4MA1 Mathematics A: Oct/Nov 2025 Paper 1HHigher Tier Paper 1

The table gives information about the number of kilometres that Ted cycled on each of the 30 days in April.

0  K < 5

5  K < 10

Calculate an estimate for the mean number of kilometres that Ted cycled on each day in April.

kilometres[4]

By rounding each number to one significant figure, work out an estimate for the value of

Show your working clearly.

[2]

Using ruler and compasses only, construct the bisector of angle ABC Show all your construction lines.

[2]

e, f and g represent integers such that

is a list of integers written in order of size.

The integers have

a range of 15 a median of 8.5 a mean of 9

Work out the value of e, the value of f and the value of g

e =

f =

g = [3]

Show that 3 57  1 23  5 821[3]

Eli and Peta share $275 in the ratio 2 : 3

Eli gives 311 of his share to charity.

Peta gives 0.32 of her share to charity.

Work out the total amount that Eli and Peta give to charity.

$ [4]

The weight of a bag of apples is 475 g correct to the nearest g

(a)Write down the lower bound of the weight.

g[1]

The height of a box is 120 cm correct to the nearest 10 cm

(b)Write down the upper bound for the height.

cm[1]

8²  8⁹_n

₁₀  8

Work out the value of n

n = [2]

Hari scored 140 points playing a game on Tuesday. This was 12% more points than he scored playing the game on Monday.

Work out the number of points that Hari scored playing the game on Monday.

[3]

(a)Simplify (6m)⁰

[1]

(b)Solve 5y + 20 < 7y + 1

[2]

(c)Factorise fully 15w² x⁵+ 25w³ x²

[2]

(d)Simplify fully 36a c12a c₂₃

[2]

ABC is a right-angled triangle.

The point D lies on AB such that DB = 9 cm

Work out the size of angle ACD Give your answer correct to one decimal place.

[4]

The diagram shows part of a regular n-sided polygon with

an interior angle of (9x + 27)° an exterior angle of (2x – 23)°

Work out the value of n

n = [4]

In a bag, there are only 2 yellow beads and 3 orange beads. In a box, there are only 3 yellow beads and 5 green beads.

Chi takes at random a bead from the bag and a bead from the box.

(a)Complete the probability tree diagram.

[2]

(b)Work out the probability that Chi takes two beads of different colours.

[3]

(a)Expand and simplify 7x(3x + 2)(2x – 5)

[3]

(b)Solve 92 y  57  5

Show clear algebraic working.

y = [3]

AOB is a sector of a circle with centre O and radius 12 cm

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

cm²[2]

Ivan asked 15 people how many books they read last year.

Here are his results.

Work out the interquartile range of the number of books read.

2[2]

Show that 7  27  3 can be written in the form a – b where a and b are integers.

Show your working clearly.[3]

Make y the subject of p  y  w3y  t

[4]

The diagram shows triangle ABC

AB = 8 cm BC = 10 cm CA = 9 cm

Work out the size of angle BAC Give your answer correct to one decimal place.

[3]

The straight line L has equation y = 4x + 7

The straight line M is perpendicular to L and passes through the point with coordinates (8, 1)

Find an equation for M Give your answer in the form y = mx + c

[3]

Express 5x² ‒ 20x + 23 in the form a(x – b)²+ c where a, b and c are integers.

[3]

There are 15 buttons in a box.

3 of the buttons are red 2 of the buttons are pink 10 of the buttons are blue

Pete takes at random three buttons from the box.

Work out the probability that there is still at least one pink button in the box.

2x  5 5  2 y[3]

a  x  1  x 3y

Write a in the form where m, n and p are integers.

Show your working clearly.

a = [3]

A curve has equation y = f (x)

There is only one turning point on the curve. The coordinates of this turning point are (4, 3)

Write down the coordinates of the turning point on the curve with equation

(i)y = f (x + 5)

( _, )[1]

(ii)y = f (x) + 7

( _, )[1]

(iii)y = f (2x)

( _, )[1]

Solve the inequality 2x²+ x – 28 > 0 Show clear algebraic working.

[3]

Here is a prism ABCDEFGH with a horizontal, rectangular base ABGF

AB = 10 cm BG = 14 cm

angle DAB = angle ABC = angle EFG = angle FGH = 90°

BC = 15 AD

The angle of elevation of E from B is 50°

Calculate the volume of the prism. Give your answer correct to 3 significant figures. Show your working clearly.

cm³[5]

OABC is a quadrilateral. ABP and ODP are straight lines.

OA = 2a AB = 4b – a OC = 5b – 3a →

(a)Find an expression in terms of a and b for the vector BC Simplify your answer.

[2]

The point D lies on BC such that BD : DC = 1 : 3 → → Given that OP = nOD

(b)use a vector method to find the value of n

n = [4]

The curve C has equation x²+ y²= d – 11x where d is an integer. The line L has equation y = 3x + e where e is an integer.

C and L intersect at the point A and at the point B

The coordinates of A are (0.2, 2.6)

Work out the coordinates of B Show your working clearly.

( _, )[6]