MOCK CAMBRIDGE IGCSE 2021
MAKTAB RENDAH SAINS MARA
International General Certificate of Secondary Education
CANDIDATE NAME
CENTRE
CANDIDATE
NUMBER
COLLEGE
NUMBER
CLASS
_____________________________________________________________________________
MATHEMATICS
Paper 2 (Extended)
Additional Materials:
0580/22
September 2021
1 hour 30 minutes
Electronic calculator
Tracing paper (optional)
Geometrical Instruments
________________________________________________________________________________
READ THESE INSTRUCTIONS FIRST
Write your name, centre number, class, college number or candidate number (if any) in the
boxes at the top of the page.
Write in dark blue or black pen.
You may use a pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue, or correction fluid.
DO NOT WRITE IN ANY BARCODES.
Answer all the questions.
If working is needed for any question it must be shown below that question.
Electronic calculators should be used.
If the degree of accuracy is not specified in the question, and if the answer is not exact, give the
answer to three significant figures. Give answers in degrees to one decimal place.
For π, use either your calculator value or 3.142.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total of the marks for this paper is 70.
__________________________________________________________________________
This document consists of 18 printed pages.
©BPM2021
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[Turn over
Name:
Class:
2
CONFIDENTIAL
1
The Venn diagram shows three sets, A, B, and C.
ξ
A
1
2
3
6
5
4
B
7
9
8
C
10
11
(a) Use set notation to complete the statement for the Venn diagram above.
(i)
A _________________ B = {2, 5, 7}
……..…………….. [1]
(ii)
3 ________________ A
……..…………….. [1]
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Name:
Class:
3
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(b)
𝜉𝜉 = {𝑥𝑥: 𝑥𝑥 𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑎𝑎𝑎𝑎𝑎𝑎 10 ≤ 𝑥𝑥 ≤ 20}
𝑃𝑃 = {𝑥𝑥: 𝑥𝑥 𝑖𝑖𝑖𝑖 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑜𝑜𝑜𝑜 3}
𝑄𝑄 = {𝑥𝑥: 𝑥𝑥 𝑖𝑖𝑖𝑖 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑜𝑜𝑜𝑜 2}
𝑅𝑅 = {𝑥𝑥: 𝑥𝑥 𝑎𝑎𝑎𝑎𝑎𝑎 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝑜𝑜𝑜𝑜 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛}
Complete the Venn diagram below to show this information.
ξ
Q
P
R
[3]
2
Calculate
3
√64
.
23
……..…………….. [1]
3
3
Write √𝑥𝑥 4 in the form of fractional indices.
……..…………….. [1]
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Name:
Class:
4
CONFIDENTIAL
4
Calculate
0.2 + (−4) 2
.
18 − 0.005 × 7
Give your answer correct to three significant figures.
……..…………….. [2]
5
A rectangular container has a volume of 150 cm3 measured to the nearest centimetre cube.
If the base area of the container is 25 cm2 measured to the nearest centimetre square, write down
the lower bound and upper bound for the height of the container.
Round off your answer to two decimal places.
Lower bound = …………………..cm
Upper bound = …………………...cm [3]
6
Factorise completely 45𝑚𝑚2 − 5𝑛𝑛2 .
……..…………….. [2]
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Name:
Class:
5
CONFIDENTIAL
7
The diagram shows a straight line M.
(a)
Work out the gradient of the line M.
……..…………….. [2]
(b)
Write down the equation of the line parallel to the line M that passes through
the point (1, –2).
……..…………….. [2]
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Name:
Class:
6
CONFIDENTIAL
8
f ( x=
) 2x + 4 .
Find
(a)
f −1 ( x)
f −1 ( x) = ……..…………….. [2]
(b)
ff −1 (6)
ff −1 (6) = ……..…………….. [1]
9
Given a sequence is
9, 14, 19, 24, …
Find
(a) nth term of the sequence,
……..…………….. [2]
(b) 50th term of the sequence.
……..…………….. [1]
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Name:
Class:
7
CONFIDENTIAL
10
Solve the simultaneous equations.
You must show all your working.
𝑦𝑦 = 𝑥𝑥 − 12
x=
3− y
2
x = ……..……………..
y = ……..…………….. [3]
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Name:
Class:
8
CONFIDENTIAL
11
Points D (3, −5) and E, are plotted on a Cartesian plane.
Given the midpoint of DE is (5, 3).
Find
(a)
coordinate of E,
E (.….…. , ….…...) [2]
(b)
distance of DE.
……..…………….. [2]
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Name:
Class:
9
CONFIDENTIAL
12
(a) Simplify
x2 − 1
.
x 2 + 3x − 4
……..…………….. [2]
(b) Write
5
6
− as a single fraction.
2x −1 x
……..…………….. [2]
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Name:
Class:
10
CONFIDENTIAL
13
Speed,
(km/h)
W
NOT TO SCALE
V
0700
0715
0745
Time (h)
0800
0830
The speed-time graph shows the journey of a train.
The speed V, is half the speed of W where W = 200 km/h.
Calculate the total distance travelled by the train correct to 1 decimal place.
……..…………….. km [3]
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Name:
Class:
11
CONFIDENTIAL
14
Find the order of rotational symmetry for the shape below.
……..…………….. [1]
15
NOT TO SCALE
Diagram shows a circular garden with 4 different pathways.
The circular garden is covered with grass.
The circle has centre O and radius 8 m.
Calculate the area of grass covered.
……..……………..m2 [2]
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Name:
Class:
12
CONFIDENTIAL
16
The triangle ABC is the image of triangle DEF under transformation X.
Describe fully the single transformation represented by X.
……………………………………………………………………………………..………
……………………………………………………………………………………..……… [2]
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Name:
Class:
13
CONFIDENTIAL
17
Find the value of y.
NOT TO SCALE
14 cm
22 cm
𝑦𝑦°
y = ……..…………….. [2]
18
Solve the equation 3 sin 𝑥𝑥 = 4 cos 𝑥𝑥, 180° ≤ 𝑥𝑥 ≤ 360°.
x = ……..…………….. ° [3]
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Name:
Class:
14
CONFIDENTIAL
19
The diagram shows a circle with centre O and a radius of 10 cm.
JRK is the tangent to the circle.
J
R
S
O
O
U
U
NOT TO SCALE
P
K
T
Given that RT = 16 cm,
(a)
find the length of PU.
PU = ……..…………….. cm [2]
(b)
calculate the ∠ JRU.
∠ JRU = .……..…………….. ° [2]
©BPM2021
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Name:
Class:
15
CONFIDENTIAL
y
20
6
5
P
4
M
3
K
2
1
N
−6 −5 −4 −3 −2 −1 0
−1
J
L
1
2
3
4
5
x
6
7
−2
−3
−4
−5
(a) Triangle MNP is the image of triangle JKL under transformation Y.
Describe fully the single transformation represented by Y.
……………………………………………………………………………………………….
………………………………………………………………………………………………. [3]
(b) Draw on the grid above image of MNP under enlargement with scale factor 2 centre at (4,2).
[3]
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Name:
Class:
16
CONFIDENTIAL
21
A model tower is 20 cm high and has a volume of 1200 cm3.
The real tower is 10 m high.
What is the volume of the real tower? Give your answers in cubic metre.
……..…………….. m3 [3]
©BPM2021
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Name:
Class:
17
CONFIDENTIAL
22
(a)
Janny brings a box of fruits which includes 24 oranges, 36 apples and 15 pears for her
students in a class.
(i)
Find the probability that the student will choose an apple.
……..…………….. [1]
(ii)
Janny adds more oranges in that box.
Find the number of oranges added if the probability that the student will choose
5
a pear is 28.
……..…………….. [3]
(b)
A florist sells several types of flowers in her shop.
There are eighty carnations, seventy roses, twenty sunflowers, fifty daffodils, thirty
chrysanthemums, and fifty tulips.
A customer chooses a flower at random.
What is the probability that it is not a carnation?
……..…………….. [2]
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Name:
Class:
18
CONFIDENTIAL
23
The stem-and-leaf diagram shows the number of customers eating in a restaurant for 20
working days.
1
1
6
6
7
9
2
2
3
3
3
3
3
4
5
6
8
4
3
6
8
9
8
7
9
Key: 22 represents 22 customers
(a)
Find the median number of customers.
……..…………….. [1]
(b)
Which type of average is suitable to represent the data. Give your reason.
……………………………………………………………………………………….
………………………………………………………………………………………. [2]
END OF QUESTION PAPER
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