Mathematics Standard • Year 11 • Module 3 • Lesson 10
Managing Money — Exam Practice
Build fluency in chaining Managing Money steps within one question: net pay, taxable income, tax + Medicare, GST, and budget surplus.
Reference — 2024–25 ATO tax brackets
| Taxable income | Tax on this income |
|---|---|
| $0 – $18,200 | Nil |
| $18,201 – $45,000 | Nil + 19c for each $1 over $18,200 |
| $45,001 – $120,000 | $5,092 + 32.5c for each $1 over $45,000 |
| $120,001 – $180,000 | $29,467 + 37c for each $1 over $120,000 |
| $180,001 + | $51,667 + 45c for each $1 over $180,000 |
Medicare levy = 2% of taxable income. GST = 10% (×1.10 to add, ÷1.10 to remove, ÷11 for component).
1. Quick recall
Answer each question in the space provided. 1 mark each
Q1.1 Complete the chain: Gross income − Allowable deductions = ____________ ; Income tax + Medicare levy = ____________.
Q1.2 A label that protects ECF marks reads ∴ ____________ = $ ____________. State why writing this line at the end of each part is so important in extended-response questions.
____________________________________________________________________________
Q1.3 Tick (✓) the operations that are correct. Cross (×) the wrong ones.
____ Medicare levy = income tax × 0.02 | ____ GST component of inclusive price = price ÷ 11
____ Taxable income = gross + deductions | ____ Net pay = gross pay − total deductions
2. Worked example — full integrated tax question
Follow each line of working. Every step has a reason on the right.
Problem. Aisha earns $84,600 salary and $310 in bank interest. Her allowable deductions total $1,840. Her PAYG withheld was $17,820. Calculate her taxable income, total tax liability and refund/debt.
Step 1 — Gross income.
Gross = $84,600 + $310 = $84,910
Step 2 — Taxable income.
∴ Taxable income = $84,910 − $1,840 = $83,070
Reason: label the answer with a "∴" line so the marker can find it.
Step 3 — Income tax (bracket $45,001 – $120,000).
Income tax = $5,092 + 0.325 × ($83,070 − $45,000)
= $5,092 + 0.325 × $38,070
= $5,092 + $12,372.75 = $17,464.75
Step 4 — Medicare levy.
Medicare = $83,070 × 0.02 = $1,661.40
Step 5 — Total tax liability.
∴ Total liability = $17,464.75 + $1,661.40 = $19,126.15
Step 6 — Reconcile against PAYG.
$17,820 < $19,126.15 → ∴ Tax debt of $1,306.15
Conclusion. Aisha has a tax debt of $1,306.15.
3. Faded example — net pay + monthly budget
Theo's fortnightly gross pay is $2,420. PAYG tax $410, union $14, health insurance $52 per fortnight. Monthly expenses: rent $1,560, groceries $620, transport $240, phone $96 (GST-inclusive). Fill the blanks. 4 marks
Step 1 — Total fortnightly deductions:
= $ ________ + $ ________ + $ ________ = $ ____________
Step 2 — Fortnightly net pay: $ ________ − $ ________ = $ ____________
Step 3 — Convert to monthly net pay: $ ________ × 26 ÷ 12 ≈ $ ____________
Step 4 — Total monthly expenses: $1,560 + $620 + $240 + $ ________ = $ ____________
Step 5 — Monthly surplus or deficit: $ ________ − $ ________ = $ ____________ → ____________
4. Graduated practice — chained Managing Money
Show every step labelled clearly with "∴". Use the tax-bracket reference above.
Foundation — single-skill recall (4 questions)
| Q | Problem | Answer |
|---|---|---|
| 4.1 1 | Gross income $68,400; deductions $1,920. Find taxable income. | |
| 4.2 1 | Gross fortnightly pay $2,180; PAYG $362; super $98; health $34. Find fortnightly net pay. | |
| 4.3 1 | Income tax on $94,200 = ? (apply the bracket formula) | |
| 4.4 1 | Find the GST component of a $957 GST-inclusive bill. |
Standard — typical HSC difficulty (6 questions)
Show substitution and label each answer with "∴".
4.5 Calculate total tax liability (income tax + Medicare) on a taxable income of $63,400. 2 marks
4.6 A worker earns $72,800 salary + $480 interest; deductions $2,140; PAYG $14,300. Find refund/debt. 2 marks
4.7 Weekly net pay $920. Weekly expenses $740. Find weekly surplus and annual surplus. 2 marks
4.8 A 91-day electricity bill: supply $1.02/day; flat usage 650 kWh × 30.6c/kWh. All pre-GST. Find GST-inclusive bill. 2 marks
4.9 Plan A: $94/month flat. Plan B: $44/month + $0.18 per GB above 10 GB. The household uses 65 GB per month. Which is cheaper? 2 marks
4.10 Gross fortnightly pay $2,640; PAYG $458; union $16; super $194; health $52. Find fortnightly net pay. 2 marks
Extension — chain three concepts (2 questions)
4.11 Mei earns $86,400 salary + $740 interest + $1,620 rental income. Deductions $2,950. PAYG $18,150. (a) Taxable income. (b) Total liability. (c) Refund/debt. 3 marks
4.12 A family has monthly net income $7,420. Expenses (monthly): mortgage $2,180; weekly groceries $290; quarterly electricity $580 (GST-inc); fortnightly fuel $140. (a) Convert all to monthly. (b) Find surplus/deficit. (c) Find GST component of the electricity. 3 marks
5. Self-check the easy 3
Tick the first three once you've checked your method works.
How did this worksheet feel?
What I'll revisit before next class:
Q1.1 — Chain labels
Gross − Deductions = Taxable income. Income tax + Medicare = Total tax liability.
Q1.2 — ECF protection
Markers can only award error-carried-forward marks if the labelled answer is visible. A clearly written "∴ X = $..." line ensures a single arithmetic slip doesn't cost marks in subsequent parts of the question.
Q1.3 — Operations
Medicare = income tax × 0.02 → × (it's taxable income × 0.02). GST ÷ 11 → ✓. Taxable = gross + deductions → × (subtract, don't add). Net = gross − deductions → ✓.
Q3 — Faded example (Theo)
Step 1: Total fortnightly deductions = $410 + $14 + $52 = $476.
Step 2: Net pay = $2,420 − $476 = $1,944 per fortnight.
Step 3: Monthly net = $1,944 × 26 ÷ 12 = $4,212.
Step 4: Total monthly expenses = $1,560 + $620 + $240 + $96 = $2,516.
Step 5: $4,212 − $2,516 = $1,696 monthly surplus.
Q4.1 — Taxable income
$68,400 − $1,920 = $66,480.
Q4.2 — Net pay
Total deductions = $362 + $98 + $34 = $494. Net pay = $2,180 − $494 = $1,686.
Q4.3 — Income tax on $94,200
$94,200 in $45,001 – $120,000 bracket. Tax = $5,092 + 0.325 × ($94,200 − $45,000) = $5,092 + $15,990 = $21,082.00.
Q4.4 — GST component
$957 ÷ 11 = $87.00.
Q4.5 — Total liability on $63,400
Income tax = $5,092 + 0.325 × ($63,400 − $45,000) = $5,092 + $5,980 = $11,072. Medicare = $63,400 × 0.02 = $1,268. Total liability = $12,340.00.
Q4.6 — Refund/debt
Gross = $73,280. Taxable income = $71,140.
Income tax = $5,092 + 0.325 × ($71,140 − $45,000) = $5,092 + $8,495.50 = $13,587.50. Medicare = $71,140 × 0.02 = $1,422.80. Total liability = $15,010.30.
$14,300 < $15,010.30 → tax debt of $710.30.
Q4.7 — Surplus
Weekly surplus = $920 − $740 = $180. Annual surplus = $180 × 52 = $9,360.
Q4.8 — Electricity bill
Supply = $1.02 × 91 = $92.82. Usage = 650 × $0.306 = $198.90. Pre-GST = $291.72. GST-inclusive = $291.72 × 1.10 = $320.89 (to nearest cent).
Q4.9 — Plan comparison
Plan A monthly = $94.00.
Plan B monthly = $44 + (65 − 10) × $0.18 = $44 + 55 × $0.18 = $44 + $9.90 = $53.90.
Plan B is cheaper by $94 − $53.90 = $40.10 per month.
Q4.10 — Fortnightly net pay
Total deductions = $458 + $16 + $194 + $52 = $720. Net pay = $2,640 − $720 = $1,920.
Q4.11 — Mei's full tax
(a) Gross = $86,400 + $740 + $1,620 = $88,760. Taxable income = $88,760 − $2,950 = $85,810.
(b) Income tax = $5,092 + 0.325 × ($85,810 − $45,000) = $5,092 + $13,263.25 = $18,355.25. Medicare = $85,810 × 0.02 = $1,716.20. Total liability = $20,071.45.
(c) PAYG $18,150 < $20,071.45 → tax debt of $1,921.45.
Q4.12 — Family budget + GST
(a) Mortgage $2,180 (already monthly). Groceries = $290 × 52 ÷ 12 ≈ $1,256.67. Electricity = $580 ÷ 3 ≈ $193.33. Fuel = $140 × 26 ÷ 12 ≈ $303.33.
Total monthly expenses ≈ $3,933.33.
(b) Surplus = $7,420 − $3,933.33 = $3,486.67 monthly surplus.
(c) GST on electricity = $580 ÷ 11 ≈ $52.73.