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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
  3. 3Measuring Systems
    1. 3.1Metric systems
    2. 3.2Imperial systems
    3. 3.3Conversions between metric and imperial systems
    4. 3.4Conversions involve squares and cubic
  4. 4Number Systems
    1. 4.1Understanding the number systems
    2. 4.2Prime factorisation
    3. 4.3Highest common factors (HCF)
    4. 4.4Least Common Multiple (LCM)
    5. 4.5Rational vs. Irrational numbers
    6. 4.6Converting repeating decimals to fractions
  5. 5Direct and Inverse Proportion
    1. 5.1Direct variation
  6. 6Algebraic Expressions
    1. 6.1Equivalent algebraic expressions
    2. 6.2Adding and subtracting algebraic expressions
    3. 6.3Multiplying monomial by monomial
    4. 6.4Multiplying monomial by binomial
    5. 6.5Multiplying binomial by binomial
    6. 6.6Multiplying polynomial by polynomial
    7. 6.7Applications of polynomials
  7. 7Surds
    1. 7.1Square and square roots
    2. 7.2Cubic and cube roots
    3. 7.3Operations with surds
    4. 7.4Conversion between entire radicals and mixed radicals
    5. 7.5Adding and subtracting surds
    6. 7.6Multiplying surds
    7. 7.7Rationalize the denominator
    8. 7.8Solving equations with surds
  8. 8Linear Functions
    1. 8.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
    2. 8.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
    3. 8.3Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
    4. 8.4Gradient intercept form: y = mx + b
    5. 8.5General form: Ax + By + C = 0
    6. 8.6Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)
    7. 8.7Rate of change
    8. 8.8Graphing linear functions using table of values
    9. 8.9Graphing linear functions using x- and y-intercepts
    10. 8.10Graphing from slope-intercept form y=mx+b
    11. 8.11Graphing linear functions using a single point and gradient
    12. 8.12Word problems of graphing linear functions
    13. 8.13Applications of linear relations
  9. 9Factorising Quadratic Functions
    1. 9.1Factorise by taking out the greatest common factor
    2. 9.2Factorise by grouping
    3. 9.3Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2
    4. 9.4Factorising difference of squares: x^2 - y^2
    5. 9.5Factorising trinomials
    6. 9.6Solving polynomials with unknown coefficients
    7. 9.7Solving polynomials with unknown constant terms
  10. 10Quadratic Functions
    1. 10.1Introduction to 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 quadratic functions: General form VS. Vertex form
    9. 10.9Finding the quadratic functions for given parabolas
    10. 10.10Applications of quadratic functions
  11. 11Quadratic Equations and Inequalities
    1. 11.1Solving quadratic equations by factoring
    2. 11.2Solving quadratic equations by completing the square
    3. 11.3Using quadratic formula to solve quadratic equations
    4. 11.4Nature of roots of quadratic equations: The discriminant
    5. 11.5Applications of quadratic equations
    6. 11.6Solving quadratic inequalities
  12. 12Algebraic Fractions
    1. 12.1Simplifying algebraic fractions and restrictions
    2. 12.2Adding and subtracting algebraic fractions
    3. 12.3Multiplying algebraic fractions
    4. 12.4Dividing algebraic fractions
    5. 12.5Solving equations with algebraic fractions
    6. 12.6Applications of equations with algebraic fractions
    7. 12.7Simplifying complex fractions
    8. 12.8Partial fraction decomposition
  13. 13Simultaneous Equations
    1. 13.1Determining number of solutions to linear equations
    2. 13.2Solving simultaneous linear equations by graphing
    3. 13.3Solving simultaneous linear equations by elimination
    4. 13.4Solving simultaneous linear equations by substitution
    5. 13.5Money related questions in linear equations
    6. 13.6Unknown number related questions in linear equations
    7. 13.7Distance and time related questions in linear equations
    8. 13.8Rectangular shape related questions in linear equations
    9. 13.9Simultaneous linear equations
    10. 13.10Simultaneous linear-quadratic equations
    11. 13.11Simultaneous quadratic-quadratic equations
  14. 14Inequalities in Two Variables
    1. 14.1Graphing linear inequalities in two variables
    2. 14.2Graphing systems of linear inequalities
    3. 14.3Graphing quadratic inequalities in two variables
    4. 14.4Graphing systems of quadratic inequalities
    5. 14.5Applications of inequalities
    6. 14.6What is linear programming?
    7. 14.7Linear programming word problems
  15. 15Laws of Indices
    1. 15.1Indices: Product rule (a^x)(a^y) = a^(x+y)
    2. 15.2Indices: Division rule (a^x / a^y) = a^(x-y)
    3. 15.3Indices: Power rule (a^x)^y = a^(x * y)
    4. 15.4Negative indices
    5. 15.5Zero index: a^0 = 1
    6. 15.6Rational indices
    7. 15.7Standard form
  16. 16Polynomial Functions
    1. 16.1Polynomial long division
    2. 16.2Polynomial synthetic division
    3. 16.3Remainder theorem
    4. 16.4Factor theorem
  17. 17Binomial expansions
    1. 17.1Factorial notation
    2. 17.2Binomial theorem
  18. 18Exponential Functions
    1. 18.1Solving exponential equations using laws of indices
    2. 18.2Graphing exponential functions
    3. 18.3Graphing transformations of exponential functions
    4. 18.4Finding an exponential function given its graph
  19. 19Logarithms
    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. 20Modulus Functions
    1. 20.1Modulus functions
    2. 20.2Solving modulus equations
  21. 21Vectors
    1. 21.1Introduction to vectors
    2. 21.2Magnitude of a vector
    3. 21.3Direction angle of a vector
    4. 21.4Scalar multiplication
    5. 21.5Adding and subtracting vectors in component form
    6. 21.6Operations on vectors in magnitude and direction form
    7. 21.7Word problems on vectors
  22. 22Matrices
    1. 22.1Notation of matrices
    2. 22.2Adding and subtracting matrices
    3. 22.3Multiplying a matrix by a scalar
    4. 22.4Multiplying a matrix by another matrix
  23. 23Trigonometric Ratios and Angle Measure
    1. 23.1Angle in standard position
    2. 23.2Coterminal angles
    3. 23.3Reference angle
    4. 23.4Find the exact value of trigonometric ratios
    5. 23.5ASTC rule in trigonometry (All Students Take Calculus)
    6. 23.6Unit circle
    7. 23.7Converting between degrees and radians
    8. 23.8Trigonometric ratios of angles in radians
    9. 23.9Radian measure and arc length
  24. 24Sine Rule and Cosine Rule
    1. 24.1Sine rule
    2. 24.2Cosine rule
    3. 24.3Sine rule and cosine rule word problems
  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. 27Applications of Trigonometric Functions
    1. 27.1Ferris wheel trig problems
    2. 27.2Tides and water depth trig problems
    3. 27.3Spring (simple harmonic motion) trig problems
  28. 28Trigonometric Identities
    1. 28.1Quotient identities and reciprocal identities
    2. 28.2Pythagorean identities
    3. 28.3Sum and difference identities
    4. 28.4Cofunction identities
    5. 28.5Double-angle identities
  29. 29Solving Trigonometric Equations
    1. 29.1Solving first degree trigonometric equations
    2. 29.2Determining non-permissible values for trig expressions
    3. 29.3Solving second degree trigonometric equations
    4. 29.4Solving trigonometric equations involving multiple angles
    5. 29.5Solving trigonometric equations using pythagorean identities
    6. 29.6Solving trigonometric equations using sum and difference identities
    7. 29.7Solving trigonometric equations using double-angle identities
  30. 30Inverse Trigonometric Functions
    1. 30.1Finding inverse trigonometric function from its graph
    2. 30.2Evaluating inverse trigonometric functions
    3. 30.3Finding inverse reciprocal trigonometric function from its graph
    4. 30.4Inverse reciprocal trigonometric function: finding the exact value
  31. 31Angles, Lines, and Transversals
    1. 31.1Pairs of lines and angles
    2. 31.2Parallel lines and transversals
    3. 31.3Parallel line proofs
    4. 31.4Perpendicular line proofs
  32. 32Scale Factors and Similarity
    1. 32.1Enlargements and reductions with scale factors
    2. 32.2Scale diagrams
    3. 32.3Similar triangles
    4. 32.4Similar polygons
  33. 33Congruent Triangles
    1. 33.1Congruence and congruent triangles
    2. 33.2Triangles congruent by SSS proofs
    3. 33.3Triangles congruent by SAS and HL proofs
    4. 33.4Triangles congruent by ASA and AAS proofs
  34. 34Circles
    1. 34.1Angles in a circle
    2. 34.2Chord properties
    3. 34.3Tangent properties
    4. 34.4Circle and circumference
    5. 34.5Arcs of a circle
    6. 34.6Areas and sectors of circles
    7. 34.7Inscribed quadrilaterals in circles
    8. 34.8Central and inscribed angles in circles
  35. 35Surface Area and Volume
    1. 35.1Surface area and volume of prisms
    2. 35.2Surface area and volume of pyramids
    3. 35.3Surface area and volume of cylinders
    4. 35.4Surface area and volume of cones
    5. 35.5Surface area and volume of spheres
  36. 36Conics
    1. 36.1Conics - Parabola
    2. 36.2Conics - Circle
  37. 37Set Theory
    1. 37.1Set notation
    2. 37.2Set builder notation
    3. 37.3Intersection and union of 2 sets
    4. 37.4Intersection and union of 3 sets
  38. 38Data and Graphs
    1. 38.1Reading and drawing bar graphs
    2. 38.2Reading and drawing histograms
    3. 38.3Reading and drawing line graphs
    4. 38.4Box-and-whisker plots and scatter plots
    5. 38.5Stem-and-leaf plots
    6. 38.6Reading and drawing Venn diagrams
    7. 38.7Frequency tables and dot diagrams
    8. 38.8Pie charts
  39. 39Statistics
    1. 39.1Median and mode
    2. 39.2Mean
    3. 39.3Range and outliers
    4. 39.4Application of averages
    5. 39.5Standard deviation, and variance
    6. 39.6Z-score, quartiles, and percentiles
  40. 40Probability
    1. 40.1Determining probabilities using tree diagrams and tables
    2. 40.2Probability of independent events
    3. 40.3Frequency distribution and histograms
    4. 40.4Addition rule for "OR"
    5. 40.5Multiplication rule for "AND"
  41. 41Differentiation
    1. 41.1Power rule
    2. 41.2Slope and equation of tangent line
    3. 41.3Chain rule
    4. 41.4Derivative of trigonometric functions
    5. 41.5Derivative of exponential functions
    6. 41.6Product rule
    7. 41.7Quotient rule
    8. 41.8Derivative of logarithmic functions
    9. 41.9Higher order derivatives
    10. 41.10Rectilinear Motion: Derivative
    11. 41.11Critical number & maximum and minimum values
  42. 42Integration
    1. 42.1Antiderivatives
    2. 42.2Definite integral
    3. 42.3Integration by parts
    4. 42.4Trigonometric substitution
    5. 42.5Integration of rational functions by partial fractions
    6. 42.6Areas between curves
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