid, reflect shape P in the line x = −1 Label the new shape R.[2]

Brendon, Asha and Julie share some money in the ratios 3 : 2 : 6 The total amount of money that Asha and Julie receive is $36

Work out the amount of money that Brendon receives.

$ [3]

Show that 3 15 × 2 58 = 8 25[3]

(a)Make a the subject of d = g + 2ac

[2]

(b)Factorise fully 9ef − 12f

[2]

(c)Expand and simplify (x + 2)(x − 5)

[2]

(d)Simplify fully × nn₅

[2]

B = {b, l, u, e}

G = {g, r, e, y}

W = {w, h, i, t, e}

(a)List all the members of the set

(i)B ∪ G

(ii)W ∩ G′

[2]

Serena writes down the statement B ∩ G ∩ W = ∅

(b)Is Serena’s statement correct? You must give a reason for your answer.

[1]

The diagram shows Yuen’s garden.

The garden is in the shape of a semicircle of radius 7.2 m. Yuen is going to cover his garden with grass seed.

Yuen has 12 boxes of grass seed. Each box of grass seed contains enough seed to cover 6 m² of the garden.

Has Yuen enough grass seed for his garden? Show your working clearly.[3]

The weight of a cat is 4.3 kg correct to 2 significant figures.

(a)Write down the upper bound of the weight of the cat.

_kg[1]

(b)Write down the lower bound of the weight of the cat.

_kg[1]

Solve x² − 5x − 36 = 0 Show clear algebraic working.

[3]

In a sale, the normal price of a hat is reduced by 15% The sale price of the hat is 20.40 euros.

Work out the normal price of the hat.

_euros[3]

5 children are playing on a trampoline. The mean weight of the 5 children is 28 kg.

2 of the children get off the trampoline. The mean weight of these 2 children is 26.5 kg.

Work out the mean weight of the 3 children who remain on the trampoline.

_kg[3]

Pablo made a solid gold statue.

He melted down some gold blocks and used the gold to make the statue. Each block of gold was a cuboid, as shown below.

The mass of the statue is 5.73 kg. The density of gold is 19.32 g/cm³

Work out the least number of gold blocks Pablo melted down in order to make the statue. Show your working clearly.

[5]

The diagram shows a regular hexagon, ABCDEF, and an isosceles triangle, GHJ.

The perimeter of the hexagon is equal to the perimeter of the triangle.

Find the length of each side of the hexagon. Show clear algebraic working.

_cm[5]