16 marksmedium
The GDP per capita for a region is defined as follows
GDP per capita = total GDP
population
Complete the table below, giving each value to 2 significant figures.
Question 1 continued
Maths B
June 2022 · Paper 2 (4MB1/02) (Edexcel IGCSE Maths): Exam Questions
Exam code:4MB111 questions · 100 marks · ≈ 2 hours
27 marksmedium
1 mark
(a)
E is the universal set and A, B and C are three sets.
E = { p, q, r, s, t }
A = { q, r, s }
B = { p, q, t }
List the members of
A ∩ B
1 mark
(a)(ii)
E is the universal set and A, B and C are three sets.
E = { p, q, r, s, t }
A = { q, r, s }
B = { p, q, t }
A ∪ B
1 mark
(a)(iii)
E is the universal set and A, B and C are three sets.
E = { p, q, r, s, t }
A = { q, r, s }
B = { p, q, t }
A¢ ∩ B
Given that A ∩ C = {r}
2 marks
(b)
E is the universal set and A, B and C are three sets.
E = { p, q, r, s, t }
A = { q, r, s }
B = { p, q, t }
write down all the possibilities for set C
One of the possibilities for set C is selected at random.
2 marks
(c)
E is the universal set and A, B and C are three sets.
E = { p, q, r, s, t }
A = { q, r, s }
B = { p, q, t }
Find the probability that this set C is such that B ∩ C = ∅
Question 2 continued
38 marksmedium
3 marks
(a)
Given that 2x × 4y = 128
show that x + 2y = 7
x
Given that 8
y = 32
4
2 marks
(b)
Given that 2x × 4y = 128
show that 3x - 2y = 5
3 marks
(c)
Given that 2x × 4y = 128
Hence, or otherwise, solve the simultaneous equations
2x × 4y = 128
x
8
y = 32
4
Question 3 continued
48 marksmedium
1 mark
(a)
Sophie conducted a survey on the time spent on the internet per day. There were 90 people
in her survey. The results are shown in the table below.
Write down the class interval that contains the median time spent on the internet per day.
4 marks
(b)
Sophie conducted a survey on the time spent on the internet per day. There were 90 people
in her survey. The results are shown in the table below.
Calculate an estimate for the mean time spent on the internet per day.
Sophie drew a histogram for the information in the table.
In her histogram, the bar for the class interval 30 ≤ t < 60 is a square with sides of
length 3 cm.
Given that the bar for the class interval 10 ≤ t < 30 is a rectangle of width w cm and of
height h cm,
3 marks
(c)
Sophie conducted a survey on the time spent on the internet per day. There were 90 people
in her survey. The results are shown in the table below.
find the value of w and the value of h
Question 4 continued
58 marksmedium
4 marks
(a)
A closed box is in the shape of a hollow cuboid.
The dimensions of the cuboid are 12 cm by 4.0 cm by 3.0 cm.
Each length is given to 2 significant figures.
A tin of paint contains enough paint to cover exactly 200 cm²
Determine if this tin of paint is definitely enough to cover the 6 outside faces of the
closed box.
4 marks
(b)
A closed box is in the shape of a hollow cuboid.
The dimensions of the cuboid are 12 cm by 4.0 cm by 3.0 cm.
Each length is given to 2 significant figures.
A tin of paint contains enough paint to cover exactly 200 cm²
Calculate the length of the longest straight rod that can definitely fit inside the box.
Give your answer to 3 significant figures.
Show your working clearly.
Question 5 continued
67 markshard
2 marks
(a)
A, P and B are three points on horizontal ground.
A is 1 km due south of P
PQ is a vertical tower.
The angle of elevation of Q from A is 16.9°
Show that the height of the tower, in metres to 3 significant figures, is 304 m.
B is 2 km due east of P
BC is a vertical radio mast.
The angle of elevation of Q from C, the top of the radio mast, is 8.2°
5 marks
(b)
A, P and B are three points on horizontal ground.
A is 1 km due south of P
PQ is a vertical tower.
The angle of elevation of Q from A is 16.9°
Calculate the size, in degrees to one decimal place, of the angle of elevation of C from A
Question 6 continued
77 marksmedium
2 marks
(a)
B
Diagram NOT
accurately drawn
C
A
E
D
Figure 1
→ = a and AD
→ = b
Figure 1 shows quadrilateral ABCD such that AB
E is the point such that ADE and BCE are straight lines.
→ = b - 1
3 a
Given that BC
show that AB is parallel to DC
→ = λb - a
Given also that λ is a scalar such that BE
2 marks
(b)
B
Diagram NOT
accurately drawn
C
A
E
D
Figure 1
→ = a and AD
→ = b
Figure 1 shows quadrilateral ABCD such that AB
E is the point such that ADE and BCE are straight lines.
→ = b - 1
3 a
Given that BC
find the value of λ
The area of triangle ABE is x square units.
Given that the area of quadrilateral ABCD is P square units,
3 marks
(c)
B
Diagram NOT
accurately drawn
C
A
E
D
Figure 1
→ = a and AD
→ = b
Figure 1 shows quadrilateral ABCD such that AB
E is the point such that ADE and BCE are straight lines.
→ = b - 1
3 a
Given that BC
find an expression for P in terms of x
Question 7 continued
Question 7 continued
Question 7 continued
811 marksmedium
3 marks
(a)
0.9 m
1.2 m
2.1 m
Figure 2
Figure 2 shows the design for a garden feature.
In the middle of the feature is a circular pond.
The pond is surrounded by 6 identical flower beds.
Each flower bed is in the shape of an isosceles trapezium.
Calculate the area, in m² to 3 significant figures, of one of the flower beds.
Each flower bed needs to be filled with compost to a depth of 10 cm.
The compost is sold in bags containing 50 litres of compost.
4 marks
(b)
Diagram NOT
accurately drawn
0.9 m
1.2 m
2.1 m
Figure 2
Figure 2 shows the design for a garden feature.
In the middle of the feature is a circular pond.
The pond is surrounded by 6 identical flower beds.
Each flower bed is in the shape of an isosceles trapezium.
Show that 16 bags of compost will be needed to fill all six flower beds to a depth of 10 cm.
Show your working clearly.
4 marks
(c)
0.9 m
1.2 m
2.1 m
Figure 2
Figure 2 shows the design for a garden feature.
In the middle of the feature is a circular pond.
The pond is surrounded by 6 identical flower beds.
Each flower bed is in the shape of an isosceles trapezium.
Find the area of the circular pond.
Give your answer in m² to 3 significant figures.
Question 8 continued
Area of trapezium = 1
2 (a + b)h
99 marksmedium
1 mark
(a)
[In this question the coordinates of the points are given in centimetres]
The points with coordinates (1, 1), (2, 4), (4, 6) and (3, 3) are the vertices of quadrilateral A
On the grid opposite, draw and label quadrilateral A
Quadrilateral A is transformed to quadrilateral B by a rotation of 90° anticlockwise about
the origin, O
2 marks
(b)
[In this question the coordinates of the points are given in centimetres]
The points with coordinates (1, 1), (2, 4), (4, 6) and (3, 3) are the vertices of quadrilateral A
On the grid opposite, draw and label quadrilateral B
Quadrilateral B is transformed to quadrilateral C under the transformation with matrix M
where
1
3
M =
1
1
3 marks
(c)
[In this question the coordinates of the points are given in centimetres]
The points with coordinates (1, 1), (2, 4), (4, 6) and (3, 3) are the vertices of quadrilateral A
On the grid opposite, draw and label quadrilateral C
1 mark
(d)
[In this question the coordinates of the points are given in centimetres]
The points with coordinates (1, 1), (2, 4), (4, 6) and (3, 3) are the vertices of quadrilateral A
Calculate the determinant of M
2 marks
(e)
[In this question the coordinates of the points are given in centimetres]
The points with coordinates (1, 1), (2, 4), (4, 6) and (3, 3) are the vertices of quadrilateral A
Calculate the area of quadrilateral A
Determinant of matrix a
b
ad
bc
=
−
Question 9 continued
y
x
Question 9 continued
Question 9 continued
Only use this grid if you need to redraw your shapes.
y
7
x
1015 markshard
2 marks
(a)
Diagrams NOT
20 cm
accurately drawn
10 cm
Figure 3
Figure 4
Figure 3 shows a rectangle with dimensions 20 cm by 10 cm from which a square with
sides of length x cm is removed from each of the corners.
The shape in Figure 3 is then folded along the dotted lines to form a box, without a lid,
in the shape of a cuboid, shown in Figure 4
The volume of the box is V cm³
Show that V = 4x3 - 60x2 + 200x
4 marks
(b)
Diagrams NOT
20 cm
accurately drawn
10 cm
Figure 3
Figure 4
Figure 3 shows a rectangle with dimensions 20 cm by 10 cm from which a square with
sides of length x cm is removed from each of the corners.
The shape in Figure 3 is then folded along the dotted lines to form a box, without a lid,
in the shape of a cuboid, shown in Figure 4
The volume of the box is V cm³
Find, to 3 significant figures, the value of x such that d
V
x = 0
d
b
b
ac
2
4
ax
bx
c
x
2
Solutions of
0
are
a
2
Question 10 continued
Question 10 continued
2 marks
(c)
Diagrams NOT
20 cm
accurately drawn
10 cm
Figure 3
Figure 4
Figure 3 shows a rectangle with dimensions 20 cm by 10 cm from which a square with
sides of length x cm is removed from each of the corners.
The shape in Figure 3 is then folded along the dotted lines to form a box, without a lid,
in the shape of a cuboid, shown in Figure 4
The volume of the box is V cm³
Complete the following table of values for V = 4x3 - 60x2 + 200x
2 marks
(d)
Diagrams NOT
20 cm
accurately drawn
10 cm
Figure 3
Figure 4
Figure 3 shows a rectangle with dimensions 20 cm by 10 cm from which a square with
sides of length x cm is removed from each of the corners.
The shape in Figure 3 is then folded along the dotted lines to form a box, without a lid,
in the shape of a cuboid, shown in Figure 4
The volume of the box is V cm³
On the grid opposite, plot the points from your completed table and, using your answer
to part (b), join them to form a smooth curve.
2 marks
(e)
Diagrams NOT
20 cm
accurately drawn
10 cm
Figure 3
Figure 4
Figure 3 shows a rectangle with dimensions 20 cm by 10 cm from which a square with
sides of length x cm is removed from each of the corners.
The shape in Figure 3 is then folded along the dotted lines to form a box, without a lid,
in the shape of a cuboid, shown in Figure 4
The volume of the box is V cm³
By drawing on the grid a tangent to the curve, find an estimate of the gradient of the
curve at the point where x = 1.5
Starting with a square of side 15 cm and removing a square with sides of length x cm from
each corner, a second box without a lid is formed by folding as in part (a).
The volume of this box is B cm³ where B = 4x3 - 60x2 + 225x
Given that B = 200
3 marks
(f)
Diagrams NOT
20 cm
accurately drawn
10 cm
Figure 3
Figure 4
Figure 3 shows a rectangle with dimensions 20 cm by 10 cm from which a square with
sides of length x cm is removed from each of the corners.
The shape in Figure 3 is then folded along the dotted lines to form a box, without a lid,
in the shape of a cuboid, shown in Figure 4
The volume of the box is V cm³
find, by drawing a suitable straight line on the grid, estimates, to one decimal place,
of the possible values of x
Question 10 continued
V
200
180
160
140
120
100
80
60
40
20
x
O
2
3
4
5
1
Question 10 continued
Question 10 continued
Only use this grid if you need to redraw your curve.
V
200
180
160
140
120
100
80
60
40
20
O
x
2
3
4
5
1
1114 marksmedium
2 marks
(a)
The function f is defined as
x
f : x ↦ 3
1
x
−
1
Find f
1 mark
(b)
The function f is defined as
x
f : x ↦ 3
1
x
−
1
State the value of x that must be excluded from any domain of the function f
4 marks
(c)
The function f is defined as
x
f : x ↦ 3
1
x
−
1
Find the inverse of the function f
Give your answer in its simplest form.
The function g is such that
fg( x) = x
−
1
x
3
1
7 marks
(d)
The function f is defined as
x
f : x ↦ 3
1
x
−
1
Find the value of a such that gf(a) = fg(a)
Question 11 continued
Question 11 continued