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

Pearson Edexcel International GCSE 4MA1 Mathematics A past paper 1HR, 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-1hr/
- PDF: https://mathvsarham.com/papers/4ma1/4MA1_january_2023_paper_1HR_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International GCSE
- Subject: 4MA1 Mathematics A (https://mathvsarham.com/past-papers/4ma1/)
- Session: January 2023
- Paper: 1HR (Higher Tier Paper 1)
- Component code: 4MA1/1HR
- 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
The table shows information about the frame size, in cm, of 60 bicycles sold in a shop.
[Diagram or table: see page 3 of the paper]
(a) Write down the modal class.
Answer: ____ [1]
(b) Work out an estimate for the mean frame size.
Answer: ____ cm [4]

Question 2
The diagram shows a solid triangular prism.
6 cm
[Diagram or table: see page 4 of the paper]
Work out the total surface area of the triangular prism. Give your answer correct to 3 significant figures.
Answer: ____ cm^2 [3]

Question 3
Here is a list of six numbers written in order of size.
[Diagram or table: see page 5 of the paper]
Find the value of x, the value of y and the value of z
Answer: x = ____
Answer: y = ____
Answer: z = ____ [3]

Question 4
Divya and Yuan each pay for a holiday at a special offer price.
[Diagram or table: see page 6 of the paper]
The amount that Divya pays is the same as the amount that Yuan pays.
Work out the value of k
Answer: k = ____ [4]

Question 5
C grams of chocolate is shared in the ratios 2 : 5 : 8 The difference between the largest share and the smallest share is 390 grams.
Work out the value of C
Answer: C = ____ [3]

Question 6
Solve the simultaneous equations
[Diagram or table: see page 7 of the paper]
Show clear algebraic working.
Answer: x = ____
Answer: y = ____ [3]

Question 7
(a) Write 9.32 × 10^–5 as an ordinary number.
Answer: ____ [1]
(b) Work out 3 × 10^5– 6 × 10^4 Give your answer in standard form.
Answer: ____ [2]
(c) Work out (3 × 10^55) × (6 × 10^65) Give your answer in standard form.
Answer: ____ [2]

Question 8
(a) Factorise fully 18c^3 d^2– 21c^2
Answer: ____ [2]
(b)(i) Factorise y^2– 3y – 18
Answer: ____ [2]
(ii) Hence, solve y^2– 3y – 18 = 0
Answer: ____ [1]

Question 9
The diagram shows an isosceles triangle ABC
[Diagram or table: see page 10 of the paper]
AB = 7 cm AC = BC = ycm
The area of the triangle is 42 cm^2
Work out the value of y
Answer: y = ____ [4]

Question 10
R and T are points on a circle, centre O
[Diagram or table: see page 11 of the paper]
RT = 12 cm M is the midpoint of RT Angle ROM = 52°
Work out the area of the circle. Give your answer correct to 3 significant figures.
Answer: ____ cm^2 [4]

Question 11
The table shows information about the times, in minutes, that 80 patients had to wait to see a doctor.
[Diagram or table: see page 12 of the paper]
(a) Complete the cumulative frequency table below.
[Diagram or table: see page 12 of the paper]
[1]
(b) On the grid opposite, draw a cumulative frequency graph for your table.
[Diagram or table: see page 13 of the paper]
[2]
(c) Use your graph to find an estimate for the median.
Answer: ____ _minutes [1]
(d) Use your graph to find an estimate for the interquartile range.
Answer: ____ _minutes [2]

Question 12
Solve 2^–4^x = 32
Answer: x = ____
[Diagram or table: see page 14 of the paper]
[2]

Question 13
Use algebra to show that 0.381 = 21/55
[Diagram or table: see page 15 of the paper]
[2]

Question 14
T =
p = 0.51 correct to 2 significant figures. r = 6.3 correct to 2 significant figures.
Work out the upper bound for the value of T Show your working clearly.
Answer: ____ [2]

Question 15
(a) Complete the table of values for y = x^3– 3x + 2
[Diagram or table: see page 16 of the paper]
[2]
(b) On the grid, draw the graph of y = x^3– 3x + 2 for values of x from –2 to 2
[Diagram or table: see page 16 of the paper]
[2]
(c) By drawing a suitable straight line on the grid, use your graph to find an estimate for the solution of
[Diagram or table: see page 17 of the paper]
Give your answer correct to one decimal place.
Answer: ____ [3]

Question 16
The function f is such that
[Diagram or table: see page 18 of the paper]
(a) Find f  1/ 3  
Answer: ____ [1]
(b) Find f ^–1(x)
Answer: f ^–1(x) = ____ [2]
The function g is such that
[Diagram or table: see page 18 of the paper]
(c) Express g(x) in the form a(x – b)^2+ c
Answer: ____ [3]

Question 17
[Diagram or table: see page 19 of the paper]
The area of triangle ABC is 12 cm²
Work out the perimeter of triangle ABC Give your answer correct to 3 significant figures.
Answer: ____ cm [5]

Question 18
Solve 3(x – 2 3) = x + 2 3
Give your answer in the form a + b 3 where a and b are integers. Show your working clearly.
Answer: x = ____ [4]

Question 19
P is inversely proportional to y^2 When y = 4, P = a
(a) Find a formula for P in terms of y and a
Answer: ____ [3]
Given also that y is directly proportional to x and when x = a, P = 4a
(b) find a formula for P in terms of x and a
Answer: ____ [3]

Question 20
Here is a sketch of the curve y = a cos(x + b)° for 0  x  360
[Diagram or table: see page 22 of the paper]
Given that 0 < b < 180
find the value of a and the value of b
Answer: a = ____
Answer: b = ____ [2]

Question 21
The diagram shows a triangular prism, ABCDEF, with a rectangular base ABCD
[Diagram or table: see page 23 of the paper]
Work out the angle that BE makes with the plane ABCD Give your answer correct to one decimal place.
[Diagram or table: see page 23 of the paper]
Answer: ____ [4]

Question 22
The diagram shows triangle OAB with OA extended to E
[Diagram or table: see page 24 of the paper]
OA = a OB = b
M is the point on OB such that OM : MB = 4 : 1 N is the point on AB such that AN : NB = 3 : 2 OA : AE = 5 : 3
(a) Find an expression for ON in terms of a and b Give your answer in its simplest form.
[Diagram or table: see page 24 of the paper]
Answer: ON = ____ [2]
(b) Use a vector method to show that MNE is a straight line. [3]

Question 23
G is the point on the curve with equation y = 8x^2– 14x – 6 where the gradient is 10 The straight line Q passes through the point G and is perpendicular to the tangent at G
Find an equation for Q Give your answer in the form ax + by + c = 0 where a, b and c are integers.
Answer: ____ [5]

Question 24
An arithmetic sequence has first term 8 and common difference 11 The sequence has k terms, where k > 21
The sum of the last 20 terms of the sequence is 10 170
Find the value of k Show clear algebraic working.
Answer: k = ____
[Diagram or table: see page 27 of the paper]
[5]