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

(a)Factorise fully 18c − 45cd

[2]

(b)Solve 5  2x6  3x  4

Show clear algebraic working.

x = [3]

Write 1400 as a product of powers of its prime factors. Show your working clearly.

[3]

Solve the simultaneous equations

Show clear algebraic working.

x =

y = [3]

Joshua is going to cover a floor with tiles for a customer. The area of the floor is 45 m²

Joshua buys one box of tiles for each 1.5 m² of floor area. Each box of tiles costs £64

Joshua also buys 5 bags of tile adhesive. Each bag of tile adhesive costs £12

Joshua charges the customer £3000

Work out his percentage profit. Give your answer correct to one decimal place.

_%[5]

(a)On the grid above, reflect shape A in the line y = x[2]

(b)On the grid above, enlarge shape B by scale factor 2 with centre (1, 1)[2]

(a)Write down the value of 5⁰

[1]

5⁹  5³_k

(b)Find the value of k

k = [2]

(c)Simplify fully 2d⁴ e⁵

[2]

The mass of a silver coin is 48.3 g The density of silver is 10.5 g/cm³

Work out the volume of the silver coin.

_cm³[2]

The mean of 7 numbers is 60

The mean of 3 of the numbers is 46

Work out the mean of the other 4 numbers.

[3]

In a sale, normal prices are reduced by 15%

The sale price of a dishwasher is 612 Swiss francs.

Work out the normal price of the dishwasher.

Swiss francs[3]

A straight line, L, is parallel to the line with equation y = 2 – 5x The line L passes through the point (0, 6)

Find an equation of the line L

[2]

The diagram shows two triangles, ADE and CDB

ABD is a straight line.

AE = 28 cm ED = 45 cm AB = 21 cm CD = 35 cm

angle AED = angle CBD = 90°

Work out the area of triangle CDB Give your answer correct to 3 significant figures.

cm²[5]

Osman buys a car for $16 000

The car depreciates at a rate of 12% each year for the first 2 years. In the third year, the car depreciates at a rate of x %

At the end of 3 years, the value of the car is $11 461.12

Work out the value of x

[3]

(a)Factorise 4x² − 25y²

[2]

(b)Show that 4x(x  3)(2x  5) can be written in the form ax³ + bx² + cx where a, b and c are integers to be found.[3]

Sara has two bags, A and B

In bag A, there are only 5 red beads and 4 green beads. In bag B, there are only 7 red beads and 3 green beads.

Sara takes at random a bead from bag A She then takes at random a bead from bag B

(a)Use this information to complete the probability tree diagram.

[2]

(b)Work out the probability that Sara takes two red beads.

[2]

Sara puts the beads back into their original bags.

Sara also has a box of beads. In the box, there are only red beads and green beads.

When a bead is taken at random from the box, the probability that it is

a green bead is 211

Sara takes at random a bead from bag A She then takes at random a bead from bag B She then takes at random a bead from the box.

(c)Work out the probability that Sara takes more red beads than green beads.

[3]

A, B and C are points on a circle, centre O

Angle BAO = 36° Angle BCO = 21°

Work out the size of angle ACO

[3]

Show that 45 + 7 can be written in the form a − b where a and b are integers.

Show each stage of your working.

[3]

Make k the subject of p  8k7  3k₂

[4]

OAB is a triangle.

P is the point on AB such that AP : PB = 1 : 3

(a)Write down in terms of a and b

[1]

(b)Express in terms of a and b Give your answer in its simplest form.

[2]

The functions f and g are such that

(a)State the value of x that cannot be included in any domain of g

[1]

(b)Find gf(x) Give your answer in its simplest form.

gf(x) = [2]

The histogram gives some information about the weights, in grams, of some books.

75 books weigh less than 100 grams.

A book is chosen at random.

Find an estimate for the probability that this book weighs between 400 grams and 600 grams.

[4]

Solve the inequality 2x²  7x  15  0

Show clear algebraic working.

[3]

The diagram shows a solid cuboid.

The volume of the cuboid is V cm³

Find the maximum value of V

[5]

The diagram shows a triangular prism, ABCDEF, with a horizontal rectangular base ABCD

M is the midpoint of the line AC

AC = 40 cm angle CAE = 35° angle ABF = 90°

Work out the size of angle CME Give your answer correct to 3 significant figures.

[3]

PQ is a straight line drawn on a square grid, with a scale of 1 cm for 1 unit on each axis.

P has coordinates 5, a and Q has coordinates 7, 3a where a > 0

The length of PQ is 4 10 cm

Find an equation of the perpendicular bisector of PQ Give your answer in the form y  mx  c where m and c are integers.

[6]

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

Find a suitable value for a, for b and for c

a =

b =

c = [3]

The diagram shows a solid hemisphere, H

The radius of H is x cm The volume of H is 6174π cm³

A bowl is made by removing a solid hemisphere from H such that the uniform thickness of the bowl is 2 cm

Diagram NOT accurately drawn

Work out the total surface area of the bowl. Give your answer in terms of π

_cm²[5]