Essential Maths Help & Practice

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  1. 1Adding and Subtracting Fractions
    1. 1.1Using models to add and subtract fractions
    2. 1.2Adding fractions with like denominators
    3. 1.3Subtracting fractions with like denominators
    4. 1.4Adding and subtracting fractions with unlike denominators
    5. 1.5Adding and subtracting mixed numbers
  2. 2Multiplying and Dividing Fractions
    1. 2.1Multiplying fractions and whole numbers
    2. 2.2Dividing fractions with whole numbers
    3. 2.3Multiplying proper fractions
    4. 2.4Multiplying improper fractions and mixed numbers
    5. 2.5Dividing fractions and mixed numbers
    6. 2.6Applications of fraction operations
  3. 3Pythagorean Theorem
    1. 3.1Squares and square roots
    2. 3.2Pythagorean theorem
    3. 3.3Estimating square roots
    4. 3.4Using the pythagorean relationship
    5. 3.5Applications of pythagorean theorem
  4. 4Percents
    1. 4.1Representing percents
    2. 4.2Percents, fractions, and decimals
    3. 4.3Percent of a number
    4. 4.4Adding and multiplying percents
    5. 4.5Taxes, discounts, tips and more
    6. 4.6Simple interest
  5. 5Surds
    1. 5.1Square and square roots
    2. 5.2Cubic and cube roots
    3. 5.3Evaluating and simplifying surds
    4. 5.4Converting radicals to mixed radicals
    5. 5.5Converting radicals to entire radicals
    6. 5.6Adding and subtracting surds
    7. 5.7Multiplying and dividing surds
    8. 5.8Rationalize the denominator
  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. 7Introduction to Relations and Functions
    1. 7.1Relationship between two variables
    2. 7.2Understand relations between x- and y-intercepts
    3. 7.3Domain and range of a function
    4. 7.4Identifying functions
    5. 7.5Function notation
  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. 8.13Parallel and perpendicular lines in linear functions
    14. 8.14Applications of linear relations
    15. 8.15Perpendicular line equation
  9. 9Simultaneous Equations
    1. 9.1Determining number of solutions to linear equations
    2. 9.2Solving simultaneous linear equations by graphing
    3. 9.3Solving simultaneous linear equations by elimination
    4. 9.4Solving simultaneous linear 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
    9. 9.9Simultaneous linear-quadratic equations
    10. 9.10Simultaneous quadratic-quadratic equations
    11. 9.11Solving 3 variable simultaneous equations by substitution
    12. 9.12Solving 3 variable simultaneous equations by elimination
    13. 9.13Solving 3 variable simultaneous equations with no solution, infinite solutions
    14. 9.14Word problems relating 3 variable simultaneous equations
  10. 10Factorisation
    1. 10.1Factorise by taking out the greatest common factor
    2. 10.2Factorise by grouping
    3. 10.3Factorising difference of squares: x^2 - y^2
    4. 10.4Factorising trinomials
    5. 10.5Factoring difference of cubes
    6. 10.6Factoring sum of cubes
  11. 11Quadratic Functions
    1. 11.1Introduction to quadratic functions
    2. 11.2Transformations of quadratic functions
    3. 11.3Quadratic function in general form: y = ax^2 + bx + c
    4. 11.4Quadratic function in vertex form: y = a(x-p)^2 + q
    5. 11.5Completing the square
    6. 11.6Converting from general to vertex form by completing the square
    7. 11.7Shortcut: Vertex formula
    8. 11.8Graphing quadratic functions: General form VS. Vertex form
    9. 11.9Finding the quadratic functions for given parabolas
    10. 11.10Applications of quadratic functions
  12. 12Solving Quadratic Equations
    1. 12.1Solving quadratic equations by factorising
    2. 12.2Solving quadratic equations by completing the square
    3. 12.3Using quadratic formula to solve quadratic equations
    4. 12.4Nature of roots of quadratic equations: The discriminant
    5. 12.5Applications of quadratic equations
  13. 13Inequalities
    1. 13.1Express linear inequalities graphically and algebraically
    2. 13.2Solving one-step linear inequalities
    3. 13.3Solving multi-step linear inequalities
    4. 13.4Compound inequalities
    5. 13.5Solving absolute value inequalities
    6. 13.6Graphing linear inequalities in two variables
    7. 13.7Graphing simultaneous inequalities
    8. 13.8Solving quadratic inequalities in one variable
  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. 16Angles, Lines, and Transversals
    1. 16.1Pairs of lines and angles
    2. 16.2Parallel lines and transversals
    3. 16.3Parallel line proofs
    4. 16.4Perpendicular line proofs
  17. 17Scale Factors and Similarity
    1. 17.1Enlargements and reductions with scale factors
    2. 17.2Scale diagrams
    3. 17.3Similar triangles
    4. 17.4Similar polygons
  18. 18Properties of Triangles
    1. 18.1Classifying Triangles
    2. 18.2Isosceles and Equilateral Triangles
  19. 19Congruent Triangles
    1. 19.1Congruence and Congruent Triangles
    2. 19.2Triangles Congruent by SSS Proofs
    3. 19.3Triangles Congruent by SAS and HL Proofs
    4. 19.4Triangles Congruent by ASA and AAS Proofs
  20. 20Functions
    1. 20.1Function notation
    2. 20.2Operations with functions
    3. 20.3Adding functions
    4. 20.4Subtracting functions
    5. 20.5Multiplying functions
    6. 20.6Dividing functions
    7. 20.7Composite functions
    8. 20.8Even and odd functions
  21. 21Rational Functions
    1. 21.1What is a rational function?
    2. 21.2Point of discontinuity
    3. 21.3Vertical asymptote
    4. 21.4Horizontal asymptote
    5. 21.5Slant asymptote
    6. 21.6Graphs of rational functions
  22. 22Indices
    1. 22.1Indices: Product rule (a^x)(a^y) = a^(x+y)
    2. 22.2Indices: Division rule (a^x / a^y) = a^(x-y)
    3. 22.3Indices: Power rule (a^x)^y = a^(x * y)
    4. 22.4Indices: Negative exponents
    5. 22.5Indices: Zero exponent: a^0 = 1
    6. 22.6Indices: Rational exponents
    7. 22.7Combining laws of indices
    8. 22.8Scientific notation
    9. 22.9Convert between radicals and rational exponents
    10. 22.10Solving for indices
  23. 23Exponential Functions
    1. 23.1Solving exponential equations using exponent rules
    2. 23.2Graphing exponential functions
    3. 23.3Graphing transformations of exponential functions
    4. 23.4Finding an exponential function given its graph
  24. 24Logarithmic Functions
    1. 24.1What is a logarithm?
    2. 24.2Converting from logarithmic form to exponential form
    3. 24.3Evaluating logarithms without a calculator
    4. 24.4Common logarithms
    5. 24.5Natural log: ln
    6. 24.6Evaluating logarithms using change-of-base formula
    7. 24.7Converting from exponential form to logarithmic form
    8. 24.8Solving exponential equations with logarithms
    9. 24.9Product rule of logarithms
    10. 24.10Quotient rule of logarithms
    11. 24.11Combining product rule and quotient rule in logarithms
    12. 24.12Evaluating logarithms using logarithm rules
    13. 24.13Solving logarithmic equations
    14. 24.14Graphing logarithmic functions
    15. 24.15Finding a logarithmic function given its graph
  25. 25Trigonometric Ratios and Angle Measure
    1. 25.1Angle in standard position
    2. 25.2Coterminal angles
    3. 25.3Reference angle
    4. 25.4Find the exact value of trigonometric ratios
    5. 25.5ASTC rule in trigonometry (All Students Take Calculus)
    6. 25.6Unit circle
    7. 25.7Converting between degrees and radians
    8. 25.8Trigonometric ratios of angles in radians
    9. 25.9Radian measure and arc length
  26. 26Sine Rule and Cosine Rule
    1. 26.1Sine rule
    2. 26.2Cosine rule
    3. 26.3Sine rule and cosine rule word problems
  27. 27Trigonometric Graphs
    1. 27.1Sine graph: y = sin x
    2. 27.2Cosine graph: y = cos x
    3. 27.3Tangent graph: y = tan x
  28. 28Inverse Trigonometric Functions
    1. 28.1Finding inverse trigonometric function from its graph
    2. 28.2Evaluating inverse trigonometric functions
    3. 28.3Finding inverse reciprocal trigonometric function from its graph
    4. 28.4Finding exact value of inverse reciprocal trig functions
  29. 29Bearings
    1. 29.1Introduction to bearings
    2. 29.2Bearings and direction word problems
    3. 29.3Angle of elevation and depression
  30. 30Series
    1. 30.1Arithmetic series
    2. 30.2Geometric series
    3. 30.3Convergence and divergence of normal infinite series
    4. 30.4Convergence & divergence of geometric series
  31. 31Growth and Decay
    1. 31.1Exponential growth and decay by a factor
    2. 31.2Exponential growth and decay by percentage
    3. 31.3Finance: Compound interest
    4. 31.4Finance: Future value and present value
  32. 32Conics
    1. 32.1Conics - Parabola
    2. 32.2Conics - Ellipse
    3. 32.3Conics - Circle
    4. 32.4Conics - Hyperbola
  33. 33Probability
    1. 33.1Addition rule for "OR"
    2. 33.2Multiplication rule for "AND"
  34. 34Limits
    1. 34.1Finding limits from graphs
    2. 34.2Continuity
    3. 34.3Finding limits algebraically - direct substitution
    4. 34.4Finding limits algebraically - when direct substitution is not possible
    5. 34.5Limit laws
  35. 35Derivatives
    1. 35.1Definition of derivative
    2. 35.2Power rule
    3. 35.3Slope and equation of tangent line
    4. 35.4Chain rule
    5. 35.5Derivative of trigonometric functions
    6. 35.6Derivative of exponential functions
    7. 35.7Product rule
    8. 35.8Quotient rule
    9. 35.9Derivative of logarithmic functions
    10. 35.10Higher order derivatives
  36. 36Derivative Applications
    1. 36.1Rectilinear Motion: Derivative
    2. 36.2Critical number & maximum and minimum values
    3. 36.3Curve sketching
  37. 37Integrals
    1. 37.1Antiderivatives
    2. 37.2Riemann sum
    3. 37.3Definite integral
    4. 37.4Fundamental theorem of calculus
  38. 38Integral Applications
    1. 38.1Areas between curves
    2. 38.2Volumes of solids of revolution - Disc method
    3. 38.3Volumes of solids of revolution - Shell method
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