12 markseasy
The nth term of a sequence is given by 5n
Find the difference between the 3rd term and the 4th term of this sequence.
Maths B
October 2025 · Paper 1 (4MB1/01) (Edexcel IGCSE Maths): Exam Questions
Exam code:4MB127 questions · 100 marks · ≈ 2 hours
22 markseasy
Make h the subject of k
2
32 markseasy
Without using a calculator and showing all your working, evaluate
15
2 2
×
6
5
Give your answer as a mixed number in its simplest form.
42 markseasy
1 mark
(a)
Write down the order of rotational symmetry of a regular hexagon.
A shape is made from a regular hexagon and a square.
The vertices of the square lie on the sides of the hexagon.
1 mark
(b)
For this shape, write down the number of lines of symmetry.
52 markseasy
Using ruler and compasses only and showing all your construction lines, construct the
perpendicular bisector of AB
A
B
62 markseasy
The bearing of point P from point Q is 304°
Calculate the bearing of point Q from point P
.......................................................°
72 markseasy
Find the value of pq
q
2
3
when p = 2 and q = –5
p
2
1
82 markseasy
Given that y = x
find d
y
d
x
d
y
= .......................................................
d
x
93 markseasy
1 mark
(a)
Here are eight numbers.
15 30 18 12 23 19 16 23
Write down the mode.
2 marks
(b)
Here are eight numbers.
15 30 18 12 23 19 16 23
Find the median.
103 markseasy
1 mark
(a)
The probability that Charlie arrives late to school is 0.35
Write down the probability that Charlie does not arrive late to school.
Charlie attends school 20 times during January.
2 marks
(b)
The probability that Charlie arrives late to school is 0.35
Calculate the expected number of times that Charlie arrives late to school
during January.
113 marksmedium
A
B
m
7
4
5
6
Find 3A - B
Give each element of the matrix in terms of m where appropriate.
123 marksmedium
A straight line L passes through the points with coordinates (4, 3) and (6, –8)
Find an equation of L in the form y = mx + c
133 marksmedium
Diagram NOT
accurately drawn
O
124
P
R
Q
P, Q and R are three points on a circle, centre O
∠POR = 124°
Calculate the size, in degrees, of ∠PQR
Give reasons for each stage of your working.
∠PQR = .......................................................°
143 marksmedium
N
A
B
Diagram NOT
accurately drawn
M
D
C
The diagram shows a square ABCD
M is the midpoint of AD
N is the midpoint of AB
Prove that DAN is congruent to CDM
153 marksmedium
Without using a calculator and showing all your working, express
11
2
3 2
1
2 where a and b are integers.
in the form a
b
163 markseasy
Write 3x
174 markseasy
2 marks
(a)
Expand and simplify 3c(2 - 5c) - 2c(5c + 1)
5 - 9de
2
2 marks
(b)
Factorise fully 2de
184 marksmedium
x cm
C
D
Diagram NOT
accurately drawn
B
E
6 cm
6 cm
A
F
14 cm
10 cm
10 cm
H
5x cm
G
The diagram shows a shape ABCDEFGH
HG = 5x cm CD = x cm AH = FG = 10 cm AB = EF = 6 cm
∠BAH = ∠AHG = ∠HGF = ∠GFE = 90°
CD is parallel to HG
The perpendicular height of the shape is 14 cm
2
The area of the shape ABCDEFGH is 534 cm
Find the value of x
x = .......................................................
194 marksmedium
Find the two values of x such that
2
x
x
2 81
2
1
x
4
6
x
8
Show clear algebraic working.
x = .......................................................
205 marksmedium
Emma asks 420 students to choose one type of movie from Horror, Adventure
and Comedy.
5% of the students choose Horror.
3
5 of the students choose Adventure.
The remaining students choose Comedy.
The students who choose Comedy are put into either group A or group B
For the students who choose Comedy
number in group A : number in group B = 1 : 6
Calculate the number of students who choose Comedy and are in group B
Show all your working.
215 marksmedium
4 marks
(a)
The table shows information about the number of points scored by people in a game.
Given that the mean number of points scored is 15.6 seconds
calculate the value of x
Show all your working.
x = .......................................................
One of the people is chosen at random.
1 mark
(b)
The table shows information about the number of points scored by people in a game.
Given that the mean number of points scored is 15.6 seconds
Calculate the probability that this person scored more than 16 points.
227 marksmedium
3 marks
(a)
E = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A = {multiples of 4}
B = {factors of 12}
C = {prime numbers}
Complete the Venn diagram for this information showing the position of each of the
numbers in the universal set.
E
B
A
C
1 mark
(b)
E = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A = {multiples of 4}
B = {factors of 12}
C = {prime numbers}
Find n(A′∩ B′ ∩ C′)
1 mark
(c)
E = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A = {multiples of 4}
B = {factors of 12}
C = {prime numbers}
Find n(A ∪ B′)
A number is chosen at random from the universal set, E
2 marks
(d)
E = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A = {multiples of 4}
B = {factors of 12}
C = {prime numbers}
Find the probability that this number is in the set A ∪ C
235 marksmedium
1 mark
(a)
Diagram NOT
accurately drawn
B
A
C
24 cm
The diagram shows a semicircle with diameter 24 cm
The diagram also shows three congruent circles A, B and C inside the semicircle.
All three circles touch the circumference of the semicircle and circle B touches both
circle A and circle C
The diameter of the semicircle is a tangent to circle A and circle C
The radius of each of the circles is r cm
Show that r = 4
2 to 3 significant figures, of the shaded region.
4 marks
(b)
Diagram NOT
accurately drawn
B
A
C
24 cm
The diagram shows a semicircle with diameter 24 cm
The diagram also shows three congruent circles A, B and C inside the semicircle.
All three circles touch the circumference of the semicircle and circle B touches both
circle A and circle C
The diameter of the semicircle is a tangent to circle A and circle C
The radius of each of the circles is r cm
Calculate the total area, in cm
2
....................................................... cm
245 marksmedium
Express
as a single fraction in its simplest form.
x
x
x
x
x
2
2
3
2
1
2
1
Show clear algebraic working.
256 marksmedium
5 cm
The diagram shows a solid shape made by fixing the flat circular face of a solid
hemisphere, with radius 5 cm, to a solid right circular cone with base radius 5 cm
The centre of the circular face of the hemisphere coincides with the centre of the base of
the cone.
550
3
3 cm
The total volume of the solid is
2 to 3 significant figures, of the solid.
Find the total surface area, in cm
Show all your working.
2
....................................................... cm
268 markshard
1 mark
(a)
Diagram NOT
D
accurately drawn
B
P
A
C
O
The diagram shows a quadrilateral OABC
→ = 2a OC
→ = 3b AB
→ = a + 2b
OA
The point P is on the line CB such that CP : PB = 4 : 1
The point D is such that ABD and OPD are straight lines.
→ in terms of a and b
Find AC
→ = .......................................................
AC
→ in terms of a and b
2 marks
(b)
Diagram NOT
D
accurately drawn
B
P
A
C
O
The diagram shows a quadrilateral OABC
→ = 2a OC
→ = 3b AB
→ = a + 2b
OA
The point P is on the line CB such that CP : PB = 4 : 1
The point D is such that ABD and OPD are straight lines.
→ in terms of a and b
Find OP
Give your answer in its simplest form.
→ = .......................................................
OP
5 marks
(c)
Diagram NOT
D
accurately drawn
B
P
A
C
O
The diagram shows a quadrilateral OABC
→ = 2a OC
→ = 3b AB
→ = a + 2b
OA
The point P is on the line CB such that CP : PB = 4 : 1
The point D is such that ABD and OPD are straight lines.
→ in terms of a and b
Using a vector method find the ratio OP : PD
Show all your working.
277 marksmedium
2 marks
(a)
(2x - 1) is a factor of 6x
Use the factor theorem to show that a = 6
3 + 17x
2 + 6x - 8
3 marks
(b)
(2x - 1) is a factor of 6x
Hence, factorise fully 6x
Show all your working.
3 + 17(3y + 1)
2 + 6(3y + 1) - 8 = 0
2 marks
(c)
(2x - 1) is a factor of 6x
Hence, solve 6(3y + 1)
Show all your working.
y = .......................................................