Year 7 Maths • AC9M7N09 • Homework
Mathematical Modelling with Rational Numbers and Percentages
Show your model, calculation, interpretation and any assumptions. Use a calculator or spreadsheet where it improves efficiency.
Part A — 5 × 2-mark questions
1. A lift starts at floor 0, rises 9 floors, then descends 14 floors. Write a signed-number model and state the final floor.
2. 55% of a Year 7 cohort of 320 students attend an event. Write a percentage model and calculate the number attending.
3. A fundraiser earns $480 and costs $525. Model the result and state the profit or loss.
4. A bank account starts at $150. A $45 debit and a $20 credit occur. Write a signed-number model and find the final balance.
5. 12% of a 900-student school votes in a survey. Calculate the number of students and write one sentence interpreting the result.
Part B — 5 × 5-mark questions
6. Submarine model. A submarine begins at −240 m, rises 85 m, descends 120 m, rises 60 m, then descends 30 m. (a) Write a signed-number expression. (b) Find the final depth. (c) Describe a number-line model. (d) Explain why negative values are useful. (e) Interpret the final answer.
7. School proportion. 23% of 1200 students vote “yes” to a uniform change. (a) Model using a percentage equation. (b) Calculate the votes. (c) Show an equivalent decimal or fraction method. (d) Explain why percentage is useful. (e) Interpret the result.
8. Fundraising model. A sausage sizzle earns $1050 and costs $780. (a) Write a profit model. (b) Find profit. (c) Find percentage profit on cost. (d) Explain why percentage profit helps compare events. (e) State one assumption or limitation of the model.
9. Account transactions. An account starts at $600 with transactions −$120, +$75, −$200 and +$40. (a) Find the final balance. (b) Present the transactions in a table. (c) Explain the role of signs. (d) Identify the largest change in magnitude. (e) Interpret the final balance.
10. Green-space model. A school site is 18,000 m² and 35% is green space. (a) Model the calculation. (b) Find green-space area. (c) Show a fraction/decimal alternative. (d) If the target is 40%, find the extra area required. (e) Interpret the result.
Part C — Enrichment investigation
Researchers want to compare two land-use proportions within the same hypothetical 2.4 million km² study region: Model A uses 18% and Model B uses 27%.
Calculate both areas; compare them using a difference, ratio and percentage; explain why proportional representations are useful; identify assumptions or limitations of this simplified model; and explain what additional reliable data would be needed before drawing conclusions about real Australian First Nations traditional grain systems or current commercial grain regions.