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

Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 2HR, 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-2hr/
- PDF: https://mathvsarham.com/papers/4ma1/4MA1_january_2023_paper_2HR_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International GCSE
- Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/)
- Session: January 2023
- 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
Show that 4 2/3 ÷ 1 5/6 = 2 6/11 [3]

Question 2
[Diagram or table: see page 4 of the paper]
(a) On the grid, rotate triangle A 180° about (1, –1) Label the new triangle B [2]
(b) On the grid, translate triangle A by the vector  −7/
Label the new triangle C [1]

Question 3
–8 < 2y  2
y is an integer.
(a) Find all the possible values of y
Answer: ____ [2]
(b) Write down the inequality shown on the number line.
[Diagram or table: see page 5 of the paper]
Answer: ____ [1]

Question 4
Using ruler and compasses only, construct the bisector of angle BAC You must show all your construction lines.
[Diagram or table: see page 5 of the paper]
[2]

Question 5
On the grid, draw the graph of 5x + 2y = 10 for values of x from –2 to 4
[Diagram or table: see page 6 of the paper]
[3]

Question 6
In a bag, there are only red counters, blue counters, green counters and yellow counters.
The total number of counters in the bag is 80
In the bag
the number of red counters is x + 7 the number of blue counters is x – 11 the number of green counters is 3x
Jude takes at random a counter from the bag.
The probability that he takes a red counter is 1/4
Work out the probability that Jude takes a yellow counter.
Answer: ____ [4]

Question 7
(a) Find the highest common factor (HCF) of 200 and 420
Answer: ____ [2]
A = 2^3 × 3 × 5 ×7^2 B = 2 × 3^2 × 7 C = 3 × 5^2 × 11
(b) Find the lowest common multiple (LCM) of A, B and C Write your answer as a product of powers of prime factors.
Answer: ____ [2]

Question 8
60 students sat a Mathematics exam.
The mean mark for the 32 students in Class A was 55 The mean mark for the 28 students in Class B was 52
Find the mean mark for all 60 students.
Answer: ____ [3]

Question 9
Teresa invests $2000 for 3 years in a savings account. She gets 4% each year compound interest.
(a) How much money will Teresa have in her savings account at the end of 3 years? Give your answer correct to the nearest dollar.
Answer: $ ____ [3]
Sam invested $T The value of his investment decreased by 9% each year.
At the end of the first year, the value of Sam’s investment was $1365
(b) Work out the value of T
Answer: ____ [3]

Question 10
The diagram shows two solids, A and B, made from two different metals.
[Diagram or table: see page 11 of the paper]
Solid A is in the shape of a cylinder with radius 3 cm and height 7 cm Solid A has a mass of 2000 g
Solid B has a mass of 3375 g Solid B has a volume of 450 cm^3
All of the metal from Solid A and Solid B is melted down to make a uniform Solid C
Given that there is no change to mass or volume during this process
work out the density of Solid C Give your answer correct to one decimal place.
Answer: ____ _g / cm^3 [3]

Question 11
A
[Diagram or table: see page 12 of the paper]
AB, BC, CD, DE and EF are five sides of a regular polygon.
RST, SCU and BCV are straight lines. RST is parallel to CD Angle RSC = 128° Angle UCV = 32°
Work out how many sides the polygon has. Show your working clearly.
Answer: ____ [4]

Question 12
(a) Simplify 2/y_0
Answer: ____ [1]
(b) Simplify fully (16a^4 )^3/4
Answer: ____ [2]
(c) Expand and simplify 5x(3x + 4)(2x – 1)
Answer: ____ [3]

Question 13
A rectangle has length L and width W
L is increased by 20% W is decreased by 35%
Calculate the percentage reduction in the area of the rectangle.
Answer: ____ % [3]

Question 14
A, B and C are points on a circle, centre O
B
[Diagram or table: see page 15 of the paper]
The radius of the circle is 8.5 cm Angle ABC = 132°
Work out the perimeter of the shaded sector AOC Give your answer correct to 3 significant figures.
Answer: ____ _cm [3]

Question 15
Here are the numbers of aces that Rutger served in each of 11 tennis matches.
[Diagram or table: see page 16 of the paper]
(a) Find the interquartile range of the numbers of aces. Show your working clearly.
Answer: ____ [2]
Kim also plays in 11 tennis matches.
For Kim the median number of aces is 11 the interquartile range of the numbers of aces is 5
(b) State, giving a reason, whether Rutger or Kim
(i) served more aces on average,
Answer: ____ [1]
(ii) was more consistent with the number of aces served.
Answer: ____ [1]

Question 16
Here are two vectors.
[Diagram or table: see page 17 of the paper]
Find AC as a column vector.
[Diagram or table: see page 17 of the paper]
Answer: ____
Answer: ____ [2]

Question 17
The table gives information about the time taken by each student in Year 11 to complete a homework task.
[Diagram or table: see page 18 of the paper]
(a) On the grid, draw a histogram for this information.
[Diagram or table: see page 18 of the paper]
[3]
One of these students who took 50 minutes or less and more than 25 minutes to complete this homework task is chosen at random.
(b) Find an estimate for the probability that this student took 45 minutes or less to complete this homework task.
Answer: ____ [2]

Question 18
A statue and a model of the statue are mathematically similar.
The statue has a total surface area of 3600 cm^2 The model has a total surface area of 625 cm^2
The volume of the model is 750 cm^3
Work out the volume of the statue.
Answer: ____ _cm^3 [3]

Question 19
Prove algebraically that, for any three consecutive even numbers,
the sum of the squares of the smallest even number and the largest even number is 8 more than twice the square of the middle even number. [3]

Question 20
A, B and C are three sets.
n(A ∩ B ∩ C ) = 5
n(A ∩ B ∩ C ′) = 2
n(A ∩ C ) = 5
n(A) = 17
n([A ∪ B ∪ C ] ) = 3
n(A′ ∩ B ∩ C ′) = 6
n(B ∩ C ) = 7
n(C ) = 14
Complete the Venn diagram to show the number of elements in each region.
[Diagram or table: see page 21 of the paper]
Answer: ____
Answer: ____
Answer: ____
Answer: C ____ [4]

Question 21
The diagram shows the graph of y = f(x)
[Diagram or table: see page 22 of the paper]
The point P has x coordinate –2
Use the graph to find an estimate for the gradient of the curve at P
Answer: ____ [3]

Question 22
Solve the simultaneous equations
[Diagram or table: see page 23 of the paper]
Show clear algebraic working.
Answer: ____ [5]

Question 23
AEC and BED are chords of a circle.
[Diagram or table: see page 24 of the paper]
Angle DAE = 48°
Work out the size of angle ADE Give your answer correct to one decimal place.
[Diagram or table: see page 25 of the paper]
Answer: ____ [5]

Question 24
The diagram shows a solid cone and a solid sphere.
[Diagram or table: see page 26 of the paper]
The cone has base radius r, slant height l and perpendicular height h The sphere has radius r
The base radius of the cone is equal to the radius of the sphere.
Given that
[Diagram or table: see page 26 of the paper]
show that the total surface area of the cone can be written in the form
[Diagram or table: see page 26 of the paper]
where a is a constant to be found. [6]

Question 25
ABCD is a trapezium with AB parallel to DC
A is the point with coordinates (–4, 6) B is the point with coordinates (2, 3) D is the point with coordinates (–1, 8)
The trapezium has one line of symmetry. The line of symmetry intersects CD at the point E
Work out the coordinates of the point E
Answer: ( ____ , ____ ) [6]

Question 26
Write
[Diagram or table: see page 30 of the paper]
as a single fraction in its simplest form.
Answer: ____ [4]