# 4MA1 Mathematics A January 2023 Paper 2H (Higher Tier Paper 2)

Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 2H, Higher Tier Paper 2, January 2023. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/4ma1/2023-january-paper-2h/
- PDF: https://mathvsarham.com/papers/4ma1/4MA1_january_2023_paper_2H_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International GCSE
- Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/)
- Session: January 2023
- Paper: 2H (Higher Tier Paper 2)
- Component code: 4MA1/2H
- 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
Show that 3 5/7 ÷ 1 5/8 = 2 2/7 [3]

Question 2
Change a speed of 90 kilometres per hour to a speed in metres per second. Show your working clearly.
Answer: ____ _m/s [3]

Question 3
ℰ = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
A = {even numbers} A ∩ B = {12, 16, 20} (A ∪ B)ʹ = {17, 19}
Complete the Venn diagram for the sets ℰ, A and B
[Diagram or table: see page 4 of the paper]
[3]

Question 4
The diagram shows rectangle ABCD
[Diagram or table: see page 5 of the paper]
Work out the perimeter of the rectangle. Show your working clearly.
Answer: ____ _cm [4]

Question 5
The weight of a cake is 2.75 kg, correct to 2 decimal places.
(a) Write down the lower bound of the weight of the cake.
Answer: ____ _kg [1]
(b) Write down the upper bound of the weight of the cake.
Answer: ____ _kg [1]
Penny has worked out 81 .3 × 59 .2/1.9_2 on her calculator.
Her answer is 13 332.299 17
Penny’s answer is not sensible.
(c) By rounding each number to one significant figure, work out a suitable estimate to show that her answer is not sensible. Show your working clearly. [2]

Question 6
The points A and B are on a coordinate grid.
The coordinates of A are (6, 4) The coordinates of B are (17, j) where j is a constant.
The midpoint of AB has coordinates (k, 15) where k is a constant.
Find the value of j and the value of k
Answer: j = ____
Answer: k = ____ [3]

Question 7
Solve the simultaneous equations
[Diagram or table: see page 7 of the paper]
Show clear algebraic working.
Answer: x = ____
Answer: y = ____ [3]

Question 8
Matteo is going to invest 5000 Swiss francs for two years.
He can invest his money in Bank G or in Bank H.
[Diagram or table: see page 8 of the paper]
The total amount of interest Matteo would receive at the end of two years from Bank G is more than the amount of interest Matteo would receive at the end of two years from Bank H.
How much more?
Answer: ____ _Swiss_francs [4]

Question 9
(a) Write down the value of (m + 2)^0 where m is a positive integer.
Answer: ____ [1]
(b) Simplify (3a^2 b^4)^3
Answer: ____ [2]
(c) Factorise fully 14x^2 y^4+ 21x^3 y^2
Answer: ____ [2]
The diagram shows a straight line drawn on a grid.
[Diagram or table: see page 9 of the paper]
(d) Write down an equation of the line.
Answer: ____ [2]

Question 10
The diagram shows an isosceles triangle, with base length 24 cm.
[Diagram or table: see page 10 of the paper]
The perimeter of the triangle is 54 cm.
Work out the area of the triangle.
Answer: ____ _cm^2 [5]

Question 11
Here are six graphs.
[Diagram or table: see page 11 of the paper]
Complete the table below with the letter of the graph that could represent each given equation. Write your answers on the dotted lines.
[Diagram or table: see page 11 of the paper]
Answer: ____
[Diagram or table: see page 11 of the paper]
Answer: ____
[Diagram or table: see page 11 of the paper]
Answer: ____ [3]

Question 12
The cumulative frequency graph gives information about the time, in minutes, each of 60 people took to shop in a market.
60
50
40
[Diagram or table: see page 12 of the paper]
(a) Use the graph to find an estimate for the median time people took to shop in the market.
Answer: ____ _minutes [1]
(b) Use the graph to find an estimate for the number of people who took longer than 55 minutes to shop in the market.
Answer: ____ [2]
(c) Use the graph to complete the frequency table to give information about the time, in minutes, each of the 60 people took to shop in the market.
[Diagram or table: see page 13 of the paper]
[2]

Question 13
Solve x + 3/4 − 7 − x/5 = 4.3
Show clear algebraic working.
Answer: x = ____ [3]

Question 14
A, B, C and D are points on a circle, centre O
EBF is the tangent to the circle at B
[Diagram or table: see page 14 of the paper]
(a)(i) Work out the size of angle DCB
[Diagram or table: see page 14 of the paper]
Answer: ____ [1]
(ii) Give a reason for your answer to (a)(i)
Answer: ____ [1]
(b) Work out the size of angle ADO
[Diagram or table: see page 14 of the paper]
Answer: ____ [3]

Question 15
Here is a list giving the numbers of runs scored last week by the eleven members of cricket team A.
[Diagram or table: see page 15 of the paper]
The interquartile range of the numbers of runs scored last week by the eleven members of cricket team B was 42
Using a suitable calculation, write down one comparison between the numbers of runs scored by the members of cricket team A and the members of cricket team B. Show your working clearly.
Answer: ____
[Diagram or table: see page 15 of the paper]
[3]

Question 16
Use algebra to show that 0.43 8 = 217/495 [2]

Question 17
Given that 8 m + 49m − 9m = k m where k is an integer and m is a prime number,
(a) work out the value of k
Answer: k = ____ [1]
(b) Show that 5 −/1 − 18/2 can be written in the form a + b 2
where a and b are integers. Show each stage of your working clearly. [3]

Question 18
The table gives information about the weights, in kg, of the parcels that Pedro delivers on Monday.
[Diagram or table: see page 17 of the paper]
0 < w  2 12
2 < w  3 7
3 < w  6 15
6 < w  9 12
9 < w  14 9
(a) On the grid, draw a histogram for this information.
8
6
[Diagram or table: see page 17 of the paper]
[3]
One of the parcels that Pedro delivered on Monday is chosen at random.
(b) Using the information in the table, find an estimate for the probability that this parcel weighs more than 7 kg.
Answer: ____ [2]

Question 19
A and B are two similar vases.
[Diagram or table: see page 18 of the paper]
The vases are such that
[Diagram or table: see page 18 of the paper]
Calculate the volume of vase B
Answer: ____ _cm^3 [4]

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

Question 21
Given that the surface area of a sphere is 49π cm^2
find the volume of the sphere. Give your answer correct to the nearest integer.
Answer: ____ _cm^3 [3]

Question 22
Solve the inequality 6x^2+ 37x  35 Show clear algebraic working.
Answer: ____ [3]

Question 23
The diagram shows a solid prism ABCDEFGHIJ
[Diagram or table: see page 22 of the paper]
The prism is such that each cross section is a pentagon where
[Diagram or table: see page 22 of the paper]
Given that AG = BH = EF = DJ = CI = 12 cm
calculate the angle that AJ makes with the base ABHG of the prism. Give your answer correct to 3 significant figures.
[Diagram or table: see page 23 of the paper]
Answer: ____ [5]

Question 24
The graph of y = a sin x° + b is drawn on the grid.
[Diagram or table: see page 24 of the paper]
Find the value of a and the value of b
Answer: a = ____
Answer: b = ____ [2]

Question 25
The function f is such that f(x) = 3x^2– 12x + 7 where x  2
Express the inverse function f^–1 in the form f^–1(x) = …
Answer: f ^–1(x) = ____ [4]

Question 26
Find the values of n such that
[Diagram or table: see page 26 of the paper]
Show clear algebraic working.
Answer: ____ [5]