4MA1 Mathematics A: May/June 2026 Paper 2HRHigher Tier Paper 2

The diagram shows a right‑angled triangle.

Work out the value of x

x = [3]

Here are the first five terms of an arithmetic sequence.

Find an expression, in terms of n, for the nth term of this sequence.

[2]

E = {integers from 1 to 12} A = {factors of 12}

List the members of the set A′

[1]

(a)Solve 3(x + 2) = 1 – 5x Show clear algebraic working.

x = [3]

P = c²– 5d

(b)Work out the value of P when c = –7 and d = 3

P = [2]

(c)Simplify m⁰

[1]

(d)Simplify (4r² t)³

[2]

Sarah and Dej each give some money to charity A and to charity B

Sarah shares $400 between charity A and charity B in the ratio 2 : 3

Dej shares $375 between the two charities. He gives twice as much money to charity B as he gives to charity A

Dej gives more money to charity B than Sarah gives to charity B

How much more?

$ [5]

Mika has six cards. There is a number on each card. The cards are arranged with the numbers in order of size. Three of the numbers are hidden.

The mode of the six numbers is 8 The range of the six numbers is 7 The sum of the six numbers is 31

Work out the median of the six numbers.

[4]

(a)Write 4 × 10^–5 as an ordinary number.

[1]

(b)Work out (6 × 10¹⁵⁸) × (2 × 10⁷²) Give your answer in standard form.

[2]

Lauren’s salary increased by 4% After the increase, her salary was 36 400 euros.

Work out Lauren’s salary before the increase.

_euros[3]

Change a speed of 198 kilometres per hour to a speed in metres per second. Show your working clearly.

_m/s[3]

The diagram shows a solid cylinder.

The cylinder has radius 4 cm and height 11 cm The cylinder is made from wood with a density of 0.6 g/cm³

Work out the mass of the cylinder. Give your answer correct to 3 significant figures.

_g[3]

The diagram shows a square ABCD and a right‑angled triangle EFG

The area of square ABCD is 36 cm² DC = EG

Work out the area of triangle EFG Give your answer correct to one decimal place. Show your working clearly.

_cm²[5]

y

6

5

The region R, shown shaded in the diagram, is bounded by the y‑axis and the straight lines with equations

2x + 5y = 12

Write down the three inequalities that define R

[3]

(a)Complete the table of values for y = x + 1x

[2]

(b)On the grid, draw the graph of y = x + 1x for 0.25  x  5

[2]

Pras has 2 bags of counters, bag A and bag B

In bag A, there are 4 green counters and 3 red counters. In bag B, there are 5 green counters and 1 red counter.

Pras is going to take at random a counter from bag A and a counter from bag B

(a)Complete the probability tree diagram.

Red[2]

(b)Work out the probability that Pras will take two green counters.

[2]

Pras also has a third bag of counters, bag C In bag C, there are only green counters and red counters. All the original counters are back in bag A and bag B

Pras is going to take at random a counter from bag A, a counter from bag B and a counter from bag C

The probability that Pras will take three red counters is 370

(c)Work out the probability that Pras will take 1 green counter and 2 red counters.

[4]

Mina recorded the times taken, in minutes, by 11 people to complete a puzzle. Here are her results.

Find the interquartile range of these times.

_minutes

 1 _n[2]

 a    a 

Work out the value of n

n =

[2]

Use algebra to show that 0.814 = 2227[2]

Here are two vectors.

Find AC as a column vector.

[2]

The table gives information about the times, in minutes, some people spent waiting to go on a rollercoaster.

Time (t minutes) Frequency

0 < t  20

20 < t  25

25 < t  35

35 < t  50

On the grid, draw a histogram for this information.

[3]

Make x the subject of y  3x  54  2x

[3]

d = 6.6 correct to 1 decimal place e = 2.8 correct to 1 decimal place f = 0.47 correct to 2 decimal places

Calculate the lower bound for the value of p Give your answer correct to 3 significant figures. Show your working clearly.

[3]

Solve the simultaneous equations

Show clear algebraic working.

[5]

K, L and M are three similar solids.

volume of K : volume of L = 125 : 216

surface area of K : surface area of M = 4 : 9

The height of M is y% greater than the height of L

Work out the value of y Show your working clearly.

y = [5]

A

AB, BC and CD are three sides of a regular polygon. ABE is a straight line.

BCE is a sector of a circle with centre B and radius 4.5 cm

The length of arc CE is 310 π cm

Work out the sum of the interior angles of the regular polygon.

[4]

The graph of y = a sin(x + b)° for 0  x  360 is drawn on the grid below.

Given that a < 0 and that 0 < b < 360

(a)find the value of a and the value of b

a =

b = [2]

A curve has equation y = f(x) The point T with coordinates (p, q) lies on the curve.

(b)Find the coordinates of the image of T on the curve with equation

Give your coordinates in terms of p and q

( , )[2]

Here are the first four terms of an arithmetic series.

The sum of the first 2n terms of the series is 4 times the sum of the first n terms of the series.

Work out the numerical value of the 100th term of the series. Show your working clearly.

[6]

Bryan owns a house.

During 2024, the value of Bryan’s house increased by x% During 2025, the value of Bryan’s house increased by 2x%

Overall, during 2024 and 2025, the value of Bryan’s house increased by 38.88%

Work out the value of x Show clear algebraic working.

x = [4]