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Mathematics questions, chapter 5
Nama / NameKelas / ClassTarikh / Date

Circles

40 marks. Use Practice to check each answer as you go, or Exam to answer everything first. Use π = 227 unless the question gives another value. Show your working for Section B.

Section A: objective questions

12 marks
Choose the correct answer.
1

Question 1

Which of these is the longest chord of a circle?
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B
A diameter is a chord that passes through the centre, and it is the longest chord. A radius is not a chord (one end is the centre), and an arc and the circumference are curved, not straight.
For the teacher: Remembering, low difficulty, standard 5.1.1
Textbook p. 76
2

Question 2

Diagram 1 shows a circle with centre O. What is the shaded region called?
A circle with centre O. A large part of the circle between two radii is shaded
Diagram 1
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C
The region is enclosed by two radii and an arc, so it is a sector. It is more than half of the circle, so it is the major sector. A segment is enclosed by a chord and an arc.
For the teacher: Remembering, low difficulty, standard 5.1.1
Textbook p. 76
3

Question 3

Syafiq opens his compasses to 3.6 cm and draws a circle. What is the diameter of the circle?
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C
The compasses are set to the radius, 3.6 cm, so the diameter is 2 × 3.6 = 7.2 cm. 11.3 cm comes from multiplying the radius by π, which is not the diameter. 1.8 cm halves the radius by mistake.
For the teacher: Understanding, low difficulty, standard 5.1.2
Textbook p. 78
4

Question 4

How many axes of symmetry does a circle have?
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D
Every straight line through the centre (every diameter) is an axis of symmetry, and there are infinitely many of them.
For the teacher: Understanding, low difficulty, standard 5.2.1
Textbook p. 81
5

Question 5

In Diagram 2, O is the centre of the circle and OM is perpendicular to the chord AB, OA = 13 cm and OM = 5 cm. Find the length of AB.
Circle with centre O and chord AB. OM is perpendicular to AB at M. OA = 13 cm and OM = 5 cm
Diagram 2
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B
AM² = 13² − 5² = 169 − 25 = 144, so AM = 12 cm. OM bisects AB, so AB = 2 × 12 = 24 cm. 12 cm is only half of the chord.
For the teacher: Applying, low difficulty, standard 5.2.1
Textbook p. 83
6

Question 6

PQ and RS are two chords of a circle with centre O. PQ = RS, and the perpendicular distance from O to PQ is 7 cm. What is the perpendicular distance from O to RS?
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A
Chords that are equal in length are the same distance from the centre of the circle, so the distance is 7 cm.
For the teacher: Understanding, low difficulty, standard 5.2.1
Textbook p. 82
7

Question 7

In Diagram 3, two parallel chords of lengths 16 cm and 30 cm are on the same side of the centre O. The radius of the circle is 17 cm. What is the distance between the two chords?
Circle with centre O and radius 17 cm. Two parallel chords above O, one of 16 cm and one of 30 cm
Diagram 3
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D
The 16 cm chord is √(17² − 8²) = 15 cm from O. The 30 cm chord is √(17² − 15²) = 8 cm from O. On the same side, the distance between them is 15 − 8 = 7 cm. 23 cm is the sum, which is only used when the chords are on opposite sides.
For the teacher: Applying, medium difficulty, standard 5.2.3
Textbook p. 85
8

Question 8

Calculate the circumference of a circle with a diameter of 35 cm. (Use π = 227)
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A
C = πd = 227 × 35 = 110 cm. 55 cm is πr, 220 cm is 2πd and 962.5 cm is the area πr².
For the teacher: Applying, low difficulty, standard 5.3.3
Textbook p. 88
9

Question 9

The circumference of a circle is 44 cm. What is its area? (Use π = 227)
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C
2πr = 44, so 2 × 227 × r = 44 and r = 7 cm. Area = 227 × 7² = 154 cm². 616 cm² comes from using the diameter 14 cm as the radius.
For the teacher: Applying, medium difficulty, standard 5.3.3
Textbook p. 89
10

Question 10

A circle has a radius of 21 cm. Find the length of the minor arc that has an angle of 120° at the centre. (Use π = 227)
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B
Arc = 120°360° × 2 × 227 × 21 = 13 × 132 = 44 cm. 132 cm is the whole circumference; 22 cm is the arc for 60°.
For the teacher: Applying, low difficulty, standard 5.3.3
Textbook p. 90
11

Question 11

A sector has an angle of 45° at the centre and a radius of 14 cm. Calculate the area of the sector. (Use π = 227)
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D
Area = 45°360° × 227 × 14² = 18 × 616 = 77 cm². 154 cm² is the sector for 90°, and 616 cm² is the whole circle.
For the teacher: Applying, low difficulty, standard 5.3.3
Textbook p. 91
12

Question 12

Calculate the perimeter of a semicircle of diameter 28 cm. (Use π = 227)
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A
The perimeter is the curved edge plus the straight diameter: 12 × 227 × 28 + 28 = 44 + 28 = 72 cm. 44 cm forgets the straight edge, and 116 cm uses the whole circumference.
For the teacher: Analysing, medium difficulty, standard 5.3.3
Textbook p. 89

Section B: structured questions

28 marks
Answer all questions. Show your working.
13

Question 13

Diagram 4 shows a circle with centre O.
Circle with centre O; PQ is a diameter through O; ST is a chord above the diameter; OR is a radius
Diagram 4
[1 mark] (a)Name the diameter of the circle.
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Tick each point you got.
[1 mark] (b)Name a chord that is not a diameter.
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Tick each point you got.
[1 mark] (c)A diameter is the longest chord of a circle.
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True
Any chord that does not pass through the centre is shorter than the diameter.
For the teacher: Remembering, low difficulty, standard 5.1.1
Textbook p. 76
14

Question 14

In Diagram 5, O is the centre of the circle. OS is perpendicular to the chord MN. The radius is 17 cm and MN = 30 cm.
Circle with centre O and radius 17 cm; chord MN = 30 cm; OS is perpendicular to MN at S
Diagram 5
[1 mark] (a)State the length of MS. Give a reason.
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Tick each point you got.
[2 marks] (b)Calculate the length of OS.
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Tick each point you got.
For the teacher: Applying, low difficulty, standard 5.2.1
Textbook p. 83
15

Question 15

Diagram 6 shows a round table top with a diameter of 50 cm. Two parallel supports, 48 cm and 14 cm long, are fixed on opposite sides of the centre O.
Circle of diameter 50 cm with centre O; a chord of 48 cm above O and a parallel chord of 14 cm below O
Diagram 6
[2 marks] (a)Calculate the distance of the 48 cm support from O.
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Tick each point you got.
[2 marks] (b)Calculate the distance between the two supports.
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They are on opposite sides of O, so the two distances are added.
Tick each point you got.
For the teacher: Analysing, medium difficulty, standard 5.2.3
Textbook p. 85
16

Question 16

The circumference of a circular pail is 88 cm and its diameter is 28 cm.
[1 mark] (a)Calculate circumference ÷ diameter. Give the answer as a fraction in its lowest terms.
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This ratio is the value of π, which is the same for every circle.
Tick each point you got.
[2 marks] (b)Hence, find the circumference of a circular plate with a radius of 10.5 cm. (Use π = 227)
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Tick each point you got.
For the teacher: Understanding, low difficulty, standard 5.3.1
Textbook p. 86
17

Question 17

Diagram 7 shows a sector POQ of a circle with centre O. The radius is 21 cm and ∠POQ = 60°. (Use π = 227)
Sector POQ with centre O, radius 21 cm and angle POQ = 60 degrees
Diagram 7
[2 marks] (a)Calculate the length of arc PQ.
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Tick each point you got.
[2 marks] (b)Calculate the area of sector POQ.
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Tick each point you got.
For the teacher: Applying, low difficulty, standard 5.3.3
Textbook p. 90
18

Question 18

Diagram 8 shows a circular fish pond of radius 10 m. A path 2 m wide goes all the way round the pond. Calculate the area of the path, correct to 2 decimal places. (Use π = 227)
A circular pond of radius 10 m with a path around it; a path 2 m wide round it
Diagram 8
[3 marks] (a)Calculate the area of the path.
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Check: outer circle 227 × 144 = 452.57; inner circle 227 × 100 = 314.29; the difference is 138.29 (using the unrounded values; the rounded figures above differ in the last digit).
Tick each point you got.
For the teacher: Analysing, medium difficulty, standard 5.3.4
Textbook p. 92
19

Question 19

A shop sells two round pizzas. Pizza A has a diameter of 20 cm and costs RM12. Pizza B has a diameter of 30 cm and costs RM24. Hakim says, "Pizza B is twice the price, so it is not worth it." (Use π = 3.142)
[2 marks] (a)Calculate the area of each pizza.
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Tick each point you got.
[2 marks] (b)Is Hakim correct? Compare the price for each cm² of pizza and give a conclusion.
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The area depends on r², so B (r = 15 cm) has more than twice the area of A (r = 10 cm) while costing exactly twice as much.
Tick each point you got.
For the teacher: Evaluating, medium difficulty, standard 5.3.3
Textbook p. 89
20

Question 20

Diagram 9 shows a rectangular garden 20 m long and 12 m wide. Amir wants a circular pond in the middle of the garden, with a strip of grass at least 2 m wide between the pond and every edge of the garden. (Use π = 227)
Rectangle 20 m by 12 m with an inner rectangle 2 m from every edge
Diagram 9
[2 marks] (a)Find the greatest radius the pond can have.
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Tick each point you got.
[2 marks] (b)Using this radius, calculate the area of the garden that is not the pond, correct to 2 decimal places.
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Tick each point you got.
For the teacher: Creating, high difficulty, standard 5.3.4
Textbook p. 92