Mathematics • Year 10 • Unit 2 • Lesson 1
Review of Algebraic Expressions — Skill Drill
Build fluency with the three tools from Lesson 1: collect like terms, substitute values (brackets around negatives!), and apply BIDMAS for the right order of operations. One worked example, one guided trace, then eight independent problems sized from foundation to extension.
1. I do — fully worked example
Substitute, then simplify. Read every step — each one has a reason underneath so you can see why, not just what.
Problem. If p = 5 and q = −3, evaluate 2p² − 3q.
Step 1 — Substitute with brackets.
2(5)² − 3(−3)
Reason: brackets around −3 keep the negative attached and stop sign errors.
Step 2 — Indices (BIDMAS: I before M).
= 2(25) − 3(−3)
Reason: 5² = 25. Powers always before multiplication.
Step 3 — Multiplication (left to right).
= 50 − (−9)
Reason: 2 × 25 = 50, and 3 × (−3) = −9.
Step 4 — Subtracting a negative becomes adding.
= 50 + 9 = 59
Reason: −(−9) = +9. The two negatives cancel.
Answer: 2p² − 3q = 59.
2. We do — fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank. 5 marks
Problem. Simplify 4m + 6n − 2m + 5n − n.
Step 1 — Identify the like-term groups: the m-group is ___________ and the n-group is ___________.
Step 2 — Group like terms together (keep each sign with its term):
(4m − 2m) + (6n + 5n − ____)
Step 3 — Combine the coefficients inside each group:
m-group: 4 − 2 = ____, so we get ____ m
n-group: 6 + 5 − 1 = ____, so we get ____ n
Step 4 — Write the final answer:
Simplified expression = ____________________
3. You do — independent practice
Show your working in the space under each problem. The first four are foundation (single skill). The middle two are standard (combine two tools). The last two are extension.
Foundation — single skill
3.1 Simplify 7x + 5x − 2x. 1 mark
3.2 Simplify 6a + 4b − a + 3b. 1 mark
3.3 If x = 4, evaluate 3x + 7. 1 mark
3.4 Evaluate 2 + 3 × 4² using BIDMAS. 1 mark
Standard — combine tools
3.5 Simplify 5x² + 3x − 2x² + x. (Careful — x² and x are NOT like terms.) 2 marks
3.6 If x = −2 and y = 3, evaluate 4x + y². Use brackets around the negative. 2 marks
Extension — push your thinking
3.7 If a = −3, evaluate a² − 4a + 1. Show every BIDMAS step. 3 marks
3.8 A student writes "3x + 5y = 8xy". Without doing any calculation, explain in one sentence what is wrong with this, then write the correct simplified form. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (faded 4m + 6n − 2m + 5n − n)
Step 1: m-group is 4m, −2m; n-group is 6n, 5n, −n.
Step 2: (4m − 2m) + (6n + 5n − n).
Step 3: m-group: 4 − 2 = 2, so 2m. n-group: 6 + 5 − 1 = 10, so 10n.
Step 4: Simplified expression = 2m + 10n.
3.1 — 7x + 5x − 2x
All like terms (each is an x). 7 + 5 − 2 = 10x.
3.2 — 6a + 4b − a + 3b
a-group: 6a − a = 5a. b-group: 4b + 3b = 7b. Answer: 5a + 7b.
3.3 — 3x + 7 when x = 4
= 3(4) + 7 = 12 + 7 = 19.
3.4 — 2 + 3 × 4²
Indices first: 4² = 16. Then multiply: 3 × 16 = 48. Then add: 2 + 48 = 50.
BIDMAS: I before M before A.
3.5 — 5x² + 3x − 2x² + x
x²-group: 5x² − 2x² = 3x². x-group: 3x + x = 4x. Answer: 3x² + 4x.
x and x² are NOT like terms — they live in separate bins.
3.6 — 4x + y² when x = −2, y = 3
= 4(−2) + (3)² = −8 + 9 = 1.
3.7 — a² − 4a + 1 when a = −3
Substitute with brackets: (−3)² − 4(−3) + 1.
Indices: (−3)² = 9. So 9 − 4(−3) + 1.
Multiplication: 4 × (−3) = −12, so 9 − (−12) + 1.
Subtracting a negative: 9 + 12 + 1 = 22.
3.8 — Why "3x + 5y = 8xy" is wrong
3x and 5y are not like terms — they have different letters — so they cannot be combined. The expression 3x + 5y is already in simplest form: 3x + 5y.
The student has glued the letters together (and added the coefficients) when neither operation is valid.