Formulating Algebraic Expressions

Part A — 5 × 2-mark questions

1. Simplify x+(x+3)+(x+6).
2. Translate: “Triple a number, then subtract twice the number.”
3. Write an expression for “five less than the product of a number and 9”.
4. Expand and simplify 4(x−7).
5. Formulate an expression for “a number increased by its double, then multiplied by 3”.

Part B — 5 × 5-mark questions

6. Translate “add 6 to a number, multiply the result by 4, then subtract twice the original number.” Write the unsimplified expression, expand, simplify, identify the coefficient of x and explain why brackets matter.
7. A pattern has Term 1 = x+2, Term 2 = 2x+4, Term 3 = 3x+6. Identify the structure, write the nth term, explain the role of n and x, and describe the growth.
8. Represent “a number is multiplied by its successor, then increased by triple the number.” Write with brackets, expand, simplify, identify quadratic/linear parts and explain why it grows faster than a linear expression.
9. A walking tour charges a fixed $18 plus $6 per participant. Define a variable, formulate a total-cost expression, find the cost for 12 participants, explain the fixed and variable parts, and state how the expression changes when one more participant joins.
10. A student says 5(x+4)=5x+4. Explain the error, correct it, verify with x=3, create a similar incorrect example, and correct that example.

Part C — Enrichment

Design a meaningful Country/Place or environmental model using at least two variables—for example water depth, distance travelled, or resource use. Define each variable, formulate an algebraic expression, test it with two sets of values, explain how the expression changes when one variable changes, and discuss why algebra is useful for communicating the relationship. Do not invent cultural claims; keep the mathematical context respectful and evidence-neutral.