4MA1 Mathematics A: May/June 2022 Paper 1FRFoundation Tier Paper 1

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

These four cards are arranged to make the number 3457

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

Darren arranges the cards to make another number.

The difference between the number 3600 and the number that Darren makes is as small as possible.

(b)Find this difference.

[2]

Here is a 5‑sided polygon.

(a)Write down the mathematical name for a 5‑sided polygon.

[1]

(b)On the diagram, mark with a letter A an acute angle.[1]

(c)On the diagram, mark with a letter R a reflex angle.[1]

The pictogram shows information about the number of loaves of bread sold in a bakery each day from Tuesday to Friday last week.

(a)How many loaves of bread were sold on Friday?

[1]

The total number of loaves sold in the bakery from Monday to Friday last week was 66

(b)(i)Work out the number of loaves sold on Monday last week.

[2]

(ii)Show this information for Monday on the pictogram.[1]

(a)Write 0.7 as a fraction.

[1]

(b)Write a number in the box so that the following statement is correct.

3 and are equivalent fractions. 4 20[1]

(c)Work out 35 of 35

[2]

The diagram shows the trapezium ABCD

(a)How many lines of symmetry has ABCD?

[1]

Here is another shape.

(b)Write down the order of rotational symmetry of this shape.

[1]

(c)Find, by measuring, the size of the angle marked x

[1]

Here is a list of seven numbers.

(a)From the numbers in the list, write down

(i)a cube number

[1]

(ii)a factor of 80

[1]

Two numbers in the list are prime numbers.

(b)Work out the sum of these two prime numbers.

[2]

The three points A, B and C are marked on a centimetre grid.

(a)Write down the coordinates of A

( , )[1]

(b)Find the coordinates of the midpoint of BC

( , )[2]

(c)Work out the area of triangle ABC

cm²[2]

D is the point on the grid so that ABCD is a rectangle.

(d)On the grid, mark with a cross (X) the point D Label this point D[1]

Masie is told that 13 203 ÷ 27 = 489

Explain how she can use this calculation to work out 489 × 28

[2]

(a)Simplify 6p + 2t + p – 3t

[2]

A = 8x – 3y

(b)Work out the value of A when x = 5 and y = 4

A = [2]

In the diagram, BCE is a right‑angled triangle. ABCD, BEF and GCEH are straight lines.

Angle BCE = 35°

(a)(i)Find the value of x

x = [1]

(ii)Give a reason for your answer.

[1]

(b)(i)Work out the value of y

y = [2]

(ii)Give a reason for your answer.

[1]

Sophia spends a total of £6.30 on cheese.

She buys 500 g of Cheddar cheese and 200 g of Stilton cheese.

The cost of the Cheddar cheese is £9.20 for 1 kg.

Work out the cost of 1 kg of the Stilton cheese.

£ [4]

The diagram below shows the trapezium PQRS

Angle PQR and angle QPS are right angles.

Find the value of x

x = [3]

Salma asked some people what type of exercise they each liked the best from walking or running or swimming or cycling.

Salma is going to draw a pie chart for her results.

The incomplete table gives some information about her results.

18 people answered walking.

(a)How many people answered running?

[2]

15 people answered cycling.

(b)How many people answered swimming?

[3]

Jakub has bought a chicken.

He is going to use this rule to work out the number of minutes it will take to cook his chicken.

The weight of Jakub’s chicken is 2.6 kg

(a)Use the rule to work out the number of minutes it will take to cook Jakub’s chicken.

_minutes[2]

The following week Jakub buys another chicken.

He uses the rule and works out that it will take 2 hours 40 minutes to cook this chicken.

(b)Work out the weight of this chicken.

kg[3]

Bella and Millie share some money in the ratio 5 : 2

Bella receives 10.50 euros more than Millie.

Work out the total amount of money they share.

_euros[3]

Work out the value of

Write down all the figures on your calculator display.

[2]

Here is a biased spinner.

When the spinner is spun once, the probabilities that it lands on red or on yellow or on green are given in the table.

(a)Work out the probability that the spinner lands on red or on yellow.

[1]

Yang is going to spin the spinner 300 times.

(b)Work out an estimate for the number of times the spinner will land on purple.

[3]

In a warehouse there are two types of shelves, type R and type S.

These two types of shelves are arranged into shelving units that form a sequence of patterns.

Here are the first three terms in the sequence.

The width of each type R shelf is 2.4 m and the width of each type S shelf is 3.5 m

(a)Work out the total width of a shelving unit that has 6 type R shelves.

m[2]

A shelving unit has n type R shelves. The total width of this shelving unit is W metres.

(b)Find an expression for W in terms of n Give your answer in its simplest form.

W = [2]

Here are five cards.

Each card has a number written on it.

The mean of the five numbers is 12

Work out the value of x

x = [3]

The language department of a college has 180 students. Each student studies exactly one of French, German, Italian or Spanish.

15 students study French. 45% of the students study German.

Express the percentage of students studying Italian or Spanish as a percentage of those studying French or German.

%[4]

(a)Expand 3c³(c + 4)

[2]

(b)(i)Factorise x²+ 8x – 9

[2]

(ii)Hence, solve x²+ 8x –9 = 0

[1]

Show that 2 23 + 3 34 = 6 512[3]

The diagram shows a solid cylinder made from iron.

The cylinder has diameter 18 cm and height 3.5 cm The mass of the cylinder is 7.04 kg

Work out the density of the iron. Give your answer in g/cm³ correct to 2 significant figures.

g/cm³[3]

Jane bought a new car for $18 000 The car depreciates in value by 15% each year.

Work out the value of the car at the end of 4 years. Give your answer correct to the nearest $

$ [3]

Solve the inequality 3 – 4x  11

[2]

Line L is drawn on the grid.

Find an equation for L Give your answer in the form y = mx + c

[3]

The diagram shows a quadrilateral ABCD

In the diagram, ABC and DAC are right‑angled triangles.

BC = 6 cm AC = 7.5 cm

The area of quadrilateral ABCD is 31.5 cm²

Work out the length of AD

cm[6]