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Maths Methods Topics

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

Linear Equations

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

Quadratic Functions

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

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

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

Transformations of Functions

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

Combining transformations of functions

Even and odd functions

Factorisation

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

Conics

Trigonometric Ratios and Angle Measure

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 and Cosine Rule

Sine rule

Cosine rule

Sine rule and cosine rule word problems

Bearings

Introduction to bearings

Bearings and direction word problems

Angle of elevation and depression

Graphing Trigonometric Functions

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

Applications of Trigonometric Functions

Ferris wheel trig problems

Tides and water depth trig problems

Spring (simple harmonic motion) trig problems

Trigonometric Identities

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Cofunction identities

Double-angle identities

Solving Trigonometric Equations

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

Permutations and Combinations

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

Addition rule for "OR"

Multiplication rule for "AND"

Conditional probability

Probability with permutations and combinations

Law of total probability

Bayes' rule

Probability with Venn diagrams

Indices

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

Exponential Functions

Solving exponential equations using exponent rules

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

Applications of Exponential Functions

Exponential growth and decay by a factor

Exponential decay: Half-life

Exponential growth and decay by percentage

Finance: Compound interest

Continuous growth and decay

Logarithmic 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

Applications of Logarithmic Functions

Logarithmic scale: Richter scale (earthquake)

Logarithmic scale: pH scale

Logarithmic scale: dB scale

Finance: Future value and present value

Sequences and Series

Infinite geometric series

Sigma notation

Arithmetic mean vs. Geometric mean

Limits and Derivatives

Finding limits from graphs

Definition of derivative

Power rule

Slope and equation of tangent line

Chain rule

Derivative of trigonometric functions

Derivative of exponential functions

Product rule

Quotient rule

Implicit differentiation

Derivative of inverse trigonometric functions

Derivative of logarithmic functions

Higher order derivatives

Derivative Applications

Position velocity acceleration

Critical number & maximum and minimum values

Curve sketching

Optimization

Related rates

Integrals

Antiderivatives

Riemann sum

Definite integral

Fundamental theorem of calculus

Integration Applications

Areas between curves

Normal Distribution and Z-score

Introduction to normal distribution

Normal distribution and continuous random variable

Z-scores and random continuous variables

Sampling distributions

Central limit theorem

Rare event rule

Discrete Probabilities

Probability distribution - histogram, mean, variance & standard deviation

Binomial distribution

Mean and standard deviation of binomial distribution

Poisson distribution

Geometric distribution

Negative binomial distribution

Confidence Intervals

Point estimates

Confidence levels and critical values

Margin of error

Making a confidence interval

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