12 markseasy
The nth term of a sequence is given by 6
n −
5
2
Find the difference between the 2nd term and the 4th term of the sequence.
Maths B
January 2023 · Paper 1 (4MB1/01) (Edexcel IGCSE Maths): Exam Questions
Exam code:4MB126 questions · 100 marks · ≈ 2 hours
22 markseasy
Find the Highest Common Factor (HCF) of 60 and 165
Show your working clearly.
32 markseasy
Factorise fully 6
30
2
42 markseasy
Without using a calculator and showing all your working, calculate
4 1
2 1
÷
3
2
Give your answer as a mixed number in its simplest form.
52 markseasy
Solve the inequality 5
x
x
3
15
62 markseasy
Calculate 4 2
.
10
5 5
.
10
72
75
Give your answer in standard form.
73 marksmedium
The price of a holiday is reduced by 4% in a sale.
Haniya pays $600 of the sale price when she books the holiday.
She pays the remainder of the sale price in 4 equal monthly payments of $180
Calculate the price of the holiday before the sale.
$.............................................................................................
83 marksmedium
The straight line L1 has equation y + 4x = 5
The straight line L2 is parallel to L1 and passes through the point (2, ‒6)
Find the equation for L2 in the form y = mx + c
93 marksmedium
y
x
Quadrilateral A and quadrilateral B are drawn on a grid.
Quadrilateral B is the image of quadrilateral A under a single transformation.
Describe fully this single transformation.
103 marksmedium
Without using a calculator and showing your working clearly, find the value of the
integer a so that
a
2 300
108
a = .............................................................................................
114 marksmedium
1 mark
(a)
Write down the value of a0 where a > 0
1 mark
(b)
Simplify fully 2
w
w
×
11
2
5
3
2 marks
(c)
Simplify fully 4
y
8
2
123 marksmedium
A
Diagram NOT
B
accurately drawn
C
75°
E
D
F
A, B, C and D are points on a circle.
EDF is the tangent to the circle at the point D
Angle BDF = 75°
Calculate, giving your reasons, the size, in degrees, of ∠BCD
............................................................................................. °
133 marksmedium
a
t
v = 8.91 to 3 significant figures.
u = 5.82 to 3 significant figures.
t = 9 to 1 significant figure.
Calculate the lower bound, to 3 significant figures, of a
Show your working clearly.
144 marksmedium
F
D
Diagram NOT
69°
accurately drawn
E
C
G
A
B
H
The diagram shows a regular pentagon ABCDE and three sides, FE, EG and GH, of a
regular n-sided polygon.
AB is horizontal.
EG is vertical.
DEF
69
Calculate the value of n
n = .............................................................................................
154 marksmedium
The diagram shows a sphere of radius r cm and a right circular cone with base
radius r cm and vertical height 20 cm.
Diagram NOT
accurately drawn
20 cm
r cm
r cm
The volume of the sphere is 1.5 times the volume of the cone.
Find the value of r
r = .............................................................................................
164 marksmedium
P is inversely proportional to the square root of W
P = 1600 when W = 1.96
Find the value of W when P = 800
W = .............................................................................................
174 markshard
Quadrilateral A is transformed to quadrilateral B under a reflection in the line y = − x
Quadrilateral B is transformed to quadrilateral C under the matrix 4
2
1
3
Quadrilateral C is the image of quadrilateral A under the matrix N
Find the matrix N
N
184 marksmedium
A
B
The diagram shows two mathematically similar solids A and B
The volume of solid A is 1125 cm³
The volume of solid B is 576 cm³
Given that
surface area of solid A + surface area of solid B = 3198 cm²
calculate the surface area of solid B
............................................................................................. cm²
195 marksmedium
1 mark
(a)
A
X
B
Y
D
Scale: 1 cm represents 2 metres
C
The quadrilateral ABCD is a scale drawing of Simon’s garden.
There is a tree at the point X and a tree at the point Y
Construct the locus of all points inside the quadrilateral that are 10 metres from C
2 marks
(b)
A
X
B
Y
D
Scale: 1 cm represents 2 metres
C
The quadrilateral ABCD is a scale drawing of Simon’s garden.
There is a tree at the point X and a tree at the point Y
Using ruler and compasses only and showing all your construction lines, construct
the locus of all points inside the quadrilateral that are equidistant from X and Y
1 mark
(c)
A
X
B
Y
D
Scale: 1 cm represents 2 metres
C
The quadrilateral ABCD is a scale drawing of Simon’s garden.
There is a tree at the point X and a tree at the point Y
Construct the locus of all points inside the quadrilateral that are 6 metres from AB
Simon is going to place a light in the garden so that it is closer to X than to Y, more than
6 metres from AB and more than 10 metres from C
1 mark
(d)
A
X
B
Y
D
Scale: 1 cm represents 2 metres
C
The quadrilateral ABCD is a scale drawing of Simon’s garden.
There is a tree at the point X and a tree at the point Y
Show, by shading, the region where Simon can place the light.
Label the region R
205 marksmedium
1 mark
(a)
Sarah records the number of visits to the cinema that each of the 19 students in her class
made in June. The table below shows her results.
Write down the mode of the number of visits to the cinema.
1 mark
(b)
Sarah records the number of visits to the cinema that each of the 19 students in her class
made in June. The table below shows her results.
Find the median number of visits to the cinema.
Bhaskor joins Sarah’s class.
The mean number of visits to the cinema, after Bhaskor joins the class, for the 20
students in June is 1.7
3 marks
(c)
Sarah records the number of visits to the cinema that each of the 19 students in her class
made in June. The table below shows her results.
Calculate the number of visits to the cinema Bhaskor makes in June.
215 marksmedium
2 marks
(a)
Diagram NOT
accurately drawn
10
Speed (m/s)
u
0
0
4
6
8
Time (t seconds)
The diagram shows a sketch of the speed-time graph of part of a cyclist’s journey along
a straight horizontal road.
Calculate the deceleration, in m/s2, for the last 2 seconds of this part of the cyclist’s
journey.
............................................................................................. m/s2
At time t = 0 seconds, the speed of the cyclist is u m/s
The cyclist travelled a total distance of 65 m in the 8 seconds.
3 marks
(b)
Diagram NOT
accurately drawn
10
Speed (m/s)
u
0
0
4
6
8
Time (t seconds)
The diagram shows a sketch of the speed-time graph of part of a cyclist’s journey along
a straight horizontal road.
Calculate the value of u
u = .............................................................................................
226 marksmedium
2 marks
(a)
The bar chart gives information about the number of pieces of music downloaded last
month for each of 30 students in a class.
9
8
7
6
5
Number of
4
students
3
2
1
0
6-8
9-11
12-14
15-17
0-2
3-5
Number of pieces of music downloaded
Calculate the percentage of students who downloaded more than 8 pieces of music
last month.
............................................................................................. %
4 marks
(b)
The bar chart gives information about the number of pieces of music downloaded last
month for each of 30 students in a class.
9
8
7
6
5
Number of
4
students
3
2
1
0
6-8
9-11
12-14
15-17
0-2
3-5
Number of pieces of music downloaded
Calculate an estimate for the mean number of pieces of music each student
downloaded last month.
235 marksmedium
Simplify x
3
x
2
4
2
Show your working clearly.
246 marksmedium
2 marks
(a)
Use the factor theorem to show that x
x
x
x
9
17
10
3
2
4 marks
(b)
Factorise fully 18
x
x
x
9
17
10
3
2
Show clear algebraic working.
256 marksmedium
2 marks
(a)
A particle P is moving along a straight line that passes through the point O
The displacement, x metres, of P from O at time t seconds (t ≥0) is given by
x
t
t
t
4
3
1
3
2
At time t seconds, the velocity of P is v m/s
Find an expression for v in terms of t
v = .............................................................................................
The particle P comes to instantaneous rest at the point A
4 marks
(b)
A particle P is moving along a straight line that passes through the point O
The displacement, x metres, of P from O at time t seconds (t ≥0) is given by
x
t
t
t
4
3
1
3
2
At time t seconds, the velocity of P is v m/s
Find, in metres, the distance OA
............................................................................................. m
268 markshard
3 marks
(a)
D
Diagram NOT
accurately drawn
60°
5
3 cm
5
15 cm
C
A
3 cm
10
B
The diagram shows a pyramid ABCD with a horizontal triangular base ABC
DC = 5 3 cm
DB = 10 3 cm
AC = 5 15 cm
60
ADB
DCA
DCB
90
Calculate the length, in cm to one decimal place, of AB
............................................................................................. cm
5 marks
(b)
D
60°
5
3 cm
5
15 cm
C
A
3 cm
10
B
The diagram shows a pyramid ABCD with a horizontal triangular base ABC
DC = 5 3 cm
DB = 10 3 cm
AC = 5 15 cm
60
ADB
DCA
DCB
90
Calculate the area, in cm² to 3 significant figures, of triangle ABC
............................................................................................. cm²