Geometry – space, measurement and data handling
Mathematics • Grade 7
Total50 marks
Time90 minutes
Questions20
Name:
Class: Date:
Instructions
- Read all the questions carefully before you begin writing.
- Answer all the questions on the question paper itself.
- Show all your working where the question asks for it.
- Write neatly. Work that cannot be read cannot be marked.
- You may use a pencil and a ruler for drawings.
- Calculators are not allowed.
Sit down with pen and paper. Work through the whole paper before you show the answers — that is how a real test feels.
The answers are right at the bottom of the page.
QUESTION 1 • Short questions
[5]
1.1
How many degrees are there in a right angle?
(1)
Answer
90°
1.2
The sum of the interior angles of a triangle is:
(1)
Answer
180°
1.3
How many sides does a hexagon have?
(1)
Answer
6
1.4
How many flat faces does a cube have?
(1)
Answer
6
1.5
One litre is how many cubic centimetres?
(1)
Answer
1 000 cm³
QUESTION 2 • Angles
[6]
2.1
PQ and RS are parallel. If angle a = 65°, calculate angle b and angle c. Give a reason for each.
(4)
Answer
b = 115° (supplementary angles on a straight line). c = 65° (corresponding angles).
Marking tip: 2 punte per hoek, met die rede.
2.2
Two angles are complementary. One is 38°. Calculate the other.
(2)
Answer
90° − 38° = 52°
Marking tip: 1 mark per step.
QUESTION 3 • Triangles
[5]
3.1
Name each triangle A to D.
(4)
Answer
A = equilateral triangle; B = right-angled triangle; C = scalene triangle; D = obtuse-angled triangle
Marking tip: 1 mark each.
3.2
In triangle ABC, angle A = 52° and angle B = 71°. Calculate angle C.
(1)
Answer
52° + 71° = 123°; 180° − 123° = 57°
QUESTION 4 • Perimeter, area, volume and surface area
[16]
4.1
Calculate the PERIMETER and the AREA of the rectangle below.
(4)
Answer
Perimeter = 2(36 + 22) = 116 cm. Area = 36 × 22 = 792 cm²
Marking tip: 2 punte elk, met die eenheid.
4.2
Calculate the area of a triangle with a base of 14 cm and a height of 9 cm.
(2)
Answer
½ × 14 × 9 = 63 cm²
Marking tip: 1 mark per step.
4.3
Calculate the volume of a rectangular prism 15 cm long, 8 cm wide and 6 cm high.
(3)
Answer
15 × 8 × 6 = 720 cm³
Marking tip: 1 mark per step.
4.4
Calculate the surface area of a cube with a side length of 7 cm.
(3)
Answer
One face = 7 × 7 = 49 cm²; 6 × 49 = 294 cm²
Marking tip: 1 mark per step.
4.5
A rectangular garden is 18 m by 11 m. Fencing costs R45 per metre. Calculate the cost.
(4)
Answer
Perimeter = 2(18 + 11) = 58 m; 58 × 45 = R2 610
Marking tip: 1 mark per step.
QUESTION 5 • Similarity and congruence
[2]
5.1
Look at the two pairs below. Which pair is CONGRUENT and which is SIMILAR? Give a reason.
(2)
Answer
A is congruent — same shape and same size. B is similar — same shape but a different size.
Marking tip: 1 mark each.
QUESTION 6 • Transformation geometry
[4]
6.1
Triangle P has been transformed to A, B and C. Name each transformation.
(3)
Answer
A = translation; B = reflection; C = rotation
Marking tip: 1 mark each.
6.2
Which transformation changes the SIZE of a shape?
(1)
Answer
None of these three — translation, reflection and rotation all keep the size. An enlargement or reduction changes the size.
QUESTION 7 • Graphs
[3]
7.1
Study the line graph below and answer the questions.
(3)
Answer
a. 12:00 b. 26 °C − 12 °C = 14 °C c. Between 12:00 and 18:00 (it falls)
Marking tip: 1 mark each.
QUESTION 8 • Data handling
[5]
8.1
The bar graph shows how many books Grade 7 borrowed each day. Answer the questions.
(5)
Answer
a. 8 + 12 + 6 + 14 + 9 = 49 books b. 49 ÷ 5 = 9,8 c. Ordered: 6; 8; 9; 12; 14 → median = 9 d. 14 − 6 = 8 e. Thursday
Marking tip: 1 mark each.
QUESTION 9 • Problem solving
[4]
9.1
A swimming pool is 12 m long, 6 m wide and 1,5 m deep. How many kilolitres of water does it hold? Show all your working.
(4)
Answer
12 × 6 × 1,5 = 108 m³; 1 m³ = 1 000 ℓ = 1 kℓ; so 108 kℓ
Marking tip: 1 mark per step.