12 markseasy
Without using a calculator and showing all your working, evaluate
3 3
45
8
Give your answer in its simplest form.
Maths B
January 2022 · Paper 1R (4MB1/01R) (Edexcel IGCSE Maths): Exam Questions
Exam code:4MB129 questions · 100 marks · ≈ 2 hours
22 markseasy
The nth term of a sequence is given by n2
3
2
Determine whether 222 is a term of this sequence.
Show your working clearly.
32 markseasy
Express 450 millilitres as a fraction of 3 litres.
Give your answer in its simplest form.
42 markseasy
All the people at a meeting were asked where they had been for their last holiday.
All the people gave one answer.
Elton recorded the continent of each person’s answer.
Elton drew an accurate pie chart for his results.
Elton’s results showed that 40 people had been to Europe for their last holiday.
The angle in the pie chart for Europe is 64°
Calculate the number of people at the meeting.
52 markseasy
The bearing of P from Q is 063°
Calculate the bearing of Q from P
.......................................................°
62 markseasy
B
5 cm
Diagram NOT
D
accurately drawn
16 cm
12 cm
A
E
C
The diagram shows triangle ABC and triangle ADE.
The point D lies on AB and the point E lies on AC such that DE is parallel to BC.
AD = 16 cm DB = 5 cm DE = 12 cm
Calculate the length, in cm, of BC.
....................................................... cm
72 markseasy
A = 2
23
35
n
B = 2
Given that the Lowest Common Multiple (LCM) of A and B is 3 375 000
find the value of the integer n.
Show your working clearly.
n = .......................................................
82 markseasy
y = 4x5 − 8
x
2
Find d
y
d
x
d
y
x = .......................................................
d
92 markseasy
A
Diagram NOT
accurately drawn
10 cm
9 cm
B
7 cm
D
P
C
A, B, C and D are four points on a circle.
The chord AC intersects the chord BD at P
AP = 10 cm BP = 9 cm PD = 7 cm
Calculate the length, in cm, of PC
....................................................... cm
102 markseasy
M =
−
−
0 5
.
1 5
.
Given that the determinant of matrix M is 0.5
find the value of x.
x = .......................................................
113 markseasy
C
Diagram NOT
150°
accurately drawn
B
D
A
E
In the diagram, AB, BD and DE are three sides of a regular polygon with n sides.
The point C is such that ABC and EDC are straight lines and ∠ BCD = 150°
Calculate the value of n.
n = .......................................................
123 marksmedium
At the end of a college course, Pierre has to take five examinations.
Each examination is marked out of 100
Pierre has to get an overall mean mark of 80% or more for the five examinations in
order to pass the course.
After taking the first four examinations, Pierre’s mean mark for these four examinations
is 78%
Calculate the lowest mark Pierre can get in his fifth examination so that he passes the course.
133 marksmedium
Solve 6
3
2
3
6
−
=
7
5
5
Show clear algebraic working.
x = .......................................................
143 marksmedium
Diagram NOT
accurately drawn
C
B
52°
63°
D
A
E
In the diagram, A, B and C are points on a circle.
DAE is the tangent to the circle at A.
∠ BAC = 52° and ∠ CAE = 63°
Calculate the size, in degrees, of ∠ ACB.
Give reasons for each stage of your working.
.......................................................°
153 marksmedium
Given that m and n are integers, write 4
20
in the form m + n 5
−
5
2
Show each stage of your working clearly.
163 marksmedium
c
a = 15 to the nearest 5
b = 8.5 to one decimal place
c = 5 to one significant figure
Calculate the lower bound of P
Show your working clearly.
173 marksmedium
Given that, for all values of x,
8x2 − 48x +10 = a(x + b)2 + c where a, b and c are integers,
find the value of a, the value of b and the value of c.
Show your working clearly.
a = .......................................................
b = .......................................................
c = .......................................................
184 marksmedium
The volume of a solid right circular cylinder is 225 cm³
The height of the cylinder is 7 cm.
Work out the total surface area, in cm² to 3 significant figures, of the cylinder.
....................................................... cm²
194 marksmedium
C
Diagram NOT
accurately drawn
8 cm
D
18 cm
5 cm
A
B
The diagram shows a right-angled triangle ABC in which ∠ ABC = 90°
D is the point on BC such that
BD = 5 cm DC = 8 cm AD = 18 cm
Calculate the size, in degrees to one decimal place, of ∠ CAD
.......................................................°
204 marksmedium
Make x the subject of the formula y = 5 + 3
4
x
−
7
Give your answer in its simplest form.
214 marksmedium
B
E
12 cm
C
16 cm
A
D
The diagram shows triangle ABC and triangle EDC.
AB is parallel to DE.
AC = 16 cm and CE = 12 cm.
Given that the area of triangle ABC is 31.5 cm² greater than the area of triangle EDC,
work out the area of triangle EDC.
....................................................... cm²
224 marksmedium
1 mark
(a)
The table shows information about the lengths of time, in minutes, that 70 people waited
for a train.
Write down the modal class.
3 marks
(b)
The table shows information about the lengths of time, in minutes, that 70 people waited
for a train.
Calculate an estimate, to one decimal place, of the mean number of minutes waited.
....................................................... minutes
234 marksmedium
The students who go to Crown Academy either live in village A or in village B such that
number of students from village A : number of students from village B = 5 : 7
15% of the students from village A travel by bus to Crown Academy.
2
7 of the students from village B travel by bus to Crown Academy.
Of the students from village A and village B who do not travel by bus to Crown Academy,
3
4 walk to Crown Academy.
Find what fraction of the students walk to Crown Academy.
244 marksmedium
Find the two values of x such that
4 2 3
×
×
12
3
3
x
x
x
−
3
=
27
24
x
2
Show your working clearly.
256 marksmedium
1 mark
(a)
ℰ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A = {2, 3, 5, 6, 9, 10}
B = {3, 4, 6, 9, 12}
List the members of
A ∩ B
1 mark
(b)
ℰ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A = {2, 3, 5, 6, 9, 10}
B = {3, 4, 6, 9, 12}
List the members of
A ∪ B
1 mark
(c)
ℰ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A = {2, 3, 5, 6, 9, 10}
B = {3, 4, 6, 9, 12}
List the members of
A'
C = {5, 6, 7}
3 marks
(d)
ℰ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A = {2, 3, 5, 6, 9, 10}
B = {3, 4, 6, 9, 12}
List the members of
Write down all the subsets of C.
268 marksmedium
2 marks
(a)
Solve the inequality 7d + 3 ≤ 5d
2 marks
(b)
Expand and simplify 5a(2a − 3) − 4a(3a + 1)
x y
2 marks
(c)
Simplify fully 30
3
4
xy
5
3
2 marks
(d)
Factorise 15n2 − 11n − 14
275 marksmedium
B
Diagram NOT
5.2 m
accurately drawn
8.2 m
C
59°
A
48°
6.7 m
D
The diagram shows quadrilateral ABCD such that
AB = 8.2 m BC = 5.2 m AD = 6.7 m
∠ CAD = 48° ∠ ACD = 59°
Find the area, in m² to 3 significant figures, of quadrilateral ABCD.
....................................................... m²
286 marksmedium
The curve C has equation y = 2x3 − 21
2 x2 + 12x + 5
The points P and Q lie on C.
P is the point with coordinates (1, 8.5)
The gradient of the tangent to C at the point P is equal to the gradient of the tangent to
C at the point Q.
Calculate the gradient of the line PQ.
Show your working clearly.
296 marksmedium
2 marks
(a)
Given that (x − 5) is a factor of 3x3 − 20x2 + kx + 10 where k is a constant,
use the factor theorem to show that k = 23
4 marks
(b)
Given that (x − 5) is a factor of 3x3 − 20x2 + kx + 10 where k is a constant,
Solve the equation 3x3 − 20x2 + 23x + 10 = 0
Show clear algebraic working.