Year 10 Topic Guide

Working with Surds

(Text ref: New Century Maths 10 Advanced, Chapter 1)

• 1.01 - Surds and Irrational Numbers

• 1.02 - Simplifying Surds

• 1.03 - Adding and Subtracting Surds

• 1.04 - Multiplying and Dividing Surds

• 1.05 - Binomial Products involving Surds

• 1.06 - Rationalising the Denominator

Finance

(Text ref: New Century Maths 10 Advanced, Chapter 2)

• 2.01 - Earning an Income

• 2.02 - Income Tax

• 2.03 - Simple Interest

• 2.04 - Compound Interest

• 2.05 - The Compound Interest Formula A = P(1 + r)ⁿ

• 2.06 - Buying on Terms

• 2.07 - Depreciation (Declining Balance)

Linear Relationships and their Graphs

(Text ref: New Century Maths 10 Advanced, Chapter 3)

• 3.01 - Length, Midpoint and Gradient of an Interval

• 3.02 - Parallel and Perpendicular Lines

• 3.03 - Graphing Linear Equations

• 3.04 - The Gradient-intercept Equation y = mx + c

• 3.05 - The General Equation ax + by + c = 0

• 3.06 - The Point-gradient Formula y - y₁ = m(x - x₁)

• 3.07 - Finding the Equation of a Line

• 3.08 - Equations of Parallel and Perpendicular Lines

• 3.09 - Coordinate Geometry Problems

Surface Area and Volume

(Text ref: New Century Maths 10 Advanced, Chapter 4)

• 4.01 - Surface Area of a Prism

• 4.02 - Surface Area of a Cylinder

• 4.03 - Surface Area of a Pyramid

• 4.04 - Surface Areas of Cones and Spheres

• 4.05 - Surface Area of Composite Solids

• 4.06 - Volumes of Prisms and Cylinders

• 4.07 - Volumes of Pyramids, Cones and Spheres

• 4.08 - Volumes of Composite Solids

• 4.09 - Areas of Similar Figures

• 4.10 - Surface Area and Volume of Similar Solids

Products and Factors

(Text ref: New Century Maths 10 Advanced, Chapter 5)

• 5.01 - The Index Laws (Exponent Rules)

• 5.02 - Fractional Indices

• 5.03 - Adding and Subtracting Algebraic Fractions

• 5.04 - Multiplying and Dividing Algebraic Fractions

• 5.05 - Expanding and Factorising Expressions

• 5.06 - Expanding Binomial Products

• 5.07 - Factorising Special Binomial Products

• 5.08 - Factorising Monic Quadratic Expressions x² + bx + c

• 5.09 - Factorising Non-monic Quadratic Expressions ax² + bx + c, a ≠ 0

• 5.10 - Mixed Factorisations

• 5.11 - Factorising Algebraic Fractions

Further Statistics

(Text ref: New Century Maths 10 Advanced, Chapter 6)

• 6.01 - The Shape of a Frequency Distribution

• 6.02 - Quartiles and Interquartile Range

• 6.03 - Standard Deviation

• 6.04 - Comparing Means and Standard Deviations

• 6.05 - Box Plots

• 6.06 - Parallel Box Plots

• 6.07 - Comparing Data Sets

• 6.08 - Scatterplots

• 6.09 - Line of Best Fit

• 6.10 - Bivariate Data Involving Time

• 6.11 - Statistics in the Media

• 6.12 - Investigating Statistical Studies

Equations and Logarithms

(Text ref: New Century Maths 10 Advanced, Chapter 7)

• 7.01 - Equations with Algebraic Fractions

• 7.02 - Solving Monic Quadratic Equations x² + bx + c = 0

• 7.03 - Solving Simple Cubic Equations ax³ = c

• 7.04 - Equation Problems

• 7.05 - Equations and Formulas

• 7.06 - Changing the Subject of a Formula

• 7.07 - Graphing Inequalities on a Number Line

• 7.08 - Solving Inequalities

• 7.09 - Logarithms

• 7.10 - Logarithm Laws

• 7.11 - Solving Logarithmic and Exponential Equations

Non-Linear Relationships and their Graphs

(Text ref: New Century Maths 10 Advanced, Chapter 8)

• 8.01 - Direct Proportion

• 8.02 - Inverse Proportion

• 8.03 - Conversion Graphs

• 8.04 - Distance-time Graphs

• 8.05 - Graphs of Variable Change

• 8.06 - The Parabola y = ax² + c

• 8.07 - The Parabola y = a(x - b)² + c

• 8.08 - The Cubic Curve y = kx³ + c

• 8.09 - The Cubic Curve y = k(x - a)(x - b)(x - c)

• 8.10 - The Power Curves y = kxⁿ + c

• 8.11 - The Hyperbola y = k / x

• 8.12 - The Exponential Curve y = aˣ

• 8.13 - The Circle (x - a)² + (y - b)² = c²

• 8.14 - Identifying Graphs

Further Trigonometry

(Text ref: New Century Maths 10 Advanced, Chapter 9)

• 9.01 - Right-angled Trigonometry

• 9.02 - Bearings

• 9.03 - Pythagoras' Theorem and Trigonometry in Three Dimensions

• 9.04 - Complementary Relations and Exact Ratios

• 9.05 - The Trigonometric Functions

• 9.06 - Solving Trigonometric Equations

• 9.07 - The Sine Rule

• 9.08 - The Sine Rule for Angles

• 9.09 - The Cosine Rule

• 9.10 - The Cosine Rule for Angles

• 9.11 - The Area Rule for Triangles

• 9.12 - Problems Involving the Sine and Cosine Rules

Simultaneous Equations

(Text ref: New Century Maths 10 Advanced, Chapter 10)

• 10.01 - Solving Simultaneous Equations Graphically

• 10.02 - The Elimination Method

• 10.03 - The Substitution Method

• 10.04 - Problems Involving Simultaneous Equations

Quadratic Equations and the Parabola

(Text ref: New Century Maths 10 Advanced, Chapter 11)

• 11.01 - Solving Non-monic Quadratic Equations ax² + bx + c = 0

• 11.02 - Completing the Square

• 11.03 - The Quadratic Formula

• 11.04 - Mixed Problems

• 11.05 - Higher-order Quadratic Equations

• 11.06 - Quadratic Equation Problems

• 11.07 - The Parabola y = ax² + bx + c

• 11.08 - The Axis of Symmetry and Vertex of a Parabola

• 11.09 - Solving Non-linear Simultaneous Equations

Probability

(Text ref: New Century Maths 10 Advanced, Chapter 12)

• 12.01 - Relative Frequency (Experimental Probability)

• 12.02 - Venn Diagrams for Non-mutually Exclusive Events

• 12.03 - Two-way Tables (Arrays) for Non-mutually Exclusive Events

• 12.04 - Tree Diagrams

• 12.05 - Selecting with and without Replacement

• 12.06 - Dependent and Independent Events

• 12.07 - Conditional Probability

Geometry

(Text ref: New Century Maths 10 Advanced, Chapter 13)

• 13.01 - Angle Sum of a Polygon

• 13.02 - Congruent Triangle Proofs

• 13.03 - Tests for Quadrilaterals

• 13.04 - Proving Properties of Triangles and Quadrilaterals

• 13.05 - Formal Geometrical Proofs

• 13.06 - Finding Unknown Sides in Similar Figures

• 13.07 - Tests for Similar Triangles

• 13.08 - Similar Triangle Proofs

Functions

(Text ref: New Century Maths 10 Advanced, Chapter 14)

• 14.01 - Functions

• 14.02 - Function Notation

• 14.03 - Inverse Functions

• 14.04 - Graphing y = aˣ and y = logₐx

• 14.05 - Graphing Translations of Functions

Polynomials

(Text ref: New Century Maths 10 Advanced, Chapter 15)

• 15.01 - Polynomials

• 15.02 - Adding and Subtracting Polynomials

• 15.03 - Multiplying Polynomials

• 15.04 - Dividing Polynomials

• 15.05 - The Remainder Theorem

• 15.06 - The Factor Theorem

• 15.07 - Graphing Polynomials

• 15.08 - Transforming Graphs of 

Circle Geometry

(Text ref: New Century Maths 10 Advanced, Chapter 16)

• 16.01 - Parts of a Circle

• 16.02 - Chord Properties of Circles

• 16.03 - Angle Properties of Circles

• 16.04 - Tangent and Secant Properties of Circles

• 16.05 - Proofs Using Circle Theorems