Space: Mathematics Darjah 6 questions

Section A: objective questions

8 marks

Choose the correct answer.

Which straight line connects two points on the circumference and passes through the centre of a circle?

Diameter
Radius
Circumference
Centre

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The diameter passes through the centre. A radius goes from the centre to the circumference only.

For the teacher: Remembering, low difficulty, standard 6.2.1

Textbook p. 179

What is the size of each interior angle of a regular hexagon?

108°
120°
135°
60°

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A regular hexagon is made of six equilateral triangles, so each interior angle is 60° + 60° = 120°.

For the teacher: Remembering, low difficulty, standard 6.1.1

Textbook p. 174

Which of these angles is an obtuse angle?

50°
90°
108°
180°

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An obtuse angle is more than 90° and less than 180°. 108° is obtuse; 50° is acute, 90° is a right angle.

For the teacher: Understanding, low difficulty, standard 6.1.2

Textbook p. 166

Diagram 1 shows a circle with a diameter of 14 cm. What is the length of its radius?

28 cm
14 cm
10 cm
7 cm

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Radius = diameter ÷ 2 = 14 ÷ 2 = 7 cm.

For the teacher: Applying, low difficulty, standard 6.2.1

Textbook p. 179

Diagram 2 shows a regular polygon. What is its name?

A regular polygon with seven equal sides — Diagram 2

Heptagon
Hexagon
Octagon
Pentagon

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Count the sides: there are 7. A polygon with seven sides is a heptagon.

For the teacher: Understanding, low difficulty, standard 6.1.1

Textbook p. 175

A regular pentagon has sides of 6.5 cm. What is its perimeter?

26 cm
32.5 cm
39 cm
13 cm

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Perimeter = 5 × 6.5 = 32.5 cm.

For the teacher: Applying, low difficulty, standard 6.3.1

Textbook p. 185

Which statement about a regular polygon is true?

Only the sides are equal.
Only the angles are equal.
All sides and all interior angles are equal.
It always has four sides.

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A regular polygon has equal sides and equal interior angles. A shape with equal sides but unequal angles is not regular.

For the teacher: Analysing, low difficulty, standard 6.1.1

Textbook p. 177

A circle-shaped cake has a radius of 10 cm. Mei Hwa buys a square cake board. Which is the smallest board that the cake fits on?

10 cm × 10 cm
15 cm × 15 cm
18 cm × 18 cm
20 cm × 20 cm

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The diameter is 2 × 10 = 20 cm, so the side of the board must be at least 20 cm.

For the teacher: Applying, medium difficulty, standard 6.3.1

Textbook p. 186

Section B: structured questions

29 marks

Answer all questions. Show your working.

Diagram 3 shows a circle with centre O. P, Q and R are on the circumference. The length of PQ is 9 cm.

Circle with centre O; PQ is a diameter of 9 cm; OR is drawn to the circumference — Diagram 3

[1 mark] (a)What is the name of the line OR?

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Radius [1]1

Tick each point you got.

[1 mark] (b)What is the name of the line PQ?

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Diameter [1]1

Tick each point you got.

[1 mark] (c)What is the length of OR?

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9 ÷ 2 = 4.5 cm [1]1

Tick each point you got.

For the teacher: Remembering, low difficulty, standard 6.2.1

Textbook p. 179

Diagram 4 shows a regular polygon. Each side is 7 cm.

Regular pentagon with each side 7 cm — Diagram 4

[1 mark] (a)Name the polygon.

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Regular pentagon [1]1

Tick each point you got.

[1 mark] (b)What is the size of each interior angle?

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108° [1]1

Tick each point you got.

[1 mark] (c)Find the perimeter of the polygon.

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5 × 7 = 35 cm [1]1

Tick each point you got.

For the teacher: Understanding, low difficulty, standard 6.1.1

Textbook p. 173

Aiman forms angle ABC of 65° with a protractor.

[1 mark] (a)What type of angle is 65°?

AcuteRightObtuse

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Acute

65° is less than 90°.

[2 marks] (b)Where must he put the baseline and the centre of the protractor?

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Baseline exactly on line AB [1]1
Centre exactly on point B (the vertex of the angle) [1]1

Tick each point you got.

For the teacher: Understanding, low difficulty, standard 6.1.2

Textbook p. 165

Anding makes a photo frame with six equal sides. The perimeter of the frame is 120 cm. What is the length of each side?

[2 marks] (a)Show your working and give the answer.

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120 ÷ 6 [1]1
20 cm [1]1

Tick each point you got.

For the teacher: Applying, medium difficulty, standard 6.3.1

Textbook p. 185

Chee Cheong wants to cut a circle of radius 8 cm from the square plank in Diagram 5.

A square plank 25 cm by 25 cm — Diagram 5

[1 mark] (a)What is the diameter of the circle?

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8 × 2 = 16 cm [1]1

Tick each point you got.

[1 mark] (b)Will the circle fit on the plank?

YesNo

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Yes

The diameter 16 cm is less than 25 cm.

[1 mark] (c)How much of the width of the plank is left over?

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25 − 16 = 9 cm [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 6.3.1

Textbook p. 185

A resting area is in the shape of a regular octagon with each side 5 m, as in Diagram 6.

[1 mark] (a)What is the size of each interior angle?

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135° [1]1

Tick each point you got.

[1 mark] (b)A fence goes round the area. How long is the fence?

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8 × 5 = 40 m [1]1

Tick each point you got.

[2 marks] (c)Another resting area is a regular hexagon with each side 5 m. How much shorter is its fence than the fence in (b)?

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6 × 5 = 30 m [1]1
40 − 30 = 10 m [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 6.3.1

Textbook p. 185

Charles and Raymond each draw a regular polygon. The number of sides of Charles's polygon is 2 times the number of sides of Raymond's polygon. Both have at most eight sides. Give two possible pairs of polygons.

[2 marks] (a)Write the name of Raymond's and Charles's polygon for each pair.

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Raymond triangle (3 sides), Charles hexagon (6 sides) [1]1
Raymond square (4 sides), Charles octagon (8 sides) [1]1

Tick each point you got.

For the teacher: Analysing, high difficulty, standard 6.1.1

Textbook p. 177

Farid says: "A circle of radius 6 cm has a diameter of 3 cm, because the diameter is half of the radius."

[1 mark] (a)Is Farid correct?

YesNo

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The diameter is twice the radius.

[2 marks] (b)Explain your answer and give the correct diameter.

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The diameter is 2 times the radius (not half) [1]1
6 × 2 = 12 cm [1]1

Tick each point you got.

For the teacher: Evaluating, medium difficulty, standard 6.2.1

Textbook p. 179

A baker receives many orders for square cakes of 25 cm × 25 cm. She wants to buy cake boards that are square.

[1 mark] (a)Which board size is the most suitable?

20 cm × 20 cm25 cm × 25 cm30 cm × 30 cm

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30 cm × 30 cm

The board must be larger than the cake.

[2 marks] (b)Give a reason for your choice.

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The board must be bigger than 25 cm in each direction [1]1
so the cake fits on the board with a margin, and a board of 20 cm would be too small [1]1

Tick each point you got.

For the teacher: Creating, high difficulty, standard 6.3.1

Textbook p. 186

Draw a circle with centre O and a radius OH of 3.5 cm. Then draw the diameter PT.

[2 marks] (a)Use a ruler and two pencils to draw the circle, then label O, OH, P and T.

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Circle drawn with radius 3.5 cm and the centre O marked [1]1
OH labelled; PT drawn through O and labelled [1]1

Tick each point you got.

[1 mark] (b)What is the length of PT?

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3.5 × 2 = 7 cm [1]1

Tick each point you got.

For the teacher: Creating, medium difficulty, standard 6.2.2

Textbook p. 182

Section A: objective questions

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Section B: structured questions

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18