4MA1 Mathematics A: January 2021 Paper 2HRHigher Tier Paper 2

w = 5y²– y³

(a)Work out the value of w when y = –2

w = [2]

(b)Factorise fully 8p²– 2p

[2]

(c)Expand 4t(3t – 2)

[2]

(d)Expand and simplify (5x – 2)(x + 4)

[2]

The diagram shows a rectangle ABCD and a semicircle with diameter AB where AB = 12 cm. The point E lies on DC and also on the semicircle.

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

cm²[3]

E = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30} A = {22, 24, 26, 28, 30} B = {21, 24, 27, 30}

(a)List the members of the set

(i)A ∩ B

(ii)Aʹ

[2]

C = {23, 25, 29}

(b)Using set notation, find an expression for C in terms of A and B.

[1]

(a)Simplify (3k²)⁴

[2]

(b)Simplify (21m⁴ n) ÷ (3n^–5)

[2]

Here is a shape P drawn on a grid of squares.

(a)On the grid, rotate shape P 180° about the point (–3, 2) Label the new shape Q.[2]

(b)On the grid, translate shape P by the vector 10 8 

Label the new shape R.[1]

Here are triangle T and triangle U drawn on a grid of squares.

(c)Describe fully the single transformation that maps triangle T onto triangle U.

[3]

On Wednesday, the price of 1 litre of petrol was £1.26 The price of petrol on Wednesday was 5% more than the price of petrol on the previous Monday.

Calculate the price of 30 litres of petrol on the previous Monday.

£ [3]

The shaded region R, shown in the diagram below, is bounded by the straight line with equation y = 3x – 2 and by two other straight lines.

Write down the three inequalities that define region R.

[3]

The table gives the length of the coastline, in kilometres, of each of five oceans.

(a)Which ocean has the greatest length of coastline?

[1]

(b)Calculate the difference between the length of the Atlantic Ocean’s coastline and the length of the Southern Ocean’s coastline. Give your answer in standard form.

km[2]

Solve x²– 21x + 20 = 0 Show your working clearly.

[3]

A mathematics teacher at a school asked a group of students how far, in kilometres, each student had travelled to get to school that day.

The table gives information about their answers.

The teacher calculated that an estimate for the mean distance travelled by the whole group of students was 4.25 km.

Work out the value of x. Show your working clearly.

x = [4]

A circle centre O has radius 9 cm.

Calculate the perimeter of the shaded sector of the circle. Give your answer correct to 3 significant figures.

cm[4]

Solve the simultaneous equations 2x + 7y = 17

Show clear algebraic working.

x =

y = [4]

The diagram shows two hot air balloons. A is a point on the base of one of the balloons and B is a point on the base of the other balloon.

The distance between A and B is 500 metres. The angle of depression of B from A is 23°

Calculate the vertical height of A above B. Give your answer correct to one decimal place.

_metres[3]

Simon bought a house at the beginning of 2018 The value of Simon’s house had decreased by 15% by the end of 2018

The house increased in value during both 2019 and 2020 The percentage increases in the value of the house during 2019 and 2020 were the same.

The value of Simon’s house at the end of 2020 was 2.85% greater than the amount he paid for his house at the beginning of 2018

Calculate the percentage increase in the value of the house during 2019

%[4]

Prove algebraically that the product of any two odd numbers is always an odd number.[4]

Two events A and B are such that n(A) = 62 n(B) = 30 and n(A ∪ B) = 68

Given that n(E ) = 80

(a)complete the Venn diagram to show the number of elements in each region.

[2]

An element is chosen at random from E.

(b)Using the Venn diagram, find the probability that this element is in

(i)A ∩ B

[1]

(ii)A ∪ Bʹ

[2]

The functions f and g are defined as

f(x) = x²+ 6 g(x) = x – 10

(a)Find fg(3)

[2]

(b)Solve the equation fg(x) = f(x) Show clear algebraic working.

[3]

The function h is defined as

(c)State the value of x that cannot be included in the domain of h

[1]

(d)Express the inverse function h^–1 in the form h^–1(x) = ...

h^–1(x) = [3]

Solve the equation

Show clear algebraic working.

[5]

(a)Simplify 8² ׳ 4⁶ Give your answer in the form 2^a where a is an integer. Show each stage of your working clearly.

[3]

Given that n^{/54//} =  1 2 where n > 0

(b)find the value of n.

n = [4]

A, B and C are points on a circle with centre O.

Angle ABC = 75°

The area of the shaded segment is 200 cm²

Calculate the radius of the circle. Give your answer correct to 3 significant figures.

cm[5]

A bag contains n beads. 6 of the beads are red and the rest are blue.

Ravi is going to take at random 2 beads from the bag.

The probability that the 2 beads will be of the same colour is 917

Using algebra, and showing each stage of your working, calculate the value of n.

n = [6]

ABC is an isosceles triangle in a horizontal plane. The point T is vertically above B.

Angle ABC = 140° AB = BC = 8 cm TB = 10 cm M is the midpoint of AC.

Calculate the size of the angle between MT and the horizontal plane ABC. Give your answer correct to one decimal place.

[4]