4MA1 Mathematics A: May/June 2025 Paper 2HHigher Tier Paper 2

Rio has six cards. He writes a number on each card so that

the range of the numbers is 10 the median of the numbers is 7.5 the mode of the numbers is 6

Rio arranges the cards so that the numbers are in order of size.

Three of the numbers are hidden.

Complete the cards above to show the three numbers that are hidden.[3]

(a)On the grid, enlarge shape A with scale factor 3 and centre (0, 1)[2]

(b)Describe fully the single transformation that maps triangle P onto triangle Q

[3]

Show that 7 13  3 47  31621[3]

Using ruler and compasses only, construct the perpendicular bisector of the line AB Show all your construction lines.

[2]

The diagram shows two similar quadrilaterals, ABCD and EFGH

(a)Work out the value of x

x = [2]

(b)Work out the value of y

y = [2]

Pau, Sam and Tia share £240 in the ratios 3 : 4 : 5

Sam and Tia each give £10 of their share to Pau.

Work out the ratios of the amounts of money that Pau, Sam and Tia now have. Give your answer in its simplest form.

_{: :} [4]

Tim buys a bracelet for 4000 Swiss francs. The value of the bracelet increases by 7% each year.

Work out the value of the bracelet at the end of 3 years. Give your answer correct to the nearest Swiss franc.

_Swissfrancs[3]

Solve the simultaneous equations

Show clear algebraic working.

x =

y = [3]

(a)Solve the inequality 7 – 3t < 2t + 15

[2]

The region R, shown shaded in the diagram, is bounded by three straight lines.

(b)Write down three inequalities that define the region R

[3]

ABD and ABC are right‑angled triangles.

AB = 16 cm BC = 12 cm AD = 1.5 × AC

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

cm[5]

Khalid has a box of counters.

17 of the counters are red 28 of the counters are blue the rest of the counters are orange

Khalid is going to take at random a counter from the box.

The probability that Khalid will take an orange counter is

Work out the number of orange counters that are in the box.

[3]

Expand and simplify 3x 2x  57x  4

[3]

The frequency table gives information about the times, in minutes, that 60 people took to complete a puzzle.

(a)Complete the cumulative frequency table.

[1]

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

[2]

(c)Use your graph to find an estimate for the median time.

minutes[1]

(d)Use your graph to find an estimate for the number of these people who took more than 45 minutes to complete the puzzle.

[2]

Here are five graphs.

(a)Write down the letter of the graph that could have the equation y  5  x²

[1]

(b)Write down the letter of the graph that could have the equation y = 2x³

[1]

Simplify fully  

[3]

Make t the subject of the formula c  t7  8t₂

[4]

y  4x³  5x²  2x

(a)Find dydx

dydx = [2]

(b)Find the coordinates of the turning points on the graph with equation y  4x³  5x²  2x Show clear algebraic working.

[4]

Use algebra to show that 0 .7 0 2  2637[2]

Solve the inequality 4x²  4x 15  0 Show clear algebraic working.

[3]

120 gardeners were asked if they grow carrots (C) or potatoes (P) or tomatoes (T)

Of these gardeners

43 grow carrots 12 grow carrots and potatoes and tomatoes 18 grow carrots and potatoes 27 grow carrots and tomatoes 32 grow potatoes and tomatoes 29 do not grow carrots or potatoes or tomatoes

The number of these gardeners who grow only potatoes is equal to the number of these gardeners who grow only tomatoes.

(a)Complete the Venn diagram to show this information.

E

[3]

(b)Find n(T   C)

[1]

One of the gardeners who grows carrots is chosen at random.

(c)Calculate the probability that this gardener also grows potatoes.

[2]

The diagram shows a cuboid.

The cuboid measures 3x cm by 2x cm by y cm

The volume of the cuboid is 1014 cm³ The total surface area of the cuboid is A cm²

Show that A  12x²  1690x

You must show all the stages of your working.[3]

The diagram shows a square inside rectangle ABCD

The total area of the region shown shaded in the diagram is X cm²

AB = 11 .5 cm correct to the nearest 0.5 cm BC = 9.2 cm correct to 2 significant figures side of square = 4.1 cm correct to 2 significant figures

By considering bounds, work out the value of X to a suitable degree of accuracy. Show your working clearly.

X = [4]

Find the value of p

Show clear algebraic working.

p = [4]

The diagram shows a square‑based pyramid ABCDE

EA = EB EC== ED

M is the centre of the horizontal square base ABCD Q is the midpoint of AB Angle EQM  80

EA : AB = n :1

Find the value of n Give your answer correct to 3 significant figures.

n = [4]

(a)Write 28  24x  6x² in the form a − b(x − c)² where a, b and c are integers.

[3]

(b)On the axes below, sketch the graph of y  28  24x  6x²

Show clearly the coordinates of the turning point and the coordinates of the point of intersection of the graph with the y‑axis.

[3]

A and B are two similar solids.

The height of solid A is 31 cm The height of solid B is 18.6 cm

Given that

find the volume of solid A

cm³[4]