# 4MA1 Mathematics A January 2022 Paper 2HR (Higher Tier Paper 2)

Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 2HR, Higher Tier Paper 2, January 2022. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/4ma1/2022-january-paper-2hr/
- PDF: https://mathvsarham.com/papers/4ma1/4MA1_january_2022_paper_2HR_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International GCSE
- Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/)
- Session: January 2022
- Paper: 2HR (Higher Tier Paper 2)
- Component code: 4MA1/2HR
- Time allowed: 120 minutes
- Total marks: 100
- Pages: 32

## Question paper text

Extracted automatically from the PDF; diagrams are missing and notation may be imperfect.

Question 1
A tin contains tea bags with a choice of four different flavours of tea. The four flavours of tea are Assam or Darjeeling or Nilgiri or Rize.
Sara takes at random a tea bag from the tin.
The table shows each of the probabilities that the flavour of the tea Sara takes is Assam or Darjeeling or Rize.
[Diagram or table: see page 3 of the paper]
(a) Work out the probability that the flavour of the tea Sara takes is Nilgiri.
Answer: ____ [2]
(b) Work out the probability that the flavour of the tea Sara takes is either Darjeeling or Rize.
Answer: ____ [2]

Question 2
Mary saves for a holiday each year.
In 2020 she saved a total of $720 In 2021, each month she saved $78
The total amount Mary saved in 2021 was P% more than the total she saved in 2020
(a) Work out the value of P
Answer: ____ [4]
Roberto is going to go on holiday.
He has two coupons that will save him money on his holiday.
Coupon A Coupon B
[Diagram or table: see page 5 of the paper]
the cost of the accommodation is $1600 the cost of the flights is $800
Roberto can only use one of the coupons. He wants to save as much money as he can.
(b) Which of the two coupons, A or B, should he use? Show your working clearly. [3]

Question 3
(a) Solve 4y + 5 > 12
Answer: ____ [2]
(b) Solve 6x  5  4x  7/2
Show clear algebraic working.
Answer: x = ____ [3]

Question 4
The diagram shows a regular octagon ABCDEFGH and a regular pentagon ABIJK
F E
[Diagram or table: see page 7 of the paper]
Work out the size of the angle x
[Diagram or table: see page 7 of the paper]
Answer: ____ [4]

Question 5
Shane invests 7200 dollars for 3 years in a savings account. He gets 2.5% per year compound interest.
How much money will Shane have in his savings account at the end of 3 years? Give your answer to the nearest dollar.
Answer: ____ _dollars [3]

Question 6
(a) Write down the value of x^0
Answer: ____ [1]
Given that 2^–3 × 2^9= 2^n
(b) find the value of n
Answer: n = ____ [1]
7^206^m__3 Given that  7/7_214  7
(c) find the value of m
Answer: m = ____ [2]

Question 7
(a) Write down an equation of the straight line with gradient –3 and which passes through the point with coordinates (0, 5)
Answer: ____ [2]
(b) Show, by shading on the grid, the region defined by all three of the inequalities
[Diagram or table: see page 10 of the paper]
Label the region R
[Diagram or table: see page 10 of the paper]
[3]

Question 8
A scientist is investigating the weight of 50 tigers.
Here is some information about these tigers.
Type of tiger
[Diagram or table: see page 11 of the paper]
Mean weight of tigers (kg) 260
The mean weight of all 50 tigers is 218 kg
Work out the mean weight of the Bengal tigers.
Answer: ____ _kg [3]

Question 9
In the diagram, ABC is a right-angled triangle and DEF is a semicircular arc.
[Diagram or table: see page 12 of the paper]
The points D and F lie on AC so that DF is the diameter of the semicircular arc DEF The radius of the semicircular arc is 3 cm.
Work out the length of AFEDC Give your answer correct to 2 significant figures.
Answer: ____ _cm [5]

Question 10
The table gives information about the population and the total amount of money, in dollars, spent on healthcare for two countries in 2016
[Diagram or table: see page 14 of the paper]
Work out how much more was spent per person on healthcare in Luxembourg than in Austria. Give your answer correct to the nearest whole number.
Answer: ____ _dollars [3]

Question 11
(a) Complete the table of values for y = 6/x
[Diagram or table: see page 15 of the paper]
[2]
(b) On the grid, draw the graph of y = 6/x for 0.5  x  6
y
[Diagram or table: see page 15 of the paper]
[2]

Question 12
The diagram shows two vertical phone masts, AB and CD, on horizontal ground.
[Diagram or table: see page 16 of the paper]
Work out the size of the angle of depression of B from D Give your answer correct to one decimal place.
[Diagram or table: see page 16 of the paper]
Answer: ____ [3]

Question 13
a = 8 + 4
b = 8 − 4
(a – b) (a + b) can be written in the form y 4 y
Find the value of y Show your working clearly.
Answer: y = ____ [3]

Question 14
A group of 60 students each sat an algebra test and a geometry test. Each test was marked out of 110
The cumulative frequency graph gives information about the marks gained by the 60 students in the algebra test.
[Diagram or table: see page 18 of the paper]
(a) Use the graph to find an estimate for the median mark in the algebra test.
Answer: ____ [1]
(b) Use the graph to find an estimate for the number of students who gained 58 marks or less in the algebra test.
Answer: ____ [1]
(c) Use the graph to find an estimate for the interquartile range of the marks gained in the algebra test.
Answer: ____ [2]
The interquartile range of the marks gained in the geometry test is 9
Luis says
“The students’ marks are more spread out in the algebra test than in the geometry test.”
(d) Is Luis correct? Give a reason for your answer.
Answer: ____ [1]
To be awarded a grade A in the algebra test, a student had to gain a mark greater than 64
Two students are to be selected at random from the 60 students in the group.
(e) Use the graph to find an estimate for the probability that both of these students were awarded a grade A in the algebra test.
Answer: ____ [3]

Question 15
Make t the subject of n^2  4d  t/t_3
Answer: ____ [4]

Question 16
The diagram shows quadrilateral ABCD
[Diagram or table: see page 21 of the paper]
The angle BCD is acute.
Given that the area of triangle BCD = 405 cm^2
work out the size of angle ABD Give your answer correct to one decimal place.
[Diagram or table: see page 21 of the paper]
Answer: ____ [5]

Question 17
Part of the curve with equation y = f (x) is shown on the grid.
[Diagram or table: see page 22 of the paper]
Find an estimate for the gradient of the curve at the point where x = 2 Show your working clearly.
Answer: ____ [3]

Question 18
The line with equation 2y = x + 1 intersects the curve with equation 3y^2+ 7y + 16 = x^2– x at the points A and B
Find the coordinates of A and the coordinates of B Show clear algebraic working.
Answer: ( ____ , ____ ) and ( ____ , ____ ) [5]

Question 19
ABCD is a horizontal rectangular field.
[Diagram or table: see page 24 of the paper]
A vertical pole, AE, is placed at the corner A of the field.
[Diagram or table: see page 24 of the paper]
Calculate the size of the angle between EC and the plane ABCD Give your answer correct to one decimal place.
[Diagram or table: see page 24 of the paper]
Answer: ____ [3]

Question 20
y is inversely proportional to x x is directly proportional to T^3
Given that y = 8 when T = 25
find the exact value of T when y = 27
Answer: T = ____ [4]

Question 21
The diagram shows a solid made from a cylinder and a hemisphere. The cylinder and the hemisphere are both made from the same metal.
[Diagram or table: see page 26 of the paper]
The plane face of the hemisphere coincides with the upper plane face of the cylinder.
The radius of the cylinder and the radius of the hemisphere are both x cm. The height of the cylinder is 3x cm.
The total surface area of the solid is 81π cm^2 The mass of the solid is 840 grams.
The following table gives the density of each of four metals.
[Diagram or table: see page 26 of the paper]
The metal used to make the solid is one of the metals in the table.
Determine the metal used to make the solid. Show your working clearly.
Answer: ____ [6]

Question 22
ABC is a triangle in which angle ABC = 90°
p and q are integers such that
the coordinates of A are ( p, 10 ) the coordinates of B are ( –1, –5 ) the coordinates of C are ( 8, q )
Given that the gradient of AC is – 6/7
work out the value of p and the value of q
Answer: p = ____
Answer: q = ____ [5]

Question 23
The functions f and g are such that
[Diagram or table: see page 30 of the paper]
The function h is such that h(x) = fg(x)
The domain of h is {x : x  6}
Express the inverse function h^–1 in the form h^–1(x) = ...
Answer: h^–1(x) = ____ [4]