12 markseasy
Write 48 seconds as a fraction of 1 day.
Give your answer in its simplest form.
Maths B
January 2023 · Paper 1R (4MB1/01R) (Edexcel IGCSE Maths): Exam Questions
Exam code:4MB126 questions · 100 marks · ≈ 2 hours
22 markseasy
Here are the numbers of items that the last 9 people who visited a shop bought.
6 1 13 20 2 4 14 11 20
Find the median of these numbers of items.
32 markseasy
Write down a formula for the nth term of the sequence.
7 11 15 19 23
42 markseasy
Simplify fully (125a9)
3
52 marksmedium
Given that y = 21x2 - 8
x
find d
y
d
x
d
y
x = ......................................................
d
62 marksmedium
A = 23 × 34 × 53 × 11
B = 22 × 33 × 54
Find the lowest common multiple (LCM) of 2A and 7B
Give your answer as a product of prime factors.
73 marksmedium
Without using a calculator, and showing all your working, evaluate
2 4
3 2
5
3
Give your answer as a mixed number in its simplest form.
83 marksmedium
A farmer keeps cows, pigs and sheep.
The ratio of the number of cows he keeps to the number of pigs he keeps is 2 : 3
The ratio of the number of pigs he keeps to the number of sheep he keeps is 7 : 11
The farmer keeps 42 cows.
Work out the number of sheep the farmer keeps.
93 marksmedium
Solve 3(2 - x)2 - 75 = 0
Show clear algebraic working.
x = ......................................................
103 marksmedium
Simplify 7
8
2
−
x
x
x
4
3
5
Give your answer in its simplest form.
113 marksmedium
A = w
x
−
y
w = 21.7
to one decimal place
x = 12
to the nearest whole number
y = 20
to the nearest ten
Find the lower bound for the value of A
Show your working clearly.
123 marksmedium
M varies inversely as the cube of p
M = 0.8 when p = 25
Find a formula for M in terms of p
133 marksmedium
Solve
x
x
−
3
2
1
=
5
7
4
Show clear algebraic working.
x = ......................................................
144 marksmedium
The diagram shows a square piece of card from which two semicircles are cut out.
5 cm
5 cm
15 cm
The square has a side of length 15 cm.
Calculate the area, in cm² to 3 significant figures, of the piece of card left when the
semicircles are cut out.
...................................................... cm²
154 marksmedium
Solve the simultaneous equations
9x + 7y = 3
5x - 4y = 6.4
Show clear algebraic working.
x = ......................................................
y = ......................................................
164 marksmedium
16 cm
B
A
68°
D
C
20 cm
The diagram shows trapezium ABCD in which
AB = 16 cm DC = 20 cm ∠BCD = 68° ∠BAD = ∠CDA = 90°
Calculate the area, in cm² to 3 significant figures, of trapezium ABCD
...................................................... cm²
174 marksmedium
1 mark
(a)
The Venn diagram shows the sets D, E and F where the numbers represent numbers
of elements.
E
E
D
6
7
1
4
3
2
9
8
F
Find n(D ∪ E)
1 mark
(b)
The Venn diagram shows the sets D, E and F where the numbers represent numbers
of elements.
E
E
D
6
7
1
4
3
2
9
8
F
Find n(D ∩ E′)
1 mark
(c)
The Venn diagram shows the sets D, E and F where the numbers represent numbers
of elements.
E
E
D
6
7
1
4
3
2
9
8
F
Find n(F′)
1 mark
(d)
The Venn diagram shows the sets D, E and F where the numbers represent numbers
of elements.
E
E
D
6
7
1
4
3
2
9
8
F
Find n([D ∪ F] ∩ E′)
184 marksmedium
Make b the subject of a =
b
d
−
195 marksmedium
F
Diagram NOT
D
C
accurately drawn
E
A
B
106°
G
In the diagram, ABCD is a trapezium and EDF is an isosceles triangle with DE = DF
EDC and GADF are straight lines.
∠GAB = 106°
Calculate the size, in degrees, of ∠DEF
Give reasons for each stage of your working.
∠DEF = ......................................................°
205 marksmedium
1 mark
(a)
B
A
D
C
The diagram shows a quadrilateral ABCD
Construct the locus of all points inside the quadrilateral that are 5 cm from D
2 marks
(b)
B
A
D
C
The diagram shows a quadrilateral ABCD
Using ruler and compasses only and showing all your construction lines, construct
the locus of all points inside the quadrilateral that are equidistant from AB and BC
1 mark
(c)
B
A
D
C
The diagram shows a quadrilateral ABCD
Construct the locus of all points inside the quadrilateral that are 3 cm from BC
The region R consists of all the points inside the quadrilateral that are more than 5 cm
from D, nearer to BC than to AB and more than 3 cm from BC
1 mark
(d)
B
A
D
C
The diagram shows a quadrilateral ABCD
Show, by shading, the region R
Label the region R
215 marksmedium
2 marks
(a)
(x + 2) is a factor of 6x3 + 31x2 + kx + 30
Use the factor theorem to show that k = 53
3 marks
(b)
(x + 2) is a factor of 6x3 + 31x2 + kx + 30
Factorise fully 6x3 + 31x2 + 53x + 30
226 markshard
2 marks
(a)
−
2
3
x
3
4
7
A =
1 C =
B =
−
4
−
2
3
2
4
Find 4A - 2B
Given the determinant of BC is 20
4 marks
(b)
−
2
3
x
3
4
7
A =
1 C =
B =
−
4
−
2
3
2
4
find the value of x
x = ......................................................
236 marksmedium
1 mark
(a)
Simplify 7y0 where y > 0
×
×
×
×
x
x x
x
x
−
−
5 marks
(b)
Solve 2
15
3
3
4
2
2
5
3
3
1
(
)
= 813
x
10
2
x = ......................................................
245 marksmedium
E
D
A
X
10 cm
C
10 cm
B
The diagram shows a solid right square‑based pyramid ABCDE
The volume of the pyramid is 1000 cm³
The pyramid is standing with its square base, ABCD, on a horizontal table.
The square base has side 10 cm.
X is the midpoint of the side AB
Calculate the size, in degrees to the nearest degree, of ∠CEX
......................................................°
257 markshard
3 marks
(a)
B
P
Diagram NOT
accurately drawn
M
3a
A
a
C
O
c
The diagram shows a quadrilateral OABC in which
→ = a OC
→ = c CB
→ = 3a
OA
The point M lies on OB such that OM : MB = 7 : 3
The point P lies on AB such that CMP is a straight line.
→
Find, in terms of a and c, simplifying your answer, the vector CM
→ = ......................................................
CM
4 marks
(b)
B
P
Diagram NOT
accurately drawn
M
3a
A
a
C
O
c
The diagram shows a quadrilateral OABC in which
→ = a OC
→ = c CB
→ = 3a
OA
The point M lies on OB such that OM : MB = 7 : 3
The point P lies on AB such that CMP is a straight line.
→
Using a vector method, and showing your working clearly, find AP : PB in the form
x : y where x and y are integers.
Show your working clearly.
AP : PB = ......................................................
268 marksmedium
4 marks
(a)
Jenny has a shop.
One Monday, each of the 40 people who went in Jenny’s shop were asked how long
they were in the shop.
The table below shows information about the results.
Calculate an estimate for the mean length of time, in minutes, that these people were
in the shop.
...................................................... minutes
The incomplete table and the incomplete histogram give information about the number
of kilometres each of the 40 people had travelled to get to the shop.
None of the people travelled more than 60 km.
4 marks
(b)
Jenny has a shop.
One Monday, each of the 40 people who went in Jenny’s shop were asked how long
they were in the shop.
The table below shows information about the results.
Complete the histogram and the frequency table.