← Maths Standard 2 syllabus

NSWMaths Standard 2

Year 11: Financial Mathematics

8 dot points across 8 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you work out a household bill from a tiered tariff with a supply charge and stepped usage rates, cost the purchase and running of a car including stamp duty from a scale, and balance a personal budget to find the surplus or shortfall?

Prepare and interpret a budget. Calculate household bills such as electricity and water from a tariff with a fixed supply charge plus stepped (tiered) usage rates. Calculate the costs of purchasing and running a motor vehicle, including stamp duty from a published scale, registration, insurance and running costs. Balance a personal budget of income against expenses and find the surplus, shortfall or the saving required
The HSC Maths Standard 2 method for budgeting and household costs: work a tiered electricity or water bill from a supply charge plus stepped usage rates, find motor-vehicle stamp duty from a published scale, total the annual running cost of a car, and balance a personal budget to a surplus or shortfall, with code-checked Australian examples.
17 min answer →

How is income calculated when pay depends on sales, output or intellectual property rather than fixed hours, and how do leave loading, bonuses and government payments add to it?

Calculate earnings from commission (flat and sliding scale), piecework, royalties, annual leave loading and bonuses, and government allowances
A focused answer to the HSC Maths Standard 2 dot point on income that is not a plain wage. Flat-rate and sliding-scale (stepped) commission, piecework from a per-item rate, royalties, the 17.5% annual leave loading and bonuses, and government allowances, with code-checked Australian worked examples and a step chart.
14 min answer →

How is the 10% GST added to a price and then pulled back out of a GST-inclusive total, and why do percentage changes only behave predictably when you treat them as multipliers?

Add the 10% GST to a pre-GST price, find the GST contained in a GST-inclusive total and the pre-GST price, calculate percentage increases and decreases, and combine successive percentage changes using multipliers
The HSC Maths Standard 2 method for GST and percentage change. Add the 10% GST with x 1.1, extract the GST from an inclusive total with /11 and the pre-GST price with /1.1, do percentage increases and decreases as multipliers, and combine successive changes by multiplying, with code-checked Australian examples and a GST split-bar diagram.
15 min answer →

How does the Australian Taxation Office turn a person's gross income into the tax they actually owe, and how does the PAYG system settle that bill across a financial year?

Calculate gross and net pay, identify allowable deductions and taxable income, compute the tax payable from a tax-bracket table, add the Medicare levy, and reconcile PAYG withheld against the tax assessed
The HSC Maths Standard 2 method for income tax. Gross vs net pay, allowable deductions and taxable income, tax payable from a marginal tax-bracket table, the 2% Medicare levy, and reconciling PAYG withheld against tax assessed for a refund or amount owing, with code-checked Australian worked examples and a tax-bracket diagram.
16 min answer →

Why does simple interest plot as a straight line, what does the gradient of that line mean, and how do you compare two interest rates and read values straight off the graph?

Graph simple interest as a straight line of interest I (or amount A) against time n, interpret the gradient as the interest earned each period, compare two rates on the same axes by their gradients, and read interest, amount or time off the line
The HSC Maths Standard 2 method for simple interest graphs. Plot I or A against time n as a straight line, read off the gradient as the interest each period (Pr), compare two rates on shared axes where the steeper line is the higher rate, and read interest, amount or time straight off the line, with code-checked Australian term-deposit examples.
15 min answer →

How does the simple interest formula I = Prn work, why does the amount grow as a straight line, and how do you rearrange it to find the principal, the rate or the time, including over part of a year?

Apply the simple interest formula I = Prn and the amount A = P + I, rearrange it to solve for the principal, the rate or the time, and calculate interest over part-years measured in months or days
The HSC Maths Standard 2 method for simple interest. Use I = Prn for the interest and A = P + I for the final amount, rearrange to solve for the principal, rate or time, and handle part-years by writing months as n/12 and days as n/365, with code-checked Australian examples and a straight-line growth diagram.
16 min answer →

Why does straight-line depreciation plot as a falling straight line, how do you find the value after n years or the annual depreciation amount, and how is it different from declining-balance depreciation?

Model the value of a depreciating asset with straight-line (prime-cost) depreciation S = V0 - Dn, find the salvage value after n years, the annual depreciation D and the time to reach a given value, work with a rate given as a percentage of the original cost, and contrast it with declining-balance depreciation
The HSC Maths Standard 2 method for straight-line (prime-cost) depreciation. Use S = V0 - Dn to find the salvage value after n years, the annual depreciation D, and when the value hits a target, handle a rate given as a percentage of the original cost, and contrast the falling straight line with declining balance, with code-checked Australian examples.
15 min answer →

How is pay calculated from a salary or an hourly wage, and how do overtime rates and allowances change a worker's earnings?

Calculate earnings from wages, salaries and overtime, including conversion between pay periods, hourly rates, penalty rates and allowances
A focused answer to the HSC Maths Standard 2 dot point on earning money as a wage or salary. Converting pay between yearly, monthly, fortnightly and weekly periods, finding an hourly rate, and computing gross pay with overtime at time-and-a-half and double time, shift loadings and allowances, with worked Australian examples.
13 min answer →