AU Maths Methods made completely easy!

Get better math marks with our complete Mathematical Methods help – be it VCAA maths methods exam, ATAR Maths Methods exam (Western Australia), WACE requirements, Maths methods SACE stage 2 (South Australia), or the national senior secondary curriculum Mathematical Methods. Our maths methods tutors got you all covered!

Just like your class or textbook, our complete help for maths methods includes topics such as Solving Linear Equations, Trigonometry, Permutations and Combinations, Exponential functions, Logarithmic functions, Limits and Derivatives, Statistics, and more. Learn the concepts with our online video tutorials that show you step-by-step solutions to even the hardest maths methods problems. Then, strengthen your understanding with tons of maths methods practice.

All our lessons are taught by experienced maths methods teachers. Let’s finish your homework in no time, and ACE that exam.

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Common Questions
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.

AU Maths Methods Topics

We have plenty of free lessons for you to watch

1.Solving Linear Equations

1.1Solving linear equations using multiplication and division (free lessons)
1.2Solving two-step linear equations: ax+b=cax + b = c, xa+b=c{x \over a} + b = c
1.3Solving linear equations using distributive property: a(x+b)=ca(x + b) = c (free lessons)
1.4Solving linear equations with variables on both sides
1.5Solving literal equations

2.Introduction to Relations and Functions

2.1Relationship between two variables (free lessons)
2.2Understand relations between x- and y-intercepts
2.3Domain and range of a function (free lessons)
2.4Identifying functions
2.5Function notation (free lessons)

3.Linear Functions

3.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} (free lessons)
3.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2) (free lessons)
3.3Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
3.4Gradient intercept form: y = mx + b (free lessons)
3.5General form: Ax + By + C = 0 (free lessons)
3.6Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1) (free lessons)
3.7Rate of change
3.8Graphing linear functions using table of values
3.9Graphing linear functions using x- and y-intercepts (free lessons)
3.10Graphing from slope-intercept form y=mx+b
3.11Graphing linear functions using a single point and gradient
3.12Word problems of graphing linear functions
3.13Parallel and perpendicular lines in linear functions (free lessons)
3.14Applications of linear relations

4.Linear Equations

4.1Introduction to linear equations (free lessons)
4.2Introduction to nonlinear equations
4.3Special case of linear equations: Horizontal lines
4.4Special case of linear equations: Vertical lines
4.5Parallel line equation (free lessons)
4.6Perpendicular line equation
4.7Combination of both parallel and perpendicular line equations
4.8Applications of linear equations

5.Quadratic Functions

5.1Introduction to quadratic functions (free lessons)
5.2Transformations of quadratic functions
5.3Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+c
5.4Quadratic function in vertex form: y = a(x−p)2+qa(x-p)^2 + q
5.5Completing the square
5.6Converting from general to vertex form by completing the square
5.7Shortcut: Vertex formula (free lessons)
5.8Finding the quadratic functions for given parabolas (free lessons)
5.9Applications of quadratic functions

6.Solving Quadratic Equations

6.1Solving quadratic equations by factorising
6.2Solving quadratic equations by completing the square
6.3Using quadratic formula to solve quadratic equations
6.4Nature of roots of quadratic equations: The discriminant
6.5Applications of quadratic equations

7.Functions

7.1Function notation (free lessons)
7.2Operations with functions
7.3Adding functions
7.4Subtracting functions
7.5Multiplying functions
7.6Dividing functions
7.7Composite functions (free lessons)
7.8Inverse functions
7.9One to one functions
7.10Difference quotient: applications of functions

8.Transformations of Functions

8.1Transformations of functions: Horizontal translations
8.2Transformations of functions: Vertical translations
8.3Reflection across the y-axis: y=f(−x)y = f(-x) (free lessons)
8.4Reflection across the x-axis: y=−f(x)y = -f(x)
8.5Transformations of functions: Horizontal stretches
8.6Transformations of functions: Vertical stretches
8.7Combining transformations of functions
8.8Even and odd functions

9.Factorisation

9.1Factorise by taking out the greatest common factor (free lessons)
9.2Factorise by grouping
9.3Factorising difference of squares: x2−y2x^2 - y^2
9.4Factorising trinomials
9.5Factoring difference of cubes
9.6Factoring sum of cubes

10.Conics

10.1Conics - Parabola
10.2Conics - Ellipse
10.3Conics - Circle
10.4Conics - Hyperbola

11.Trigonometric Ratios and Angle Measure

11.1Angle in standard position
11.2Coterminal angles (free lessons)
11.3Reference angle
11.4Find the exact value of trigonometric ratios
11.5ASTC rule in trigonometry (All Students Take Calculus) (free lessons)
11.6Unit circle (free lessons)
11.7Converting between degrees and radians
11.8Trigonometric ratios of angles in radians
11.9Radian measure and arc length

12.Sine Rule and Cosine Rule

12.1Sine rule
12.2Cosine rule
12.3Sine rule and cosine rule word problems

13.Graphing Trigonometric Functions

13.1Sine graph: y = sin x
13.2Cosine graph: y = cos x
13.3Tangent graph: y = tan x
13.4Cotangent graph: y = cot x
13.5Secant graph: y = sec x
13.6Cosecant graph: y = csc x
13.7Graphing transformations of trigonometric functions
13.8Determining trigonometric functions given their graphs

14.Applications of Trigonometric Functions

14.1Ferris wheel trig problems
14.2Tides and water depth trig problems
14.3Spring (simple harmonic motion) trig problems

15.Trigonometric Identities

15.1Quotient identities and reciprocal identities (free lessons)
15.2Pythagorean identities
15.3Sum and difference identities
15.4Cofunction identities
15.5Double-angle identities (free lessons)

16.Solving Trigonometric Equations

16.1Solving first degree trigonometric equations (free lessons)
16.2Determining non-permissible values for trig expressions
16.3Solving second degree trigonometric equations
16.4Solving trigonometric equations involving multiple angles (free lessons)
16.5Solving trigonometric equations using pythagorean identities
16.6Solving trigonometric equations using sum and difference identities
16.7Solving trigonometric equations using double-angle identities

17.Permutations and Combinations

17.1Fundamental counting principle
17.2Factorial notation
17.3Path counting problems
17.4Permutation vs. Combination
17.5Permutations
17.6Combinations
17.7Problems involving both permutations and combinations
17.8Pascal's triangle
17.9Binomial theorem

18.Probability

18.1Addition rule for "OR"
18.2Multiplication rule for "AND"
18.3Conditional probability
18.4Probability with permutations and combinations
18.5Law of total probability
18.6Bayes' rule
18.7Probability with Venn diagrams

19.Indices

19.1Indices: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
19.2Indices: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
19.3Indices: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
19.4Indices: Negative exponents
19.5Indices: Zero exponent: a0=1 a^0 = 1
19.6Indices: Rational exponents
19.7Combining laws of indices
19.8Scientific notation
19.9Convert between radicals and rational exponents (free lessons)
19.10Solving for indices

20.Exponential Functions

20.1Solving exponential equations using exponent rules
20.2Graphing exponential functions
20.3Graphing transformations of exponential functions
20.4Finding an exponential function given its graph

21.Applications of Exponential Functions

21.1Exponential growth and decay by a factor
21.2Exponential decay: Half-life (free lessons)
21.3Exponential growth and decay by percentage
21.4Finance: Compound interest
21.5Continuous growth and decay

22.Logarithmic Functions

22.1What is a logarithm?
22.2Converting from logarithmic form to exponential form (free lessons)
22.3Evaluating logarithms without a calculator
22.4Common logarithms
22.5Natural log: ln
22.6Evaluating logarithms using change-of-base formula
22.7Converting from exponential form to logarithmic form (free lessons)
22.8Solving exponential equations with logarithms
22.9Product rule of logarithms (free lessons)
22.10Quotient rule of logarithms
22.11Combining product rule and quotient rule in logarithms
22.12Evaluating logarithms using logarithm rules
22.13Solving logarithmic equations (free lessons)
22.14Graphing logarithmic functions
22.15Finding a logarithmic function given its graph

23.Applications of Logarithmic Functions

23.1Logarithmic scale: Richter scale (earthquake)
23.2Logarithmic scale: pH scale
23.3Logarithmic scale: dB scale
23.4Finance: Future value and present value

24.Sequences and Series

24.1Arithmetic sequences (free lessons)
24.2Arithmetic series (free lessons)
24.3Geometric sequences
24.4Geometric series
24.5Infinite geometric series
24.6Sigma notation
24.7Arithmetic mean vs. Geometric mean

25.Limits and Derivatives

25.1Finding limits from graphs
25.2Definition of derivative
25.3Power rule
25.4Slope and equation of tangent line
25.5Chain rule
25.6Derivative of trigonometric functions
25.7Derivative of exponential functions
25.8Product rule
25.9Quotient rule
25.10Implicit differentiation
25.11Derivative of inverse trigonometric functions
25.12Derivative of logarithmic functions
25.13Higher order derivatives

26.Derivative Applications

26.1Position velocity acceleration
26.2Critical number & maximum and minimum values
26.3Curve sketching
26.4Optimization
26.5Related rates

27.Integrals

27.1Antiderivatives
27.2Riemann sum
27.3Definite integral
27.4Fundamental theorem of calculus

28.Integration Applications

28.1Areas between curves

29.Normal Distribution and Z-score

29.1Introduction to normal distribution
29.2Normal distribution and continuous random variable
29.3Z-scores and random continuous variables
29.4Sampling distributions
29.5Central limit theorem
29.6Rare event rule

30.Discrete Probabilities

30.1Probability distribution - histogram, mean, variance & standard deviation
30.2Binomial distribution
30.3Mean and standard deviation of binomial distribution
30.4Poisson distribution
30.5Geometric distribution
30.6Negative binomial distribution

31.Confidence Intervals

31.1Point estimates
31.2Confidence levels and critical values
31.3Margin of error
31.4Making a confidence interval
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