Space: Mathematics Darjah 4 questions

Section A: objective questions

8 marks

Choose the correct answer.

Diagram 1 shows three angles. Which angle is an acute angle?

Angle P is wider than a right angle, angle Q is a right angle, angle R is narrower than a right angle — Diagram 1

P
Q
R
None of them

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An acute angle is smaller than a right angle. Angle R is narrower than the right angle Q. P is obtuse.

For the teacher: Remembering, low difficulty, standard 6.1.1

Textbook p. 199

Two straight lines cross each other at a right angle. The lines are called ______ lines.

parallel
perpendicular
acute
equal

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Lines that intersect at a right angle are perpendicular lines. Parallel lines never meet.

For the teacher: Remembering, low difficulty, standard 6.2.1

Textbook p. 201

Diagram 2 shows four straight lines. Which pair of lines is parallel?

Horizontal lines AB and CD, a vertical line EF crossing both, and a slanted line GH — Diagram 2

AB and CD
AB and EF
CD and GH
EF and GH

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AB and CD are both horizontal and always the same distance apart, so they are parallel. EF crosses them at right angles, so EF is perpendicular to both.

For the teacher: Understanding, low difficulty, standard 6.2.1

Textbook p. 203

A regular hexagon has sides of 9 cm. What is its perimeter?

27 cm
36 cm
45 cm
54 cm

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A regular hexagon has 6 equal sides. 6 × 9 cm = 54 cm.

For the teacher: Applying, low difficulty, standard 6.3.1

Textbook p. 205

A rectangular wall is 9 m long and 6 m wide. What is its area?

30 m²
54 m²
15 m²
54 m

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Area = length × width = 9 m × 6 m = 54 m². Area is stated in square units, so not m.

For the teacher: Applying, low difficulty, standard 6.3.2

Textbook p. 206

What is the volume of a cube with sides of 5 cm?

15 cm³
25 cm³
20 cm³
125 cm³

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Volume = 5 cm × 5 cm × 5 cm = 125 cm³.

For the teacher: Applying, low difficulty, standard 6.4.1

Textbook p. 210

The base area of a cuboid is 15 cm². Its height is 4 cm. What is its volume?

60 cm³
19 cm³
60 cm²
11 cm³

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Volume = base area × height = 15 cm² × 4 cm = 60 cm³. Volume is stated in cubic units.

For the teacher: Applying, low difficulty, standard 6.4.1

Textbook p. 210

Diagram 3 shows a rectangle made of unit squares. What is its area?

Rectangle made of unit squares, 5 columns and 4 rows — Diagram 3

9 square units
18 square units
20 square units
24 square units

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There are 5 squares in each row and 4 rows. 5 × 4 = 20 square units. (18 is the perimeter.)

For the teacher: Understanding, low difficulty, standard 6.3.2

Textbook p. 206

Section B: structured questions

33 marks

Answer all questions. Show your working.

Answer the questions about shapes and angles.

[1 mark] (a)A triangle has 3 equal sides. What is the name of the triangle?

equilateral triangleisosceles trianglescalene triangleright-angled triangle

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equilateral triangle

An equilateral triangle has 3 equal sides and 3 acute angles.

[1 mark] (b)A regular hexagon has 6 vertices. How many angles does it have?

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6 angles (number of angles = number of vertices) [1]1

Tick each point you got.

[1 mark] (c)State the type of angle that is smaller than a right angle.

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Acute angle [1]1

Tick each point you got.

For the teacher: Remembering, low difficulty, standard 6.1.1

Textbook p. 199

Refer to Diagram 2 (lines AB, CD, EF and GH).

[1 mark] (a)Name the line that is perpendicular to AB.

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EF [1]1

Tick each point you got.

[1 mark] (b)Name the line that is parallel to AB.

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CD [1]1

Tick each point you got.

[1 mark] (c)Line GH is not perpendicular to CD. Give a reason.

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It does not meet CD at a right angle / the angle is not a right angle [1]1

Tick each point you got.

For the teacher: Understanding, low difficulty, standard 6.2.1

Textbook p. 203

Diagram 4 shows an L-shaped garden drawn on a square grid. The length of one square is 1 unit.

L-shaped figure on a grid, 6 squares wide and 4 squares high with a 3 by 2 corner missing — Diagram 4

[1 mark] (a)Find the area of the garden, in square units.

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Full 6 × 4 = 24; missing 3 × 2 = 6; 24 − 6 = 18 square units [1]1

Tick each point you got.

[2 marks] (b)Find the perimeter of the garden, in units.

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Add the sides: 6 + 2 + 3 + 2 + 3 + 4 [1]1
= 20 units [1]1

Tick each point you got.

For the teacher: Applying, medium difficulty, standard 6.3.2

Textbook p. 206

A fence of 44 m surrounds a rectangular playground. The length of the playground is 15 m.

A rectangular playground with its length of 15 m shown — Diagram 5

[2 marks] (a)Calculate the width of the playground.

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44 ÷ 2 = 22 (length + width) [1]1
22 − 15 = 7 m [1]1

Tick each point you got.

[1 mark] (b)Calculate the area of the playground.

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15 × 7 = 105 m² [1]1

Tick each point you got.

For the teacher: Applying, medium difficulty, standard 6.5.1

Textbook p. 211

Diagram 6 shows a right-angled triangle.

Right-angled triangle with base 12 cm and height 9 cm — Diagram 6

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

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½ × 12 × 9 [1]1
= 54 cm² [1]1

Tick each point you got.

[1 mark] (b)A rectangle has the same base and height as this triangle. What is the area of the rectangle?

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12 × 9 = 108 cm² (twice the triangle) [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 6.3.2

Textbook p. 207

Diagram 7 shows a cuboid.

Cuboid 5 cm long, 4 cm wide and 3 cm high — Diagram 7

[1 mark] (a)What is the area of the base?

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5 × 4 = 20 cm² [1]1

Tick each point you got.

[2 marks] (b)Calculate the volume of the cuboid.

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20 × 3 (or 5 × 4 × 3) [1]1
= 60 cm³ [1]1

Tick each point you got.

For the teacher: Understanding, low difficulty, standard 6.4.1

Textbook p. 210

A box is 20 cm long, 12 cm wide and 8 cm high. Cubes with sides of 4 cm are packed into the box.

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

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20 × 12 × 8 = 1 920 cm³ [1]1

Tick each point you got.

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

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4 × 4 × 4 = 64 cm³ [1]1

Tick each point you got.

[1 mark] (c)How many cubes can be packed in the box?

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1 920 ÷ 64 = 30 cubes [1]1

Tick each point you got.

For the teacher: Analysing, medium difficulty, standard 6.5.1

Textbook p. 212

Diagram 8 shows cuboid A and cube B. The volume of A is equal to the volume of B.

Cuboid A with length 12 cm, width 9 cm and height p; cube B with sides of 6 cm — Diagram 8

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

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6 × 6 × 6 = 216 cm³ [1]1

Tick each point you got.

[2 marks] (b)Calculate the value of p.

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12 × 9 = 108 (base area of A) [1]1
216 ÷ 108 = 2 [1]1

Tick each point you got.

For the teacher: Analysing, high difficulty, standard 6.5.1

Textbook p. 214

Hana says: "Rectangle X (8 m × 2 m) and square Y (5 m × 5 m) have the same perimeter, so they have the same area."

[1 mark] (a)Is Hana correct?

YesNo

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The perimeters are equal, but the areas are 16 m² and 25 m².

[2 marks] (b)Show your working to explain your answer.

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Perimeter X = 2 × (8 + 2) = 20 m; Y = 4 × 5 = 20 m (equal) [1]1
Area X = 8 × 2 = 16 m²; Y = 5 × 5 = 25 m² (not equal) [1]1

Tick each point you got.

For the teacher: Evaluating, medium difficulty, standard 6.3.2

Textbook p. 213

Make your own rectangle with a perimeter of 24 cm. The length and the width must be whole numbers.

[1 mark] (a)Write a possible length and width.

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Length + width = 12 cm, for example 8 cm and 4 cm (accept 11 and 1, 10 and 2, 9 and 3, 7 and 5, 6 and 6) [1]1

Tick each point you got.

[2 marks] (b)Show that the perimeter is 24 cm and calculate the area.

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Perimeter check: 2 × (length + width) = 24 cm [1]1
Area = length × width, e.g. 8 × 4 = 32 cm² (follow the pair chosen) [1]1

Tick each point you got.

For the teacher: Creating, low difficulty, standard 6.3.1

Textbook p. 213

A square tile has a perimeter of 36 cm.

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

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36 ÷ 4 = 9 cm [1]1

Tick each point you got.

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

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Area = side × side = 9 × 9 [1]1
= 81 cm² [1]1

Tick each point you got.

For the teacher: Applying, medium difficulty, standard 6.3.2

Textbook p. 207

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

Question 19