Mathematics Standard • Year 11 • Module 3 • Lesson 9
GST, Budgeting and Household Expenses
Practise HSC Mathematics Standard 2-style writing on GST, budgets and household bills — short answers and one structured extended response.
1. Short-answer questions
1.1 A plumber's pre-GST invoice for a hot-water installation is $1,640. Calculate the GST-inclusive amount the customer must pay. 2 marks Band 3
1.2 A receipt shows a GST-inclusive total of $748.
(a) Calculate the GST component of this receipt.
(b) Calculate the pre-GST amount. 3 marks Band 3-4
1.3 A household receives a 91-day electricity bill (pre-GST): supply $1.04/day; usage — first 700 kWh at 28.6c/kWh, remaining at 36.4c/kWh. Total usage 950 kWh.
(a) Calculate the pre-GST bill total.
(b) Calculate the GST-inclusive total. 4 marks Band 4
2. Extended response
2.1 The Tran family has the following weekly/monthly/quarterly finances:
Income: Combined monthly net wages $7,840; weekly child-care subsidy $112.
Expenses: Mortgage $2,420 per month; weekly groceries $290; quarterly electricity bill $612 (GST-inclusive); fortnightly fuel $148; phone and internet $128 per month (GST-inclusive); annual home insurance $1,560 (GST-inclusive); discretionary monthly spending $640.
(a) Convert all income items to a monthly figure and calculate total monthly income.
(b) Convert all expense items to a monthly figure and calculate total monthly expenses.
(c) Calculate the monthly surplus or deficit and state a clear conclusion. Also calculate the GST component of the electricity bill, and explain in one sentence why this calculation uses ÷11 rather than ×0.10. 7 marks Band 5-6
Explicit marking criteria
Part (a) — 1 mark
• 1 mark — correct monthly income (wages already monthly; weekly subsidy × 52 ÷ 12).
Part (b) — 3 marks
• 1 mark — correct conversion of weekly groceries (× 52 ÷ 12) and fortnightly fuel (× 26 ÷ 12).
• 1 mark — correct conversion of quarterly electricity (÷ 3) and annual insurance (÷ 12).
• 1 mark — correct total monthly expenses (sum of all converted items).
Part (c) — 3 marks
• 1 mark — correct monthly surplus or deficit with conclusion sentence.
• 1 mark — correct GST component using ÷ 11 on the GST-inclusive electricity total.
• 1 mark — brief, accurate one-sentence explanation: GST-inclusive prices already contain the 10% — ÷11 extracts it, while ×0.10 on an inclusive price overcounts.
Your response:
Stuck on (c)? An inclusive price = 110% of pre-GST = 11 equal parts; the GST is 1 of those 11 parts (1/11 = ÷11). ×0.10 only works on the pre-GST amount.How did this worksheet feel?
What I'll revisit before next class:
1.1 — Pre-GST $1,640 → inclusive (2 marks)
Sample response.
GST-inclusive amount = $1,640 × 1.10 = $1,804.00.
Marking notes. 1 mark — correct method (multiplying by 1.10). 1 mark — correct numerical answer with units. Common error: adding 10 (i.e. $1,650) instead of multiplying by 1.10.
1.2 — GST component and pre-GST from inclusive $748 (3 marks)
Sample response.
(a) GST component = $748 ÷ 11 = $68.00.
(b) Pre-GST = $748 ÷ 1.10 = $680.00. (Check: $680 + $68 = $748 ✓.)
Marking notes. (a) 1 mark — uses ÷11 (not ×0.10) on inclusive price. 1 mark — correct numerical answer. (b) 1 mark — uses ÷1.10 (not ÷11). Common error: ×0.10 on $748 gives $74.80 (overcounted GST) — a 1-mark loss.
1.3 — Tiered electricity bill with GST (4 marks)
Sample response.
(a) Supply = $1.04 × 91 = $94.64.
Tier 1 = 700 × $0.286 = $200.20.
Tier 2 = (950 − 700) × $0.364 = 250 × $0.364 = $91.00.
Pre-GST total = $94.64 + $200.20 + $91.00 = $385.84.
(b) GST-inclusive total = $385.84 × 1.10 = $424.42 (to nearest cent).
Marking notes. (a) 1 mark — correct supply charge. 1 mark — correct tier-split usage (Tier 1 capped at 700; Tier 2 on remainder). 1 mark — correct pre-GST total. (b) 1 mark — correct GST-inclusive total using ×1.10. Common errors: applying Tier 1 rate to all 950 kWh; or adding GST tier-by-tier (wasteful but not wrong if executed correctly).
2.1 — Tran family budget (7 marks): sample Band-6 response with annotations
Sample Band-6 response.
(a) Total monthly income.
Monthly wages = $7,840.
Monthly child-care subsidy = $112 × 52 ÷ 12 ≈ $485.33.
Total monthly income = $7,840 + $485.33 ≈ $8,325.33. [1 mark — correct income total with weekly subsidy converted.]
(b) Total monthly expenses.
Mortgage = $2,420.
Groceries = $290 × 52 ÷ 12 ≈ $1,256.67.
Fuel = $148 × 26 ÷ 12 ≈ $320.67. [1 mark — weekly groceries and fortnightly fuel correctly converted.]
Electricity = $612 ÷ 3 = $204.
Insurance = $1,560 ÷ 12 = $130. [1 mark — quarterly electricity and annual insurance correctly converted.]
Phone/internet = $128.
Discretionary = $640.
Total monthly expenses ≈ $2,420 + $1,256.67 + $320.67 + $204 + $130 + $128 + $640 = $5,099.34. [1 mark — correct total expenses.]
(c) Surplus/deficit + GST on electricity.
Monthly surplus = $8,325.33 − $5,099.34 = $3,225.99.
Conclusion: The Trans have a monthly surplus of about $3,226. [1 mark — correct surplus + conclusion sentence.]
GST component of electricity = $612 ÷ 11 = $55.64 (to nearest cent). [1 mark — correct GST component using ÷11.]
We use ÷11 because the $612 is already GST-inclusive — the pre-GST portion is 10 parts and the GST itself is 1 part, making 11 parts in total. Multiplying $612 by 0.10 would calculate 10% of an already-inflated amount and overcount the GST. [1 mark — accurate one-sentence explanation linking ÷11 to the 1-in-11-parts structure of an inclusive price.]
Total: 7/7.
Band descriptors for marker.
Band 3: Converts at least one income and one expense item correctly; gets some of the totals; surplus/deficit attempted but errors in conversion. ≈ 3 marks.
Band 4: All conversions correct; total income and total expenses correct; surplus or deficit calculated; either GST or its explanation missing. ≈ 5 marks.
Band 5: Full numerical solution including correct GST component, but explanation in (c) is muddled or missing the 1-in-11 logic. ≈ 6 marks.
Band 6: Complete: all conversions, correct surplus with sentence, correct GST using ÷11, AND a clear one-sentence justification for ÷11 vs ×0.10. 7/7.