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  1. 1Solving Linear Equations
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    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. 3Factorising Quadratic Equations
    1. 3.1Factorise by taking out the greatest common factor
    2. 3.2Factorise by grouping
    3. 3.3Factorising difference of squares: x^2 - y^2
    4. 3.4Factorising trinomials
    5. 3.5Factoring difference of cubes
    6. 3.6Factoring sum of cubes
  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. 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. 7Linear Functions
    1. 7.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
    2. 7.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
    3. 7.3Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
    4. 7.4Gradient intercept form: y = mx + b
    5. 7.5General form: Ax + By + C = 0
    6. 7.6Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)
    7. 7.7Rate of change
    8. 7.8Graphing linear functions using table of values
    9. 7.9Graphing linear functions using x- and y-intercepts
    10. 7.10Graphing from gradient-intercept form y=mx+b
    11. 7.11Graphing linear functions using a single point and gradient
    12. 7.12Word problems of graphing linear functions
    13. 7.13Parallel and perpendicular lines in linear functions
    14. 7.14Applications of linear relations
  8. 8Linear equations (Advanced)
    1. 8.1Introduction to linear equations
    2. 8.2Introduction to nonlinear equations
    3. 8.3Special case of linear equations: Horizontal lines
    4. 8.4Special case of linear equations: Vertical lines
    5. 8.5Parallel line equation
    6. 8.6Perpendicular line equation
    7. 8.7Combination of both parallel and perpendicular line equations
    8. 8.8Applications of linear equations
  9. 9Solving Simultaneous Equations
    1. 9.1Determining number of solutions to linear equations
    2. 9.2Solving simultaneous equations by graphing
    3. 9.3Solving simultaneous equations by elimination
    4. 9.4Solving simultaneous equations by substitution
    5. 9.5Money related questions in linear equations
    6. 9.6Unknown number related questions in linear equations
    7. 9.7Distance and time related questions in linear equations
    8. 9.8Rectangular shape related questions in linear equations
  10. 10Imaginary and Complex Numbers
    1. 10.1Introduction to imaginary numbers
    2. 10.2Complex numbers and complex planes
    3. 10.3Adding and subtracting complex numbers
    4. 10.4Complex conjugates
    5. 10.5Multiplying and dividing complex numbers
    6. 10.6Distance and midpoint of complex numbers
    7. 10.7Angle and absolute value of complex numbers
    8. 10.8Polar form of complex numbers
    9. 10.9Operations on complex numbers in polar form
  11. 11Operations of polynomials
    1. 11.1What is a polynomial?
    2. 11.2Polynomial components
    3. 11.3Multiplying monomial by monomial
    4. 11.4Multiplying monomial by binomial
    5. 11.5Multiplying binomial by binomial
    6. 11.6Multiplying polynomial by polynomial
    7. 11.7Applications of polynomials
    8. 11.8Fundamental theorem of algebra
    9. 11.9Pascal's triangle
    10. 11.10Binomial theorem
  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. 14Algebraic Fractions
    1. 14.1Simplifying algebraic fractions and restrictions
    2. 14.2Adding and subtracting algebraic fractions
    3. 14.3Multiplying algebraic fractions
    4. 14.4Dividing algebraic fractions
    5. 14.5Solving equations with algebraic fractions
    6. 14.6Applications of equations with algebraic fractions
    7. 14.7Simplifying complex fractions
    8. 14.8Partial fraction decomposition
  15. 15Reciprocal Functions
    1. 15.1Graphing reciprocals of linear functions
    2. 15.2Graphing reciprocals of quadratic functions
  16. 16Rational Functions
    1. 16.1What is a rational function?
    2. 16.2Point of discontinuity
    3. 16.3Vertical asymptote
    4. 16.4Horizontal asymptote
    5. 16.5Slant asymptote
    6. 16.6Graphs of rational functions
    7. 16.7Solving rational inequalities
  17. 17Operations of Functions
    1. 17.1Function notation
    2. 17.2Operations with functions
    3. 17.3Adding functions
    4. 17.4Subtracting functions
    5. 17.5Multiplying functions
    6. 17.6Dividing functions
    7. 17.7Composite functions
    8. 17.8Inequalities of combined functions
    9. 17.9Inverse functions
    10. 17.10One to one functions
    11. 17.11Difference quotient: applications of functions
  18. 18Transformations of Functions
    1. 18.1Transformations of functions: Horizontal translations
    2. 18.2Transformations of functions: Vertical translations
    3. 18.3Reflection across the y-axis: y = f(-x)
    4. 18.4Reflection across the x-axis: y = -f(x)
    5. 18.5Transformations of functions: Horizontal stretches
    6. 18.6Transformations of functions: Vertical stretches
    7. 18.7Combining transformations of functions
    8. 18.8Even and odd functions
  19. 19Exponential Functions
    1. 19.1Exponents: Product rule (a^x)(a^y) = a^(x+y)
    2. 19.2Exponents: Division rule (a^x / a^y) = a^(x-y)
    3. 19.3Exponents: Power rule (a^x)^y = a^(x * y)
    4. 19.4Exponents: Negative exponents
    5. 19.5Exponents: Zero exponent: a^0 = 1
    6. 19.6Exponents: Rational exponents
    7. 19.7Graphing exponential functions
    8. 19.8Graphing transformations of exponential functions
    9. 19.9Finding an exponential function given its graph
  20. 20Applications of Exponential Functions
    1. 20.1Exponential growth and decay by a factor
    2. 20.2Exponential decay: Half-life
    3. 20.3Exponential growth and decay by percentage
    4. 20.4Finance: Compound interest
    5. 20.5Continuous growth and decay
  21. 21Logarithmic Functions
    1. 21.1What is a logarithm?
    2. 21.2Converting from logarithmic form to exponential form
    3. 21.3Evaluating logarithms without a calculator
    4. 21.4Common logarithms
    5. 21.5Natural log: ln
    6. 21.6Evaluating logarithms using change-of-base formula
    7. 21.7Converting from exponential form to logarithmic form
    8. 21.8Solving exponential equations with logarithms
    9. 21.9Product rule of logarithms
    10. 21.10Quotient rule of logarithms
    11. 21.11Combining product rule and quotient rule in logarithms
    12. 21.12Evaluating logarithms using logarithm rules
    13. 21.13Solving logarithmic equations
    14. 21.14Graphing logarithmic functions
    15. 21.15Finding a logarithmic function given its graph
  22. 22Conics
    1. 22.1Conics - Parabola
    2. 22.2Conics - Ellipse
    3. 22.3Conics - Circle
    4. 22.4Conics - Hyperbola
  23. 23Introduction to Trigonometry
    1. 23.1Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h} )
    2. 23.2Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
    3. 23.3Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a} )
    4. 23.4Combination of SohCahToa questions
    5. 23.5Solving expressions using 45-45-90 special right triangles
    6. 23.6Solving expressions using 30-60-90 special right triangles
    7. 23.7Word problems relating ladder in trigonometry
    8. 23.8Word problems relating guy wire in trigonometry
    9. 23.9Other word problems relating angles in trigonometry
  24. 24Trigonometry
    1. 24.1Angle in standard position
    2. 24.2Coterminal angles
    3. 24.3Reference angle
    4. 24.4Find the exact value of trigonometric ratios
    5. 24.5ASTC rule in trigonometry (All Students Take Calculus)
    6. 24.6Unit circle
    7. 24.7Converting between degrees and radians
    8. 24.8Trigonometric ratios of angles in radians
    9. 24.9Radian measure and arc length
    10. 24.10Law of sines
    11. 24.11Law of cosines
    12. 24.12Applications of the sine law and cosine law
  25. 25Bearings
    1. 25.1Introduction to bearings
    2. 25.2Bearings and direction word problems
    3. 25.3Angle of elevation and depression
  26. 26Graphing Trigonometric Functions
    1. 26.1Sine graph: y = sin x
    2. 26.2Cosine graph: y = cos x
    3. 26.3Tangent graph: y = tan x
    4. 26.4Cotangent graph: y = cot x
    5. 26.5Secant graph: y = sec x
    6. 26.6Cosecant graph: y = csc x
    7. 26.7Graphing transformations of trigonometric functions
    8. 26.8Determining trigonometric functions given their graphs
  27. 27Trigonometric Identities
    1. 27.1Quotient identities and reciprocal identities
    2. 27.2Pythagorean identities
    3. 27.3Sum and difference identities
    4. 27.4Cofunction identities
    5. 27.5Double-angle identities
  28. 28Sequences
    1. 28.1Arithmetic sequences
    2. 28.2Geometric sequences
    3. 28.3Sigma notation
  29. 29Derivatives
    1. 29.1Definition of derivative
    2. 29.2Power rule
    3. 29.3Chain rule
    4. 29.4Derivative of exponential functions
    5. 29.5Product rule
    6. 29.6Quotient rule
    7. 29.7Derivative of logarithmic functions
  30. 30Probability
    1. 30.1Determining probabilities using tree diagrams and tables
    2. 30.2Probability of independent events
    3. 30.3Probability with Venn diagrams
    4. 30.4Addition rule for "OR"
    5. 30.5Multiplication rule for "AND"
    6. 30.6Conditional probability
  31. 31Statistics
    1. 31.1Median and mode
    2. 31.2Mean
    3. 31.3Range and outliers
    4. 31.4Application of averages
  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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