Year 13 Maths Help & Practice

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  1. 1Functions
    1. 1.1Domain and range of a function
    2. 1.2Function notation
    3. 1.3Operations with functions
    4. 1.4Adding functions
    5. 1.5Subtracting functions
    6. 1.6Multiplying functions
    7. 1.7Dividing functions
    8. 1.8Composite functions
    9. 1.9Inequalities of combined functions
    10. 1.10Inverse functions
    11. 1.11One to one functions
    12. 1.12Difference quotient: applications of functions
  2. 2Transformations of Functions
    1. 2.1Transformations of functions: Horizontal translations
    2. 2.2Transformations of functions: Vertical translations
    3. 2.3Reflection across the y-axis: y = f(-x)
    4. 2.4Reflection across the x-axis: y = -f(x)
    5. 2.5Transformations of functions: Horizontal stretches
    6. 2.6Transformations of functions: Vertical stretches
    7. 2.7Combining transformations of functions
    8. 2.8Even and odd functions
  3. 3Quadratic Functions
    1. 3.1Characteristics of quadratic functions
    2. 3.2Transformations of quadratic functions
    3. 3.3Quadratic function in general form: y = ax^2 + bx + c
    4. 3.4Quadratic function in vertex form: y = a(x-p)^2 + q
    5. 3.5Completing the square
    6. 3.6Converting from general to vertex form by completing the square
    7. 3.7Shortcut: Vertex formula
    8. 3.8Graphing parabolas for given quadratic functions
    9. 3.9Finding the quadratic functions for given parabolas
    10. 3.10Applications of quadratic functions
  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. 5Polynomial Functions
    1. 5.1What is a polynomial function?
    2. 5.2Polynomial long division
    3. 5.3Polynomial synthetic division
    4. 5.4Remainder theorem
    5. 5.5Factor theorem
    6. 5.6Rational zero theorem
    7. 5.7Characteristics of polynomial graphs
    8. 5.8Multiplicities of polynomials
    9. 5.9Imaginary zeros of polynomials
    10. 5.10Determining the equation of a polynomial function
    11. 5.11Applications of polynomial functions
    12. 5.12Solving polynomial inequalities
    13. 5.13Fundamental theorem of algebra
    14. 5.14Descartes' rule of signs
  6. 6Rational Functions
    1. 6.1What is a rational function?
    2. 6.2Point of discontinuity
    3. 6.3Vertical asymptote
    4. 6.4Horizontal asymptote
    5. 6.5Slant asymptote
    6. 6.6Graphs of rational functions
    7. 6.7Solving equations with algebraic fractions
    8. 6.8Solving rational inequalities
  7. 7Exponential Functions
    1. 7.1Exponents: Product rule (a^x)(a^y) = a^(x+y)
    2. 7.2Exponents: Division rule (a^x / a^y) = a^(x-y)
    3. 7.3Exponents: Power rule (a^x)^y = a^(x * y)
    4. 7.4Exponents: Negative exponents
    5. 7.5Exponents: Zero exponent: a^0 = 1
    6. 7.6Exponents: Rational exponents
    7. 7.7Solving exponential equations using exponent rules
    8. 7.8Graphing exponential functions
    9. 7.9Graphing transformations of exponential functions
    10. 7.10Finding an exponential function given its graph
  8. 8Logarithmic Functions
    1. 8.1What is a logarithm?
    2. 8.2Converting from logarithmic form to exponential form
    3. 8.3Evaluating logarithms without a calculator
    4. 8.4Common logarithms
    5. 8.5Natural log: ln
    6. 8.6Evaluating logarithms using change-of-base formula
    7. 8.7Converting from exponential form to logarithmic form
    8. 8.8Solving exponential equations with logarithms
    9. 8.9Product rule of logarithms
    10. 8.10Quotient rule of logarithms
    11. 8.11Combining product rule and quotient rule in logarithms
    12. 8.12Evaluating logarithms using logarithm rules
    13. 8.13Solving logarithmic equations
    14. 8.14Graphing logarithmic functions
    15. 8.15Finding a logarithmic function given its graph
  9. 9Radical Functions
    1. 9.1Basic radical functions
    2. 9.2Transformations of radical functions
    3. 9.3Square root of a function
    4. 9.4Solving radical equations
  10. 10Solving Simultaneous Equations
    1. 10.1Determining number of solutions to linear equations
    2. 10.2Solving simultaneous equations by graphing
    3. 10.3Solving simultaneous equations by elimination
    4. 10.4Solving simultaneous equations by substitution
    5. 10.5Money related questions in linear equations
    6. 10.6Unknown number related questions in linear equations
    7. 10.7Distance and time related questions in linear equations
    8. 10.8Rectangular shape related questions in linear equations
  11. 11Trigonometry
    1. 11.1Sine rule
    2. 11.2Cosine rule
    3. 11.3Applications of the sine rule and cosine rule
  12. 12Bearings
    1. 12.1Introduction to bearings
    2. 12.2Bearings and direction word problems
    3. 12.3Angle of elevation and depression
  13. 13Trigonometric Ratios and Angle Measure
    1. 13.1Angle in standard position
    2. 13.2Coterminal angles
    3. 13.3Reference angle
    4. 13.4Find the exact value of trigonometric ratios
    5. 13.5ASTC rule in trigonometry (All Students Take Calculus)
    6. 13.6Unit circle
    7. 13.7Converting between degrees and radians
    8. 13.8Trigonometric ratios of angles in radians
    9. 13.9Radian measure and arc length
  14. 14Graphing Trigonometric Functions
    1. 14.1Sine graph: y = sin x
    2. 14.2Cosine graph: y = cos x
    3. 14.3Tangent graph: y = tan x
    4. 14.4Cotangent graph: y = cot x
    5. 14.5Secant graph: y = sec x
    6. 14.6Cosecant graph: y = csc x
    7. 14.7Graphing transformations of trigonometric functions
    8. 14.8Determining trigonometric functions given their graphs
  15. 15Trigonometric Identities
    1. 15.1Quotient identities and reciprocal identities
    2. 15.2Pythagorean identities
    3. 15.3Sum and difference identities
    4. 15.4Cofunction identities
    5. 15.5Double-angle identities
  16. 16Parabolas and Circles
    1. 16.1Conics - Parabola
    2. 16.2Conics - Circle
  17. 17Two-dimensional vectors
    1. 17.1Introduction to vectors
    2. 17.2Magnitude of a vector
    3. 17.3Direction angle of a vector
    4. 17.4Scalar multiplication
    5. 17.5Equivalent vectors
    6. 17.6Adding and subtracting vectors in component form
    7. 17.7Operations on vectors in magnitude and direction form
    8. 17.8Unit Vector
    9. 17.9Word problems on vectors
  18. 18Sequences and Series
    1. 18.1Arithmetic sequences
    2. 18.2Arithmetic series
    3. 18.3Geometric sequences
    4. 18.4Geometric series
    5. 18.5Infinite geometric series
    6. 18.6Sigma notation
    7. 18.7Arithmetic mean vs. Geometric mean
  19. 19Data Interpretation
    1. 19.1Center of a data set: mean, median, mode
    2. 19.2Spread of a data set - standard deviation & variance
    3. 19.3Measures of relative standing - z-score, quartiles, percentiles
    4. 19.4Bivariate, scatter plots and correlation
    5. 19.5Regression analysis
    6. 19.6Equation of the best fit line
  20. 20Discrete Probabilities
    1. 20.1Probability distribution - histogram, mean, variance & standard deviation
    2. 20.2Binomial distribution
    3. 20.3Mean and standard deviation of binomial distribution
    4. 20.4Poisson distribution
    5. 20.5Geometric distribution
    6. 20.6Negative binomial distribution
  21. 21Probability
    1. 21.1Addition rule for "OR"
    2. 21.2Multiplication rule for "AND"
    3. 21.3Conditional probability
    4. 21.4Probability with permutations and combinations
    5. 21.5Law of total probability
    6. 21.6Bayes' rule
  22. 22Permutations and Combinations
    1. 22.1Fundamental counting principle
    2. 22.2Factorial notation
    3. 22.3Path counting problems
    4. 22.4Permutation vs. Combination
    5. 22.5Permutations
    6. 22.6Combinations
    7. 22.7Problems involving both permutations and combinations
    8. 22.8Pascal's triangle
    9. 22.9Binomial theorem
  23. 23Integration Techniques
    1. 23.1U-Substitution
    2. 23.2Integration by parts
    3. 23.3Integration using trigonometric identities
    4. 23.4Trigonometric substitution
    5. 23.5Integration of rational functions by partial fractions
    6. 23.6Improper integrals
  24. 24Derivatives
    1. 24.1Definition of derivative
    2. 24.2Power rule
    3. 24.3Slope and equation of tangent line
    4. 24.4Chain rule
    5. 24.5Derivative of trigonometric functions
    6. 24.6Derivative of exponential functions
    7. 24.7Product rule
    8. 24.8Quotient rule
    9. 24.9Implicit differentiation
    10. 24.10Derivative of inverse trigonometric functions
    11. 24.11Derivative of logarithmic functions
    12. 24.12Higher order derivatives
    13. 24.13Tangent and concavity of parametric equations
  25. 25Integration Applications
    1. 25.1Areas between curves
    2. 25.2Volumes of solids with known cross-sections
    3. 25.3Volumes of solids of revolution - Disc method
    4. 25.4Volumes of solids of revolution - Shell method
    5. 25.5Average value of a function
    6. 25.6Arc length
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  • What class should I take after year 13 maths?

    You should take this course after you are comfortable with Year 12 Maths. Your follow up course can be Differentiation or Statistics.

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