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1Introduction to Relations and Functions
2Functions
3Transformations of Functions
- 3.1Transformations of functions: Horizontal translations
- 3.2Transformations of functions: Vertical translations
- 3.3Reflection across the y-axis: y = f(-x)
- 3.4Reflection across the x-axis: y = -f(x)
- 3.5Transformations of functions: Horizontal stretches
- 3.6Transformations of functions: Vertical stretches
- 3.7Combining transformations of functions
- 3.8Even and odd functions
- 3.1Transformations of functions: Horizontal translations
4Quadratic Functions
- 4.1Characteristics of quadratic functions
- 4.2Transformations of quadratic functions
- 4.3Quadratic function in general form: y = ax^2 + bx + c
- 4.4Quadratic function in vertex form: y = a(x-p)^2 + q
- 4.5Completing the square
- 4.6Converting from general to vertex form by completing the square
- 4.7Shortcut: Vertex formula
- 4.8Graphing parabolas for given quadratic functions
- 4.9Finding the quadratic functions for given parabolas
- 4.10Applications of quadratic functions
- 4.1Characteristics of quadratic functions
5Quadratic Equations and Inequalities
6Polynomial Functions
- 6.1What is a polynomial function?
- 6.2Polynomial long division
- 6.3Polynomial synthetic division
- 6.4Remainder theorem
- 6.5Factor theorem
- 6.6Rational zero theorem
- 6.7Characteristics of polynomial graphs
- 6.8Multiplicities of polynomials
- 6.9Imaginary zeros of polynomials
- 6.10Determining the equation of a polynomial function
- 6.11Applications of polynomial functions
- 6.12Solving polynomial inequalities
- 6.13Fundamental theorem of algebra
- 6.14Descartes' rule of signs
- 6.1What is a polynomial function?
7Rational Functions
8Solving Simultaneous Equations
- 8.1Determining number of solutions to linear equations
- 8.2Solving simultaneous equations by graphing
- 8.3Solving simultaneous equations by elimination
- 8.4Solving simultaneous equations by substitution
- 8.5Money related questions in linear equations
- 8.6Unknown number related questions in linear equations
- 8.7Distance and time related questions in linear equations
- 8.8Rectangular shape related questions in linear equations
- 8.1Determining number of solutions to linear equations
9Inequalities in two variables
10Introduction to Matrices
11Determinants and Inverses of Matrices
- 11.1The determinant of a 2 x 2 matrix
- 11.2The determinant of a 3 x 3 matrix (General & Shortcut Method)
- 11.3The inverse of a 2 x 2 matrix
- 11.4The inverse of 3 x 3 matrices with matrix row operations
- 11.5The inverse of 3 x 3 matrix with determinants and adjugate
- 11.62 x 2 invertible matrix
- 11.7Solving linear systems using Cramer's Rule
- 11.8Solving linear systems using 2 x 2 inverse matrices
- 11.1The determinant of a 2 x 2 matrix
12Conics
13Imaginary and Complex Numbers
- 13.1Introduction to imaginary numbers
- 13.2Complex numbers and complex planes
- 13.3Adding and subtracting complex numbers
- 13.4Complex conjugates
- 13.5Multiplying and dividing complex numbers
- 13.6Distance and midpoint of complex numbers
- 13.7Angle and absolute value of complex numbers
- 13.8Polar form of complex numbers
- 13.9Operations on complex numbers in polar form
- 13.1Introduction to imaginary numbers
14Vectors
15Sequences and Series
16Limits
- 16.1Finding limits from graphs
- 16.2Continuity
- 16.3Finding limits algebraically - direct substitution
- 16.4Finding limits algebraically - when direct substitution is not possible
- 16.5Infinite limits - vertical asymptotes
- 16.6Limits at infinity - horizontal asymptotes
- 16.7Intermediate value theorem
- 16.8Squeeze theorem
- 16.1Finding limits from graphs
17Derivatives
- 17.1Definition of derivative
- 17.2Power rule
- 17.3Gradient and equation of tangent line
- 17.4Chain rule
- 17.5Derivative of trigonometric functions
- 17.6Derivative of exponential functions
- 17.7Product rule
- 17.8Quotient rule
- 17.9Implicit differentiation
- 17.10Derivative of inverse trigonometric functions
- 17.11Derivative of logarithmic functions
- 17.12Higher order derivatives
- 17.1Definition of derivative
18Permutations and Combinations
19Probability
20Data Interpretation
21Discrete Probabilities
- 21.1Probability distribution - histogram, mean, variance & standard deviation
- 21.2Binomial distribution
- 21.3Mean and standard deviation of binomial distribution
- 21.4Poisson distribution
- 21.5Geometric distribution
- 21.6Negative binomial distribution
- 21.7Hypergeometric distribution
- 21.8Properties of expectation
- 21.1Probability distribution - histogram, mean, variance & standard deviation
22Normal Distribution and Z-score
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