12 markseasy
Without using a calculator and showing all your working, work out
5 5
8 − 3 3
4
Give your answer as a mixed number in its simplest form.
Maths B
January 2021 · Paper 1 (4MB1/01) (Edexcel IGCSE Maths): Exam Questions
Exam code:4MB126 questions · 100 marks · ≈ 2 hours
22 marksmedium
Some students at a school are asked the following question
“Did you walk to school today?”
52% of the students asked are in Year 7 and the rest of the students asked are in Year 8.
20% of the students asked are Year 8 students who walked to school.
42% of the students asked did not walk to school.
Find as a percentage of all students asked, those who are in Year 7 and did not walk to school.
.................................................................... %
32 markseasy
Each interior angle of a regular polygon is 176º
Calculate the number of sides of the polygon.
42 markseasy
Q = 10 − At
Work out the value of Q when A = −2 and t = 3
Q = ....................................................................
52 marksmedium
Given that
x
x
−
4
3
1
4
x
=
y
y
−
−
1
0
1
1
find the value of x.
x = ....................................................................
63 marksmedium
Here are four numbers written in order of size.
1.5 2 p 19.5
The mean of the four numbers is three times the median of the four numbers.
Find the value of p.
p = ....................................................................
73 markseasy
Here is hexagon ABCDEF.
All the corners of ABCDEF are right angles.
AB = 8 cm AF = 14 cm BC = 9 cm CD = 12 cm
Calculate the area, in cm², of ABCDEF.
.................................................................... cm²
83 marksmedium
1 mark
(a)
Paul is carrying out an investigation into people’s wages in the United Kingdom.
Paul asks two of his friends, Abdul and Sue, about the pay rise each received in the last year.
Abdul says that he has had a 5% pay rise in the last year.
Sue says that she has had a 7% pay rise in the last year.
Paul says that, in the last year, Sue’s wages have risen by more than Abdul’s wages.
Explain why Paul might not be correct.
Paul has also read an article about the National Minimum Wage in the United Kingdom.
The article says that, from April 2017 to April 2018, the national minimum hourly wage
increased by 4.4% to £7.83
2 marks
(b)
Paul is carrying out an investigation into people’s wages in the United Kingdom.
Paul asks two of his friends, Abdul and Sue, about the pay rise each received in the last year.
Abdul says that he has had a 5% pay rise in the last year.
Sue says that she has had a 7% pay rise in the last year.
Paul says that, in the last year, Sue’s wages have risen by more than Abdul’s wages.
Find the value of the National Minimum Wage before this increase.
£ ....................................................................
93 marksmedium
C
Diagram NOT
accurately drawn
4 cm
A
B
3 cm
5 cm
D
The diagram shows triangle ABC.
The point D lies on AB such that ∠ADC = 90°
AC = 4 cm AD = 3 cm BD = 5 cm
Calculate the size, in degrees to one decimal place, of ∠ABC.
.................................................................... °
103 marksmedium
The nth term of a sequence is an where an = 2
3
1
2
n
2
2
By simplifying the expression for an or otherwise, explain why no term in the sequence
is an integer.
Show algebraic working and clearly explain your reasoning.
113 markshard
1 mark
(a)
Factorise x2 − 1
p and q are integers greater than 260 000 and p < q
2 marks
(b)
Find the value of p and the value of q such that pq = 236 − 1
p = ....................................................................
q = ....................................................................
123 marksmedium
The density, d grams/cm³, of an object of mass m grams and volume V cm³ is given by the formula
m
d
=
V
m = 2800 to the nearest 10
V = 1600 to 3 significant figures.
Calculate the lower bound, to 3 significant figures, of d.
Show your working clearly.
133 marksmedium
Without using your calculator and showing all your working, express
13
11
−
13
11
b where a and b are integers.
in the form a +
143 marksmedium
Jill travels to work either by car or by train.
Each day that Jill travels to work, the probability that she travels to work by train is 0.1
On a day that Jill travels to work by train, the probability that she will be late for work is 0.05
On a day that Jill travels to work by car, the probability that she will be late for work is 0.01
On a randomly chosen day that Jill travels to work, she is late for work.
Find the probability that Jill travelled to work by train on that day.
154 markseasy
2 marks
(a)
Simplify 4x − 3y + x + 5y
2 marks
(b)
Simplify 2a34a3
164 markseasy
2 marks
(a)
Factorise fully 10ab − 24a2
2 marks
(b)
Factorise p2 + 10p − 24
174 marksmedium
2 marks
(a)
Given that a = 2. and b =
calculate ab
Give your answer in standard form.
n where k and n are integers,
Given that a + b = k10
2 marks
(b)
Given that a = 2. and b =
find the smallest value of k and the corresponding value of n
k = ....................................................................
n = ....................................................................
184 marksmedium
Solve the simultaneous equations
5x + 3y = 2
3x − 8y = 4
Show clear algebraic working.
x = ....................................................................
y = ....................................................................
194 marksmedium
2 marks
(a)
f (x) = x3 + ax − 3 where a is an integer.
(x − 3) is a factor of f (x)
Use the factor theorem to show that a = −8
Given that f (x) = (x − 3)Q(x) where Q(x) is a quadratic expression in x
2 marks
(b)
f (x) = x3 + ax − 3 where a is an integer.
(x − 3) is a factor of f (x)
find Q(x)
Q(x) = ....................................................................
205 markshard
2 marks
(a)
A
C
B
The diagram shows triangle ABC.
Showing all your construction lines, construct
the perpendicular bisector of AB,
2 marks
(b)
A
C
B
The diagram shows triangle ABC.
Showing all your construction lines, construct
the bisector of ∠ACB.
The region R consists of all the points inside the triangle that are closer to A than to B
and closer to BC than to AC.
1 mark
(c)
A
C
B
The diagram shows triangle ABC.
Showing all your construction lines, construct
Show, by shading, the region R.
Label the region R.
215 marksmedium
B
Diagram NOT
accurately drawn
C
80°
D
120°
O
A
E
The diagram shows the circle ABCDE with centre O.
AC is the diameter of the circle.
AB is parallel to ED.
∠ACD = 80° ∠CDE = 120°
Giving your reasons, find the size, in degrees, of ∠ACB.
∠ACB = ....................................................................°
225 marksmedium
2 marks
(a)
20 cm
S
20 cm
The diagram above shows a right circular solid cone S with base diameter 20 cm and height 20 cm.
Calculate the volume, in cm³ to 3 significant figures, of S.
.................................................................... cm³
A
B
20 cm
The shape B is formed from cone S by cutting S parallel to its base and removing
cone A, as shown in the diagram above.
The height of B is 10 cm.
3 marks
(b)
20 cm
S
20 cm
The diagram above shows a right circular solid cone S with base diameter 20 cm and height 20 cm.
Calculate the volume, in cm³ to 3 significant figures, of B.
.................................................................... cm³
235 marksmedium
The incomplete histogram and the incomplete table give information about the daily
mean temperature for 184 days measured at Heathrow.
None of the daily mean temperatures were less than 5°C and all the daily mean
temperatures were less than 25°C.
Complete the histogram and the table.
248 marksmedium
2 marks
(a)
The functions f and g are defined as
f : x ↦ x − 3
g : x ↦ x2 − 2
Find fg
The function h is defined as
h(x) = gf (x)
2 marks
(b)
The functions f and g are defined as
f : x ↦ x − 3
g : x ↦ x2 − 2
Show that h(x) = x2 − 6x + 7
The domain of h is {x : x ≥ n}
The inverse of h is h−1
1 mark
(c)
The functions f and g are defined as
f : x ↦ x − 3
g : x ↦ x2 − 2
State the least value of n for which h−1 is a function.
n = ....................................................................
3 marks
(d)
The functions f and g are defined as
f : x ↦ x − 3
g : x ↦ x2 − 2
For this value of n, find h−1(x)
h−1(x) = ....................................................................
258 markshard
6 marks
(a)
E
Diagram NOT
accurately drawn
M
32.3 m
D
C
N
34 m
A
B
The diagram shows a solid right pyramid ABCDE with a square base ABCD on a horizontal plane.
The vertex E of the pyramid is vertically above the centre of the base.
BC = 34 m EA = EB = EC = ED = 32.3 m
The point M is the midpoint of CE and the point N is the midpoint of BE.
Given that AN + NM = x metres
calculate the value, to 2 significant figures, of x.
x = ....................................................................
2 marks
(b)
E
Diagram NOT
accurately drawn
M
32.3 m
D
C
N
34 m
A
B
The diagram shows a solid right pyramid ABCDE with a square base ABCD on a horizontal plane.
The vertex E of the pyramid is vertically above the centre of the base.
BC = 34 m EA = EB = EC = ED = 32.3 m
The point M is the midpoint of CE and the point N is the midpoint of BE.
Given that AN + NM = x metres
Calculate the size, to the nearest degree, of angle BAN.
.................................................................... °
267 marksmedium
4 marks
(a)
A particle P is moving along a straight line. At time t seconds, the displacement,
s metres, of P from a fixed point O on the line is given by
s = 5t 2 − t 3 0 ≤ t ≤ 5
At time T seconds, where T > 0 , P comes to instantaneous rest.
Find the exact value of T.
T = ....................................................................
3 marks
(b)
A particle P is moving along a straight line. At time t seconds, the displacement,
s metres, of P from a fixed point O on the line is given by
s = 5t 2 − t 3 0 ≤ t ≤ 5
At time T seconds, where T > 0 , P comes to instantaneous rest.
Find the total distance travelled by the particle between t = 0 and t = 5
.................................................................... m