Maths Methods Help & Practice

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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 = 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. 2Introduction to Relations and Functions
    1. 2.1Relationship between two variables
    2. 2.2Understand relations between x- and y-intercepts
    3. 2.3Domain and range of a function
    4. 2.4Identifying functions
    5. 2.5Function notation
  3. 3Linear Functions
    1. 3.1Distance formula: d=(x2−x1)2+(y2−y1)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=y2−y1x2−x1m = \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: y−y1=m(x−x1)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 slope-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. 4Linear Equations
    1. 4.1Introduction to linear equations
    2. 4.2Introduction to nonlinear equations
    3. 4.3Special case of linear equations: Horizontal lines
    4. 4.4Special case of linear equations: Vertical lines
    5. 4.5Parallel line equation
    6. 4.6Perpendicular line equation
    7. 4.7Combination of both parallel and perpendicular line equations
    8. 4.8Applications of linear equations
  5. 5Quadratic Functions
    1. 5.1Introduction to quadratic functions
    2. 5.2Transformations of quadratic functions
    3. 5.3Quadratic function in general form: y = ax^2 + bx + c
    4. 5.4Quadratic function in vertex form: y = a(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 quadratic functions: General form VS. Vertex form
    9. 5.9Finding the quadratic functions for given parabolas
    10. 5.10Applications of quadratic functions
  6. 6Solving Quadratic Equations
    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
  7. 7Functions
    1. 7.1Function notation
    2. 7.2Operations with functions
    3. 7.3Adding functions
    4. 7.4Subtracting functions
    5. 7.5Multiplying functions
    6. 7.6Dividing functions
    7. 7.7Composite functions
    8. 7.8Inequalities of combined functions
    9. 7.9Inverse functions
    10. 7.10One to one functions
    11. 7.11Difference quotient: applications of functions
  8. 8Transformations of Functions
    1. 8.1Transformations of functions: Horizontal translations
    2. 8.2Transformations of functions: Vertical translations
    3. 8.3Reflection across the y-axis: y = f(-x)
    4. 8.4Reflection across the x-axis: y = -f(x)
    5. 8.5Transformations of functions: Horizontal stretches
    6. 8.6Transformations of functions: Vertical stretches
    7. 8.7Combining transformations of functions
    8. 8.8Even and odd functions
  9. 9Factorisation
    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. 10Conics
    1. 10.1Conics - Parabola
    2. 10.2Conics - Ellipse
    3. 10.3Conics - Circle
    4. 10.4Conics - Hyperbola
  11. 11Trigonometric Ratios and Angle Measure
    1. 11.1Angle in standard position
    2. 11.2Coterminal angles
    3. 11.3Reference angle
    4. 11.4Find the exact value of trigonometric ratios
    5. 11.5ASTC rule in trigonometry (All Students Take Calculus)
    6. 11.6Unit circle
    7. 11.7Converting between degrees and radians
    8. 11.8Trigonometric ratios of angles in radians
    9. 11.9Radian measure and arc length
  12. 12Sine Rule and Cosine Rule
    1. 12.1Sine rule
    2. 12.2Cosine rule
    3. 12.3Sine rule and cosine rule word problems
  13. 13Bearings
    1. 13.1Introduction to bearings
    2. 13.2Bearings and direction word problems
    3. 13.3Angle of elevation and depression
  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. 15Applications of Trigonometric Functions
    1. 15.1Ferris wheel trig problems
    2. 15.2Tides and water depth trig problems
    3. 15.3Spring (simple harmonic motion) trig problems
  16. 16Trigonometric Identities
    1. 16.1Quotient identities and reciprocal identities
    2. 16.2Pythagorean identities
    3. 16.3Sum and difference identities
    4. 16.4Cofunction identities
    5. 16.5Double-angle identities
  17. 17Solving Trigonometric Equations
    1. 17.1Solving first degree trigonometric equations
    2. 17.2Determining non-permissible values for trig expressions
    3. 17.3Solving second degree trigonometric equations
    4. 17.4Solving trigonometric equations involving multiple angles
    5. 17.5Solving trigonometric equations using pythagorean identities
    6. 17.6Solving trigonometric equations using sum and difference identities
    7. 17.7Solving trigonometric equations using double-angle identities
  18. 18Permutations and Combinations
    1. 18.1Fundamental counting principle
    2. 18.2Factorial notation
    3. 18.3Path counting problems
    4. 18.4Permutation vs. Combination
    5. 18.5Permutations
    6. 18.6Combinations
    7. 18.7Problems involving both permutations and combinations
    8. 18.8Pascal's triangle
    9. 18.9Binomial theorem
  19. 19Probability
    1. 19.1Addition rule for "OR"
    2. 19.2Multiplication rule for "AND"
    3. 19.3Conditional probability
    4. 19.4Probability with permutations and combinations
    5. 19.5Law of total probability
    6. 19.6Bayes' rule
    7. 19.7Probability with Venn diagrams
  20. 20Indices
    1. 20.1Indices: Product rule (a^x)(a^y) = a^(x+y)
    2. 20.2Indices: Division rule (a^x / a^y) = a^(x-y)
    3. 20.3Indices: Power rule (a^x)^y = a^(x * y)
    4. 20.4Indices: Negative exponents
    5. 20.5Indices: Zero exponent: a^0 = 1
    6. 20.6Indices: Rational exponents
    7. 20.7Combining laws of indices
    8. 20.8Scientific notation
    9. 20.9Convert between radicals and rational exponents
    10. 20.10Solving for indices
  21. 21Exponential Functions
    1. 21.1Solving exponential equations using exponent rules
    2. 21.2Graphing exponential functions
    3. 21.3Graphing transformations of exponential functions
    4. 21.4Finding an exponential function given its graph
  22. 22Applications of Exponential Functions
    1. 22.1Exponential growth and decay by a factor
    2. 22.2Exponential decay: Half-life
    3. 22.3Exponential growth and decay by percentage
    4. 22.4Finance: Compound interest
    5. 22.5Continuous growth and decay
  23. 23Logarithmic Functions
    1. 23.1What is a logarithm?
    2. 23.2Converting from logarithmic form to exponential form
    3. 23.3Evaluating logarithms without a calculator
    4. 23.4Common logarithms
    5. 23.5Natural log: ln
    6. 23.6Evaluating logarithms using change-of-base formula
    7. 23.7Converting from exponential form to logarithmic form
    8. 23.8Solving exponential equations with logarithms
    9. 23.9Product rule of logarithms
    10. 23.10Quotient rule of logarithms
    11. 23.11Combining product rule and quotient rule in logarithms
    12. 23.12Evaluating logarithms using logarithm rules
    13. 23.13Solving logarithmic equations
    14. 23.14Graphing logarithmic functions
    15. 23.15Finding a logarithmic function given its graph
  24. 24Applications of Logarithmic Functions
    1. 24.1Logarithmic scale: Richter scale (earthquake)
    2. 24.2Logarithmic scale: pH scale
    3. 24.3Logarithmic scale: dB scale
    4. 24.4Finance: Future value and present value
  25. 25Sequences and Series
    1. 25.1Arithmetic sequences
    2. 25.2Arithmetic series
    3. 25.3Geometric sequences
    4. 25.4Geometric series
    5. 25.5Infinite geometric series
    6. 25.6Sigma notation
    7. 25.7Arithmetic mean vs. Geometric mean
  26. 26Limits and Derivatives
    1. 26.1Finding limits from graphs
    2. 26.2Definition of derivative
    3. 26.3Power rule
    4. 26.4Slope and equation of tangent line
    5. 26.5Chain rule
    6. 26.6Derivative of trigonometric functions
    7. 26.7Derivative of exponential functions
    8. 26.8Product rule
    9. 26.9Quotient rule
    10. 26.10Implicit differentiation
    11. 26.11Derivative of inverse trigonometric functions
    12. 26.12Derivative of logarithmic functions
    13. 26.13Higher order derivatives
  27. 27Derivative Applications
    1. 27.1Position velocity acceleration
    2. 27.2Critical number & maximum and minimum values
    3. 27.3Curve sketching
    4. 27.4Optimization
    5. 27.5Related rates
  28. 28Integrals
    1. 28.1Antiderivatives
    2. 28.2Riemann sum
    3. 28.3Definite integral
    4. 28.4Fundamental theorem of calculus
  29. 29Integration Applications
    1. 29.1Areas between curves
  30. 30Normal Distribution and Z-score
    1. 30.1Introduction to normal distribution
    2. 30.2Normal distribution and continuous random variable
    3. 30.3Z-scores and random continuous variables
    4. 30.4Sampling distributions
    5. 30.5Central limit theorem
    6. 30.6Rare event rule
  31. 31Discrete Probabilities
    1. 31.1Probability distribution - histogram, mean, variance & standard deviation
    2. 31.2Binomial distribution
    3. 31.3Mean and standard deviation of binomial distribution
    4. 31.4Poisson distribution
    5. 31.5Geometric distribution
    6. 31.6Negative binomial distribution
  32. 32Confidence Intervals
    1. 32.1Point estimates
    2. 32.2Confidence levels and critical values
    3. 32.3Margin of error
    4. 32.4Making a confidence interval
  • I am from Victoria. Would your mathematical methods course help?

    You bet! This course follows VCAA study design for Units 1- 4. The course also contains help in the maths methods course in Western Australia for ATAR or WACE, South Australia for SACE and the national curriculum for Mathematical Methods.

  • My VCE exam on maths methods is coming up soon. How should I study for it with StudyPug?

    You can first start with trying out some VCAA past exams to find out which areas you need help with. Then, look for the help in our Mathematical methods course to sharpen your understanding on those topics. If you want to revise some of the materials you have learned in the previous years, no worries, your subscription gives you unlimited access to all maths help in all courses. Same goes to anyone who is taking the ATAR Maths methods assessment too – you can find the ATAR past exams here.

  • What course should I take after General Maths?

    The prerequisite for this course is Year 10 maths or General Maths, and after you mastered mathematical methods, your follow up course should be Calculus 1 or Statistics.

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