4MA1 Mathematics A: May/June 2024 Paper 2HRHigher Tier Paper 2

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

[3]

(a)Describe fully the single transformation that maps shape A onto shape B

[2]

(b)On the grid above, rotate shape A 180° about (−1, 0) Label your shape C[2]

Here is a list of four numbers written in ascending order of size

where x and y are integers.

The numbers have

a median of 12.5 a range of 4

Find the value of x and the value of y

x =

y = [2]

E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {factors of 6} B = {prime numbers}

(a)List the members of the set

(i)A ∪ B

[1]

(ii)A′

[1]

Harpreet states that A  B  

Harpreet is incorrect.

(b)Explain why.

[1]

C is a set with 4 members such that

the set A ∩ C has 2 members the set B ∩ C has 2 members

Set A ∩ C and set B ∩ C have no members in common.

(c)List the 4 members of set C

[2]

The diagram shows the design for a badge, which will be made using wire. The design is a circle inside a square ABCD

The circle touches the square at the points E, F, G and H

The area of the square is 81 cm²

Calculate the total length of wire that will be needed to make the square and the circle. Give your answer correct to 3 significant figures.

cm[4]

(a)Solve 2 f3  4 f  17

Show clear algebraic working.

f = [3]

(b)Simplify (e + 12)⁰ where e > 0

[1]

(c)Simplify fully

[2]

(d)Factorise fully 20x⁵ y + 12x³ y⁴

[2]

3²  3⁵_n

Find the value of n

n = [2]

In a sale, all normal prices are reduced by 17%

The sale price of a fridge is 6225 rupees.

Work out the normal price of the fridge.

rupees[3]

(a)Write 6.04 × 10⁵ as an ordinary number.

[1]

(b)Write 0.000 07 in standard form.

[1]

(c)Work out

Give your answer in standard form.

[2]

The diagram shows a hexagon ABCDEF

Angle BCF = 30° AB, FC and ED are parallel.

Calculate the area of ABCDEF Show your working clearly.

cm²[5]

The cumulative frequency table gives information about the time, in hours, that each of 60 workers spent working from home in one week.

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

[2]

(b)Use your graph to find an estimate for the interquartile range of the times.

hours[2]

25 workers spent more than W hours working from home.

(c)Use your graph to find an estimate for the value of W

W = [2]

One of the 60 workers is chosen at random. This worker spent H hours working from home.

(d)Find the probability that 5 < H „ 10

[1]

In the diagram, ABC and AED are straight lines. BE is parallel to CD

(a)Work out the length of ED

cm[2]

AB = (2x + 5) cm and BC = (3x – 5) cm

(b)Work out the value of x

x = [2]

OAB is a sector of a circle with centre O and radius r cm.

Angle AOB = 60° The perimeter of the sector is P cm.

Find a formula for P in terms of r Give your answer in the form P = r(cπ + k) where c and k are values to be found.

[3]

Adriana is going to roll a biased dice and spin a biased coin.

The probability that the coin will land on Heads is 0.8 The probability that the dice will land on 6 and the coin will land on Heads is 0.24

Work out the probability that the dice will land on 6 and the coin will land on Tails.

[3]

AB, BC and CD are three sides of a regular pentagon and CDE is a triangle. BCE is a straight line.

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

cm²[3]

Here are six graphs.

Write down the letter of the graph that could have the equation 1

(i)y   x

[1]

(ii)y = sin x°

[1]

x

f(x)  g(x)  3x  1

Given that fg(k) = 2

work out the value of k

k =

[3]

Use algebra to show that 0.30. 30606 = 34111[2]

Aviv goes on a cycle journey.

For the cycle journey

average speed = 19 km/h correct to the nearest whole number

Work out the upper bound for the distance Aviv travels. Give your answer correct to 3 significant figures.

km[3]

Solve 6x²  7x  20  0 Show clear algebraic working.

[4]

ABCD is a square.

The point A has coordinates (−5, 2) The point B has coordinates (3, 5)

Find an equation of the line that passes through B and C Give your answer in the form ax + by + c = 0 where a, b and c are integers.

[4]

Solve the simultaneous equations

Show clear algebraic working.

[5]

A curve has equation y = f(x) The coordinates of the minimum point on this curve are (6, −3)

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

(i)y  f(x)  10

( , )[1]

(ii)y = f(3x)

( , )[1]

The diagram shows a solid, S, made from a cone and a hemisphere.

The centre of the circular face of the cone coincides with the centre of the flat surface of the hemisphere.

The radius of the circular face of the cone, x cm, is equal to the radius of the hemisphere.

The total height of S is 4 × the radius of the hemisphere.

A separate sphere has radius kx cm. The volume of this sphere is 12.5 × the volume of S

(a)Work out the value of k

k = [4]

A solid, T, is similar to solid S

The volume of T is 512 × the volume of S

The total surface area of T is d × the total surface area of S

(b)Find the value of d

d = [1]

OPQR is a parallelogram.

OP = 2a and OR = 3b

The point M lies on PQ such that PM = 14 PQ

The point N lies on RQ such that RN = 45 RQ

(a)Find, in terms of a and b, giving your answers in simplest form

(i)ON

[1]

(ii)MR

[1]

MR and ON intersect at the point Y

Given that

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

k = [4]

Write 4  3x  5   x  10  as a single fraction in its simplest form.

[4]