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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=cax + b = c, xa+b=c{x \over a} + b = c
    3. 1.3Solving linear equations using distributive property: a(x+b)=ca(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. 3Linear Functions
    1. 3.1Distance formula: d=(x2x1)2+(y2y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
    2. 3.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
    3. 3.3Gradient equation: m=y2y1x2x1m = \frac{y_2-y_1}{x_2- x_1}
    4. 3.4Gradient intercept form: y = mx + b
    5. 3.5General form: Ax + By + C = 0
    6. 3.6Gradient-point form: yy1=m(xx1)y - y_1 = m (x - x_1)
    7. 3.7Rate of change
    8. 3.8Graphing linear functions using table of values
    9. 3.9Graphing linear functions using x- and y-intercepts
    10. 3.10Graphing from gradient-intercept form y=mx+b
    11. 3.11Graphing linear functions using a single point and gradient
    12. 3.12Word problems of graphing linear functions
    13. 3.13Parallel and perpendicular lines in linear functions
    14. 3.14Applications of linear relations
  4. 4Factorising
    1. 4.1Factorise by taking out the greatest common factor
    2. 4.2Factorise by grouping
    3. 4.3Factorising difference of squares: x2y2x^2 - y^2
    4. 4.4Factorising trinomials: ax2+bx+cax^2 + bx + c
  5. 5Quadratic Functions
    1. 5.1Characteristics of quadratic functions
    2. 5.2Transformations of quadratic functions
    3. 5.3Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+c
    4. 5.4Quadratic function in vertex form: y = a(xp)2+qa(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. 6Quadratic Equations and Inequalities
    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. 7Solving Simultaneous Equations
    1. 7.1Determining number of solutions to linear equations
    2. 7.2Solving simultaneous equations by graphing
    3. 7.3Solving simultaneous equations by elimination
    4. 7.4Solving simultaneous equations by substitution
    5. 7.5Money related questions in linear equations
    6. 7.6Unknown number related questions in linear equations
    7. 7.7Distance and time related questions in linear equations
    8. 7.8Rectangular shape related questions in linear equations
  8. 8Simultaneous Equations (Advanced)
    1. 8.1Simultaneous linear equations
    2. 8.2Simultaneous linear-quadratic equations
    3. 8.3Simultaneous quadratic-quadratic equations
    4. 8.4Solving 3 variable simultaneous equations by substitution
    5. 8.5Solving 3 variable simultaneous equations by elimination
    6. 8.6Solving 3 variable simultaneous equations with no or infinite solutions
    7. 8.7Word problems relating 3 variable simultaneous equations
  9. 9Inequalities in two variables (Advanced)
    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. 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. 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. 13Exponents
    1. 13.1Product rule of exponents
    2. 13.2Quotient rule of exponents
    3. 13.3Power of a product rule
    4. 13.4Power of a quotient rule
    5. 13.5Power of a power rule
    6. 13.6Negative exponent rule
    7. 13.7Combining the exponent rules
    8. 13.8Scientific notation
    9. 13.9Convert between radicals and rational exponents
    10. 13.10Solving for exponents
  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)y = f(-x)
    4. 18.4Reflection across the x-axis: y=f(x)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 (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)}
    2. 19.2Exponents: Division rule axay=a(xy){a^x \over a^y}=a^{(x-y)}
    3. 19.3Exponents: Power rule (ax)y=a(xy) (a^x)^y = a^{(x\cdot y)}
    4. 19.4Exponents: Negative exponents
    5. 19.5Exponents: Zero exponent: a0=1 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. 20Logarithmic Functions
    1. 20.1What is a logarithm?
    2. 20.2Converting from logarithmic form to exponential form
    3. 20.3Evaluating logarithms without a calculator
    4. 20.4Common logarithms
    5. 20.5Natural log: ln
    6. 20.6Evaluating logarithms using change-of-base formula
    7. 20.7Converting from exponential form to logarithmic form
    8. 20.8Solving exponential equations with logarithms
    9. 20.9Product rule of logarithms
    10. 20.10Quotient rule of logarithms
    11. 20.11Combining product rule and quotient rule in logarithms
    12. 20.12Evaluating logarithms using logarithm rules
    13. 20.13Solving logarithmic equations
    14. 20.14Graphing logarithmic functions
    15. 20.15Finding a logarithmic function given its graph
  21. 21Applications of Exponential and Logarithmic Functions
    1. 21.1Exponential growth and decay by a factor
    2. 21.2Exponential decay: Half-life
    3. 21.3Exponential growth and decay by percentage
    4. 21.4Finance: Compound interest
    5. 21.5Continuous growth and decay
    6. 21.6Logarithmic scale: Richter scale (earthquake)
    7. 21.7Logarithmic scale: pH scale
    8. 21.8Logarithmic scale: dB scale
    9. 21.9Finance: Future value and present value
  22. 22Introduction to Trigonometry
    1. 22.1Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h} )
    2. 22.2Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
    3. 22.3Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a} )
    4. 22.4Combination of SohCahToa questions
    5. 22.5Solving expressions using 45-45-90 special right triangles
    6. 22.6Solving expressions using 30-60-90 special right triangles
    7. 22.7Word problems relating ladder in trigonometry
    8. 22.8Word problems relating guy wire in trigonometry
    9. 22.9Other word problems relating angles in trigonometry
  23. 23Trigonometric Ratios and Angle Measure
    1. 23.1Standard angle
    2. 23.2Coterminal angles
    3. 23.3Reference angles
    4. 23.4Find the exact value of trigonometric ratios
    5. 23.5ASTC rule in trigonometry (All Students Take Calculus)
    6. 23.6Unit circle
    7. 23.7Law of sines
    8. 23.8Law of cosines
    9. 23.9Applications of the sine law and cosine law
  24. 24Bearings
    1. 24.1Introduction to bearings
    2. 24.2Bearings and direction word problems
    3. 24.3Angle of elevation and depression
  25. 25Graphing Trigonometric Functions
    1. 25.1Sine graph: y = sin x
    2. 25.2Cosine graph: y = cos x
    3. 25.3Tangent graph: y = tan x
    4. 25.4Cotangent graph: y = cot x
    5. 25.5Secant graph: y = sec x
    6. 25.6Cosecant graph: y = csc x
    7. 25.7Graphing transformations of trigonometric functions
    8. 25.8Determining trigonometric functions given their graphs
  26. 26Trigonometric Identities
    1. 26.1Quotient identities and reciprocal identities
    2. 26.2Pythagorean identities
    3. 26.3Sum and difference identities
    4. 26.4Cofunction identities
    5. 26.5Double-angle identities
  27. 27Conics
    1. 27.1Conics - Parabola
    2. 27.2Conics - Ellipse
    3. 27.3Conics - Circle
    4. 27.4Conics - Hyperbola
  28. 28Surface Area and Volume
    1. 28.1Surface area and volume of prisms
    2. 28.2Surface area and volume of pyramids
    3. 28.3Surface area and volume of cylinders
    4. 28.4Surface area and volume of cones
    5. 28.5Surface area and volume of spheres
  29. 29Sequences and Series
    1. 29.1Arithmetic sequences
    2. 29.2Arithmetic series
    3. 29.3Geometric sequences
    4. 29.4Geometric series
    5. 29.5Infinite geometric series
    6. 29.6Sigma notation
    7. 29.7Arithmetic mean vs. Geometric mean
  30. 30Probability
    1. 30.1Determining probabilities using tree diagrams and tables
    2. 30.2Probability of independent events
    3. 30.3Probability with Venn diagrams
  31. 31Permutations and Combinations
    1. 31.1Fundamental counting principle
    2. 31.2Factorial notation
    3. 31.3Path counting problems
    4. 31.4Permutation vs. Combination
    5. 31.5Permutations
    6. 31.6Combinations
    7. 31.7Problems involving both permutations and combinations
    8. 31.8Pascal's triangle
    9. 31.9Binomial theorem
  32. 32Statistics
    1. 32.1Median and mode
    2. 32.2Mean
    3. 32.3Range and outliers
    4. 32.4Application of averages
  33. 33Data and Graphs
    1. 33.1Reading and drawing bar graphs
    2. 33.2Reading and drawing histograms
    3. 33.3Reading and drawing line graphs
    4. 33.4Box-and-whisker plots and scatter plots
    5. 33.5Stem-and-leaf plots
    6. 33.6Reading and drawing Venn diagrams
    7. 33.7Frequency tables and dot plots
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