4MA1 Mathematics A: May/June 2026 Paper 1HHigher Tier Paper 1

Show that 4 17  2 35  11935[3]

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

x = [3]

E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19}

A = {factors of 20}

B = {multiples of 5}

(a)List the members of the set

(i)A ∪ B

[1]

(ii)A  B

[1]

C = {prime numbers}

Ana writes down the statement A  C   Ana’s statement is wrong.

(b)Explain why.

[1]

Henri competes in a race.

For the first part of the race Henri cycles 60 km at an average speed of 24 km/h For the remaining part of the race Henri runs for 1 hour and 15 minutes at an average speed of 12 km/h

Work out Henri’s average speed for the whole race. Give your answer in km/h Show your working clearly.

_km/h[4]

(a)Expand 4e2e  3

[1]

(b)Expand and simplify  f  3 f  6

[2]

(c)Make x the subject of t  ax  2n

[2]

(d)On the number line, represent the inequality −1< y  3

[2]

Simplify 4x⁵ y⁶

[2]

Here is a biased 4-sided spinner.

The table gives information about the probability that, when the spinner is spun once, it will land on each number.

Nevan spins the spinner 500 times.

Work out the expected number of times that the spinner lands on an even number.

[4]

Change a speed of 70 metres per second to a speed in kilometres per hour. Show your working clearly.

_km/h[3]

(a)Write 0.0651 in standard form.

[1]

(b)Work out 4  10⁵⁶ 8  10⁷⁴

Give your answer in standard form.

[2]

Solve the simultaneous equations

Show clear algebraic working.

[3]

The diagram shows a shaded shape ABCDEO made from a semicircle BCD and two identical right-angled triangles ABO and EDO

BD is the diameter of the semicircle. O is the midpoint of BD

angle ABO  angle EDO  90 AO  EO  15 cm

The area of semicircle BCD is 227 cm²

Work out the perimeter of the shaded shape. Show your working clearly. Give your answer correct to one decimal place.

_cm

2^x/3[5]

(a)Find the value of x Show clear algebraic working.

x = [3]

(b)Expand and simplify 4t(t  5)(2t  3)

[3]

On any school day, Paulo either walks to school or travels by bus to school.

The probability that it rains on any school day is 0.15

If it rains on a school day, the probability that Paulo walks to school is 0.2 If it does not rain on a school day, the probability that Paulo walks to school is 0.75

(a)Complete the probability tree diagram for this information.

[2]

(b)Work out the probability that on a school day, it rains and Paulo walks to school.

[2]

In September, the sales in a shop increased by 20% In October, the sales in the same shop decreased by x%

Over these two months, the sales in the shop decreased by 10%

Work out the value of x

[3]

Point A has coordinates 3, 4 Point B has coordinates 2,  6

Work out the gradient of the line AB

[2]

The diagram shows triangle ABC

(a)Work out the length of BC Give your answer correct to 3 significant figures.

cm[3]

(b)Work out the area of the triangle. Give your answer correct to 3 significant figures.

cm ²[2]

Show that 4  20 5  2 5 can be written in the form a − b

where a and b are integers.

[3]

Simplify fully₂4x− 5x − 12

Show clear algebraic working.

[3]

M is directly proportional to p²

M = 2 when p = 5

(a)Find a formula for M in terms of p

[3]

(b)Work out the value of M when p = 15

M = [1]

The final velocity, v m/s, of an object is given by

s = 100 correct to the nearest integer t = 1. 68 correct to 2 decimalm places u = 0.5 correct to 1 decimal place

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

[5]

The diagram shows a solid cuboid.

The volume of the cuboid is V cm³

Find the maximum value of V Show clear algebraic working.

[5]

The histogram gives information about the weights, in grams, of all the apples in a shop.

There are 9 apples with a weight between 140 grams and 155 grams.

(a)Work out the number of apples with a weight less than 175 grams.

[3]

An apple is classified as a large apple if it has a weight of more than 180 grams. One of the large apples is chosen at random.

(b)Work out the probability that it has a weight of more than 190 grams.

[2]

A bag contains x marbles. 12 of the marbles are pink and the rest are yellow.

Greta takes at random 2 marbles from the bag.

The probability that Greta takes a pink marble and a yellow marble is 1847

Work out the value of x Show clear algebraic working.

x = [5]

(a)Express 10 − 24x − 3x² in the form a  bx  c² where a, b and c are integers.

[3]

T is the curve with equation y  10  24 x  1  3 x  1  The point P is the maximum point on T

(b)Use your answer to part (a) to find the coordinates of P

( , )[1]

(c)Write down the equation for the line of symmetry of T

[1]

The diagram shows a triangular prism ABCDEF with horizontal rectangular base ABCD F is vertically above A

T is the point on the line BC such that BF : BT = 3: 2

Work out the size of the angle between the line FT and the plane ABCD Give your answer correct to one decimal place. Show your working clearly.

[5]