12 markseasy
The nth term of a sequence is given by 4n - 12
Write down the first 2 terms of the sequence.
1st term .......................................................
2nd term .......................................................
Maths B
June 2022 · Paper 1 (4MB1/01) (Edexcel IGCSE Maths): Exam Questions
Exam code:4MB127 questions · 100 marks · ≈ 2 hours
22 markseasy
Bronze is made from copper and tin in the ratio of 22 : 3 by weight.
Calculate the weight of copper, in kg, needed to make 12.5 kg of bronze.
....................................................... kg
32 markseasy
A pattern on a white grid is made from 6 shaded squares.
Shade exactly 2 more squares so that the 8 shaded squares will make a pattern with
rotational symmetry of order 4
42 marksmedium
Make u the subject of
s = ut + 1
2 at2
52 markseasy
Without using a calculator and showing all your working, evaluate
3 1
8 × 2 4
5
Give your answer as a mixed number in its simplest form.
62 markseasy
Factorise completely
2mc2 + 6p2c4
72 markseasy
Inzamam cycles 6.4 km from his home to school.
He leaves home at 07 40 and arrives at school at 08 20
Calculate his average speed, in km/h, for the journey.
....................................................... km/h
83 marksmedium
Rohan asked each of the students in his school what colour paper they would prefer him
to use for their worksheets.
There are 150 students in Rohan’s school.
Using his results, Rohan drew the following accurate pie chart.
red
orange
blue
green
yellow
Find how many of the 150 students preferred blue paper.
93 marksmedium
Solve
2(x + 7) = 5x - 6
x = .......................................................
103 marksmedium
E
∞
′
Above is a Venn diagram showing the sets ∞, ′, and E
∞ is the set of natural numbers,
′ is the set of integers,
is the set of rational numbers
E is the universal set.
Place each of the following four numbers in the correct place in the above diagram.
−4
22
169
17
11
7
113 marksmedium
The diagram shows a biased spinner with four colours blue, red, green and yellow.
When the spinner is spun once
•
the probability it lands on blue is twice the probability it lands on red
•
the probability it lands on yellow is three times the probability it lands on blue
•
the probability it lands on green is 0.25
Find the probability the spinner lands on yellow.
red
Diagram NOT
green
accurately drawn
blue
yellow
123 marksmedium
Here is a list of four numbers.
1.1 × 1015
2.1 × 1013
3.2 × 1014
3.7 × 1016
Find the median of these four numbers.
Give your answer in standard form.
133 marksmedium
Given that x ≠ –4
x
x
4
2
simplify
x
2
8
143 markseasy
D
C
E
Diagram NOT
accurately drawn
A
B
Using the diagram above, prove that the sum of the angles of triangle ABC is the same
as the sum of the angles on the straight line DCE
Give a reason for each stage of your proof.
154 marksmedium
2 marks
(a)
The numbers A, B, and C are given as products of their prime factors.
A = 35 × 74 × 1039
B = 316 × 79 × 114
C = 38 × 74 × 2692
Find the Highest Common Factor (HCF) of A, B and C
Exactly one of the three numbers is the square of an integer N
2 marks
(b)
The numbers A, B, and C are given as products of their prime factors.
A = 35 × 74 × 1039
B = 316 × 79 × 114
C = 38 × 74 × 2692
Calculate the value of N
N =.......................................................
164 markseasy
2 marks
(a)
A =
B =
3 1
−
−
6
1
Calculate A + 2B
2 marks
(b)
A =
B =
3 1
−
−
6
1
Calculate AB
174 marksmedium
A
O
100°
B
C
OABC is a sector of a circle, centre O, with ∠AOC = 100°
The area of the sector is 27 cm²
Calculate the perimeter, in cm to 3 significant figures, of the sector.
....................................................... cm
183 marksmedium
Given that p = 1
5
2
show that 1
p = p - 1
Show your working clearly.
194 markshard
There are 1000 cm³ of orange juice in a carton.
The total surface area of this carton is 700 cm²
For a special offer, a new carton is designed.
The volume of orange juice in the new carton is 33.1% more than the volume of orange juice
in the original carton.
The new carton is mathematically similar to the original carton.
Calculate the total surface area of the new carton.
....................................................... cm²
204 marksmedium
Given that a =
5
2
x
find the exact value of x
x = .......................................................
213 marksmedium
The diagram shows triangle ABC
A
C
B
The region R consists of all the points inside the triangle that are closer to C than to B
and also closer to AB than to AC
Using ruler and compasses only and showing all your construction lines,
construct and show by shading the region R
Label the region R
225 marksmedium
2 marks
(a)
y
y = x
8
6
4
y = 2
2
O
x
2
4
6
8
10
The diagram above shows the line L, the line with equation y = 2 and the line with
equation y = x drawn on a grid.
Find an equation of the line L
3 marks
(b)
y
y = x
8
6
4
y = 2
2
O
x
2
4
6
8
10
The diagram above shows the line L, the line with equation y = 2 and the line with
equation y = x drawn on a grid.
Write down the three inequalities that define the region shaded in the diagram.
235 marksmedium
Diagram NOT
B
accurately drawn
E
3 cm
C
A
D
ABCD is a kite so that the points A, B, C and D lie on a circle with radius 7.5 cm.
The diagonals, AC and BD, of the kite intersect at point E, so that AE = 3 cm.
The line AEC is a diameter of the circle.
Find the area of the kite ABCD
....................................................... cm²
246 marksmedium
In a triangle ABC
AC = 6.5 cm
BC = 12 cm
∠ABC = 30°
Calculate, in cm² to 3 significant figures, the smaller of the areas of the two possible triangles ABC
....................................................... cm²
257 markshard
1 mark
(a)
There are 25 sweets in a bag.
n of the sweets are orange.
The rest of the sweets are yellow.
Chana takes a sweet at random from the bag.
She eats the sweet.
Chana takes at random another sweet from the bag.
She eats the sweet.
The probability that Chana eats one orange sweet and one yellow sweet is 1
3
Write down the probability that both sweets taken by Chana are the same colour.
6 marks
(b)
There are 25 sweets in a bag.
n of the sweets are orange.
The rest of the sweets are yellow.
Chana takes a sweet at random from the bag.
She eats the sweet.
Chana takes at random another sweet from the bag.
She eats the sweet.
The probability that Chana eats one orange sweet and one yellow sweet is 1
3
Find the possible values of n
Show clear algebraic working.
267 markshard
2 marks
(a)
f(x) = 2x3 + 9x2 - 14x - 9
Using the factor theorem, show that (2x - 1) is not a factor of f(x)
x
3 marks
(b)
f(x) = 2x3 + 9x2 - 14x - 9
Express f ( )
in the form (x + a)2 + b
x
2
1
where a and b are integers to be found.
2 marks
(c)
f(x) = 2x3 + 9x2 - 14x - 9
Hence find the exact solutions of f(x) = 0
279 markshard
5 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
0 ≤ t ≤ 9
s = t3 - 18t2 + 81t
At time T seconds, where T < 9, P is at the point A on the line.
At A, particle P instantaneously reverses its direction of motion and moves back towards O
Find the value of T
T = .......................................................
As P moves from A back towards O, the greatest speed of P is V m/s
4 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
0 ≤ t ≤ 9
s = t3 - 18t2 + 81t
At time T seconds, where T < 9, P is at the point A on the line.
At A, particle P instantaneously reverses its direction of motion and moves back towards O
Find the value of V
V = .......................................................