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  1. 1Factoring Polynomials
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    1. 1.1Factor by taking out the greatest common factor
    2. 1.2Factor by grouping
    3. 1.3Factoring difference of squares: x^2 - y^2
    4. 1.4Factoring trinomials of greater degree
    5. 1.5Factoring difference of cubes
    6. 1.6Factoring sum of cubes
  2. 2Quadratic Functions
    1. 2.1Introduction to quadratic functions
    2. 2.2Transformations of quadratic functions
    3. 2.3Quadratic function in general form: y = ax^2 + bx + c
    4. 2.4Quadratic function in vertex form: y = a(x-p)^2 + q
    5. 2.5Completing the square
    6. 2.6Converting from general to vertex form by completing the square
    7. 2.7Shortcut: Vertex formula
    8. 2.8Graphing quadratic functions: General form VS. Vertex form
    9. 2.9Finding the quadratic functions for given parabolas
    10. 2.10Applications of quadratic functions
  3. 3Functions
    1. 3.1Function notation
    2. 3.2Operations with functions
    3. 3.3Adding functions
    4. 3.4Subtracting functions
    5. 3.5Multiplying functions
    6. 3.6Dividing functions
    7. 3.7Composite functions
    8. 3.8Inverse functions
    9. 3.9One to one functions
    10. 3.10Difference quotient: applications of functions
  4. 4Transformations of Functions
    1. 4.1Transformations of functions: Horizontal translations
    2. 4.2Transformations of functions: Vertical translations
    3. 4.3Reflection across the y-axis: y = f(-x)
    4. 4.4Reflection across the x-axis: y = -f(x)
    5. 4.5Transformations of functions: Horizontal stretches
    6. 4.6Transformations of functions: Vertical stretches
    7. 4.7Combining transformations of functions
  5. 5Polynomial Functions
    1. 5.1What is a polynomial function?
    2. 5.2Polynomial long division
    3. 5.3Polynomial synthetic division
    4. 5.4Remainder theorem
    5. 5.5Factor theorem
    6. 5.6Rational zero theorem
    7. 5.7Characteristics of polynomial graphs
    8. 5.8Multiplicities of polynomials
    9. 5.9Imaginary zeros of polynomials
    10. 5.10Determining the equation of a polynomial function
    11. 5.11Applications of polynomial functions
    12. 5.12Solving polynomial inequalities
    13. 5.13Fundamental theorem of algebra
    14. 5.14Descartes' rule of signs
  6. 6Radical Functions
    1. 6.1Basic radical functions
    2. 6.2Transformations of radical functions
    3. 6.3Square root of a function
    4. 6.4Solving radical equations
  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 rational equations
    8. 7.8Solving rational inequalities
  8. 8Exponential Functions
    1. 8.1Exponents: Product rule (a^x)(a^y) = a^(x+y)
    2. 8.2Exponents: Division rule (a^x / a^y) = a^(x-y)
    3. 8.3Exponents: Power rule (a^x)^y = a^(x * y)
    4. 8.4Exponents: Negative exponents
    5. 8.5Exponents: Zero exponent: a^0 = 1
    6. 8.6Exponents: Rational exponents
    7. 8.7Solving exponential equations using exponent rules
    8. 8.8Graphing exponential functions
    9. 8.9Graphing transformations of exponential functions
    10. 8.10Finding an exponential function given its graph
  9. 9Logarithmic Functions
    1. 9.1What is a logarithm?
    2. 9.2Converting from logarithmic form to exponential form
    3. 9.3Evaluating logarithms without a calculator
    4. 9.4Common logarithms
    5. 9.5Natural log: ln
    6. 9.6Evaluating logarithms using change-of-base formula
    7. 9.7Converting from exponential form to logarithmic form
    8. 9.8Solving exponential equations with logarithms
    9. 9.9Product rule of logarithms
    10. 9.10Quotient rule of logarithms
    11. 9.11Combining product rule and quotient rule in logarithms
    12. 9.12Evaluating logarithms using logarithm rules
    13. 9.13Solving logarithmic equations
    14. 9.14Graphing logarithmic functions
    15. 9.15Finding a logarithmic function given its graph
  10. 10Applications of Exponential and Logarithmic Functions
    1. 10.1Exponential growth and decay by a factor
    2. 10.2Exponential decay: Half-life
    3. 10.3Exponential growth and decay by percentage
    4. 10.4Finance: Compound interest
    5. 10.5Continuous growth and decay
    6. 10.6Logarithmic scale: Richter scale (earthquake)
    7. 10.7Logarithmic scale: pH scale
    8. 10.8Logarithmic scale: dB scale
    9. 10.9Finance: Future value and present value
  11. 11Trigonometric Ratios and Angle Measure
    1. 11.1Angle in standard position
    2. 11.2Coterminal angles
    3. 11.3Reference angle
    4. 11.4Find the exact value of trigonometric ratios
    5. 11.5ASTC rule in trigonometry (All Students Take Calculus)
    6. 11.6Unit circle
    7. 11.7Converting between degrees and radians
    8. 11.8Trigonometric ratios of angles in radians
    9. 11.9Radian measure and arc length
  12. 12Graphing Trigonometric Functions
    1. 12.1Sine graph: y = sin x
    2. 12.2Cosine graph: y = cos x
    3. 12.3Tangent graph: y = tan x
    4. 12.4Cotangent graph: y = cot x
    5. 12.5Secant graph: y = sec x
    6. 12.6Cosecant graph: y = csc x
    7. 12.7Graphing transformations of trigonometric functions
    8. 12.8Determining trigonometric functions given their graphs
  13. 13Applications of Trigonometric Functions
    1. 13.1Ferris wheel trig problems
    2. 13.2Tides and water depth trig problems
    3. 13.3Spring (simple harmonic motion) trig problems
  14. 14Trigonometric Identities
    1. 14.1Quotient identities and reciprocal identities
    2. 14.2Pythagorean identities
    3. 14.3Sum and difference identities
    4. 14.4Cofunction identities
    5. 14.5Double-angle identities
  15. 15Solving Trigonometric Equations
    1. 15.1Solving first degree trigonometric equations
    2. 15.2Determining non-permissible values for trig expressions
    3. 15.3Solving second degree trigonometric equations
    4. 15.4Solving trigonometric equations involving multiple angles
    5. 15.5Solving trigonometric equations using pythagorean identities
    6. 15.6Solving trigonometric equations using sum and difference identities
    7. 15.7Solving trigonometric equations using double-angle identities
  16. 16Permutations and Combinations
    1. 16.1Fundamental counting principle
    2. 16.2Factorial notation
    3. 16.3Path counting problems
    4. 16.4Permutation vs. Combination
    5. 16.5Permutations
    6. 16.6Combinations
    7. 16.7Problems involving both permutations and combinations
    8. 16.8Pascal's triangle
    9. 16.9Binomial theorem
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