12 markseasy
Find the Lowest Common Multiple (LCM) of 180 and 198
Show your working clearly.
Maths B
January 2022 · Paper 1 (4MB1/01) (Edexcel IGCSE Maths): Exam Questions
Exam code:4MB127 questions · 100 marks · ≈ 2 hours
22 markseasy
Factorise fully 6 p3 q5 r − 15 pq3
32 markseasy
Find the value of 11
2
2
when a = − 2 and b = −3
b
42 markseasy
A
Diagram NOT
accurately drawn
15 cm
C
B
8 cm
The diagram shows the right-angled triangle in which
AB = 15 cm BC = 8 cm ∠ ACB = 90°
Calculate the size, in degrees to 3 significant figures, of ∠ ABC
∠ ABC = .......................................................°
52 markseasy
4
3
2
5
A =
B =
−
−
2
2
2
5
Calculate 4A − 3B
63 markseasy
1 mark
(a)
The nth term of a sequence is given by 3n − 5
Write down the first two terms of this sequence.
......................................... , .........................................
The mth term of this sequence is 103
2 marks
(b)
The nth term of a sequence is given by 3n − 5
Find the value of m
m = .......................................................
73 markseasy
A straight line L passes through the points with coordinates (4, 8) and (0, −6)
Find an equation of L
Give your answer in the form y = mx + c
83 markseasy
A
Diagram NOT
accurately drawn
6.5 cm
55°
O
B
OAB is a sector of a circle, centre O and radius 6.5 cm
∠ AOB = 55°
Calculate the perimeter, in cm to 3 significant figures, of the sector OAB
....................................................... cm
93 markseasy
Simplify 25
4
2
2
x
25
3
103 marksmedium
A
B
Diagram NOT
accurately drawn
D
C
In the diagram, triangles ABC and ABD are such that
AD = BC and ∠ BAD = ∠ ABC
Prove that AC = BD
113 marksmedium
24 cm
18 cm
A solid is made by joining a hemisphere, of diameter 18 cm, to a right circular cone whose
base has a diameter of 18 cm. The height of the cone is 24 cm.
The plane face of the cone coincides with the plane face of the hemisphere.
Calculate the volume, in cm³, of the solid.
Give your answer in terms of
....................................................... cm³
123 marksmedium
Given that y =
where x ≠ 0
x
find d
y
d
x
d
y
x = .......................................................
d
133 marksmedium
Without using a calculator and showing your working clearly, express
432 −
147
in the form
n where n is an integer.
143 marksmedium
A and B are two similar solids.
The volume of A is 500 cm³
The volume of B is 32 cm³
The total surface area of A is 250 cm²
Calculate the total surface area, in cm², of B.
....................................................... cm²
154 marksmedium
3 marks
(a)
The table gives information about the weights, in grams, of 40 adult mice.
Calculate an estimate for the mean weight, in grams to 3 significant figures, of these adult mice.
....................................................... grams
One of these adult mice is selected at random.
1 mark
(b)
The table gives information about the weights, in grams, of 40 adult mice.
Find the probability that this mouse weighs less than 22 grams.
164 marksmedium
1 mark
(a)
Andrew borrowed some money from Sarah.
He borrowed $21 250 on 1st January 2018
On 31st December each year, starting on 31st December 2018, Sarah charged Andrew
interest of 4% on the amount of money that he owed her. This interest was added to the
amount of money that Andrew owed Sarah.
On 1st January each year, starting on 1st January 2019, Andrew repaid $4000 to Sarah.
Show that before Andrew had repaid $4000 to Sarah on 1st January 2019, he owed
Sarah $22 100
After Andrew had repaid $4000 to Sarah on 1st January 2020,
3 marks
(b)
Andrew borrowed some money from Sarah.
He borrowed $21 250 on 1st January 2018
On 31st December each year, starting on 31st December 2018, Sarah charged Andrew
interest of 4% on the amount of money that he owed her. This interest was added to the
amount of money that Andrew owed Sarah.
On 1st January each year, starting on 1st January 2019, Andrew repaid $4000 to Sarah.
calculate how much money Andrew now owed Sarah.
$.......................................................
174 marksmedium
A
B
fountain
D
C
Scale: 1 cm represents 1 m
The diagram shows a scale drawing of a garden in the shape of the rectangle ABCD.
The position of a fountain in the garden is marked by a cross.
Tarik is going to plant a tree in the garden.
The tree must be
less than 2 metres from AB,
greater than 3 metres from the fountain,
closer to AB than to AC.
Using ruler and compasses only and showing all your construction lines, construct and
show by shading the region in which Tarik can plant the tree. Label the region R.
184 marksmedium
5 cm
Diagram NOT
A
B
accurately drawn
D
C
9 cm
The diagram shows a trapezium ABCD.
∠ ABC = ∠ BCD = 90°
AB = 5 cm
DC = 9 cm
The area of the trapezium ABCD is 29.4 cm²
Calculate the length, in cm, of AD.
....................................................... cm
194 marksmedium
The sum of the interior angles of a regular polygon is 8280°
Calculate the size, in degrees, of each exterior angle of the regular polygon.
.......................................................°
204 marksmedium
The numbers p and q are positive such that p is inversely proportional to
p = 420 when q = 9
Calculate the value of q when p = 28
q = .......................................................
214 marksmedium
a cm
A cm²
C °
b cm
The diagram shows a triangle of area A cm² in which
a = 5.2 to 1 decimal place
b = 8.4 to 1 decimal place
A = 13 to 2 significant figures.
Given that the angle marked C ° is an acute angle,
calculate the lower bound, to 3 significant figures, of C.
224 marksmedium
Express
÷
−
as a single fraction in its simplest form.
x
x
x
x
−
−
6
7
10
5
1
2
2
Show clear algebraic working.
236 marksmedium
3 marks
(a)
A bag contains 20 balls. Each ball has either the number 5 on it or the number 6 on it.
5
6
There are 12 balls with the number 5
There are 8 balls with the number 6
Ben takes at random 2 balls from the bag.
Complete the probability tree diagram.
First ball
Second ball
5
5
12
20
6
5
6
6
3 marks
(b)
A bag contains 20 balls. Each ball has either the number 5 on it or the number 6 on it.
5
6
There are 12 balls with the number 5
There are 8 balls with the number 6
Ben takes at random 2 balls from the bag.
Calculate the probability that the sum of the numbers on the two balls is greater than 10
Give your answer as a fraction.
245 marksmedium
The two digit number M has tens digit p and units digit q
The two digit number N has tens digit q and units digit p
Given that N − M = 9 and that p + q = 13
find the value of M
Show clear algebraic working.
M = .......................................................
256 marksmedium
By writing 8x2 − 56x + 17 in the form p(x + q)2 + r find the exact solutions of the equation
8x2 − 56x + 17 = 0
2 where a, b and c are integers.
Give your answer in the form a
b
±
c
Show your working clearly.
x = .......................................................
267 markshard
V
A
O
B
M
C
The diagram shows a solid pyramid with a triangular base ABC, which is an equilateral
triangle of side 8 3 cm.
The base of the pyramid is on a horizontal surface and the vertex V of the pyramid is
vertically above the point O of the base.
The edges AV, BV and CV of the pyramid are the same length and O lies on AM, where
M is the midpoint of CB and AO : OM = 2 : 1
Given that the total surface area of the pyramid is 150 3 cm²,
find the length, in cm, of VO.
....................................................... cm
277 marksmedium
Egan cycled 168 km at an average speed of x km/h,
Rohan cycled the 168 km at an average speed that was 2 km/h less than Egan’s average speed.
Given that it took Rohan 12 minutes longer than Egan to cycle the 168 km,
calculate the value of x
x = .......................................................