4MA1 Mathematics A: May/June 2025 Paper 1HRHigher Tier Paper 1

Find the lowest common multiple (LCM) of 45 and 70

[2]

The length of a ship is 142.8 m, correct to 1 decimal place.

(i)Write down the lower bound of the length of the ship.

m[1]

(ii)Write down the upper bound of the length of the ship.

m[1]

Show that 2 14  157  3 67[3]

Here is a biased 5-sided spinner. When the spinner is spun, it can land on blue or on green or on purple or on red or on yellow.

The table gives information about the probability of the spinner landing on each colour.

Sophie spins the spinner once.

(a)Work out the probability that the spinner lands on blue or on green or on purple.

[1]

Max spins the spinner 350 times.

(b)Work out an estimate for the number of times the spinner lands on red.

[4]

E  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

A  2, 4, 6, 8, 10, 12

B  3, 6, 9, 12

C  1, 3, 5, 7, 9, 11

(a)List the members of the set

(i)A ∪ B

(ii)Bʹ

[2]

E  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

A  2, 4, 6, 8, 10, 12

B  3, 6, 9, 12

C  1, 3, 5, 7, 9, 11

(b)Write a symbol from the box on each dotted line to make each of the following a true statement.

(i)A  C 

(ii)13 E[2]

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

[2]

(b)Solve the inequality 7a  5  3a  28 Show clear algebraic working.

[2]

Change a speed of 50x metres per second to a speed in kilometres per hour.

_km/h[3]

(a)Simplify a⁶ × a¹⁰

[1]

(b)Simplify c³⁰ ÷ c¹²

[1]

(c)(i)Factorise y²  10 y  21

[2]

(ii)Hence, solve y²  10 y  21  0

[1]

The diagram shows triangle PQR

Work out the length of QR Give your answer correct to 3 significant figures.

_cm[3]

The diagram shows two water containers. One is a cuboid and one is a cylinder.

The cuboid measures 35 cm by 28 cm by 20 cm The surface of the water in the cuboid is 9 cm above the base of the cuboid.

The cylinder has a radius of 10 cm and a height of 33 cm The cylinder is completely full of water.

Izzy is going to pour all the water from the cylinder into the cuboid.

Show that the cuboid will not be completely full of water.[3]

Zhou invests some money for 2 years. He invests $2500 with Bank A and $3000 with Bank B.

4% per year compound interest for 2 years

Zhou receives more interest from Bank A than from Bank B.

How much more?

$ [5]

The table gives information about the ages of 80 people in a cinema.

Age (n years) Frequency

(a)Complete the cumulative frequency table.

Age (n years) Cumulative frequency

[1]

(b)On the grid below, draw a cumulative frequency graph for your table.

[2]

(c)Use your graph to find an estimate for the percentage of the 80 people who are more than 46 years of age. Give your answer correct to the nearest whole number.

%[3]

Here are the numbers of eggs laid by some hens on each of 11 days in June.

Work out the interquartile range of the numbers of eggs.

[2]

Work out 6.7  10¹³⁵  3  10¹³⁴

Give your answer in standard form.

[2]

(a)Solve 5a  83  2a  54  23

Show clear algebraic working.

[4]

(b)Express   in the form cy where c and n are numbers to be found.

[2]

Use algebra to show that the recurring decimal 0. 612 = 101165[2]

Prove that, for any three numbers which are consecutive multiples of 4, the difference between the square of the largest number and the square of the smallest number is always a multiple of 64

Show clear algebraic working.[3]

F is inversely proportional to the cube of r

F = 6 when r = 2

(a)Find a formula for F in terms of r

[3]

(b)Find the value of r when F = 3072

r = [2]

Kannika has 9 counters. There is a number on each counter.

Kannika puts the 9 counters in a bag. She takes at random a counter from the bag and does not replace the counter. She then takes at random a second counter from the bag.

Work out the probability that the sum of the numbers on the two counters is less than 5

[3]

The diagram shows cuboid ABCDEFGH

Calculate the length of BC Give your answer correct to 3 significant figures.

cm[3]

The curve with equation y = f(x) has one turning point. The coordinates of this turning point are (−6, 9)

(a)Write down the coordinates of the turning point on the curve with equation y = f (3x)

( , )[1]

The curve C with equation y = g(x) is transformed to give the curve S with equation y = g(x + a) + b

The point (4, −5) on C is mapped to the point (1, −16) on S

(b)Write down the value of a and the value of b

a =

b = [2]

Solve the simultaneous equations

Show clear algebraic working.

[5]

PTR and QTS are chords of a circle.

Find an expression for y in terms of x

y = [5]

The first 3 terms of an arithmetic series are

where x and y are constants.

The sum of the first 9 terms of the series is 216

Find the value of x and the value of y Show clear algebraic working.

x =

y = [6]

BAC is a sector of a circle, centre A

BCD is a sector of a circle, centre C

Angle BAC = 40° Angle BCD = 130° Area of shaded segment = 28 cm²

Find the length of the arc BD Give your answer correct to 3 significant figures.

_cm[6]

R, S and T are three similar vases.

The volume of vase S is 72.8% more than the volume of vase R

The height of vase R is h cm The height of vase T is 6h cm

The surface area of vase S is A cm² The surface area of vase T is kA cm²

Work out the value of k

k = [4]