12 markseasy
Factorise fully 28ab + 21b
Maths B
November 2024 · Paper 1 (4MB1/01) (Edexcel IGCSE Maths): Exam Questions
Exam code:4MB127 questions · 100 marks · ≈ 2 hours
22 markseasy
1 mark
(a)
A pattern is made with white squares and shaded squares.
Shade one more square to make a pattern with rotational symmetry of order 2
Here is a different pattern made from white squares and shaded squares.
1 mark
(b)
A pattern is made with white squares and shaded squares.
Shade one more square to make a pattern with exactly one line of symmetry.
32 markseasy
Using ruler and compasses only and showing all your construction lines, construct the
perpendicular bisector of AB
B
A
42 markseasy
The bearing of Port A from Port B is 276°
Find the bearing of Port B from Port A
.............................................................. °
52 markseasy
Solve 5
2
x
x
18
7
7
x = ..............................................................
62 marksmedium
x
2
4
A
2
3
7
y
2
5
B
2
3
5
7
Given that x > 2 and y > 4
find the highest common factor (HCF) of A and B
72 markseasy
A biased dice has six faces numbered 1, 2, 3, 4, 5 and 6
The table below shows information about the probability that, when the dice is thrown
once, it will land on each of the numbers.
The dice is thrown 300 times.
Calculate the expected number of times the dice will land on a number greater than 3
83 marksmedium
3 kg of onions cost £1.71
2 kg of onions and 5 kg of potatoes cost £5.34
Calculate the total cost, in £, of 3 kg of onions and 4 kg of potatoes.
£..............................................................
93 marksmedium
A
B
6 cm
D
C
G
F
5.5 cm
E
H
12 cm
The diagram shows a solid cuboid ABCDEFGH
EH = 12 cm GH = 5.5 cm BG = 6 cm
Calculate the total surface area, in cm², of the cuboid.
.............................................................. cm²
103 marksmedium
y
5
x
−5
−5
The straight line L1 is drawn on the grid.
The straight line L2 is parallel to L1 and passes through the point
with coordinates
9,12
Find an equation for L2
Give your answer in the form y
mx
c
112 markseasy
Calculate 2 3
.
10
4 6
.
10
Give your answer in standard form.
123 marksmedium
A, B, C and D are numbers such that
A B
= 2 5
:
:
A D
= 3 8
:
:
B C
= 9 11
:
:
Find C D
:
Give your answer in its simplest form.
133 marksmedium
D
Diagram NOT
accurately drawn
A
1.7 m
B
C
12.2 m
The diagram shows quadrilateral ABCD where B and C are on horizontal ground
and BA and CD are vertical.
BC = 12.2 metres
AB = 1.7 metres
ABC
BCD
90
The angle of elevation of D from A is 32°
Calculate the length, in metres to 3 significant figures, of CD
.............................................................. metres
143 marksmedium
Write as a single fraction in its simplest form
x
x
5
1
2 2
5
7
4
154 marksmedium
A team takes part in a sports league.
After 12 games its mean score per game is 96
After 14 games its mean score per game is 98
The ratio of its score in game 13 to its score in game 14 is 2 3
:
Calculate its score in game 14
164 marksmedium
In the diagram, BGE is an isosceles triangle with EG
BG
=
ABC, DEF and EGH are straight lines.
ABC is parallel to DEF
113
DEB
BGH
94
Find the size, in degrees, of ∠CBG
Give a reason for each stage of your working.
.............................................................. °
CBG
174 markshard
At the start of 2012, Fatima bought a car for $15 500
From the start of 2012 to the start of 2014, the value of the car decreased by 8%
From the start of 2014 to the start of 2016, the value of the car decreased by 2.2%
From the start of 2016 to the start of 2018, the value of the car decreased by x%
At the start of 2018, the value of the car was $13 137.40
Calculate, to 2 significant figures, the value of x
x = ..............................................................
184 markseasy
Make t the subject of r
t
8
3
194 marksmedium
2 marks
(a)
B
3
4
0
2
Find AB
3
2
C
5
6
2 marks
(b)
B
3
4
0
2
Find C −1
204 marksmedium
C
Diagram NOT
accurately drawn
D
B
O
61°
E
27°
A
F
In the diagram A, B, C and E are points on a circle with centre O
DEF is the tangent to the circle at the point E
27
BA
BC
OAE
CED
=
61
Find the size, in degrees, of ∠BCE
.............................................................. °
BCE
214 markshard
v
2
u
as
v = 25 4. to 1 decimal place
to 4 significant figures
u = 9 512
.
s = 15 to the nearest 5
Calculate the upper bound, to 3 significant figures, of a
Show your working clearly.
225 marksmedium
2 marks
(a)
On the number line, represent the inequality
5
3
y
−6
−5
−4
−3
−2
−1
0
1
2
3
4
5
6
≥3 7
3 marks
(b)
Solve the inequality 4
x
x +
2
2
236 markshard
2 marks
(a)
Use the factor theorem to show that x
5 is a factor of 2
3
2
x
x
x
9
11
30
4 marks
(b)
Hence, factorise completely 2
3
2
x
x
x
9
11
30
Show clear algebraic working.
245 markshard
2 marks
(a)
The probability that Lethna takes the bus to work on Monday is 0.32
If Lethna takes the bus on Monday, the probability that she takes the bus
on Tuesday is 0.47
If Lethna does not take the bus on Monday, the probability she will not take the bus
on Tuesday is 0.71
Complete the tree diagram for this information.
Monday
Tuesday
bus
bus
0.32
not bus
bus
not bus
not bus
E is the event that Lethna takes the bus on exactly one of either Monday or Tuesday.
F is the event that Lethna does not take the bus on Monday and does not take the bus on
Tuesday.
3 marks
(b)
The probability that Lethna takes the bus to work on Monday is 0.32
If Lethna takes the bus on Monday, the probability that she takes the bus
on Tuesday is 0.47
If Lethna does not take the bus on Monday, the probability she will not take the bus
on Tuesday is 0.71
Find which of the events, E or F, has the greater probability.
Show your working clearly.
257 markshard
y
C
P
Q
O
x
R
L
The diagram shows part of the curve C with equation y
2
x
x
3
16
35
and part of the line L with equation 2
y
x
11
110
P and Q are the points of intersection of C and L
R is the point on the x-axis such that PR is parallel to the y-axis.
Show that the area of triangle PQR is 442.75 cm²
You must show clear algebraic working.
Question 25 continued
269 markshard
2 marks
(a)
B
Diagram NOT
C
accurately drawn
E
D
A
The diagram shows a solid pyramid P with vertices A, B, C and D
ACD is the horizontal triangular base of P
= 3
E is the point on AC such that AE
AC
5
AC = 15.5 cm
CD =8.2 cm
AED
90
Calculate, in cm to 3 significant figures, the length of ED
.............................................................. cm
The solid pyramid T is mathematically similar to P
The area of the triangular base of T is 64.9 cm²
EBD
Given that vertex B is vertically above point E and
71
7 marks
(b)
B
Diagram NOT
C
accurately drawn
E
D
A
The diagram shows a solid pyramid P with vertices A, B, C and D
ACD is the horizontal triangular base of P
= 3
E is the point on AC such that AE
AC
5
AC = 15.5 cm
CD =8.2 cm
AED
90
calculate, in cm³ to 3 significant figures, the volume of T
Question 26 continued
.............................................................. cm³
276 markshard
A curve with equation y
2
x
x
is drawn on a grid where
9
16
5
1 unit = 1 cm on each axis.
P and Q are two points on the curve.
P is the point with coordinates 1
,
2
The gradient of the tangent to the curve at Q is 6.5
Find the length, in cm to 3 significant figures, of PQ
You must show clear algebraic working.
.............................................................. cm