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Higher 1 Maths 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 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

Linear equations (Advanced)

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

Solving Simultaneous Equations

Determining number of solutions to linear equations

Solving simultaneous equations by graphing

Solving simultaneous equations by elimination

Solving simultaneous equations by substitution

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Imaginary and Complex Numbers

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

Operations of polynomials

What is a polynomial?

Polynomial components

Multiplying monomial by monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Applications of polynomials

Fundamental theorem of algebra

Pascal's triangle

Binomial theorem

Radicals

Operations with radicals

Conversion between entire radicals and mixed radicals

Adding and subtracting radicals

Multiplying radicals

Solving radical equations

Radical Functions

Basic radical functions

Transformations of radical functions

Square root of a function

Algebraic Fractions

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

Reciprocal Functions

Graphing reciprocals of linear functions

Graphing reciprocals of quadratic functions

Rational Functions

What is a rational function?

Point of discontinuity

Vertical asymptote

Horizontal asymptote

Slant asymptote

Graphs of rational functions

Solving rational inequalities

Operations of 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

Exponential Functions

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

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

Conics

Introduction to Trigonometry

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

Trigonometry

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

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

Trigonometric Identities

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Cofunction identities

Double-angle identities

Sequences

Arithmetic sequences

Geometric sequences

Sigma notation

Derivatives

Definition of derivative

Power rule

Chain rule

Derivative of exponential functions

Product rule

Quotient rule

Derivative of logarithmic functions

Probability

Determining probabilities using tree diagrams and tables

Probability of independent events

Probability with Venn diagrams

Addition rule for "OR"

Multiplication rule for "AND"

Conditional probability

Statistics

Median and mode

Mean

Range and outliers

Application of averages

Introduction to Matrices

Notation of matrices

Adding and subtracting matrices

Scalar multiplication

Matrix multiplication

The three types of matrix row operations

Representing a linear system as a matrix

Solving a linear system with matrices using Gaussian elimination

Determinants and Inverses of Matrices

The determinant of a 2 x 2 matrix

The determinant of a 3 x 3 matrix (General & Shortcut Method)

The inverse of a 2 x 2 matrix

The inverse of 3 x 3 matrices with matrix row operations

The inverse of 3 x 3 matrix with determinants and adjugate

2 x 2 invertible matrix

Solving linear systems using Cramer's Rule

Solving linear systems using 2 x 2 inverse matrices

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