HSC Maths Standard 1 Financial Mathematics and Algebra: exam question types and methods

What this guide covers

Financial mathematics and algebra make up a large share of the Standard 1 course, and they appear throughout both sections of the HSC paper. The multiple-choice items test whether you pick the right formula and the right values; the longer Section II questions ask you to show working and interpret the answer in context. Try the practice quiz on this page first, then use this guide to fix whatever you missed.

NESA's exam specification for Standard 1 is an 80-mark written paper (2 hours plus 10 minutes reading time): 10 marks of objective-response questions in Section I and 30 to 35 items in Section II.

The formulas you must choose between

These come from the reference sheet, but the marks come from choosing the right one and substituting correctly.

Revise investment, simple and compound interest and shares and depreciation, credit cards and reducing balance loans.

Question types you should expect

1. Calculate a value after some periods

Depreciation, compound interest and inflation all ask for a value after $n$ periods. Write the formula, substitute, then state the answer with units and sensible rounding (money to the nearest cent unless told otherwise). Inflation compounds exactly like interest.

2. Read or complete a table

Reducing balance loans and credit card statements are often given as tables. For each row of a loan table: add the period's interest to the balance owing, then subtract the repayment. For a credit card, interest applies to the unpaid balance and cash advances, usually from the day of the advance.

3. Break-even and linear models

Set up income and cost as linear equations, find where they are equal, and interpret the result. The y-intercept of the cost line is the fixed cost; the region to the right of the intersection is the profit zone.

Revise simultaneous linear equations and break-even.

4. Identify a graph from its shape

Straight lines mean a constant rate of change; exponential growth gets steeper; exponential decay levels off. On a distance-time graph the gradient is the speed, and a horizontal segment means the object is stopped. Revise graphs of practical situations.

Worked example

Question (exam style, 3 marks). A phone costs $1200 and depreciates at 25% per year using the declining-balance method. Find its value after 3 years.

Answer. Using $S = V_0(1 - r)^n$ with $r = 0.25$ and $n = 3$ gives $S = 1200(0.75)^3 = 506.25$. The phone is worth $506.25 after 3 years.

Keep going

Continue with the Measurement, Networks and Statistics practice, then work through the practice questions on each dot point page.