# 4MA1 Mathematics A January 2023 Paper 1H (Higher Tier Paper 1)

Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 1H, Higher Tier Paper 1, January 2023. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/4ma1/2023-january-paper-1h/
- PDF: https://mathvsarham.com/papers/4ma1/4MA1_january_2023_paper_1H_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International GCSE
- Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/)
- Session: January 2023
- Paper: 1H (Higher Tier Paper 1)
- Component code: 4MA1/1H
- 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
80 students entered a dancing competition.
The table gives information about the length of time, in minutes, for which each student spent dancing.
[Diagram or table: see page 3 of the paper]
12 < m  24 25
24 < m  36 23
36 < m  48 15
48 < m  60 6
Work out an estimate for the mean length of time the students spent dancing.
Answer: ____ _minutes [4]

Question 2
Solve 3(2 – 4x) = 5 – 8x Show clear algebraic working.
Answer: x = ____ [3]

Question 3
Use ruler and compasses only to construct the perpendicular bisector of line AB You must show all your construction lines.
[Diagram or table: see page 5 of the paper]
[2]

Question 4
The diagram shows a pentagon.
[Diagram or table: see page 6 of the paper]
Work out the value of x
Answer: x = ____ [3]

Question 5
In a box, there are only green sweets, orange sweets and yellow sweets.
There are 280 sweets in the box so that
the number of green sweets : the number of orange sweets = 2 : 3 and the number of orange sweets : the number of yellow sweets = 1 : 5
Work out how many green sweets there are in the box.
Answer: ____ [3]

Question 6
Shane bought a car.
The amount Shane paid for the car was $32 000
Theresa also bought a car. To pay for this car, Theresa paid a deposit of $18 000 together with 14 monthly payments of $1160
Theresa paid more for her car than Shane paid for his car.
(a) Work out how much more Theresa paid as a percentage of the amount Shane paid.
Answer: ____ % [4]
Kylie bought a van.
After 1 year, the value of the van was $39 865 During this year, the value of the van decreased by 15%
(b) Work out the value of the van when Kylie bought it.
Answer: $ ____ [3]

Question 7
Some members of a library were asked to name the type of book that they each liked to read the best.
One of the members is chosen at random. The table shows information about the probability of the type of book that this member answered.
[Diagram or table: see page 9 of the paper]
48 members answered comedy books.
Work out how many of the members answered mystery books.
Answer: ____ [4]

Question 8
The diagram shows a triangle ABC inside a semicircle.
[Diagram or table: see page 10 of the paper]
A, B and C are points on the semicircle.
AB is the diameter of the semicircle.
Angle ACB = 90° Angle BAC = 50° AC = 18 cm
Work out the perimeter of the semicircle. Give your answer correct to 2 significant figures.
Answer: ____ cm [5]

Question 9
(a) Write 6.25 × 10^−4 as an ordinary number.
Answer: ____ [1]
(b) Work out (2.4 × 10^12) ÷ (9.6 × 10^4) Give your answer in standard form.
Answer: ____ [2]

Question 10
(a) Factorise y^2– 2y – 48
Answer: ____ [2]
(b) Write down the inequality shown on the number line
[Diagram or table: see page 12 of the paper]
Answer: ____ [1]
(c) Solve the inequality 7w + 6 > 12w + 14
Answer: ____ [3]

Question 11
[Diagram or table: see page 13 of the paper]
The region R, shown shaded in the diagram, is bounded by the straight lines with equations
[Diagram or table: see page 13 of the paper]
3y + 2x = 4
Write down the three inequalities that define R
Answer: ____ [3]

Question 12
3^1/2 × 3^2/5 = 3^m
(a) Work out the value of m
Answer: m = ____ [1]
5^–10÷ 5^–^4= 5^n
(b) Work out the value of n
Answer: n = ____ [1]

Question 13
Expand and simplify 3x(2x – 5)^2 Show clear algebraic working.
Answer: ____ [3]

Question 14
(a) Complete the table of values for y  2 /x  5  1 /x 
[Diagram or table: see page 15 of the paper]
[1]
(b) On the grid, draw the graph of y  2 /x  5  1 /x  for 0.5  x  5
[Diagram or table: see page 15 of the paper]
[2]

Question 15
Here are 9 cards. Each card has either a number on it or a letter on it.
[Diagram or table: see page 16 of the paper]
Tomas is playing a game.
Tomas takes at random one of the cards and keeps it.
Tomas then takes at random another card and keeps it.
(a) Complete the probability tree diagram.
[Diagram or table: see page 16 of the paper]
Answer: ____
[Diagram or table: see page 16 of the paper]
Answer: ____
Answer: ____ letter
[Diagram or table: see page 16 of the paper]
Answer: ____
Answer: ____ letter
Answer: ____ letter [2]
(b) Work out the probability that each of the two cards has a number on it.
Answer: ____ [2]
(c) Work out the probability that there will be one card with a number on it and one card with a letter on it.
Answer: ____ [3]

Question 16
Here is a shape formed from two triangles ABC and CDE ACD and BCE are straight lines.
[Diagram or table: see page 18 of the paper]
AC = 24 cm BC = 31 cm CE = 19 cm CD = 16 cm
Angle BAC = 64°
Work out the length of DE Give your answer correct to 3 significant figures.
Answer: ____ cm [5]

Question 17
y is inversely proportional to x
y = c^4 when x = c^2 where c is a positive constant.
Find a formula for y in terms of x and c Give your answer in its simplest form.
Answer: ____ [3]

Question 18
The function f is such that f(x) = k/x where x ≠ 0 and k is an integer.
(a) Express the inverse function f^−1 in the form f^−1(x) = ...
Answer: f^−1(x) = ____ [1]
The function g is such that g(x) = 2 – 3x^4 where x ≠ 0
The function h is such that h(x) = 3x/2 − x where x ≠ 2
(b)(i) Find g(−2)
Answer: ____ [1]
(ii) Express the composite function hg in the form hg(x) = ... Give your answer in its simplest form.
Answer: hg(x) = ____ [2]

Question 19
The acceleration, a, of an object is given by
[Diagram or table: see page 21 of the paper]
v = 45.23 correct to 2 decimal places u = 5.12 correct to 2 decimal places t = 8.5 correct to 2 significant figures
By considering bounds, work out the value of a to a suitable degree of accuracy. Show your working clearly and give a reason for your answer.
Answer: a = ____ [5]

Question 20
The radius of a right circular cylinder is x cm.
The height of the cylinder is  800/π x − x cm.
The volume of the cylinder is V cm^3
Find the maximum value of V Give your answer correct to the nearest whole number.
Answer: ____ [5]

Question 21
The diagram shows the cross section of a circular water pipe.
[Diagram or table: see page 24 of the paper]
OABC is a sector of the circle, centre O
The shaded region in the diagram represents the water flowing in the pipe.
The water flows at 14 cm/s in the pipe.
Work out the volume of water that has flowed through the pipe in 3 minutes. Give your answer in cm^3 correct to 3 significant figures.
Answer: ____ cm^3 [5]

Question 22
The first term of an arithmetic series is (2t + 1) where t > 0 The nth term of this arithmetic series is (14t – 5)
The common difference of the series is 3
The sum of the first n terms of the series can be written as p(qt – 1)^r where p, q and r are integers.
Find the value of p, the value of q and the value of r Show clear algebraic working.
Answer: p = ____ q = ____ r = ____ [4]

Question 23
ABCD is a kite.
AB = AD and CB = CD
The point B has coordinates (k, 1) where k is a negative constant. The point D has coordinates (8, 7)
The straight line L passes through the points B and D
The straight line L is parallel to the line with equation 5y – 3x = 6
Find an equation of AC Give your answer in the form px + qy = r where p, q and r are integers. Show your working clearly.
Answer: ____ [6]

Question 24
OAED is a quadrilateral.
[Diagram or table: see page 30 of the paper]
OA = 2a OB = 2b DE = 7a + 3b
AB : BD = 1 : 2
The point C on AB is such that OCE is a straight line.
Use a vector method to find the ratio of OC : CE
Answer: ____ [5]