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Financial Mathematics, Indices and Measurement

Build essential mathematical skills for life and further study. Master earning and spending money, simple and compound interest, index laws, scientific notation, and the measurement of area, surface area and volume. Fully mapped to the NESA Mathematics K-10 Syllabus (2022) Stage 5 Core.

20 Lessons 3 Checkpoints 1 Unit Quiz Stage 5 Core + Paths

NESA Syllabus Outcomes

MAS-FIN-C-01

Solves financial problems involving simple interest, earning money and spending money.

MAS-FIN-C-02

Solves financial problems involving compound interest and depreciation.

MAS-IND-C-01

Simplifies algebraic expressions involving positive-integer and zero indices, and establishes the meaning of negative indices for numerical bases.

MAS-MAG-C-01

Solves measurement problems by using scientific notation to represent numbers and rounding to a given number of significant figures.

MAS-ARE-C-01

Solves problems involving the surface area of right prisms and practical problems involving the area of composite shapes and solids.

MAS-VOL-C-01

Solves problems involving the volume of composite solids, consisting of right prisms and cylinders.

Lessons

Block A — Financial Mathematics Lessons 1-7

Earning Money — Wages, Salaries and Awards

Calculate earnings from wages, salaries, overtime, penalties, commissions and piecework.

Earning Money — Overtime, Penalties and Commissions

Calculate overtime, penalty rates, commissions, bonuses and allowances.

Spending Money — Budgets and GST

Create personal budgets, calculate GST, and apply the 50/30/20 rule.

Discounts, Mark-ups and Best Buys

Calculate percentage discounts, mark-ups, successive discounts and unit pricing.

Simple Interest

Use I = PRT to calculate interest, total amounts and rearrange for any variable.

Compound Interest

Understand compounding periods, use A = P(1 + R)^n and compare with simple interest.

Depreciation and Financial Decision Making

Straight-line and reducing balance depreciation. Make informed financial decisions.

Checkpoint 1 — Financial Mathematics

Covers Lessons 1-7. Earning, spending, simple interest, compound interest and depreciation.

Block B — Indices and Numbers of Any Magnitude Lessons 8-14

Index Laws — Multiplication and Division

Apply a^m x a^n = a^(m+n) and a^m / a^n = a^(m-n) to numerical and algebraic bases.

Index Laws — Power of a Power and Mixed Practice

Combine multiple index laws including (a^m)^n = a^(mn) in complex expressions.

Zero and Negative Indices

Why a^0 = 1 and how negative indices create reciprocals.

Scientific Notation

Represent huge and tiny numbers. Convert, order and operate in standard form.

Significant Figures

Count, round and calculate with appropriate precision for real measurements.

Fractional Indices

Connect roots to powers: a^(1/n) and a^(m/n). [PATHS extension]

Surds and Operations

Simplify, add, subtract, multiply and rationalise simple surds. [PATHS extension]

Checkpoint 2 — Indices and Numbers of Any Magnitude

Covers Lessons 8-14. Index laws, zero and negative indices, scientific notation, significant figures, fractional indices and surds.

Block C — Measurement: Area, Surface Area and Volume Lessons 15-20

Area of Composite Shapes

Dissect complex shapes into triangles, quadrilaterals and circles to find total area.

Surface Area of Prisms

Use nets and formulas to find the surface area of rectangular and triangular prisms.

Surface Area of Cylinders and Cones

Extend to curved surfaces and composite solids. [PATHS: cones]

Volume of Prisms and Cylinders

Apply V = A_base x h to solve practical volume and capacity problems.

Volume of Pyramids, Cones and Spheres

The one-third relationship and sphere formula. [PATHS extension]

Measurement Problem Solving and Mixed Contexts

Multi-step problems, optimisation, scale factors and practical projects.

Checkpoint 3 — Measurement

Covers Lessons 15-20. Area, surface area and volume of prisms, cylinders and composite solids.

Unit Quiz — Financial Mathematics, Indices and Measurement

Comprehensive assessment covering all 20 lessons, 3 checkpoints and Working Mathematically.