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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.

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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

1Solving 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

2Introduction 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)

3Linear 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

4Linear 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

5Quadratic 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 (free lessons)
5.6Converting from general to vertex form by completing the square
5.7Shortcut: Vertex formula (free lessons)
5.8Graphing quadratic functions: General form VS. Vertex form
5.9Finding the quadratic functions for given parabolas (free lessons)
5.10Applications of quadratic functions

6Solving 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

7Functions

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)
7.8Inequalities of combined functions
7.9Inverse functions (free lessons)
7.10One to one functions
7.11Difference quotient: applications of functions

8Transformations 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

9Factorisation

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

10Conics

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

11Trigonometric 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

12Sine Rule and Cosine Rule

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

13Bearings

13.1Introduction to bearings
13.2Bearings and direction word problems
13.3Angle of elevation and depression

14Graphing Trigonometric Functions

14.1Sine graph: y = sin x
14.2Cosine graph: y = cos x
14.3Tangent graph: y = tan x
14.4Cotangent graph: y = cot x
14.5Secant graph: y = sec x
14.6Cosecant graph: y = csc x
14.7Graphing transformations of trigonometric functions
14.8Determining trigonometric functions given their graphs

15Applications of Trigonometric Functions

15.1Ferris wheel trig problems
15.2Tides and water depth trig problems
15.3Spring (simple harmonic motion) trig problems

16Trigonometric Identities

16.1Quotient identities and reciprocal identities (free lessons)
16.2Pythagorean identities
16.3Sum and difference identities
16.4Cofunction identities
16.5Double-angle identities (free lessons)

17Solving Trigonometric Equations

17.1Solving first degree trigonometric equations (free lessons)
17.2Determining non-permissible values for trig expressions
17.3Solving second degree trigonometric equations
17.4Solving trigonometric equations involving multiple angles (free lessons)
17.5Solving trigonometric equations using pythagorean identities
17.6Solving trigonometric equations using sum and difference identities
17.7Solving trigonometric equations using double-angle identities

18Permutations and Combinations

18.1Fundamental counting principle
18.2Factorial notation
18.3Path counting problems
18.4Permutation vs. Combination
18.5Permutations
18.6Combinations
18.7Problems involving both permutations and combinations
18.8Pascal's triangle
18.9Binomial theorem

19Probability

19.1Addition rule for "OR"
19.2Multiplication rule for "AND"
19.3Conditional probability
19.4Probability with permutations and combinations
19.5Law of total probability
19.6Bayes' rule
19.7Probability with Venn diagrams

20Indices

20.1Indices: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
20.2Indices: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
20.3Indices: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
20.4Indices: Negative exponents
20.5Indices: Zero exponent: a0=1 a^0 = 1
20.6Indices: Rational exponents
20.7Combining laws of indices
20.8Scientific notation
20.9Convert between radicals and rational exponents (free lessons)
20.10Solving for indices

21Exponential Functions

21.1Solving exponential equations using exponent rules
21.2Graphing exponential functions
21.3Graphing transformations of exponential functions
21.4Finding an exponential function given its graph

22Applications of Exponential Functions

22.1Exponential growth and decay by a factor
22.2Exponential decay: Half-life (free lessons)
22.3Exponential growth and decay by percentage
22.4Finance: Compound interest
22.5Continuous growth and decay

23Logarithmic Functions

23.1What is a logarithm?
23.2Converting from logarithmic form to exponential form (free lessons)
23.3Evaluating logarithms without a calculator
23.4Common logarithms
23.5Natural log: ln
23.6Evaluating logarithms using change-of-base formula
23.7Converting from exponential form to logarithmic form (free lessons)
23.8Solving exponential equations with logarithms
23.9Product rule of logarithms (free lessons)
23.10Quotient rule of logarithms
23.11Combining product rule and quotient rule in logarithms
23.12Evaluating logarithms using logarithm rules
23.13Solving logarithmic equations (free lessons)
23.14Graphing logarithmic functions
23.15Finding a logarithmic function given its graph

24Applications of Logarithmic Functions

24.1Logarithmic scale: Richter scale (earthquake)
24.2Logarithmic scale: pH scale
24.3Logarithmic scale: dB scale
24.4Finance: Future value and present value

25Sequences and Series

25.1Arithmetic sequences (free lessons)
25.2Arithmetic series (free lessons)
25.3Geometric sequences
25.4Geometric series
25.5Infinite geometric series
25.6Sigma notation
25.7Arithmetic mean vs. Geometric mean

26Limits and Derivatives

26.1Finding limits from graphs
26.2Definition of derivative
26.3Power rule
26.4Slope and equation of tangent line
26.5Chain rule
26.6Derivative of trigonometric functions
26.7Derivative of exponential functions
26.8Product rule
26.9Quotient rule
26.10Implicit differentiation
26.11Derivative of inverse trigonometric functions
26.12Derivative of logarithmic functions
26.13Higher order derivatives

27Derivative Applications

27.1Position velocity acceleration
27.2Critical number & maximum and minimum values
27.3Curve sketching
27.4Optimization
27.5Related rates

28Integrals

28.1Antiderivatives
28.2Riemann sum
28.3Definite integral
28.4Fundamental theorem of calculus

29Integration Applications

29.1Areas between curves

30Normal Distribution and Z-score

30.1Introduction to normal distribution
30.2Normal distribution and continuous random variable
30.3Z-scores and random continuous variables
30.4Sampling distributions
30.5Central limit theorem
30.6Rare event rule

31Discrete Probabilities

31.1Probability distribution - histogram, mean, variance & standard deviation
31.2Binomial distribution
31.3Mean and standard deviation of binomial distribution
31.4Poisson distribution
31.5Geometric distribution
31.6Negative binomial distribution

32Confidence Intervals

32.1Point estimates
32.2Confidence levels and critical values
32.3Margin of error
32.4Making a confidence interval
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