Master Third Year Maths

Understanding the number systems

Prime factorisation

Greatest Common Factors (GCF)

Least Common Multiple (LCM)

Rational vs. Irrational numbers

Converting repeating decimals to fractions

Ratios

Rates

Proportions

Representing percents

Percents, fractions, and decimals

Percent of a number

Adding and multiplying percents

Taxes, discounts, tips and more

Simple interest

Metric systems

Imperial systems

Conversions between metric and imperial systems

Conversions involve squares and cubic

Cartesian plane

Draw on coordinate planes

Introduction to transformations

Horizontal and vertical distances

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Classifying triangles

Isosceles and equilateral triangles

Circles and circumference

Angles in a circle

Arcs of a circle

Areas and sectors of circles

Congruence and congruent triangles

Triangles congruent by SSS proofs

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS proofs

Line symmetry

Rotational symmetry and transformations

Surface area of 3-dimensional shapes

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Squares and square roots

Pythagorean theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface area of cylinders

Introduction to volume

Volume of prisms

Volume of cylinders

Word problems relating volume of prisms and cylinders

Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )

Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ )

Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ )

Combination of SohCahToa questions

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Other word problems relating angles in trigonometry

Patterns

Evaluating algebraic expressions

Solving one - step equations: x + a = b

Graphing linear relations

Representing patterns in linear relations

Reading linear relation graphs

Solving linear equations by graphing

Express linear inequalities graphically and algebraically

Solving one-step linear inequalities

Solving multi-step linear inequalities

Compound inequalities

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Reading and drawing bar graphs

Reading and drawing histograms

Reading and drawing line graphs

Box-and-whisker plots and scatter plots

Stem-and-leaf plots

Circle graphs

Reading and drawing Venn diagrams

Frequency tables and dot plots

Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$

Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$

Gradient intercept form: y = mx + b

General form: Ax + By + C = 0

Gradient-point form: $y - y_1 = m (x - x_1)$

Rate of change

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from gradient-intercept form y=mx+b

Graphing linear functions using a single point and gradient

Word problems of graphing linear functions

Parallel and perpendicular lines in linear functions

Applications of linear relations

Introduction to linear equations

Introduction to nonlinear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Applications of linear equations

Determining number of solutions to linear equations

Solving simultaneous equations by graphing

Solving simultaneous equations by elimination

Solving simultaneous equations by substitution

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Negative exponent rule

Combining the exponent rules

Scientific notation

Convert between radicals and rational exponents

Solving for exponents

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Quadratic function in vertex form: y = a(x-p)^2 + q

Completing the square

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Graphing parabolas for given quadratic functions

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Characteristics of polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

What is a polynomial?

Using algebra tiles to factorise polynomials

Common factors of polynomials

Factorising polynomials by grouping

Solving polynomials with the unknown "b" from x^2 + bx + c

Solving polynomials with the unknown "c" from x^2 + bx + c

Factorising polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

Solving polynomials with the unknown "b" from $ax^2 + bx + c$

Factorising polynomials: $ax^2 + bx + c$

Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Evaluating polynomials

Solving polynomial equations

Word problems of polynomials

Square and square roots

Cubic and cube roots

Evaluating and simplifying radicals

Converting radicals to mixed radicals

Converting radicals to entire radicals

Adding and subtracting radicals

Multiplying and dividing radicals

Rationalize the denominator

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions

Multiplying rational expressions

Dividing rational expressions

Solving rational equations

Applications of rational equations

Simplifying complex fractions

Partial fraction decomposition

Graphing reciprocals of linear functions

Graphing reciprocals of quadratic functions

Determining probabilities using tree diagrams and tables

Probability of independent events

Probability with Venn diagrams