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  1. 1Introduction to Relations and Functions
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    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. 4Factorising Polynomial
    1. 4.1Factorise by taking out the greatest common factor
    2. 4.2Factorise by grouping
    3. 4.3Factorising difference of squares: x^2 - y^2
    4. 4.4Factorising trinomials
    5. 4.5Factoring difference of cubes
    6. 4.6Factoring sum of cubes
  5. 5Quadratic Functions
    1. 5.1Characteristics of quadratic functions
    2. 5.2Transformations of quadratic functions
    3. 5.3Quadratic function in general form: y = ax^2 + bx + c
    4. 5.4Quadratic function in vertex form: y = a(x-p)^2 + q
    5. 5.5Completing the square
    6. 5.6Converting from general to vertex form by completing the square
    7. 5.7Shortcut: Vertex formula
    8. 5.8Graphing parabolas for given quadratic functions
    9. 5.9Finding the quadratic functions for given parabolas
    10. 5.10Applications of quadratic functions
  6. 6Polynomial Functions
    1. 6.1Solving quadratic equations by factorising
    2. 6.2Solving quadratic equations by completing the square
    3. 6.3Using quadratic formula to solve quadratic equations
    4. 6.4Nature of roots of quadratic equations: The discriminant
    5. 6.5Applications of quadratic equations
    6. 6.6Solving quadratic inequalities
  7. 7Radicals
    1. 7.1Operations with radicals
    2. 7.2Conversion between entire radicals and mixed radicals
    3. 7.3Adding and subtracting radicals
    4. 7.4Multiplying radicals
    5. 7.5Solving radical equations
  8. 8Radical Functions
    1. 8.1Basic radical functions
    2. 8.2Transformations of radical functions
    3. 8.3Square root of a function
  9. 9Exponents
    1. 9.1Product rule of exponents
    2. 9.2Quotient rule of exponents
    3. 9.3Power of a product rule
    4. 9.4Power of a quotient rule
    5. 9.5Power of a power rule
    6. 9.6Negative exponent rule
    7. 9.7Combining the exponent rules
    8. 9.8Scientific notation
    9. 9.9Convert between radicals and rational exponents
    10. 9.10Solving for exponents
  10. 10Rational Functions
    1. 10.1What is a rational function?
    2. 10.2Point of discontinuity
    3. 10.3Vertical asymptote
    4. 10.4Horizontal asymptote
    5. 10.5Slant asymptote
    6. 10.6Graphs of rational functions
    7. 10.7Solving equations with algebraic fractions
    8. 10.8Solving rational inequalities
  11. 11Exponential Functions
    1. 11.1Exponents: Product rule (a^x)(a^y) = a^(x+y)
    2. 11.2Exponents: Division rule (a^x / a^y) = a^(x-y)
    3. 11.3Exponents: Power rule (a^x)^y = a^(x * y)
    4. 11.4Exponents: Negative exponents
    5. 11.5Exponents: Zero exponent: a^0 = 1
    6. 11.6Exponents: Rational exponents
    7. 11.7Graphing exponential functions
    8. 11.8Graphing transformations of exponential functions
    9. 11.9Finding an exponential function given its graph
  12. 12Logarithmic Functions
    1. 12.1What is a logarithm?
    2. 12.2Converting from logarithmic form to exponential form
    3. 12.3Evaluating logarithms without a calculator
    4. 12.4Common logarithms
    5. 12.5Natural log: ln
    6. 12.6Evaluating logarithms using change-of-base formula
    7. 12.7Converting from exponential form to logarithmic form
    8. 12.8Solving exponential equations with logarithms
    9. 12.9Product rule of logarithms
    10. 12.10Quotient rule of logarithms
    11. 12.11Combining product rule and quotient rule in logarithms
    12. 12.12Evaluating logarithms using logarithm rules
    13. 12.13Solving logarithmic equations
    14. 12.14Graphing logarithmic functions
    15. 12.15Finding a logarithmic function given its graph
  13. 13Applications of Exponential and Logarithmic Functions
    1. 13.1Exponential growth and decay by a factor
    2. 13.2Exponential decay: Half-life
    3. 13.3Exponential growth and decay by percentage
    4. 13.4Finance: Compound interest
    5. 13.5Continuous growth and decay
    6. 13.6Logarithmic scale: Richter scale (earthquake)
    7. 13.7Logarithmic scale: pH scale
    8. 13.8Logarithmic scale: dB scale
    9. 13.9Finance: Future value and present value
  14. 14Solving Simultaneous Equations
    1. 14.1Determining number of solutions to linear equations
    2. 14.2Solving simultaneous equations by graphing
    3. 14.3Solving simultaneous equations by elimination
    4. 14.4Solving simultaneous equations by substitution
    5. 14.5Money related questions in linear equations
    6. 14.6Unknown number related questions in linear equations
    7. 14.7Distance and time related questions in linear equations
    8. 14.8Rectangular shape related questions in linear equations
  15. 15Inequalities in Two Variables
    1. 15.1Graphing linear inequalities in two variables
    2. 15.2Graphing simultaneous linear inequalities
    3. 15.3Graphing quadratic inequalities in two variables
    4. 15.4Graphing simultaneous quadratic inequalities
    5. 15.5Applications of inequalities
    6. 15.6What is linear programming?
    7. 15.7Linear programming word problems
  16. 16Introduction to Trigonometry
    1. 16.1Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h} )
    2. 16.2Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
    3. 16.3Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a} )
    4. 16.4Combination of SohCahToa questions
    5. 16.5Solving expressions using 45-45-90 special right triangles
    6. 16.6Solving expressions using 30-60-90 special right triangles
    7. 16.7Word problems relating ladder in trigonometry
    8. 16.8Word problems relating guy wire in trigonometry
    9. 16.9Other word problems relating angles in trigonometry
  17. 17Trigonometric Ratios and Angle Measure
    1. 17.1Standard angle
    2. 17.2Coterminal angles
    3. 17.3Reference angles
    4. 17.4Find the exact value of trigonometric ratios
    5. 17.5ASTC rule in trigonometry (All Students Take Calculus)
    6. 17.6Unit circle
    7. 17.7Sine rule
    8. 17.8Cosine rule
    9. 17.9Applications of the sine rule and cosine rule
  18. 18Bearings
    1. 18.1Introduction to bearings
    2. 18.2Bearings and direction word problems
    3. 18.3Angle of elevation and depression
  19. 19Graphing Trigonometric Functions
    1. 19.1Sine graph: y = sin x
    2. 19.2Cosine graph: y = cos x
    3. 19.3Tangent graph: y = tan x
    4. 19.4Cotangent graph: y = cot x
    5. 19.5Secant graph: y = sec x
    6. 19.6Cosecant graph: y = csc x
    7. 19.7Graphing transformations of trigonometric functions
    8. 19.8Determining trigonometric functions given their graphs
  20. 20Applications of Trigonometric Functions
    1. 20.1Ferris wheel trig problems
    2. 20.2Tides and water depth trig problems
    3. 20.3Spring (simple harmonic motion) trig problems
  21. 21Trigonometric Identities
    1. 21.1Quotient identities and reciprocal identities
    2. 21.2Pythagorean identities
    3. 21.3Sum and difference identities
    4. 21.4Cofunction identities
    5. 21.5Double-angle identities
  22. 22Conics
    1. 22.1Conics - Parabola
    2. 22.2Conics - Ellipse
    3. 22.3Conics - Circle
    4. 22.4Conics - Hyperbola
  23. 23Imaginary and Complex Numbers
    1. 23.1Introduction to imaginary numbers
    2. 23.2Complex numbers and complex planes
    3. 23.3Adding and subtracting complex numbers
    4. 23.4Complex conjugates
    5. 23.5Multiplying and dividing complex numbers
    6. 23.6Distance and midpoint of complex numbers
    7. 23.7Angle and absolute value of complex numbers
    8. 23.8Polar form of complex numbers
    9. 23.9Operations on complex numbers in polar form
  24. 24Vectors
    1. 24.1Introduction to vectors
    2. 24.2Magnitude of a vector
    3. 24.3Direction angle of a vector
    4. 24.4Scalar multiplication
    5. 24.5Equivalent vectors
    6. 24.6Adding and subtracting vectors in component form
    7. 24.7Operations on vectors in magnitude and direction form
    8. 24.8Unit Vector
    9. 24.9Word problems on vectors
  25. 25Sequences and Series
    1. 25.1Arithmetic sequences
    2. 25.2Arithmetic series
    3. 25.3Geometric sequences
    4. 25.4Geometric series
    5. 25.5Infinite geometric series
    6. 25.6Sigma notation
    7. 25.7Arithmetic mean vs. Geometric mean
  26. 26Permutations and Combinations
    1. 26.1Fundamental counting principle
    2. 26.2Factorial notation
    3. 26.3Path counting problems
    4. 26.4Permutation vs. Combination
    5. 26.5Permutations
    6. 26.6Combinations
    7. 26.7Problems involving both permutations and combinations
    8. 26.8Pascal's triangle
    9. 26.9Binomial theorem
  27. 27Introduction to Probability
    1. 27.1Introduction to probability
    2. 27.2Organizing outcomes
    3. 27.3Probability of independent events
    4. 27.4Comparing experimental and theoretical probability
  28. 28Probability
    1. 28.1Determining probabilities using tree diagrams and tables
    2. 28.2Probability of independent events
    3. 28.3Probability with Venn diagrams
  29. 29Derivatives
    1. 29.1Definition of derivative
    2. 29.2Power rule
    3. 29.3Gradient and equation of tangent line
    4. 29.4Chain rule
    5. 29.5Derivative of trigonometric functions
    6. 29.6Derivative of exponential functions
    7. 29.7Product rule
    8. 29.8Quotient rule
    9. 29.9Implicit differentiation
    10. 29.10Derivative of inverse trigonometric functions
    11. 29.11Derivative of logarithmic functions
    12. 29.12Higher order derivatives
  30. 30Introduction to Matrices
    1. 30.1Notation of matrices
    2. 30.2Adding and subtracting matrices
    3. 30.3Scalar multiplication
    4. 30.4Matrix multiplication
    5. 30.5The three types of matrix row operations
    6. 30.6Representing a linear system as a matrix
    7. 30.7Solving a linear system with matrices using Gaussian elimination
  31. 31Properties of Matrices
    1. 31.1Zero matrix
    2. 31.2Identity matrix
    3. 31.3Properties of matrix addition
    4. 31.4Properties of scalar multiplication
  32. 32Determinants and Inverses of Matrices
    1. 32.1The determinant of a 2 x 2 matrix
    2. 32.2The determinant of a 3 x 3 matrix (General & Shortcut Method)
    3. 32.3The inverse of a 2 x 2 matrix
    4. 32.4The inverse of 3 x 3 matrices with matrix row operations
    5. 32.5The inverse of 3 x 3 matrix with determinants and adjugate
    6. 32.62 x 2 invertible matrix
    7. 32.7Solving linear systems using Cramer's Rule
    8. 32.8Solving linear systems using 2 x 2 inverse matrices
  33. 33Transformations with Matrices
    1. 33.1Transforming vectors with matrices
    2. 33.2Transforming shapes with matrices
    3. 33.3Finding the transformation matrix
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