4MA1 Mathematics A: May/June 2024 Paper 1HHigher Tier Paper 1

Here are the first four terms of an arithmetic sequence.

(a)Find an expression, in terms of n, for the nth term of this sequence.

[2]

The nth term of a different arithmetic sequence is 5n + 17

(b)Find the 12th term of this sequence.

[1]

450 students were asked how they travelled to school on Monday. Each student walked or travelled by bus or travelled by car or travelled by bicycle. Each student used just one method of travel.

One of these students is chosen at random. The table shows information about the probability of each method of travel.

Work out how many of the 450 students travelled by car.

[4]

Find the highest common factor (HCF) of 72 and 108 Show your working clearly.

[2]

Ava records the number of kilometres she drives each month.

In April, Ava drove 943 kilometres. This is 15% more than the number of kilometres she drove in March.

Work out the number of kilometres Ava drove in March.

_kilometres[3]

In the diagram, ABCDE is a regular pentagon.

Angle AEF = 96°

Work out the size of the obtuse angle FED Show your working clearly.

[4]

(a)Expand and simplify (m + 5)(m – 8)

[2]

(b)Solve 3n – 4 = 5n + 63

Show clear algebraic working.

n = [3]

ℰ = {23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34} A = {even numbers} B = {23, 29, 31} C = {multiples of 3}

(a)List the members of the set

(i)B ∪ C

[1]

(ii)A′ ∩ C

[1]

(b)Is it true that B ∩ C = ∅ ?

Tick ( ) one of the boxes below.  Yes No

Give a reason for your answer.

[1]

The set D has 4 members and is such that D ∩ (A ∪ C) = ∅

(c)List the members of set D

[2]

A cylinder is placed on a table.

The volume of the cylinder is 1575 cm³ The force exerted by the cylinder on the table is 84 newtons.

Work out the pressure on the table due to the cylinder.

_newtons/cm²[3]

The table gives the amount of rice produced by each of two countries in 2020

Country Amount of rice (tonnes)

(a)Write 3.5 × 10⁷ as an ordinary number.

[1]

In 2020, Japan produced 6 780 000 more tonnes of rice than Argentina.

(b)Work out the amount of rice Japan produced in 2020 Give your answer in standard form.

_tonnes[2]

(a)Simplify (2p)⁰ where p > 0

[1]

y⁹ × y^–3= yⁿ

(b)Find the value of n

n = [1]

(c)Simplify fully (5a⁴ c²)³

[2]

The diagram shows a roof support.

The roof support is made from four lengths of wood, AB, AC, BC and MC

AC = BC = 9 m AB = 12 m

angle AMC = 90°

Lewis is going to buy lengths of wood to make the roof support.

The wood costs 21.50 euros per metre. Each length of wood he buys has to be a whole number of metres.

Work out the total cost of the wood Lewis needs to buy. Show your working clearly.

_euros[4]

(a)Factorise fully 6y²– 5y – 4

[2]

(b)Express 2x  14x  7  5x3x as a single fraction in its simplest form.

[3]

Harman has two bags of beads.

In bag A, there are 3 white beads and 7 black beads. In bag B, there are 5 white beads and 4 black beads.

Harman takes at random a bead from bag A and a bead from bag B

(a)Complete the probability tree diagram.

[2]

(b)Work out the probability that Harman takes two beads of the same colour.

[3]

The combined savings of Abel and Bahira are 15 435 dinars.

The savings of Bahira are 45% more than the savings of Abel.

The savings of Bahira are 32 times the savings of Chanda.

Work out the savings of Chanda.

_dinars[5]

The function f is defined as

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

[1]

(b)Express the inverse function f^–1 in the form f^–1(x) = ...

f ^–1(x) = [3]

There are 20 sweets in a box.

15 of the sweets are red

Fred takes at random 3 sweets from the box.

Work out the probability that Fred takes at least one sweet of each colour from the box.

[4]

Show that 1 3  55 can be written in the form a + b where a and b are integers.

Show each stage of your working clearly.[3]

A curve C has equation y = x³ ‒ 40x + 1

Find the coordinates of both the points on C at which the gradient is 8

( , )

( , )[5]

Here is quadrilateral ABCD

B

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

x = [5]

The diagram shows a sector OABC of a circle centre O

A

Angle AOC = 60°

The area of the shaded segment ABC is 38 cm²

Work out the perimeter of the shaded segment ABC Give your answer correct to one decimal place.

_cm[4]

A curve has equation y = f (x)

There is one minimum point on this curve. The coordinates of this minimum point are (5, ‒4)

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

(i)y = f (x + 7)

( , )[1]

(ii)y = f (x) ‒ 6

( , )[1]

The incomplete histogram shows some information about the distances, in kilometres, that 100 adults ran last week.

All of the adults ran at least 5 kilometres. None of the adults ran more than 55 kilometres. 14 adults ran between 15 kilometres and 20 kilometres.

Complete the histogram.[3]

A solid shape is made by removing a hemisphere, shown shaded, from a cone as shown in the diagram.

The radius of the hemisphere is 2x cm The radius of the base of the cone is 5x cm The vertical height of the cone is 6x cm

The volume of the solid shape is 6948π cm³

Work out the total surface area of the solid hemisphere that has been removed from the cone. Give your answer correct to the nearest integer.

cm²[5]

A polygon has n sides, where n > 5

The interior angles of the polygon form an arithmetic sequence.

The smallest angle of the polygon is 84° The common difference of the sequence is 4°

Work out the sum of the interior angles of the polygon. Show clear algebraic working.

[6]

f (x) = 17 − 3x²+ 12x

Write f (x) in the form a – b(x − c)² where a, b and c are constants.

f (x) = [4]