Algebra – numbers, operations and patterns
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 |
|---|---|
| −7 + 12 = 5 | |
| (−3) × (−4) = −12 | |
| 2⁴ = 8 | |
| The HCF of 12 and 18 is 6 | |
| 0,25 = ¼ |
Answer
1. True 2. False 3. False 4. True 5. True
Marking tip: 1 mark each.
QUESTION 2 • Short questions
[15]
2.1
Calculate: −15 + 8
(1)
Answer
−7
2.2
Calculate: −6 − (−11)
(1)
Answer
5
2.3
Calculate: (−4) × 7
(1)
Answer
−28
2.4
Calculate: −36 ÷ (−9)
(1)
Answer
4
2.5
Write 3 × 3 × 3 × 3 in exponent form.
(1)
Answer
3⁴
2.6
Calculate: 5² + 3³
(1)
Answer
52
2.7
Write 0,6 as a common fraction in simplest form.
(1)
Answer
3/5
2.8
Write ⅜ as a decimal fraction.
(1)
Answer
0,375
2.9
Calculate 20% of R450.
(1)
Answer
R90
2.10
Simplify: 7a + 3a − 2a
(1)
Answer
8a
2.11
Solve for x: x + 9 = 17
(1)
Answer
x = 8
2.12
Write the ratio 18 : 24 in simplest form.
(1)
Answer
3 : 4
2.13
Round 8 473 off to the nearest 100.
(1)
Answer
8 500
2.14
Write 4 062 in expanded notation.
(1)
Answer
4 000 + 60 + 2
2.15
What is the value of √49?
(1)
Answer
7
QUESTION 3 • Exponents and square roots
[3]
3.1
Calculate: 2⁵
(2)
Answer
32
Marking tip: 1 mark per step.
3.2
Calculate: √81 + √16
(1)
Answer
9 + 4 = 13
QUESTION 4 • Multiples and factors
[5]
4.1
Write down all the factors of 36.
(2)
Answer
1, 2, 3, 4, 6, 9, 12, 18, 36
Marking tip: 1 mark per step.
4.2
Write down the first four multiples of 7.
(1)
Answer
7, 14, 21, 28
4.3
Write 84 as a product of its prime factors.
(2)
Answer
84 = 2² × 3 × 7
Marking tip: 1 mark per step.
QUESTION 5 • Ratio and rate
[4]
5.1
Divide R960 in the ratio 3 : 5.
(2)
Answer
3 + 5 = 8 parts; 960 ÷ 8 = 120; R360 and R600
Marking tip: 1 mark per step.
5.2
A car travels 420 km on 35 litres of petrol. How many kilometres per litre?
(2)
Answer
420 ÷ 35 = 12 km per litre
Marking tip: 1 mark per step.
QUESTION 6 • Financial mathematics
[3]
6.1
A shopkeeper buys a bicycle for R1 600 and sells it for R2 000. Calculate the profit as a percentage of the cost price.
(3)
Answer
Profit = 2 000 − 1 600 = R400; 400 ÷ 1 600 × 100 = 25%
Marking tip: 1 mark per step.
QUESTION 7 • Fractions
[3]
7.1
Calculate: ⅔ + ⅕
(2)
Answer
10/15 + 3/15 = 13/15
Marking tip: 1 mark per step.
7.2
Calculate: ¾ × ⅘
(1)
Answer
15/32
QUESTION 8 • Functions and relationships
[2]
8.1
The rule is T = 2p − 3. Complete the table.
(2)
| p | 2 | 4 | 7 |
|---|---|---|---|
| T | 1 |
Answer
p = 4 → T = 5; p = 7 → T = 11
Marking tip: 1 mark each.
QUESTION 9 • Percentages
[5]
9.1
A pair of takkies costs R1 250. The shop gives 15% discount. How much do you pay?
(3)
Answer
15% of 1 250 = R187,50; 1 250 − 187,50 = R1 062,50
Marking tip: 1 mark per step.
9.2
A test is out of 40 marks. Thabo scores 34. What is his percentage?
(2)
Answer
34 ÷ 40 × 100 = 85%
Marking tip: 1 mark per step.
QUESTION 10 • Algebraic expressions
[5]
10.1
Simplify: 6x + 4y − 2x + 3y
(2)
Answer
4x + 7y
Marking tip: 1 mark per step.
10.2
Simplify: 3(a + 5) − a
(2)
Answer
2a + 15
Marking tip: 1 mark per step.
10.3
Solve for x: 4x − 7 = 21
(1)
Answer
4x = 28; x = 7