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  1. 1Solving Linear Equations
    1. 1.1Solving linear equations using multiplication and division
    2. 1.2Solving two-step linear equations: ax + b = c, x/a + b = c
    3. 1.3Solving linear equations using distributive property: a(x + b) = c
    4. 1.4Solving linear equations with variables on both sides
    5. 1.5Solving literal equations
  2. 2Linear Inequalities
    1. 2.1Express linear inequalities graphically and algebraically
    2. 2.2Solving one-step linear inequalities
    3. 2.3Solving multi-step linear inequalities
    4. 2.4Compound inequalities
  3. 3Quadratic Equations and Inequalities
    1. 3.1Solving quadratic equations by factoring
    2. 3.2Solving quadratic equations by completing the square
    3. 3.3Solving quadratic equations using the quadratic formula
    4. 3.4Nature of roots of quadratic equations: The discriminant
    5. 3.5Applications of quadratic equations
    6. 3.6Solving quadratic inequalities
  4. 4Solving Simultaneous Equations
    1. 4.1Determining number of solutions to linear equations
    2. 4.2Solving simultaneous equations by graphing
    3. 4.3Solving simultaneous equations by elimination
    4. 4.4Solving simultaneous equations by substitution
    5. 4.5Money related questions in linear equations
    6. 4.6Unknown number related questions in linear equations
    7. 4.7Distance and time related questions in linear equations
    8. 4.8Rectangular shape related questions in linear equations
  5. 5Linear programming
    1. 5.1What is linear programming?
    2. 5.2Linear programming word problems
  6. 6Introduction to Relations and Functions
    1. 6.1Relationship between two variables
    2. 6.2Understand relations between x- and y-intercepts
    3. 6.3Domain and range of a function
    4. 6.4Identifying functions
    5. 6.5Function notation
  7. 7Direct Variation
    1. 7.1Identifying proportional relationships
    2. 7.2Writing and solving for proportions
    3. 7.3Understanding graphs of proportional relationships
    4. 7.4Graphing and writing equations of proportional relationships
    5. 7.5Applications of proportional relationships
  8. 8Imaginary and Complex Numbers
    1. 8.1Introduction to imaginary numbers
    2. 8.2Complex numbers and complex planes
    3. 8.3Adding and subtracting complex numbers
    4. 8.4Complex conjugates
    5. 8.5Multiplying and dividing complex numbers
    6. 8.6Distance and midpoint of complex numbers
    7. 8.7Angle and absolute value of complex numbers
    8. 8.8Polar form of complex numbers
    9. 8.9Operations on complex numbers in polar form
  9. 9Factorising Polynomial
    1. 9.1Factorise by taking out the greatest common factor
    2. 9.2Factorise by grouping
    3. 9.3Factorising difference of squares: x^2 - y^2
    4. 9.4Factorising trinomials
    5. 9.5Factoring difference of cubes
    6. 9.6Factoring sum of cubes
  10. 10Quadratic Functions
    1. 10.1Characteristics of quadratic functions
    2. 10.2Transformations of quadratic functions
    3. 10.3Quadratic function in general form: y = ax^2 + bx + c
    4. 10.4Quadratic function in vertex form: y = a(x-p)^2 + q
    5. 10.5Completing the square
    6. 10.6Converting from general to vertex form by completing the square
    7. 10.7Shortcut: Vertex formula
    8. 10.8Graphing parabolas for given quadratic functions
    9. 10.9Finding the quadratic functions for given parabolas
    10. 10.10Applications of quadratic functions
  11. 11Polynomial Functions
    1. 11.1What is a polynomial function?
    2. 11.2Polynomial long division
    3. 11.3Polynomial synthetic division
    4. 11.4Remainder theorem
    5. 11.5Factor theorem
    6. 11.6Rational zero theorem
    7. 11.7Characteristics of polynomial graphs
    8. 11.8Multiplicities of polynomials
    9. 11.9Imaginary zeros of polynomials
    10. 11.10Determining the equation of a polynomial function
    11. 11.11Applications of polynomial functions
    12. 11.12Solving polynomial inequalities
    13. 11.13Fundamental theorem of algebra
    14. 11.14Descartes' rule of signs
  12. 12Radicals
    1. 12.1Operations with radicals
    2. 12.2Conversion between entire radicals and mixed radicals
    3. 12.3Adding and subtracting radicals
    4. 12.4Multiplying radicals
    5. 12.5Solving radical equations
  13. 13Radical Functions
    1. 13.1Basic radical functions
    2. 13.2Transformations of radical functions
    3. 13.3Square root of a function
  14. 14Exponents
    1. 14.1Product rule of exponents
    2. 14.2Quotient rule of exponents
    3. 14.3Power of a product rule
    4. 14.4Power of a quotient rule
    5. 14.5Power of a power rule
    6. 14.6Negative exponent rule
    7. 14.7Combining the exponent rules
    8. 14.8Scientific notation
    9. 14.9Convert between radicals and rational exponents
    10. 14.10Solving for exponents
  15. 15Exponential Functions
    1. 15.1Exponents: Product rule (a^x)(a^y) = a^(x+y)
    2. 15.2Exponents: Division rule (a^x / a^y) = a^(x-y)
    3. 15.3Exponents: Power rule (a^x)^y = a^(x * y)
    4. 15.4Exponents: Negative exponents
    5. 15.5Exponents: Zero exponent: a^0 = 1
    6. 15.6Exponents: Rational exponents
    7. 15.7Graphing exponential functions
    8. 15.8Graphing transformations of exponential functions
    9. 15.9Finding an exponential function given its graph
  16. 16Logarithmic Functions
    1. 16.1What is a logarithm?
    2. 16.2Converting from logarithmic form to exponential form
    3. 16.3Evaluating logarithms without a calculator
    4. 16.4Common logarithms
    5. 16.5Natural log: ln
    6. 16.6Evaluating logarithms using change-of-base formula
    7. 16.7Converting from exponential form to logarithmic form
    8. 16.8Solving exponential equations with logarithms
    9. 16.9Product rule of logarithms
    10. 16.10Quotient rule of logarithms
    11. 16.11Combining product rule and quotient rule in logarithms
    12. 16.12Evaluating logarithms using logarithm rules
    13. 16.13Solving logarithmic equations
    14. 16.14Graphing logarithmic functions
    15. 16.15Finding a logarithmic function given its graph
  17. 17Applications of Exponential and Logarithmic Functions
    1. 17.1Exponential growth and decay by a factor
    2. 17.2Exponential decay: Half-life
    3. 17.3Exponential growth and decay by percentage
    4. 17.4Finance: Compound interest
    5. 17.5Continuous growth and decay
    6. 17.6Logarithmic scale: Richter scale (earthquake)
    7. 17.7Logarithmic scale: pH scale
    8. 17.8Logarithmic scale: dB scale
    9. 17.9Finance: Future value and present value
  18. 18Conics
    1. 18.1Conics - Parabola
    2. 18.2Conics - Ellipse
    3. 18.3Conics - Circle
    4. 18.4Conics - Hyperbola
  19. 19Introduction to Trigonometry
    1. 19.1Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h} )
    2. 19.2Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
    3. 19.3Use tangent ratio to calculate angles and side (Tan = oa \frac{o}{a} )
    4. 19.4Combination of SohCahToa questions
    5. 19.5Solving expressions using 45-45-90 special right triangles
    6. 19.6Solving expressions using 30-60-90 special right triangles
    7. 19.7Word problems relating ladder in trigonometry
    8. 19.8Word problems relating guy wire in trigonometry
    9. 19.9Other word problems relating angles in trigonometry
  20. 20Trigonometric Ratios and Angle Measure
    1. 20.1Standard angle
    2. 20.2Coterminal angles
    3. 20.3Reference angles
    4. 20.4Find the exact value of trigonometric ratios
    5. 20.5ASTC rule in trigonometry (All Students Take Calculus)
    6. 20.6Unit circle
    7. 20.7Sine rule
    8. 20.8Cosine rule
    9. 20.9Applications of the sine rule and cosine rule
  21. 21Bearings
    1. 21.1Introduction to bearings
    2. 21.2Bearings and direction word problems
    3. 21.3Angle of elevation and depression
  22. 22Graphing Trigonometric Functions
    1. 22.1Sine graph: y = sin x
    2. 22.2Cosine graph: y = cos x
    3. 22.3Tangent graph: y = tan x
    4. 22.4Cotangent graph: y = cot x
    5. 22.5Secant graph: y = sec x
    6. 22.6Cosecant graph: y = csc x
    7. 22.7Graphing transformations of trigonometric functions
    8. 22.8Determining trigonometric functions given their graphs
  23. 23Applications of Trigonometric Functions
    1. 23.1Ferris wheel trig problems
    2. 23.2Tides and water depth trig problems
    3. 23.3Spring (simple harmonic motion) trig problems
  24. 24Trigonometric Identities
    1. 24.1Quotient identities and reciprocal identities
    2. 24.2Pythagorean identities
    3. 24.3Sum and difference identities
    4. 24.4Cofunction identities
    5. 24.5Double-angle identities
  25. 25Circle Geometry
    1. 25.1Angles in a circle
    2. 25.2Chord properties
    3. 25.3Tangent properties
    4. 25.4Circles and circumference
    5. 25.5Arcs of a circle
    6. 25.6Areas and sectors of circles
    7. 25.7Inscribed Angles and Proofs
    8. 25.8Central and inscribed angles in circles
  26. 26Sequences and Series
    1. 26.1Arithmetic sequences
    2. 26.2Arithmetic series
    3. 26.3Geometric sequences
    4. 26.4Geometric series
    5. 26.5Infinite geometric series
    6. 26.6Sigma notation
    7. 26.7Arithmetic mean vs. Geometric mean
  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. 29Statistics
    1. 29.1Median and mode
    2. 29.2Mean
    3. 29.3Range and outliers
    4. 29.4Application of averages
  30. 30Limits
    1. 30.1Finding limits from graphs
    2. 30.2Continuity
    3. 30.3Finding limits algebraically - direct substitution
    4. 30.4Finding limits algebraically - when direct substitution is not possible
    5. 30.5Infinite limits - vertical asymptotes
    6. 30.6Limits at infinity - horizontal asymptotes
    7. 30.7Intermediate value theorem
    8. 30.8Squeeze theorem
  31. 31Derivatives
    1. 31.1Definition of derivative
    2. 31.2Power rule
    3. 31.3Gradient and equation of tangent line
    4. 31.4Chain rule
    5. 31.5Derivative of trigonometric functions
    6. 31.6Derivative of exponential functions
    7. 31.7Product rule
    8. 31.8Quotient rule
    9. 31.9Implicit differentiation
    10. 31.10Derivative of inverse trigonometric functions
    11. 31.11Derivative of logarithmic functions
    12. 31.12Higher order derivatives
    13. 31.13Position velocity acceleration
  32. 32Introduction to Matrices
    1. 32.1Notation of matrices
    2. 32.2Adding and subtracting matrices
    3. 32.3Scalar multiplication
    4. 32.4Matrix multiplication
    5. 32.5The three types of matrix row operations
    6. 32.6Representing a linear system as a matrix
    7. 32.7Solving a linear system with matrices using Gaussian elimination
  33. 33Determinants and Inverses of Matrices
    1. 33.1The determinant of a 2 x 2 matrix
    2. 33.2The determinant of a 3 x 3 matrix (General & Shortcut Method)
    3. 33.3The inverse of a 2 x 2 matrix
    4. 33.4The inverse of 3 x 3 matrices with matrix row operations
    5. 33.5The inverse of 3 x 3 matrix with determinants and adjugate
    6. 33.62 x 2 invertible matrix
    7. 33.7Solving linear systems using Cramer's Rule
    8. 33.8Solving linear systems using 2 x 2 inverse matrices
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