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Three printable worksheets that build from foundations to mastery, or build your own from any module’s questions.

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Practise this lesson

Three printable worksheets that build from foundations to mastery, or build your own from any module’s questions.

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Module 3 · Financial Mathematics · Lesson 5 of 14

Earning Money, Exam Practice

Bring together all Earning Money concepts in integrated, HSC-style problems that mirror real exam structure and decision-making.

55 min MS-F1 4 WE 5 MC 3 SAQ

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Think First

In a real HSC exam, you won't get a question that says "this is a commission question" or "this is a leave loading question." The examiner combines multiple concepts into one scenario, a worker who earns a wage, works overtime, gets an allowance, and takes annual leave all in the same question. The skill being tested isn't just whether you know each formula, it's whether you can identify which formula applies, in what order, and whether your final answer actually makes sense. Before you start, think: what's your strategy when you open an exam paper and see a multi-part financial maths question?

Learning Intentions

Know

All Earning Money formulas from Lessons 1–4
The decomposition strategy: list every component, calculate each, then sum
That extended response marks are awarded for each step, not just the final answer

Understand

How to identify which formula applies from an unfamiliar context
Why conclusions must be stated explicitly in comparison questions
How to carry forward a part (a) answer correctly into part (b)

Can Do

Solve multi-component pay questions in exam conditions
Compare two earning structures and state a clear conclusion
Find the piecework output that matches an hourly wage

Gross PayTotal earnings before any deductions are taken out.

Net PayThe amount received after all deductions have been subtracted.

CommissionPayment calculated as a percentage of total sales made.

OvertimeHours worked beyond normal hours, paid at higher penalty rates.

AllowanceAdditional payment for specific work conditions or expenses.

Formula Summary, Earning Money

$W = r_h \times h \quad A = W \times 52 \quad F = A \div 26 \quad M = A \div 12$

Weekly wage, Annual, Fortnightly, Monthly, always convert through annual

$r_{\text{OT}} = r_h \times m \quad \text{Total pay} = (h_n \times r_h) + (h_{\text{OT}} \times r_{\text{OT}}) + \text{Allowances}$

$m$ = 1.5 (time-and-a-half) or 2.0 (double time) | each component calculated separately

$\text{Commission} = S \times r \quad \text{Piecework} = n \times r_p \quad \text{Leave loading} = 0.175 \times 4W$

Tiered commission: apply each rate to its slice only | Leave loading: based on weekly wage, not annual

$\text{Gross} = \text{all earnings summed} \quad \text{Net} = \text{Gross} - \text{Deductions} \quad \text{Gross} = \text{Net} + \text{Deductions}$

Last form is the reverse formula, use when net and deductions are known

Reading the Question Before Writing Anything

In multi-part HSC questions, the most important skill is identifying exactly what is being asked before reaching for a formula.

Reading the Question Before Writing Anything

In multi-part HSC questions, the most important skill is identifying exactly what is being asked before reaching for a formula.

A common trap in exam conditions is to start calculating immediately without checking whether the question asks for gross pay or net pay, weekly pay or annual pay, the commission amount or the total earnings including commission.

Develop a two-step habit before every question:

Underline or circle the key quantity being asked for
Identify which pay components are mentioned in the stimulus

In extended response questions, marks are allocated to each part independently, a wrong answer in part (a) does not prevent you from scoring full marks in part (b) if you use the correct method from that point on. Always carry forward your part (a) answer with a clear label, even if you're unsure it's right.

Re-read the final line of the question before writing your answer: The last sentence of an HSC question usually states exactly what form the answer must take, e.g. "express your answer to the nearest dollar" or "determine whether Job A or Job B pays more." Answer that specific question, not a related one.

Common error, Don't leave answers without units or conclusions: A numerical answer alone is not enough for extended response marks. "Job A pays $\$3,120$ more per year" earns the conclusion mark; "$\$3,120$" alone may not.

Book notes

True or false: In a multi-part exam question, getting part (a) wrong means you cannot earn any marks on part (b).

Strategy for Multi-Component Pay Questions

Complex pay questions always decompose into the same building blocks, identify each block, calculate it separately, then combine.

Strategy for Multi-Component Pay Questions

Complex pay questions always decompose into the same building blocks, identify each block, calculate it separately, then combine.

When a question describes a worker's full pay situation, use this reliable decomposition strategy:

Step	Action	Mark value (typical)
1	List every income source mentioned	Setup mark
2	Calculate each component in isolation	1 mark each
3	Sum for gross pay	1 mark
4	Apply deductions if asked for net pay	1 mark
5	Convert to requested time period if needed	1 mark

Set out working as a table or numbered list: "Ordinary pay: $\$\square$ | Overtime: $\$\square$ | Allowance: $\$\square$ | Gross: $\$\square$", this structure mirrors HSC marking guidelines and makes it impossible for a marker to miss your method.

Common error, Forgetting to convert pay periods at the end: A question may give hourly rates and weekly hours, then ask for annual income or fortnightly pay. Always check the question's requested unit against your answer's unit.

Insight: If your final answer seems unrealistically large or small, trust that instinct. Most full-time workers earn $\$800$–$\$2{,}500$ per week gross, use this to sense-check arithmetic.

Book notes

Quick check: Fatima worked 76 ordinary hours at $\$34.20$/hr and 8 Saturday hours at time-and-a-half. What is her ordinary pay for the fortnight?

Comparing Earning Options

Some of the most demanding HSC questions ask you to compare two different pay structures and determine which is better under...

Comparing Earning Options

Some of the most demanding HSC questions ask you to compare two different pay structures and determine which is better under given conditions.

Comparison questions typically involve two workers or two job offers described using different pay structures, for example, a flat salary vs a retainer-plus-commission arrangement, or an hourly wage vs a piecework rate. The strategy:

Convert both options to the same unit (annual or weekly)
Calculate each fully
State a clear conclusion with supporting numbers

A common variation asks "how many items must a piecework employee produce to match the salary worker's weekly pay?", this is a reverse calculation requiring division. Another variation gives a commission structure and asks for the sales volume required to reach a target income. In all cases, define a variable, write an equation, and solve, this earns method marks even if arithmetic errors occur later.

Always state a conclusion: Comparison questions require a judgement, "Option A is better by $\$X$ per year" or "the employee needs to sell at least Y units." A calculation without a conclusion is incomplete and will lose the final mark.

Common error, Don't assume more pay is always better: Some questions introduce additional conditions, e.g. "the commission role requires purchasing a car for $\$8{,}500$." This additional cost changes the comparison. Read every sentence of the stimulus before concluding.

Book notes

A factory worker under Option A earns $\$19.80$/hr for 38 hours = $\$752.40$ per week. Under Option B they earn $\$2.75$ per component. To meet the same target, they must produce at least components (round up).

How to Maximise Marks in Extended Response Questions

In exam practice lessons, presentation is part of performance.

How to Maximise Marks in Extended Response Questions

In exam practice lessons, presentation is part of performance. A marker should be able to follow your work line by line without guessing what you meant.

For multi-part earning-money questions, a strong layout usually looks like this:

Label the part clearly: (a), (b), (c)
Write the relevant formula or relationship
Substitute values on the next line
Show the numerical result with units
If it is a comparison question, finish with a sentence conclusion

ECF reminder: Error-carried-forward marks are only possible when each part is clearly shown. If part (b) uses your answer from part (a), label it so the marker can see the method is sound even if the earlier number was wrong.

Best habit: Box or underline the final answer for each part. This makes it much easier to keep long responses organised and prevents you from losing marks for ambiguity.

Book notes

Match each exam strategy tip to its purpose.

Underline the key quantity
Label each part (a), (b), (c)
State a sentence conclusion
Convert both options to same unit

Required in comparison questions
Essential before comparing job offers
Ensures you answer what is actually asked
Makes ECF marks possible

Worked Examples

PROBLEM 1 · INTEGRATED PAY SLIP

Fatima works as a nurse. Her ordinary rate is $\$34.20$ per hour. This fortnight she worked 76 ordinary hours, 8 hours on Saturday at time-and-a-half, and 4 hours on a public holiday at double time. She also received a uniform allowance of $\$22.50$ per week. Calculate Fatima's gross pay for the fortnight.

$\text{Ordinary pay} = \$34.20 \times 76 = \$2{,}599.20$

76 ordinary hours at base rate

Book notes

PROBLEM 2 · COMMISSION VS SALARY

Maya is choosing between two sales jobs. Job A offers a salary of $\$52,000$ per year. Job B offers a retainer of $\$650$ per fortnight plus 3.5% commission on all sales. In a typical fortnight Maya expects to make $\$28{,}000$ in sales. Which job pays more annually, and by how much?

$\text{Job A annual} = \$52{,}000$

Already given as annual, no conversion needed

Book notes

PROBLEM 3 · PIECEWORK BREAK-EVEN

A factory offers two pay options for assembling components. Option A: $\$19.80$ per hour for a 38-hour week. Option B: $\$2.75$ per component assembled. How many components per week must a worker produce under Option B to earn at least as much as Option A?

$\text{Option A weekly pay} = \$19.80 \times 38 = \$752.40$

Calculate the target income to match

Book notes

PROBLEM 4 · MULTI-PART EXAM QUESTION

A worker earns $\$27.80$ per hour for 38 hours per week. They also work 5 overtime hours at time-and-a-half and receive a $\$72$ weekly allowance. (a) Calculate the weekly gross pay. (b) Calculate the equivalent annual gross pay. (c) Another job pays $\$69{,}500$ per year. Which job pays more annually, and by how much?

$(a)\; \text{Ordinary pay} = \$27.80 \times 38 = \$1{,}056.40$

Start with ordinary weekly pay

Book notes

List the three things you must do after completing a comparison question to ensure full marks.

Revisit Your Initial Thinking

Look back at what you wrote in the Think First section. What has changed? What did you get right? What surprised you?

Show what you have learned

Multiple choice, then short answer under exam conditions.

Multiple Choice, 5 Questions

Multiple Choice

5 random questions from the lesson bank, feedback shown immediately.

Short Answer Questions

SAQ 1

A worker earns $\$26.50$ per hour for 38 hours, plus 4 overtime hours at time-and-a-half, and a $\$48$ weekly allowance. Calculate the weekly gross pay.

Show sample answer

$\text{Ordinary pay} = \$26.50 \times 38 = \$1{,}007.00$

$\text{OT rate} = \$26.50 \times 1.5 = \$39.75\text{/hr}$

$\text{OT pay} = \$39.75 \times 4 = \$159.00$

$\text{Gross pay} = \$1{,}007.00 + \$159.00 + \$48.00 = \mathbf{\$1{,}214.00}$

SAQ 2

A salesperson receives a $\$720$ fortnightly retainer plus 2.8% commission on all sales. If they make $\$34,500$ in sales in a fortnight, calculate their total fortnightly earnings and equivalent annual earnings.

Show sample answer

$\text{Commission} = \$34{,}500 \times 0.028 = \$966.00$

$\text{Fortnightly earnings} = \$720 + \$966 = \$1{,}686.00$

$\text{Annual earnings} = \$1{,}686.00 \times 26 = \mathbf{\$43{,}836.00}$

SAQ 3

A worker earns $\$1{,}050$ per week. Calculate the total amount they receive over a 4-week leave period including leave loading.

Show sample answer

$\text{4 weeks' leave pay} = \$1{,}050 \times 4 = \$4{,}200$

$\text{Leave loading} = \$4{,}200 \times 0.175 = \$735$

$\text{Total received} = \$4{,}200 + \$735 = \mathbf{\$4{,}935.00}$

Consolidate and move on

Sit the module quiz, then close the lesson off.

Boss Battle

Earning Money Exam Sprint

Face the boss using all your knowledge of wages, overtime, commission, piecework, pay slips and exam strategy. Pool: lessons 1–5.

✓

Lesson Complete!

You've worked through integrated pay questions, the decomposition strategy, job comparisons, piecework break-even, and multi-part exam technique.

Mark this lesson as done

Year 11 Index Module 3 Index Maths Standard