Mathematics questions, unit 6

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Space

42 marks. Use Practice to check each answer as you go, or Exam to answer everything against the clock first.

Section A: objective questions

8 marks

Choose the correct answer for each question.

Question 1

Which statement is true for every regular polygon?

It has at least one right angle.
Its sides are equal but its angles may be different.
All its sides are equal and all its interior angles are equal.
It has no diagonals.

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A regular polygon has equal sides and equal interior angles. A rhombus has equal sides but unequal angles, so it is not regular.

For the teacher: Remembering, low difficulty, standard 6.1.1

Textbook p. 217

Question 2

How many diagonals does a regular heptagon have?

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A heptagon has 7 corners and each corner joins to 4 corners that are not next to it. 7 × 4 ÷ 2 = 14. 7 is the number of sides.

For the teacher: Understanding, low difficulty, standard 6.1.1

Textbook p. 218

Question 3

Diagram 1 shows a protractor placed on an angle. What is the size of the angle?

A protractor with one arm of the angle along the baseline on the right and the other arm at the 70 mark of the scale that starts at 0 on the right — Diagram 1

70°
110°
20°
80°

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The arm on the baseline points to 0 on the right, so we read the scale that starts at 0 on the right. The other arm is at 70°. 110° is the reading on the other scale (70 + 110 = 180).

For the teacher: Understanding, medium difficulty, standard 6.2.1

Textbook p. 219

Question 4

Diagram 2 shows a square and a regular pentagon joined along one side. Each side is 6 cm long. What is the perimeter of the composite shape?

A square with a regular pentagon on top; each side is 6 cm — Diagram 2

54 cm
48 cm
30 cm
42 cm

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The shared side is inside the shape. Outer sides = 4 + 5 − 2 = 7. 7 × 6 cm = 42 cm. 54 cm counts all 9 sides.

For the teacher: Applying, low difficulty, standard 6.3.1

Textbook p. 221

Question 5

Diagram 3 shows a rectangle 6 m by 4 m with a right-angled triangle on top. The triangle has a base of 6 m and a height of 3 m. What is the area of the whole shape?

A rectangle 6 m wide and 4 m high with a right-angled triangle on top, base 6 m and height 3 m — Diagram 3

24 m²
33 m²
42 m²
27 m²

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Rectangle: 6 × 4 = 24 m². Triangle: ½ × 6 × 3 = 9 m². 24 + 9 = 33 m². 42 m² forgets the half of the triangle (24 + 18).

For the teacher: Applying, low difficulty, standard 6.3.2

Textbook p. 224

Question 6

Diagram 4 shows a cube of side 3 cm on top of a cuboid. What is the volume of the composite shape?

A cuboid 6 cm long, 4 cm deep and 3 cm high with a cube of side 3 cm on top — Diagram 4

72 cm³
81 cm³
90 cm³
99 cm³

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Cuboid: 6 × 4 × 3 = 72 cm³. Cube: 3 × 3 × 3 = 27 cm³. 72 + 27 = 99 cm³. 81 cm³ uses 3 × 3 = 9 for the cube.

For the teacher: Applying, medium difficulty, standard 6.4.1

Textbook p. 226

Question 7

Diagram 5 shows a block 10 cm long, 8 cm deep and 6 cm high. A piece 4 cm long, 8 cm deep and 3 cm high is cut from the top right corner. What is the volume of the block that is left?

A block 10 cm long, 8 cm deep and 6 cm high with a piece cut from the top right corner — Diagram 5

384 cm³
96 cm³
576 cm³
480 cm³

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Whole block: 10 × 8 × 6 = 480 cm³. Piece cut away: 4 × 8 × 3 = 96 cm³. Left: 480 − 96 = 384 cm³. 576 cm³ adds the piece instead of subtracting it.

For the teacher: Analysing, high difficulty, standard 6.5.1

Textbook p. 229

Question 8

Aini says, "A rectangle has 4 equal angles, so a rectangle is a regular polygon." Which reason shows that she is not correct?

A rectangle has no diagonals.
A rectangle has only 2 corners.
A rectangle that is not a square does not have all its sides equal.
A rectangle has no interior angles.

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A regular polygon needs equal sides and equal angles. A rectangle that is not a square has equal angles (90°) but its sides are not all equal.

For the teacher: Evaluating, high difficulty, standard 6.1.1

Textbook p. 217

Section B: structured questions

34 marks

Answer all questions. Show your working.

Question 9

Choose the correct answer.

[1 mark] (a)A regular polygon with 5 sides is a ______

AhexagonBpentagonCoctagon

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pentagon

[1 mark] (b)A regular hexagon has ______ symmetrical axes.

A3B6C9

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[1 mark] (c)A straight line drawn from one corner to a corner that is not next to it is called a ______

AsideBdiagonalCsymmetrical axis

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diagonal

For the teacher: Remembering, low difficulty, standard 6.1.1

Textbook p. 218

Question 10

Diagram 6 shows two polygons, P and Q.

P is a rectangle 6 cm by 3 cm. Q is a regular hexagon with each side 4 cm. — Diagram 6

[1 mark] (a)Which shape is a regular polygon?

APBQ

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[1 mark] (b)Give one reason why the other shape is not a regular polygon.

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Its sides are not all equal in length (6 cm and 3 cm) [1]1

Tick each point you got.

[1 mark] (c)How many diagonals does shape Q have?

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A hexagon has 6 corners: 6 × 3 ÷ 2 = 9 diagonals [1]1

Tick each point you got.

For the teacher: Understanding, low difficulty, standard 6.1.1

Textbook p. 217

Question 11

Diagram 7 shows an angle measured with a protractor. One arm is on the baseline at the left.

A protractor with one arm along the baseline on the left and the other arm at the 50 mark on the scale that starts at 0 on the left — Diagram 7

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

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50°

50° (the arm on the left starts at 0° of the scale that begins on the left) [1]1

Tick each point you got.

[1 mark] (b)What type of angle is it? Give a reason.

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Acute angle, because it is less than 90° [1]1

Tick each point you got.

[1 mark] (c)Mei Ling reads the angle as 130°. What mistake did she make?

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She read the scale that starts at 0 on the right, but the baseline arm is on the left, so she should read the scale that starts at 0 on the left [1]1

Tick each point you got.

For the teacher: Understanding, medium difficulty, standard 6.2.1

Textbook p. 220

Question 12

Diagram 8 shows a regular hexagon and an equilateral triangle joined along one side. Each side is 5 cm.

A regular hexagon with an equilateral triangle on top; each side is 5 cm — Diagram 8

[1 mark] (a)How many outer sides does the composite shape have?

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6 + 3 − 2 = 7 [1]1

Tick each point you got.

[2 marks] (b)Calculate the perimeter of the composite shape.

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35 cm

7 × 5 cm [1]1
35 cm [1]1

Tick each point you got.

[1 mark] (c)Why is the dashed side not counted in the perimeter?

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It is inside the composite shape, not on the outside [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 6.3.1

Textbook p. 221

Question 13

Diagram 9 shows the plan of an L-shaped plot of land.

An L-shaped plot with sides 12 m, x, 5 m, 3 m, 7 m and 8 m — Diagram 9

[1 mark] (a)Find the length of the side marked x.

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5 m

x = 8 m − 3 m = 5 m [1]1

Tick each point you got.

[2 marks] (b)Calculate the perimeter of the plot.

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40 m

12 + 5 + 5 + 3 + 7 + 8 [1]1
40 m [1]1

Tick each point you got.

For the teacher: Applying, medium difficulty, standard 6.3.1

Textbook p. 222

Question 14

Diagram 10 shows a rectangle and a right-angled triangle joined together. The triangle has a base of 4 cm and a height of 6 cm.

A rectangle 10 cm by 6 cm with a right-angled triangle of base 4 cm and height 6 cm joined on its right — Diagram 10

[1 mark] (a)Calculate the area of the rectangle.

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60 cm²

10 × 6 = 60 cm² [1]1

Tick each point you got.

[2 marks] (b)Calculate the area of the triangle.

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12 cm²

½ × 4 × 6 [1]1
12 cm² [1]1

Tick each point you got.

[1 mark] (c)Find the area of the whole composite shape.

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72 cm²

60 + 12 = 72 cm² [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 6.3.2

Textbook p. 224

Question 15

Diagram 11 shows a cube of side 4 cm placed on top of a cuboid.

A cuboid 10 cm long, 5 cm deep and 3 cm high with a cube of side 4 cm on top — Diagram 11

[1 mark] (a)Calculate the volume of the cuboid.

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150 cm³

10 × 5 × 3 = 150 cm³ [1]1

Tick each point you got.

[1 mark] (b)Calculate the volume of the cube.

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64 cm³

4 × 4 × 4 = 64 cm³ [1]1

Tick each point you got.

[1 mark] (c)Find the volume of the composite shape.

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214 cm³

150 + 64 = 214 cm³ [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 6.4.1

Textbook p. 227

Question 16

Diagram 12 shows a wooden block of length 20 cm, breadth 15 cm and height 12 cm. Jafri cuts off a piece 8 cm long, 15 cm broad and 5 cm high from the top right corner.

A wooden block 20 cm by 15 cm by 12 cm with a piece 8 cm long and 5 cm high cut from the top right — Diagram 12

[1 mark] (a)Calculate the volume of the block before it was cut.

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3 600 cm³

20 × 15 × 12 = 3 600 cm³ [1]1

Tick each point you got.

[1 mark] (b)Calculate the volume of the piece that was cut off.

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600 cm³

8 × 15 × 5 = 600 cm³ [1]1

Tick each point you got.

[1 mark] (c)Find the volume of the block that is left.

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3 000 cm³

3 600 − 600 = 3 000 cm³ [1]1

Tick each point you got.

[1 mark] (d)Rina says the volume left is 3 200 cm³. Is she correct? Prove it.

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No. The volume left is 3 000 cm³, not 3 200 cm³ [1]1

Tick each point you got.

For the teacher: Analysing, medium difficulty, standard 6.5.1

Textbook p. 229

Question 17

Diagram 13 shows Mr Lim's garden. He plants grass on the whole garden except the pond. Grass costs RM15 for each m². Mr Lim has RM1 500.

A garden 12 m by 9 m with a pond 4 m by 3 m inside it — Diagram 13

[2 marks] (a)Calculate the area of the grass.

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96 m²

Garden 12 × 9 = 108 m² and pond 4 × 3 = 12 m² [1]1
108 − 12 = 96 m² [1]1

Tick each point you got.

[1 mark] (b)Calculate the cost of the grass.

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RM1 440

96 × RM15 = RM1 440 [1]1

Tick each point you got.

[1 mark] (c)Is Mr Lim's money enough? Give a reason.

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Yes, because RM1 440 is less than RM1 500 (RM60 left over) [1]1

Tick each point you got.

For the teacher: Evaluating, medium difficulty, standard 6.5.1

Textbook p. 230

Question 18

Two regular polygons with the same side length are joined along one side to make a composite shape. The composite shape has 7 outer sides and its perimeter is 42 cm.

[1 mark] (a)Find the length of one side.

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6 cm

42 ÷ 7 = 6 cm [1]1

Tick each point you got.

[2 marks] (b)Name two regular polygons that could be joined to make this composite shape.

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A square and a pentagon (or a hexagon and an equilateral triangle: 6 + 3 − 2 = 7).

Square and pentagon (4 + 5 − 2 = 7), or hexagon and equilateral triangle (6 + 3 − 2 = 7) [2]2

Tick each point you got.

For the teacher: Creating, high difficulty, standard 6.3.1

Textbook p. 221

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