Algebra – numbers, operations and patterns (weergawe 2)
Mathematics • Grade 7
Total50 marks
Time90 minutes
Questions32
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 • True or false
[5]
1.1
State whether each statement is TRUE or FALSE.
(5)
| Statement | True / False |
|---|---|
| -9 + 15 = 6 | |
| (-6) × 8 = 48 | |
| 2³ = 6 | |
| The HCF of 35 and 56 is 7 | |
| 20% = 1/5 |
Answer
1. True 2. False 3. False 4. True 5. True
Marking tip: 1 mark each.
QUESTION 2 • Short questions
[15]
2.1
Calculate: -9 + 15
(1)
Answer
6
2.2
Calculate: -7 − (-13)
(1)
Answer
6
2.3
Calculate: (-6) × 8
(1)
Answer
-48
2.4
Calculate: -45 ÷ (-9)
(1)
Answer
5
2.5
Write 2 × 2 × 2 × 2 in exponent form.
(1)
Answer
2⁴
2.6
Calculate: 4^3 + 2^4
(1)
Answer
80
2.7
What is √64?
(1)
Answer
8
2.8
What is √25?
(1)
Answer
5
2.9
Calculate: 20% of R760
(1)
Answer
R152
2.10
Simplify: 9a + 5a - 3a
(1)
Answer
11a
2.11
Solve for x: x + 8 = 17
(1)
Answer
x = 9
2.12
Write the ratio 35 : 56 in simplest form.
(1)
Answer
5 : 8
2.13
Round 6 165 off to the nearest 100.
(1)
Answer
6 200
2.14
Write 4 582 in expanded notation.
(1)
Answer
4 000 + 500 + 80 + 2
2.15
Calculate: 2²
(1)
Answer
4
QUESTION 3 • Exponents and square roots
[3]
3.1
Calculate: 4^3
(2)
Answer
64
Marking tip: 1 mark per step.
3.2
Calculate: √64 + √25
(1)
Answer
8 + 5 = 13
QUESTION 4 • Multiples and factors
[5]
4.1
Write down all the factors of 48.
(2)
Answer
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Marking tip: 1 mark each.
4.2
Write down the first 4 multiples of 8.
(1)
Answer
8, 16, 24, 32
4.3
Write 540 as a product of its prime factors.
(2)
Answer
540 = 2² × 3³ × 5
Marking tip: 1 mark per step.
QUESTION 5 • Ratio and rate
[4]
5.1
Divide R1 080 in the ratio 4 : 5.
(2)
Answer
4 + 5 = 9; 1 080 ÷ 9 = 120; R480 and R600
Marking tip: 1 mark per step.
5.2
A car travels 608 km on 38 litres of petrol. How many kilometres per litre?
(2)
Answer
608 ÷ 38 = 16 km
Marking tip: 1 mark per step.
QUESTION 6 • Financial mathematics
[3]
6.1
A shopkeeper buys a bicycle for R2 400 and sells it for R3 000. Calculate the profit as a percentage of the cost price.
(3)
Answer
3 000 − 2 400 = R600; 600 ÷ 2400 × 100 = 25%
Marking tip: 1 mark per step.
QUESTION 7 • Fractions
[3]
7.1
Calculate: 3/5 + 2/7
(2)
Answer
21/35 + 10/35 = 31/35
Marking tip: 1 mark per step.
7.2
Calculate: 3/5 × 2/7
(1)
Answer
6/35
QUESTION 8 • Functions and relationships
[2]
8.1
The rule is T = 3p − 4. Complete the table.
(2)
| p | 2 | 5 | 8 |
|---|---|---|---|
| T | 2 |
Answer
p = 5 → T = 11; p = 8 → T = 20
Marking tip: 1 mark each.
QUESTION 9 • Percentages
[5]
9.1
A pair of takkies costs R1 450. The shop gives 20% discount. How much do you pay?
(3)
Answer
20% of 1 450 = R290; 1 450 − 290 = R1 160
Marking tip: 1 mark per step.
9.2
A test is out of 45 marks. Thabo scores 38. What is his percentage?
(2)
Answer
38 ÷ 45 × 100 = 84,4%
Marking tip: 1 mark per step.
QUESTION 10 • Algebraic expressions
[5]
10.1
Simplify: 8x + 5y - 3x + 2y
(2)
Answer
5x + 7y
Marking tip: 1 mark per step.
10.2
Simplify: 4(m + 6) - 2m
(2)
Answer
2m + 24
Marking tip: 1 mark per step.
10.3
Simplify: 15p² ÷ 3p
(1)
Answer
5p