12 markseasy
Factorise fully 9
2
x
x y
12
Maths B
June 2025 · Paper 1R (4MB1/01R) (Edexcel IGCSE Maths): Exam Questions
Exam code:4MB126 questions · 100 marks · ≈ 2 hours
22 markseasy
N
Diagram NOT
accurately drawn
N
K
214°
J
The diagram shows the position of two towns, J and K
The bearing of J from K is 214°
Find the bearing, in degrees, of K from J
.............................................................. °
32 markseasy
Make x the subject of t
x
6
4
42 markseasy
The price of a television is reduced by 8% in a sale.
The price of the television in the sale is $1012
Calculate the price of the television before the sale.
$..............................................................
52 markseasy
xy
4
5 Simplify fully
xy
2
62 markseasy
Given that, for all values of x,
2
where a and b are integers
2
x
x
x
a
b
6
15
find the value of a and the value of b
a = ..............................................................
b = ..............................................................
73 marksmedium
Diagram NOT
A
B
C
accurately drawn
72°
56°
D
E
F
G
In the diagram ABC and DEFG are parallel straight lines.
56° and
BEF
CBF
72°
Find the size, in degrees, of ∠EBF
Give reasons for each stage of your working.
.............................................................. °
EBF
83 markseasy
1 mark
(a)
Here are the marks that 10 students scored in a test.
25 11 24 6 4 28 19 11 15 10
Write down the mode of these 10 marks.
2 marks
(b)
Here are the marks that 10 students scored in a test.
25 11 24 6 4 28 19 11 15 10
Find the median of these 10 marks.
93 markseasy
2 marks
(a)
Solve the inequality 5
y
y
20
3
≥1 on the number line below.
1 mark
(b)
Represent the inequality x
x
−5
−4
−3
−2
−1
0
1
2
3
4
5
103 marksmedium
The cost, including delivery, of a mobile phone in the UK is £624
The cost of an identical mobile phone in the USA is $448 plus an additional cost of $d
for delivery.
The cost, including delivery, of the mobile phone in the UK is £224 more than the cost,
including delivery, of the mobile phone in the USA.
Using the exchange rate £1 = $1.28
calculate the value of d
d = .............................................................
113 marksmedium
A and B are two points on horizontal ground.
The distance from A to B is 1.5 kilometres
BC is a vertical pole
The angle CAB = 6°
Calculate the height, in metres to 3 significant figures, of the pole.
............................................................ metres
123 marksmedium
Solid A and solid B are similar.
cm
The surface area of solid A is 25
2
cm
2
The surface area of solid B is 900
3
The volume of solid A is 50
cm
Calculate the volume, in cm³, of solid B
............................................................ cm³
134 marksmedium
On a trip, a powerboat travels at an average speed of 40 km/h for 1 hour 18 minutes and
then travels at an average speed of 22 km/h for 30 minutes.
Calculate the average speed of the powerboat, in km/h, for the whole trip.
............................................................ km/h
144 marksmedium
Xiou records the time, in minutes, it takes each of the 30 students in his class to
complete the same puzzle.
The table shows information about his results.
Calculate an estimate for the mean number of minutes that these students take to
complete the puzzle.
............................................................ minutes
154 markshard
The points O, A and B are such that
5 and
2
The point C is such that AC
125 and AC is parallel to OB
=
Find
Give your answer in the form c
where c and d are integers
d
such that c < 0 and d > 0
Show all your working.
BC
164 marksmedium
A
B
120°
O
C
AOC
OABC is a sector of a circle, centre O with
120°
The length of arc ABC is 17.2 cm
Calculate the area, in cm² to 3 significant figures, of the sector.
............................................................ cm²
174 marksmedium
Without using a calculator and showing all your working, express
4
2 7
3
7
in the form a
where a and b are integers.
b
185 marksmedium
2 marks
(a)
B
Diagram NOT
accurately drawn
52°
x°
O
A
C
D
In the diagram A, B, C and D are points on a circle, centre O
52 and the reflex angle AOC
ABC
x
Find the size, in degrees, of ∠ADC
Give a reason for your answer.
............................................................ °
ADC
3 marks
(b)
B
Diagram NOT
accurately drawn
52°
x°
O
A
C
D
In the diagram A, B, C and D are points on a circle, centre O
52 and the reflex angle AOC
ABC
x
Find the value of x
Give a reason for your answer.
x = ............................................................
195 marksmedium
2 marks
(a)
Calculate 3 6
103
101
×
×
×
.
10
7 5
.
10
Give your answer in standard form.
10 8 where n is an integer.
n
c
4
−1
2 in terms of n
3 marks
(b)
Find an expression for c
Give your answer in standard form.
205 marksmedium
2 marks
(a)
The width of a rectangle is x metres.
The length of the rectangle is 8 metres longer than the width of the rectangle.
Find an expression in terms of x for the perimeter, in metres, of the rectangle.
Simplify your answer.
........................................................... m.
2
2 marks
(b)
The width of a rectangle is x metres.
The length of the rectangle is 8 metres longer than the width of the rectangle.
Factorise x
x
8
20
1 mark
(c)
The width of a rectangle is x metres.
The length of the rectangle is 8 metres longer than the width of the rectangle.
Hence write down the range of values of x for which the area of the rectangle is
2
greater than 20
m
215 marksmedium
Diagram NOT
E
accurately drawn
C
D
A
B
The diagram shows a right solid pyramid ABCDE, made of silver, with horizontal
rectangular base ABCD and vertex E
AB = 9 cm to 1 significant figure.
BC = 6 5. cm to the nearest 0.5 cm.
The mass of the pyramid is 5080 grams to the nearest 10 grams.
. g/cm to 3 significant figures.
3
The density of the silver is 10 5
mass
Given that density
=
volume
calculate the upper bound, in cm to 3 significant figures, of the perpendicular height of
the pyramid.
Show all your working.
............................................................ cm
226 marksmedium
2 marks
(a)
The weights, in grams, of tomatoes harvested by a gardener last month were measured.
The incomplete table and incomplete histogram below give information about the
weight, in grams, of each tomato harvested last month.
Show that y = 16
A tomato for which w≤35 grams is classed as a small tomato.
A small tomato is selected at random.
The probability that this tomato weighs less than or equal to 15 grams is 3

8
4 marks
(b)
The weights, in grams, of tomatoes harvested by a gardener last month were measured.
The incomplete table and incomplete histogram below give information about the
weight, in grams, of each tomato harvested last month.
Complete the histogram.
235 markshard
1
x
8
2
BA
A =
x where x > 0
1
2
1
0
1
Given that the determinant of matrix B−1 is −1
6
find matrix B –1
Give the elements of this matrix as numbers.
Show all your working.
B
1
246 marksmedium
Solve the simultaneous equations
2
xy
x
9
y
x
4
11
Show clear algebraic working.
255 marksmedium
Diagram NOT
accurately drawn
E
h cm
H
F
G
D
X
A
C
Y
B
A cube ABCDEFGH of side 6 cm is placed inside a hollow cone of height h cm.
The face ABCD of the cube rests on the circular base of the cone.
The vertices E, F, G and H of the cube touch the curved surface of the cone.
X and Y are points on the circumference of the base of the cone such that XACY is a
straight line.
Given that XF =
134 cm
find the value of h
Show all your working.
h = ...........................................................
268 markshard
1 mark
(a)
The function g is defined by g : x
−
↦3
x
Find g
2
2 marks
(b)
The function g is defined by g : x
−
↦3
x
Find the range of g
3 marks
(c)
The function g is defined by g : x
−
↦3
x
Express the inverse function g−1 in the form g−1 :
x ↦
...
g−1 : x ↦...........................................................
2
x < 0
The function h is defined by h : x

↦
x
−
2
3
ax
b
2 marks
(d)
The function g is defined by g : x
−
↦3
x
Express the composite functiongh in the form gh : x
where a, b and c
↦
c
are integers.
gh : x ↦...........................................................