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  1. 1Number System and Radicals
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    1. 1.1Understanding the number systems
    2. 1.2Prime factorisation
    3. 1.3Greatest Common Factors (GCF)
    4. 1.4Least Common Multiple (LCM)
    5. 1.5Rational vs. Irrational numbers
    6. 1.6Converting repeating decimals to fractions
  2. 2Exponents
    1. 2.1Product rule of exponents
    2. 2.2Quotient rule of exponents
    3. 2.3Power of a product rule
    4. 2.4Power of a quotient rule
    5. 2.5Power of a power rule
    6. 2.6Negative exponent rule
    7. 2.7Combining the exponent rules
    8. 2.8Scientific notation
    9. 2.9Convert between radicals and rational exponents
    10. 2.10Solving for exponents
  3. 3Linear Inequalities
    1. 3.1Express linear inequalities graphically and algebraically
    2. 3.2Solving one-step linear inequalities
    3. 3.3Solving multi-step linear inequalities
    4. 3.4Compound inequalities
  4. 4Quadratic Equations and Inequalities
    1. 4.1Solving quadratic equations by factorising
    2. 4.2Solving quadratic equations by completing the square
    3. 4.3Using quadratic formula to solve quadratic equations
    4. 4.4Nature of roots of quadratic equations: The discriminant
    5. 4.5Applications of quadratic equations
    6. 4.6Solving quadratic inequalities
  5. 5Introduction to Relations and Functions
    1. 5.1Relationship between two variables
    2. 5.2Understand relations between x- and y-intercepts
    3. 5.3Domain and range of a function
    4. 5.4Identifying functions
    5. 5.5Function notation
  6. 6Solving Simultaneous Equations
    1. 6.1Determining number of solutions to linear equations
    2. 6.2Solving simultaneous equations by graphing
    3. 6.3Solving simultaneous equations by elimination
    4. 6.4Solving simultaneous equations by substitution
    5. 6.5Money related questions in linear equations
    6. 6.6Unknown number related questions in linear equations
    7. 6.7Distance and time related questions in linear equations
    8. 6.8Rectangular shape related questions in linear equations
  7. 7Inequalities in two variables
    1. 7.1Graphing linear inequalities in two variables
    2. 7.2Graphing simultaneous linear inequalities
    3. 7.3Graphing quadratic inequalities in two variables
    4. 7.4Graphing simultaneous quadratic inequalities
    5. 7.5Applications of inequalities
    6. 7.6What is linear programming?
    7. 7.7Linear programming word problems
  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 Quadratic Functions
    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. 11Operations of Polynomials
    1. 11.1What is a polynomial?
    2. 11.2Using algebra tiles to factorise polynomials
  12. 12Polynomial Functions
    1. 12.1What is a polynomial function?
    2. 12.2Polynomial long division
    3. 12.3Polynomial synthetic division
    4. 12.4Remainder theorem
    5. 12.5Factor theorem
    6. 12.6Rational zero theorem
    7. 12.7Characteristics of polynomial graphs
    8. 12.8Multiplicities of polynomials
    9. 12.9Imaginary zeros of polynomials
    10. 12.10Determining the equation of a polynomial function
    11. 12.11Applications of polynomial functions
    12. 12.12Solving polynomial inequalities
    13. 12.13Fundamental theorem of algebra
    14. 12.14Descartes' rule of signs
  13. 13Radicals
    1. 13.1Operations with radicals
    2. 13.2Conversion between entire radicals and mixed radicals
    3. 13.3Adding and subtracting radicals
    4. 13.4Multiplying radicals
    5. 13.5Solving radical equations
  14. 14Radical Functions
    1. 14.1Basic radical functions
    2. 14.2Transformations of radical functions
    3. 14.3Square root of a function
  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. 16Rational Expressions
    1. 16.1Simplifying rational expressions and restrictions
    2. 16.2Adding and subtracting rational expressions
    3. 16.3Multiplying rational expressions
    4. 16.4Dividing rational expressions
    5. 16.5Solving rational equations
    6. 16.6Applications of rational equations
    7. 16.7Simplifying complex fractions
    8. 16.8Partial fraction decomposition
  17. 17Reciprocal Functions
    1. 17.1Graphing reciprocals of linear functions
    2. 17.2Graphing reciprocals of quadratic functions
  18. 18Function Operations
    1. 18.1Function notation
    2. 18.2Operations with functions
    3. 18.3Adding functions
    4. 18.4Subtracting functions
    5. 18.5Multiplying functions
    6. 18.6Dividing functions
    7. 18.7Composite functions
    8. 18.8Inequalities of combined functions
    9. 18.9Inverse functions
    10. 18.10One to one functions
    11. 18.11Difference quotient: applications of functions
  19. 19Logarithmic Functions
    1. 19.1What is a logarithm?
    2. 19.2Converting from logarithmic form to exponential form
    3. 19.3Evaluating logarithms without a calculator
    4. 19.4Common logarithms
    5. 19.5Natural log: ln
    6. 19.6Evaluating logarithms using change-of-base formula
    7. 19.7Converting from exponential form to logarithmic form
    8. 19.8Solving exponential equations with logarithms
    9. 19.9Product rule of logarithms
    10. 19.10Quotient rule of logarithms
    11. 19.11Combining product rule and quotient rule in logarithms
    12. 19.12Evaluating logarithms using logarithm rules
    13. 19.13Solving logarithmic equations
    14. 19.14Graphing logarithmic functions
    15. 19.15Finding a logarithmic function given its graph
  20. 20Exponential Growth and Decay
    1. 20.1Exponential growth and decay by a factor
    2. 20.2Exponential decay: Half-life
    3. 20.3Exponential growth and decay by percentage
    4. 20.4Continuous growth and decay
  21. 21Trigonometry
    1. 21.1Angle in standard position
    2. 21.2Coterminal angles
    3. 21.3Reference angle
    4. 21.4Find the exact value of trigonometric ratios
    5. 21.5ASTC rule in trigonometry (All Students Take Calculus)
    6. 21.6Unit circle
    7. 21.7Converting between degrees and radians
    8. 21.8Trigonometric ratios of angles in radians
    9. 21.9Radian measure and arc length
    10. 21.10Law of sines
    11. 21.11Law of cosines
    12. 21.12Applications of the sine law and cosine law
  22. 22Bearings
    1. 22.1Introduction to bearings
    2. 22.2Bearings and direction word problems
    3. 22.3Angle of elevation and depression
  23. 23Graphing Trigonometric Functions
    1. 23.1Sine graph: y = sin x
    2. 23.2Cosine graph: y = cos x
    3. 23.3Tangent graph: y = tan x
    4. 23.4Cotangent graph: y = cot x
    5. 23.5Secant graph: y = sec x
    6. 23.6Cosecant graph: y = csc x
    7. 23.7Graphing transformations of trigonometric functions
    8. 23.8Determining trigonometric functions given their graphs
  24. 24Applications of Trigonometric Functions
    1. 24.1Ferris wheel trig problems
    2. 24.2Tides and water depth trig problems
    3. 24.3Spring (simple harmonic motion) trig problems
  25. 25Trigonometric Identities
    1. 25.1Quotient identities and reciprocal identities
    2. 25.2Pythagorean identities
    3. 25.3Sum and difference identities
    4. 25.4Cofunction identities
    5. 25.5Double-angle identities
  26. 26Scale Factors and Similarity
    1. 26.1Enlargements and reductions with scale factors
    2. 26.2Scale diagrams
    3. 26.3Similar triangles
    4. 26.4Similar polygons
  27. 27Circle Geometry
    1. 27.1Angles in a circle
    2. 27.2Chord properties
    3. 27.3Tangent properties
    4. 27.4Circles and circumference
    5. 27.5Arcs of a circle
    6. 27.6Areas and sectors of circles
    7. 27.7Inscribed Angles and Proofs
    8. 27.8Central and inscribed angles in circles
  28. 28Conics
    1. 28.1Conics - Parabola
    2. 28.2Conics - Ellipse
    3. 28.3Conics - Circle
    4. 28.4Conics - Hyperbola
  29. 29Surface Area and Volume
    1. 29.1Surface area and volume of prisms
    2. 29.2Surface area and volume of pyramids
    3. 29.3Surface area and volume of cylinders
    4. 29.4Surface area and volume of cones
    5. 29.5Surface area and volume of spheres
  30. 30Sequences and series
    1. 30.1Arithmetic sequences
    2. 30.2Arithmetic series
    3. 30.3Geometric sequences
    4. 30.4Geometric series
    5. 30.5Infinite geometric series
    6. 30.6Sigma notation
    7. 30.7Arithmetic mean vs. Geometric mean
  31. 31Probability
    1. 31.1Determining probabilities using tree diagrams and tables
    2. 31.2Probability of independent events
    3. 31.3Probability with Venn diagrams
  32. 32Permutations and Combinations
    1. 32.1Fundamental counting principle
    2. 32.2Factorial notation
    3. 32.3Path counting problems
    4. 32.4Permutation vs. Combination
    5. 32.5Permutations
    6. 32.6Combinations
    7. 32.7Problems involving both permutations and combinations
    8. 32.8Pascal's triangle
    9. 32.9Binomial theorem
  33. 33Statistics
    1. 33.1Median and mode
    2. 33.2Mean
    3. 33.3Range and outliers
    4. 33.4Application of averages
  34. 34Data and Graphs
    1. 34.1Reading and drawing bar graphs
    2. 34.2Reading and drawing histograms
    3. 34.3Reading and drawing line graphs
    4. 34.4Box-and-whisker plots and scatter plots
    5. 34.5Stem-and-leaf plots
    6. 34.6Pie charts
    7. 34.7Reading and drawing Venn diagrams
    8. 34.8Frequency tables and dot plots
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