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Year 8 Mathematics · Algebraic expressions

Name: ______________________

Date: ____________

1. Which expression means “7 less than m”?
- ☐ (a) 7 − m
- ☐ (b) m − 7
- ☐ (c) 7m
- ☐ (d) m + 7
2. Simplify 5x + 2x − 3x.
- ☐ (a) 10x
- ☐ (b) 4
- ☐ (c) 4x
- ☐ (d) 7x − 3
3. Which pair are like terms?
- ☐ (a) 3a and 3b
- ☐ (b) 4x and 4x²
- ☐ (c) 2y and 7y
- ☐ (d) 5 and 5p
4. What is the value of 2p + 3 when p = 6?
- ☐ (a) 11
- ☐ (b) 26
- ☐ (c) 29
- ☐ (d) 15
5. Find the value of 4k − 5 when k = 3.
6. Simplify 6m + 4 − 2m + 1.
7. Find the value of n² + 1 when n = 5.
8. A taxi charges a $4 flag fall plus $2 for each kilometre, so the cost in dollars for k kilometres is 4 + 2k. How many dollars does a 9 km trip cost?

Answer sheet

1. m − 7 — Start with m and take 7 away: m − 7.
2. 4x — All three are like terms: 5 + 2 − 3 = 4, so the answer is 4x.
3. 2y and 7y — 2y and 7y have exactly the same pronumeral part (y), so they are like terms.
4. 15 — 2 × 6 + 3 = 12 + 3 = 15.
5. 7 — 4 × 3 − 5 = 12 − 5 = 7.
6. 4m + 5 — Collect the m terms: 6m − 2m = 4m. Collect the numbers: 4 + 1 = 5. The answer is 4m + 5.
7. 26 — n² means n × n, so 5 × 5 + 1 = 25 + 1 = 26.
8. $22 — 4 + 2 × 9 = 4 + 18 = 22, so the trip costs $22.