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

Show that 2 45 ´ 3 37 = 9 35[3]

Write 504 as a product of powers of its prime factors. Show your working clearly.

[3]

(a)Simplify e⁷ × e³

[1]

(b)Simplify g⁵ ÷ g²

[1]

The weight of a giraffe is 1178 kg, correct to the nearest kg

(i)Write down the lower bound of the weight of the giraffe.

_kg[1]

(ii)Write down the upper bound of the weight of the giraffe.

_kg[1]

A bag contains only blue counters, green counters, red counters and yellow counters.

Danny takes a counter at random from the bag.

The table gives information about the probabilities that he takes a blue counter or a green counter or a red counter or a yellow counter.

There are 400 counters in the bag.

Work out the number of red counters in the bag.

[4]

8 cm 24 cm

A and B are similar parallelograms.

Work out the area of B

_cm²[3]

(a)Represent the inequality x < 1 on the number line above.[1]

2  y + 3 < 7 y is an integer.

(b)Write down all the possible values of y

[2]

(c)Solve the inequality 8 – 5w > –10

[2]

Factorise x²– 12x + 32

[2]

Caleb owns 11 sheep.

The mean weight of all 11 sheep is 77 kg The mean weight of 8 of the sheep is 75.2 kg

Work out the mean weight of the other 3 sheep.

kg[3]

Arwa invests 200 000 yen in a savings account for 3 years. She gets 1.4% per year compound interest.

Work out how much money Arwa will have in her savings account at the end of 3 years. Give your answer correct to the nearest yen.

_yen[3]

The diagram shows a solid cuboid.

The cuboid measures 3 cm by 11 cm by x cm

The volume of the cuboid is 264 cm³

Work out the total surface area of the cuboid.

_cm²[4]

Solve the simultaneous equations

Show clear algebraic working.

x =

y = [3]

The straight line L has equation 4y – 10x – 5 = 0

(a)Find the gradient of L

[2]

(b)Find the coordinates of the point where L crosses the y‑axis.

( , )[1]

The cumulative frequency table gives information about the ages, in years, of 80 people who went to a cinema on Saturday.

(a)On the grid below, draw a cumulative frequency graph for this information.

[2]

(b)Use your graph to find an estimate for the median age of the 80 people.

_years[1]

(c)Use your graph to find an estimate for the number of the 80 people aged 16 and under.

[1]

BCDEF is a pentagon. AB, BC and CD are three sides of a regular 10‑sided polygon.

Find the value of x

x =

[3]

(a)Express as a single fraction in its simplest form.

[3]

(b)Expand and simplify 3x(2x – 1)(x + 4)

[3]

y = x³+ 5x²– 8x

(a)Find dydx

=

[2]

The curve with equation y = x³+ 5x²– 8x has two stationary points, P and Q The x‑coordinate of P is less than the x‑coordinate of Q

(b)Work out the coordinates of P Show clear algebraic working.

( , )[3]

Here are 8 cards. There is a number on each card.

Gordon puts the 8 cards in a bag. He takes at random a card from the bag and does not replace it. Gordon then takes at random a second card from the bag.

Calculate the probability that the number on the second card is 3 more than the number on the first card.

[3]

P, Q, R and S are points on a circle, centre O

Angle POR = 170° Angle ORS = 53°

Find the size of angle SPO Give a reason for each stage of your working.

[5]

y is directly proportional to t² y = 40 when t = 4

t is directly proportional to the cube root of x t = 12 when x = 8

Work out the value of y when x = 27

y = [5]

60 students were asked if they study French (F), German (G) or Italian (I)

Of these students

32 students study French 24 students study German 27 students study Italian 16 students study French and German 15 students study German and Italian

The incomplete Venn diagram gives some more information about the languages the 60 students study.

(a)Work out the value of x

x = [3]

(b)Work out how many of the 60 students study none of French or German or Italian.

[2]

The diagram shows triangle ABC

Calculate the area of the triangle. Give your answer correct to 3 significant figures.

_cm²[4]

The function f is such that f(x) = 1x

(a)Write down the value of x that cannot be included in any domain of f

[1]

The function g is such that g(x) = 4x²– 8x + 15 The domain of g is x  1

(b)Work out gf(0.5)

[2]

(c)Express the inverse function g^–1 in the form g^–1(x) = ...

g^–1(x) = [4]

The centre of a circle is the point with coordinates (3, 1)

The point P with coordinates (7, 6) lies on the circle.

The line L is the tangent to the circle at P

Find an equation for L Give your answer in the form ax + by + c = 0 where a, b and c are integers.

[4]

OA = 3a OB = 4b AC = 2a + 2b CD = 32 × AC

P is the point on BC such that OPD is a straight line. →

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

[2]

(b)Find the ratio OP : PD Show your working clearly.

[4]

Express x in terms of n Show your working clearly and simplify your expression.

x = [3]