# 4MA1 Mathematics A January 2022 Paper 1H (Higher Tier Paper 1)

Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 1H, Higher Tier Paper 1, January 2022. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/4ma1/2022-january-paper-1h/
- PDF: https://mathvsarham.com/papers/4ma1/4MA1_january_2022_paper_1H_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International GCSE
- Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/)
- Session: January 2022
- Paper: 1H (Higher Tier Paper 1)
- Component code: 4MA1/1H
- Time allowed: 120 minutes
- Total marks: 100
- Pages: 28

## Question paper text

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

Question 1
(a) Simplify a^7 × a^4
Answer: ____ [1]
(b) Simplify w^15÷ w^3
Answer: ____ [1]
(c) Simplify (8x^5 y^3)^2
Answer: ____ [2]
(d) Make t the subject of c = t^3 – 8v
Answer: ____ [2]

Question 2
Danil, Gabriel and Hadley share some money in the ratios 3 : 5 : 9 The difference between the amount of money that Gabriel receives and the amount of money that Hadley receives is 196 euros.
Work out the amount of money that Danil receives.
Answer: ____ _euros [3]

Question 3
The diagram shows triangle ABC
[Diagram or table: see page 4 of the paper]
Work out the length of the side AB Give your answer correct to 3 significant figures.
Answer: ____ _cm [3]

Question 4
Sarah makes and sells mugs.
One day she makes 150 mugs. Her total cost for making these mugs is £1140
Of these mugs
[Diagram or table: see page 5 of the paper]
and the rest are large mugs
Here is Sarah’s price list for selling each mug.
[Diagram or table: see page 5 of the paper]
Sarah sells all 150 mugs.
Work out her percentage profit. Give your answer correct to the nearest whole number.
Answer: ____ % [5]

Question 5
Jenny has six cards.
Each card has a whole number written on it so that
the smallest number is 5 the largest number is 24 the median of the six numbers is 14 the mode of the six numbers is 8
Jenny arranges her cards so that the numbers are in order of size.
5 24
Answer: ____
(a) For the remaining four cards, write on each dotted line a number that could be on the card. [3]
A basketball team plays 6 games. After playing 5 games, the team has a mean score of 21 points per game. After playing 6 games, the team has a mean score of 23 points per game.
(b) Work out the number of points the team scored in its 6th game.
Answer: ____ [3]

Question 6
(a) Solve the inequality 5x – 7  2
Answer: ____ [2]
(b)(i) Factorise y^2– 2y – 35
Answer: ____ [2]
(ii) Hence, solve y^2– 2y – 35 = 0
Answer: ____ [1]

Question 7
[Diagram or table: see page 8 of the paper]
A ∩ B = {5, 10, 15}
B¢ = {7, 8, 9, 11, 12, 13, 14}
A¢ = {4, 6, 7, 8, 14}
Complete the Venn diagram for this information.
[Diagram or table: see page 8 of the paper]
[3]

Question 8
[Diagram or table: see page 8 of the paper]
Work out the value of a × b Give your answer in standard form.
Answer: ____ [2]

Question 9
The diagram shows isosceles triangle ABC
[Diagram or table: see page 9 of the paper]
AB = AC = 17.5 cm BC = 28 cm
Calculate the area of triangle ABC
Answer: ____ _cm^2 [4]

Question 10
The straight line L has equation 2y + 7x = 10
(a) Find the gradient of L
Answer: ____ [2]
(b) Find the coordinates of the point where L crosses the y‑axis.
Answer: ( ____ , ____ ) [1]

Question 11
Himari invests 200 000 yen for 3 years in a savings account paying compound interest.
The rate of interest is 1.8% for the first year and x% for each of the second year and the third year.
The value of the investment at the end of the third year is 209 754 yen.
Work out the value of x Give your answer correct to one decimal place.
Answer: x = ____ [3]

Question 12
The table gives information about the times, in minutes, taken by 80 customers to do their shopping in a supermarket.
Time taken (t minutes) Frequency
[Diagram or table: see page 12 of the paper]
(a) Complete the cumulative frequency table.
[Diagram or table: see page 12 of the paper]
Time taken (t minutes) frequency
[Diagram or table: see page 12 of the paper]
[1]
(b) On the grid opposite, draw a cumulative frequency graph for your table.
80
70
60
50
[Diagram or table: see page 13 of the paper]
[2]
(c) Use your graph to find an estimate for the median time taken.
Answer: ____ _minutes [1]
One of the 80 customers is chosen at random.
(d) Use your graph to find an estimate for the probability that the time taken by this customer was more than 42 minutes.
Answer: ____ [2]

Question 13
(a) Expand and simplify 5x(x + 2)(3x – 4)
Answer: ____ [3]
(b) Simplify completely
[Diagram or table: see page 14 of the paper]
Answer: ____ [3]

Question 14
Aika has 2 packets of seeds, packet A and packet B
There are 12 seeds in packet A and 7 of these are sunflower seeds. There are 15 seeds in packet B and 8 of these are sunflower seeds.
Aika is going to take at random a seed from packet A and a seed from packet B
(a) Complete the probability tree diagram.
[Diagram or table: see page 15 of the paper]
Answer: ____
[Diagram or table: see page 15 of the paper]
Answer: ____
[Diagram or table: see page 15 of the paper]
Answer: ____
[Diagram or table: see page 15 of the paper]
Answer: ____
[Diagram or table: see page 15 of the paper]
[2]
(b) Calculate the probability that Aika will take two sunflower seeds.
Answer: ____ [2]

Question 15
A is inversely proportional to C^2
A = 40 when C = 1.5
Calculate the value of C when A = 1000
Answer: C = ____ [3]

Question 16
The diagram shows a circle with centre O
[Diagram or table: see page 17 of the paper]
A, B and C are points on the circle so that the length of the arc ABC is 5 cm.
Given that angle AOC = 55°
work out the area of the circle. Give your answer correct to one decimal place.
Answer: ____ cm^2 [4]

Question 17
A and B are two similar vases.
[Diagram or table: see page 18 of the paper]
Vase A has height 10 cm. Vase B has height 15 cm.
The difference between the volume of vase A and the volume of vase B is 1197 cm^3
Calculate the volume of vase A
Answer: ____ cm^3
[Diagram or table: see page 19 of the paper]
[4]

Question 18
A = w – y
w = 3.45 correct to 2 decimal places. x = 1.9 correct to 1 decimal place. y = 5 correct to the nearest whole number.
Work out the lower bound of the value of A Show your working clearly.
Answer: ____ [3]

Question 19
Solve the simultaneous equations
[Diagram or table: see page 20 of the paper]
Show clear algebraic working.
Answer: ____ [5]

Question 20
(a) Express 7 + 12x – 3x^2 in the form a + b(x + c)^2 where a, b and c are integers.
Answer: ____ [3]
C is the curve with equation y = 7 + 12x – 3x^2 The point A is the maximum point on C
(b) Use your answer to part (a) to write down the coordinates of A
Answer: ( ____ , ____ ) [1]

Question 21
The diagram shows the prism ABCDEFGHJK with horizontal base AEFG
[Diagram or table: see page 22 of the paper]
ABCDE is a cross section of the prism where ABDE is a square BCD is an equilateral triangle
EF = 2 × AE M is the midpoint of GF so that JM is vertical.
Angle MAJ = y°
Given that tan y° = T
[Diagram or table: see page 22 of the paper]
are integers.
Answer: T = ____ [5]

Question 22
The diagram shows triangle OAB
[Diagram or table: see page 24 of the paper]
OA = 8a OB = 6b
M is the point on OB such that OM : MB = 1 : 2 N is the midpoint of AB P is the point of intersection of ON and AM
Using a vector method, find OP as a simplified expression in terms of a and b Show your working clearly.
[Diagram or table: see page 25 of the paper]
Answer: OP = ____ [5]

Question 23
The diagram shows a sketch of the curve with equation y = f(x)
[Diagram or table: see page 26 of the paper]
There is only one maximum point on the curve. The coordinates of this maximum point are (5, 7)
Write down the coordinates of the maximum point on the curve with equation
(i) y = f(x + 9)
Answer: ( ____ , ____ )
(ii) y = f(x) + 3
Answer: ( ____ , ____ ) [2]

Question 24
The curve C has equation y = ax^3+ bx^2– 12x + 6 where a and b are constants.
The point A with coordinates (2, –6) lies on C The gradient of the curve at A is 16
Find the y coordinate of the point on the curve whose x coordinate is 3 Show clear algebraic working.
Answer: y = ____ [6]