Master Fifth 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

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

Express linear inequalities graphically and algebraically

Solving one-step linear inequalities

Solving multi-step linear inequalities

Compound inequalities

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

Solving quadratic inequalities

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

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

Graphing linear inequalities in two variables

Graphing simultaneous linear inequalities

Graphing quadratic inequalities in two variables

Graphing simultaneous quadratic inequalities

Applications of inequalities

What is linear programming?

Linear programming word problems

Introduction to imaginary numbers

Complex numbers and complex planes

Adding and subtracting complex numbers

Complex conjugates

Multiplying and dividing complex numbers

Distance and midpoint of complex numbers

Angle and absolute value of complex numbers

Polar form of complex numbers

Operations on complex numbers in polar form

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

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

What is a polynomial?

Using algebra tiles to factorise polynomials

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

Operations with radicals

Conversion between entire radicals and mixed radicals

Adding and subtracting radicals

Multiplying radicals

Solving radical equations

Basic radical functions

Transformations of radical functions

Square root of a function

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

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

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

Exponents: Negative exponents

Exponents: Zero exponent: a^0 = 1

Exponents: Rational exponents

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

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

Function notation

Operations with functions

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Composite functions

Inequalities of combined functions

Inverse functions

One to one functions

Difference quotient: applications of functions

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

Exponential growth and decay by a factor

Exponential decay: Half-life

Exponential growth and decay by percentage

Continuous growth and decay

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

Law of sines

Law of cosines

Applications of the sine law and cosine law

Introduction to bearings

Bearings and direction word problems

Angle of elevation and depression

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

Cotangent graph: y = cot x

Secant graph: y = sec x

Cosecant graph: y = csc x

Graphing transformations of trigonometric functions

Determining trigonometric functions given their graphs

Ferris wheel trig problems

Tides and water depth trig problems

Spring (simple harmonic motion) trig problems

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Cofunction identities

Double-angle identities

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Angles in a circle

Chord properties

Tangent properties

Circles and circumference

Arcs of a circle

Areas and sectors of circles

Inscribed Angles and Proofs

Central and inscribed angles in circles

Conics - Parabola

Conics - Ellipse

Conics - Circle

Conics - Hyperbola

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Arithmetic sequences

Arithmetic series

Geometric sequences

Geometric series

Infinite geometric series

Sigma notation

Arithmetic mean vs. Geometric mean

Determining probabilities using tree diagrams and tables

Probability of independent events

Probability with Venn diagrams

Fundamental counting principle

Factorial notation

Path counting problems

Permutation vs. Combination

Permutations

Combinations

Problems involving both permutations and combinations

Pascal's triangle

Binomial theorem

Median and mode

Mean

Range and outliers

Application of averages

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

Pie charts

Reading and drawing Venn diagrams

Frequency tables and dot plots