Master Maths Extension 1

Using models to add and subtract fractions

Adding fractions with like denominators

Subtracting fractions with like denominators

Adding and subtracting fractions with unlike denominators

Adding and subtracting mixed numbers

Multiplying fractions and whole numbers

Dividing fractions with whole numbers

Multiplying proper fractions

Multiplying improper fractions and mixed numbers

Dividing fractions and mixed numbers

Applications of fraction operations

Squares and square roots

Pythagorean theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

Representing percents

Percents, fractions, and decimals

Percent of a number

Adding and multiplying percents

Taxes, discounts, tips and more

Simple interest

Square and square roots

Cubic and cube roots

Evaluating and simplifying surds

Converting radicals to mixed radicals

Converting radicals to entire radicals

Adding and subtracting surds

Multiplying and dividing surds

Rationalize the denominator

Equivalent algebraic expressions

Adding and subtracting algebraic expressions

Multiplying monomial by monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Applications of polynomials

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

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 slope-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

Perpendicular line equation

Determining number of solutions to linear equations

Solving simultaneous linear equations by graphing

Solving simultaneous linear equations by elimination

Solving simultaneous linear 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

Simultaneous linear-quadratic equations

Simultaneous quadratic-quadratic equations

Solving 3 variable simultaneous equations by substitution

Solving 3 variable simultaneous equations by elimination

Solving 3 variable simultaneous equations with no or infinite solutions

Word problems relating 3 variable simultaneous equations

Factorise by taking out the greatest common factor

Factorise by grouping

Factorising difference of squares: x^2 - y^2

Factorising trinomials

Factoring difference of cubes

Factoring sum of cubes

Introduction to 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 quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Solving quadratic equations by factorising

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

Express linear inequalities graphically and algebraically

Solving one-step linear inequalities

Solving multi-step linear inequalities

Compound inequalities

Solving absolute value inequalities

Graphing linear inequalities in two variables

Graphing simultaneous inequalities

Solving quadratic inequalities in one variable

Simplifying algebraic fractions and restrictions

Adding and subtracting algebraic fractions

Multiplying algebraic fractions

Dividing algebraic fractions

Solving equations with algebraic fractions

Applications of equations with algebraic fractions

Simplifying complex fractions

Partial fraction decomposition

Graphing reciprocals of linear functions

Graphing reciprocals of quadratic functions

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Classifying Triangles

Isosceles and Equilateral Triangles

Congruence and Congruent Triangles

Triangles Congruent by SSS Proofs

Triangles Congruent by SAS and HL Proofs

Triangles Congruent by ASA and AAS Proofs

Angles in a circle

Chord properties

Tangent properties

Circle and circumference

Arcs of a circle

Areas and sectors of circles

Inscribed Angles and Proofs

Central and inscribed angles in circles

Function notation

Operations with functions

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Composite functions

Even and odd functions

What is a polynomial function?

Polynomial long division

Polynomial synthetic division

Remainder theorem

Factor theorem

Rational zero theorem

Characteristics of polynomial graphs

Multiplicities of polynomials

Imaginary zeros of polynomials

Determining the equation of a polynomial function

Applications of polynomial functions

Solving polynomial inequalities

Fundamental theorem of algebra

Descartes' rule of signs

What is a rational function?

Point of discontinuity

Vertical asymptote

Horizontal asymptote

Slant asymptote

Graphs of rational functions

Solving rational inequalities

Indices: Product rule (a^x)(a^y) = a^(x+y)

Indices: Division rule (a^x / a^y) = a^(x-y)

Indices: Power rule (a^x)^y = a^(x * y)

Indices: Negative exponents

Indices: Zero exponent: a^0 = 1

Indices: Rational exponents

Combining laws of indices

Scientific notation

Convert between radicals and rational exponents

Solving for indices

Solving exponential equations using exponent rules

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

What is a logarithm?

Converting from logarithmic form to exponential form

Evaluating logarithms without a calculator

Common logarithms

Natural log: ln

Evaluating logarithms using change-of-base formula

Converting from exponential form to logarithmic form

Solving exponential equations with logarithms

Product rule of logarithms

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

Evaluating logarithms using logarithm rules

Solving logarithmic equations

Graphing logarithmic functions

Finding a logarithmic function given its graph

Angle in standard position

Coterminal angles

Reference angle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

Unit circle

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

Sine rule

Cosine rule

Sine rule and cosine rule word problems

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Cofunction identities

Double-angle identities

Solving first degree trigonometric equations

Determining non-permissible values for trig expressions

Solving second degree trigonometric equations

Solving trigonometric equations involving multiple angles

Solving trigonometric equations using pythagorean identities

Solving trigonometric equations using sum and difference identities

Solving trigonometric equations using double-angle identities

Finding inverse trigonometric function from its graph

Evaluating inverse trigonometric functions

Finding inverse reciprocal trigonometric function from its graph

Finding exact value of inverse reciprocal trig functions

Introduction to bearings

Bearings and direction word problems

Angle of elevation and depression

Arithmetic series

Geometric series

Convergence and divergence of normal infinite series

Convergence & divergence of geometric series

Exponential growth and decay by a factor

Exponential growth and decay by percentage

Finance: Compound interest

Finance: Future value and present value

Conics - Parabola

Conics - Ellipse

Conics - Circle

Conics - Hyperbola

Fundamental counting principle

Factorial notation

Path counting problems

Permutation vs. Combination

Permutations

Combinations

Problems involving both permutations and combinations

Pascal's triangle

Binomial theorem

Probability distribution - histogram, mean, variance & standard deviation