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

Write 4500 as a product of powers of its prime factors. Show your working clearly.

[3]

The nth term of an arithmetic sequence is given by 8n − 5

(a)Work out the ratio of the 40th term of the sequence to the 60th term of the sequence. Give your ratio in its simplest form.

[3]

Here are the first five terms of a different arithmetic sequence.

(b)Find an expression for the nth term of this sequence.

[2]

The table shows information about the number of hours each of 40 candles burned.

Number of hours (h) Frequency

15 < h 19 2

19 < h  23 5

23 < h  27 12

27 < h  31 15

31< h  35 6

(a)Write down the modal class.

[1]

(b)Work out an estimate for the mean number of hours.

hours[4]

Sara sells water bottles.

In July, she sold 450 water bottles. In August, she sold 612 water bottles.

Work out the percentage increase in the number of water bottles she sold from July to August.

%[3]

(a)Describe fully the single transformation that maps triangle A onto triangle B

[3]

(b)On the grid, translate triangle A by the vector 3     Label your triangle C[1]

ABCDE is a pentagon.

Diagram NOT

angle EAB  96 angle BCD  91 angle CDE  93 angle DEA = angle ABC  x

Work out the value of x

[3]

The diagram shows a cylinder and a prism.

The radius of the cylinder is 7 cm The height of the cylinder is 18 cm

The area of the cross section of the prism, shown shaded in the diagram, is 120 cm² The length of the prism is L cm

The volume of the cylinder is equal to the volume of the prism.

Work out the value of L Give your answer correct to 3 significant figures.

L = [3]

A golf club increases the cost of membership by 17% After the increase, the cost of membership is 3276 zloty.

Work out the cost of membership before the increase.

zloty[3]

(a)Find the value of 7n⁰ where n > 0

[1]

(b)Simplify fully 2m⁵ p⁴

[2]

(c)Factorise fully 18c⁵ w² + 30cw³

[2]

(d)Factorise x²  6x  27

[2]

Johan owns a car.

The current value of the car is 32 000 euros. The value of the car will now depreciate by 15% per year.

Lena is going to save up and buy Johan’s car in 3 years’ time. She has already saved 2516 euros.

She will save an equal amount of money each month for the next 3 years.

Work out how much money Lena needs to save each month.

euros[4]

Find the highest prime number that is a factor of 3.6 × 10²⁴

[2]

E  integers x such that 20  x  32

A  x such that x < 27

B  x such tthat 25  x  30

(a)List the members of the set A ∩ B

[1]

(b)List the members of the set  A  B'

[1]

Leo collects apples from three trees. The incomplete table gives some information about the apples he collects from these trees.

Work out the mean weight of all the apples Leo collects from these three trees.

grams[4]

The cumulative frequency graph gives information about the weights, in kg, of 60 crates.

60

50

40

(a)Use the graph to find an estimate for the median weight.

kg[1]

(b)Use the graph to find an estimate for the interquartile range.

kg[2]

The diagram shows a sector OABC of a circle, centre O

OA = OC r cm= angle AOC = 80^

The area of the sector OABC is 32π cm²

Work out the perimeter of the sector OABC Give your answer correct to one decimal place.

cm[4]

The functions f and g are such that

(a)Find g(4)

[1]

(b)Find f⁻¹(7)

[2]

(c)Express gf(x) in the form ax² + bx + c where a, b and c are integers.

[2]

Use algebra to show that 0. 539 = 89165[2]

Make x the subject of the formula a  3w  xx₂

[4]

B, D and E are points on a circle.

ABC is the tangent to the circle at B

angle ABE  52 ED = BD

Work out the size of angle BED

[2]

A box only contains green counters and red counters.

Nuno chooses at random a counter from the box. He puts the counter back into the box.

Nuno then chooses at random a second counter from the box.

The probability that Nuno chooses at least one red counter is 3964

Work out the probability that Nuno chooses exactly one red counter.

[3]

The curve with equation y = f(x) is drawn on a grid.

y

(a)By drawing a suitable straight line (at least 3 cm long) on the grid, work out an estimate for the gradient of the curve at the point where x = 1 Show your working clearly.

[2]

(b)By drawing a suitable straight line on the grid, find the solutions

of the equation x  3  12 f(x)

Show your working clearly.

[3]

The diagram shows a quadrilateral OABC where O, A, B and C represent the positions of four houses.

Ria walks directly from A to B Anna walks directly from A to C and then walks directly from C to B

Work out how much further Anna walks than Ria walks. Give your answer correct to one decimal place.

metres[4]

The straight line L has equation y  3x  2

The curve C has equation x²  y²  2 y  12

Find the coordinates of the points where L and C intersect. Show clear algebraic working.

( , ) and ( , )[5]

The diagram shows two cones C₁ and C₂

The vertex of C₁ coincides with the vertex of C₂ at the point A C₁ and C₂ have the same axis of symmetry.

total surface area of C₁ : total surface area of C₂ = 4 : 9

Work out the radius of the base of C₂ Show your working clearly.

cm[5]

An arithmetic series has first term 3 and common difference 8

The nth term of the series is U n The sum of the first n terms of the series is Sn

Given that S_5k  S_3k  25 560

find the value of U_4k Show clear algebraic working.

[5]

The curve P has equation y  f  x The coordinates of the minimum point on P are 5, 4

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

( , )[1]

The curve Q has equation y  2   x  3

The curve R has equation y  2  3  x

(b)Describe fully the single transformation that maps Q to R

[1]

The graph of y  a cos x  b  c for −180  x  360 is drawn on the grid.

Given that a > 0 and 0 < b < 360

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

a =

b =

c = [3]