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  1. 1Introduction to Relations and Functions
    1. 1.1Relationship between two variables
    2. 1.2Understand relations between x- and y-intercepts
    3. 1.3Domain and range of a function
    4. 1.4Identifying functions
    5. 1.5Function notation
  2. 2Functions
    1. 2.1Function notation
    2. 2.2Operations with functions
    3. 2.3Adding functions
    4. 2.4Subtracting functions
    5. 2.5Multiplying functions
    6. 2.6Dividing functions
    7. 2.7Composite functions
    8. 2.8Inequalities of combined functions
    9. 2.9Inverse functions
    10. 2.10One to one functions
    11. 2.11Difference quotient: applications of functions
  3. 3Transformations of Functions
    1. 3.1Transformations of functions: Horizontal translations
    2. 3.2Transformations of functions: Vertical translations
    3. 3.3Reflection across the y-axis: y = f(-x)
    4. 3.4Reflection across the x-axis: y = -f(x)
    5. 3.5Transformations of functions: Horizontal stretches
    6. 3.6Transformations of functions: Vertical stretches
    7. 3.7Combining transformations of functions
    8. 3.8Even and odd functions
  4. 4Quadratic Functions
    1. 4.1Characteristics of quadratic functions
    2. 4.2Transformations of quadratic functions
    3. 4.3Quadratic function in general form: y = ax^2 + bx + c
    4. 4.4Quadratic function in vertex form: y = a(x-p)^2 + q
    5. 4.5Completing the square
    6. 4.6Converting from general to vertex form by completing the square
    7. 4.7Shortcut: Vertex formula
    8. 4.8Graphing parabolas for given quadratic functions
    9. 4.9Finding the quadratic functions for given parabolas
    10. 4.10Applications of quadratic functions
  5. 5Quadratic Equations and Inequalities
    1. 5.1Solving quadratic equations by factorising
    2. 5.2Solving quadratic equations by completing the square
    3. 5.3Using quadratic formula to solve quadratic equations
    4. 5.4Nature of roots of quadratic equations: The discriminant
    5. 5.5Applications of quadratic equations
    6. 5.6Solving quadratic inequalities
  6. 6Polynomial Functions
    1. 6.1What is a polynomial function?
    2. 6.2Polynomial long division
    3. 6.3Polynomial synthetic division
    4. 6.4Remainder theorem
    5. 6.5Factor theorem
    6. 6.6Rational zero theorem
    7. 6.7Characteristics of polynomial graphs
    8. 6.8Multiplicities of polynomials
    9. 6.9Imaginary zeros of polynomials
    10. 6.10Determining the equation of a polynomial function
    11. 6.11Applications of polynomial functions
    12. 6.12Solving polynomial inequalities
    13. 6.13Fundamental theorem of algebra
    14. 6.14Descartes' rule of signs
  7. 7Rational Functions
    1. 7.1What is a rational function?
    2. 7.2Point of discontinuity
    3. 7.3Vertical asymptote
    4. 7.4Horizontal asymptote
    5. 7.5Slant asymptote
    6. 7.6Graphs of rational functions
    7. 7.7Solving equations with algebraic fractions
    8. 7.8Solving rational inequalities
  8. 8Solving Simultaneous Equations
    1. 8.1Determining number of solutions to linear equations
    2. 8.2Solving simultaneous equations by graphing
    3. 8.3Solving simultaneous equations by elimination
    4. 8.4Solving simultaneous equations by substitution
    5. 8.5Money related questions in linear equations
    6. 8.6Unknown number related questions in linear equations
    7. 8.7Distance and time related questions in linear equations
    8. 8.8Rectangular shape related questions in linear equations
  9. 9Inequalities in two variables
    1. 9.1Graphing linear inequalities in two variables
    2. 9.2Graphing simultaneous linear inequalities
    3. 9.3Graphing quadratic inequalities in two variables
    4. 9.4Graphing simultaneous quadratic inequalities
    5. 9.5Applications of inequalities
    6. 9.6What is linear programming?
    7. 9.7Linear programming word problems
  10. 10Introduction to Matrices
    1. 10.1Notation of matrices
    2. 10.2Adding and subtracting matrices
    3. 10.3Scalar multiplication
    4. 10.4Matrix multiplication
    5. 10.5The three types of matrix row operations
    6. 10.6Representing a linear system as a matrix
    7. 10.7Solving a linear system with matrices using Gaussian elimination
  11. 11Determinants and Inverses of Matrices
    1. 11.1The determinant of a 2 x 2 matrix
    2. 11.2The determinant of a 3 x 3 matrix (General & Shortcut Method)
    3. 11.3The inverse of a 2 x 2 matrix
    4. 11.4The inverse of 3 x 3 matrices with matrix row operations
    5. 11.5The inverse of 3 x 3 matrix with determinants and adjugate
    6. 11.62 x 2 invertible matrix
    7. 11.7Solving linear systems using Cramer's Rule
    8. 11.8Solving linear systems using 2 x 2 inverse matrices
  12. 12Conics
    1. 12.1Conics - Parabola
    2. 12.2Conics - Ellipse
    3. 12.3Conics - Circle
    4. 12.4Conics - Hyperbola
  13. 13Imaginary and Complex Numbers
    1. 13.1Introduction to imaginary numbers
    2. 13.2Complex numbers and complex planes
    3. 13.3Adding and subtracting complex numbers
    4. 13.4Complex conjugates
    5. 13.5Multiplying and dividing complex numbers
    6. 13.6Distance and midpoint of complex numbers
    7. 13.7Angle and absolute value of complex numbers
    8. 13.8Polar form of complex numbers
    9. 13.9Operations on complex numbers in polar form
  14. 14Vectors
    1. 14.1Introduction to vectors
    2. 14.2Magnitude of a vector
    3. 14.3Direction angle of a vector
    4. 14.4Scalar multiplication
    5. 14.5Equivalent vectors
    6. 14.6Adding and subtracting vectors in component form
    7. 14.7Operations on vectors in magnitude and direction form
    8. 14.8Unit Vector
    9. 14.9Word problems on vectors
  15. 15Sequences and Series
    1. 15.1Arithmetic sequences
    2. 15.2Arithmetic series
    3. 15.3Geometric sequences
    4. 15.4Geometric series
    5. 15.5Infinite geometric series
    6. 15.6Sigma notation
    7. 15.7Arithmetic mean vs. Geometric mean
  16. 16Limits
    1. 16.1Finding limits from graphs
    2. 16.2Continuity
    3. 16.3Finding limits algebraically - direct substitution
    4. 16.4Finding limits algebraically - when direct substitution is not possible
    5. 16.5Infinite limits - vertical asymptotes
    6. 16.6Limits at infinity - horizontal asymptotes
    7. 16.7Intermediate value theorem
    8. 16.8Squeeze theorem
  17. 17Derivatives
    1. 17.1Definition of derivative
    2. 17.2Power rule
    3. 17.3Gradient and equation of tangent line
    4. 17.4Chain rule
    5. 17.5Derivative of trigonometric functions
    6. 17.6Derivative of exponential functions
    7. 17.7Product rule
    8. 17.8Quotient rule
    9. 17.9Implicit differentiation
    10. 17.10Derivative of inverse trigonometric functions
    11. 17.11Derivative of logarithmic functions
    12. 17.12Higher order derivatives
  18. 18Permutations and Combinations
    1. 18.1Fundamental counting principle
    2. 18.2Factorial notation
    3. 18.3Path counting problems
    4. 18.4Permutation vs. Combination
    5. 18.5Permutations
    6. 18.6Combinations
    7. 18.7Problems involving both permutations and combinations
    8. 18.8Pascal's triangle
    9. 18.9Binomial theorem
  19. 19Probability
    1. 19.1Addition rule for "OR"
    2. 19.2Multiplication rule for "AND"
    3. 19.3Conditional probability
    4. 19.4Probability with permutations and combinations
    5. 19.5Law of total probability
    6. 19.6Bayes' rule
    7. 19.7Probability with Venn diagrams
  20. 20Data Interpretation
    1. 20.1Center of a data set: mean, median, mode
    2. 20.2Spread of a data set - standard deviation & variance
    3. 20.3Measures of relative standing - z-score, quartiles, percentiles
    4. 20.4Bivariate, scatter plots and correlation
    5. 20.5Regression analysis
    6. 20.6Equation of the best fit line
  21. 21Discrete Probabilities
    1. 21.1Probability distribution - histogram, mean, variance & standard deviation
    2. 21.2Binomial distribution
    3. 21.3Mean and standard deviation of binomial distribution
    4. 21.4Poisson distribution
    5. 21.5Geometric distribution
    6. 21.6Negative binomial distribution
    7. 21.7Hypergeometric distribution
    8. 21.8Properties of expectation
  22. 22Normal Distribution and Z-score
    1. 22.1Introduction to normal distribution
    2. 22.2Normal distribution and continuous random variable
    3. 22.3Z-scores and random continuous variables
    4. 22.4Sampling distributions
    5. 22.5Central limit theorem
    6. 22.6Rare event rule
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