Mathematics Standard • Year 11 • Module 3 • Lesson 5
Earning Money — Exam Practice
Practise HSC Mathematics Standard 2-style writing on Earning Money — multi-mark short answers and one structured extended response.
1. Short-answer questions
1.1 A factory worker is paid $22.80 per hour for a 38-hour week. They also work 6 hours of overtime at time-and-a-half. Calculate the worker's gross weekly pay. 3 marks Band 3
1.2 A car salesperson earns a fortnightly retainer of $800 plus 3.5% commission on all sales above a threshold of $6,000. This fortnight the salesperson made $34,000 in sales. Calculate the total fortnightly earnings. 3 marks Band 3-4
1.3 An employee earns $1,180 per week. They take 4 weeks of annual leave and receive 17.5% leave loading.
(a) Calculate the total amount they receive for their 4 weeks of leave (leave pay + loading).
(b) The employee says they will be paid "an extra $826 for going on leave". Explain in one sentence whether this statement is correct or misleading. 4 marks Band 4
2. Extended response
2.1 Marcus is choosing between two job offers as a delivery driver.
Job X: A salary of $61,000 per year, paid fortnightly.
Job Y: A retainer of $580 per week, plus piecework pay of $4.20 per delivery. Marcus expects to complete 165 deliveries per week on average. Job Y also requires Marcus to pay $1,200 per year for fuel and vehicle costs that Job X would cover.
(a) Calculate Job X's fortnightly pay.
(b) Calculate Job Y's expected weekly earnings, and convert to an annual figure.
(c) After accounting for Job Y's $1,200 yearly fuel/vehicle cost, compare the two jobs annually. State which one pays more, and by how much, in a clear conclusion sentence. 6 marks Band 5-6
Explicit marking criteria
Part (a) — 1 mark
• 1 mark — correct Job X fortnightly pay using $61,000 ÷ 26.
Part (b) — 2 marks
• 1 mark — correct weekly earnings: retainer + (165 × $4.20).
• 1 mark — correct conversion to annual using × 52.
Part (c) — 3 marks
• 1 mark — applies the $1,200 cost as a subtraction from Job Y's annual earnings (or equivalent treatment).
• 1 mark — correct numerical comparison of the two annual figures.
• 1 mark — explicit conclusion sentence naming the higher-paying job and the dollar difference, with units (per year).
Your response:
Stuck on (c)? Convert both annual figures, subtract the $1,200 from Job Y's annual before comparing, then write a sentence — "Job ___ pays more by $___ per year".How did this worksheet feel?
What I'll revisit before next class:
1.1 — Gross weekly pay with overtime (3 marks)
Sample response.
Ordinary pay = $22.80 × 38 = $866.40.
Overtime rate = $22.80 × 1.5 = $34.20/hr.
Overtime pay = $34.20 × 6 = $205.20.
Gross weekly pay = $866.40 + $205.20 = $1,071.60.
Marking notes. 1 mark — correct ordinary pay. 1 mark — correct overtime rate and overtime pay (one line each). 1 mark — correct sum with units. A bare "$1,071.60" with no working scores 1/3 even if numerically correct.
1.2 — Retainer + commission above threshold (3 marks)
Sample response.
Sales above threshold = $34,000 − $6,000 = $28,000.
Commission = $28,000 × 0.035 = $980.
Total fortnightly earnings = $800 + $980 = $1,780.00.
Marking notes. 1 mark — correctly identifies the commission-eligible amount as $28,000 (not $34,000). 1 mark — correct commission calculation. 1 mark — correct sum of retainer + commission, with units. Common error: applying 3.5% to the full $34,000 gives $1,190 commission (and $1,990 total) — this is the most common loss-of-mark answer.
1.3 — Annual leave pay and loading (4 marks)
(a) Sample response. Leave pay = $1,180 × 4 = $4,720. Leave loading = 0.175 × $4,720 = $826. Total = $4,720 + $826 = $5,546.00.
(b) Sample response. The statement is misleading. The $826 is the extra loading on top of the regular 4 weeks of leave pay, not an additional amount above the employee's normal earnings. The employee would have earned $4,720 over those 4 weeks anyway; the actual "extra" because they took leave is only the $826 loading.
Marking notes. (a) 1 mark — correct leave pay. 1 mark — correct loading. 1 mark — correct total with units. (b) 1 mark — identifies the statement as misleading with the reasoning that $826 is the loading on top, not a windfall above regular pay. A response saying only "correct" or "incorrect" without explanation = 0.
2.1 — Comparing Job X and Job Y (6 marks): sample Band-6 response with annotations
Sample Band-6 response.
(a) Job X fortnightly pay.
Job X fortnightly = $61,000 ÷ 26 = $2,346.15 (to 2 d.p.). [1 mark — fortnightly conversion.]
(b) Job Y weekly and annual earnings.
Piecework pay = 165 × $4.20 = $693.00.
Weekly earnings = $580 (retainer) + $693.00 (piecework) = $1,273.00. [1 mark — weekly earnings.]
Annual = $1,273.00 × 52 = $66,196.00. [1 mark — annual conversion.]
(c) Compare annually after Job Y's $1,200 cost.
Job Y net annual (after costs) = $66,196.00 − $1,200.00 = $64,996.00. [1 mark — applies the $1,200 cost to Job Y's annual figure.]
Job X annual = $61,000.00.
Difference = $64,996.00 − $61,000.00 = $3,996.00. [1 mark — correct numerical comparison.]
Conclusion: Job Y pays more, by $3,996.00 per year, even after accounting for the $1,200 yearly fuel and vehicle costs. [1 mark — explicit conclusion naming the higher-paying job, dollar difference, with units.]
Total: 6/6.
Band descriptors for marker.
Band 3: Calculates one of Job X or Job Y fortnightly/weekly correctly but does not convert to the same unit or apply the $1,200 cost. ≈ 2-3 marks.
Band 4: Both jobs converted to annual figures correctly; numerical comparison attempted; either forgets the $1,200 cost or omits the concluding sentence. ≈ 4 marks.
Band 5: Full numerical solution including the $1,200 cost, but the conclusion is bare numbers without a clear sentence (e.g. just "$3,996" with no naming of which job). ≈ 5 marks.
Band 6: Complete, correctly converted, $1,200 cost properly applied, AND a clear conclusion sentence that names the winning job, the dollar difference, and the time unit (per year). 6/6.