Mathematics Standard • Year 11 • Module 3 • Lesson 1
Wages, Salaries and Pay Periods
Practise HSC-style writing on pay-period conversions — multi-mark short answers and one structured extended response.
1. Short-answer questions
1.1 Leah earns $29.40 per hour and works 32 hours each week. Calculate her annual income. 2 marks Band 3
1.2 An employee earns $84,500 per year, paid fortnightly. State (i) her fortnightly pay and (ii) her monthly pay, each to the nearest cent. 3 marks Band 3-4
1.3 Job X pays $63,500 per year. Job Y pays $31.25 per hour for 38 hours per week.
(a) Convert Job Y to an annual figure.
(b) Which job pays more per year, and by how much? Write a one-sentence conclusion. 4 marks Band 4
2. Extended response
2.1 Sienna is choosing between two job offers as a hospitality supervisor.
Job P: A salary of $68,640 per year, paid fortnightly. Job P includes 4 weeks of paid annual leave (i.e. she is paid for 52 weeks even though she works 48).
Job Q: Casual hourly pay of $34.80 per hour for 38 hours per week. Job Q has no paid annual leave — she is paid only for weeks she actually works (assume she takes 4 weeks unpaid leave, so works 48 weeks per year).
(a) Calculate Job P's fortnightly pay.
(b) Calculate Job Q's annual income assuming Sienna works the full 48 weeks.
(c) State which job pays more annually and by how much. Then write a one-sentence comment on which extra factor (other than the annual figure) Sienna should consider. 6 marks Band 5-6
Explicit marking criteria
Part (a) — 1 mark
• 1 mark — correct Job P fortnightly pay using $68,640 ÷ 26.
Part (b) — 2 marks
• 1 mark — correct weekly pay: $34.80 × 38.
• 1 mark — multiplied by 48 weeks (not 52) because Job Q has no paid annual leave.
Part (c) — 3 marks
• 1 mark — correctly subtracts the two annual figures.
• 1 mark — explicit conclusion sentence naming the higher-paying job, dollar difference, with units (per year).
• 1 mark — sensible comment on one extra factor (e.g. paid leave, super, job security, sick leave entitlement).
Your response:
Stuck on (b)? Job Q's annual = weekly × 48 weeks worked. Casual hourly jobs do not get paid for leave weeks.How did this worksheet feel?
What I'll revisit before next class:
1.1 — Annual income from hourly rate (2 marks)
Sample response.
Weekly pay = $29.40 × 32 = $940.80.
Annual income = $940.80 × 52 = $48,921.60.
Marking notes. 1 mark — correct weekly pay (substitution shown). 1 mark — correct annual figure with units. Bare "$48,921.60" with no working scores 1/2.
1.2 — Salary to fortnightly and monthly (3 marks)
Sample response.
(i) Fortnightly = $84,500 ÷ 26 = $3,250.00.
(ii) Monthly = $84,500 ÷ 12 = $7,041.666... ≈ $7,041.67.
Marking notes. 1 mark — correct fortnightly. 1 mark — correct monthly calculation. 1 mark — correctly rounded to the nearest cent and stated with units. Common slip: writing $7,041.66 (truncation, not rounding) — loses the rounding mark.
1.3 — Compare two jobs (4 marks)
(a) Sample response. Weekly = $31.25 × 38 = $1,187.50. Annual = $1,187.50 × 52 = $61,750.00.
(b) Sample response. Job X = $63,500.00; Job Y = $61,750.00. Difference = $63,500 − $61,750 = $1,750. Job X pays more by $1,750 per year.
Marking notes. (a) 1 mark — correct weekly figure. 1 mark — correct annual conversion. (b) 1 mark — correct subtraction. 1 mark — conclusion sentence naming the winning job and the dollar gap and the time unit (per year). A bare "$1,750" with no naming = 0 for the conclusion mark.
2.1 — Comparing Job P and Job Q (6 marks): sample Band-6 response with annotations
Sample Band-6 response.
(a) Job P fortnightly pay.
Job P fortnightly = $68,640 ÷ 26 = $2,640.00. [1 mark — fortnightly conversion.]
(b) Job Q annual income (48 worked weeks).
Weekly pay = $34.80 × 38 = $1,322.40. [1 mark — weekly pay.]
Annual = $1,322.40 × 48 = $63,475.20 per year (working 48 weeks, no paid leave). [1 mark — correctly used 48 weeks, not 52.]
(c) Compare and recommend.
Difference = $68,640.00 − $63,475.20 = $5,164.80. [1 mark — correct subtraction.]
Conclusion: Job P pays more, by $5,164.80 per year, even after accounting for the 4 weeks of unpaid leave Sienna would take on Job Q. [1 mark — explicit conclusion.]
Other factor. Job P also provides paid annual leave, sick leave entitlements, and employer-paid superannuation on top — Job Q's casual rate may not include these benefits. [1 mark — sensible extra factor.]
Total: 6/6.
Band descriptors for marker.
Band 3: Calculates one of Job P or Job Q correctly but uses 52 weeks for Job Q (ignoring "no paid leave"). ≈ 2-3 marks.
Band 4: Both jobs converted correctly including 48-week rule for Job Q; numerical comparison attempted; conclusion or extra factor omitted. ≈ 4 marks.
Band 5: Full numerical solution with clear conclusion sentence but no extra-factor comment. ≈ 5 marks.
Band 6: Complete, both jobs converted with correct week count, clear comparison, conclusion sentence naming winning job and dollar gap with units, AND a sensible extra factor. 6/6.