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Maths Methods Topics

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1. Solving Linear Equations

1.1 Solving linear equations using multiplication and division
1.2 Solving two-step linear equations: ax + b = c, x/a + b = c
1.3 Solving linear equations using distributive property: a(x + b) = c
1.4 Solving linear equations with variables on both sides
1.5 Solving literal equations

2. Introduction to Relations and Functions

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

3. Linear Functions

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

4. Linear Equations

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

5. Quadratic Functions

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

6. Solving Quadratic Equations

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

7. Functions

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

8. Transformations of Functions

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

9. Factorisation

9.1 Factorise by taking out the greatest common factor
9.2 Factorise by grouping
9.3 Factorising difference of squares: x^2 - y^2
9.4 Factorising trinomials
9.5 Factoring difference of cubes
9.6 Factoring sum of cubes

10. Conics

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

11. Trigonometric Ratios and Angle Measure

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

12. Sine Rule and Cosine Rule

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

13. Bearings

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

14. Graphing Trigonometric Functions

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

15. Applications of Trigonometric Functions

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

16. Trigonometric Identities

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

17. Solving Trigonometric Equations

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

18. Permutations and Combinations

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

19. Probability

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

20. Indices

20.1 Indices: Product rule (a^x)(a^y) = a^(x+y)
20.2 Indices: Division rule (a^x / a^y) = a^(x-y)
20.3 Indices: Power rule (a^x)^y = a^(x * y)
20.4 Indices: Negative exponents
20.5 Indices: Zero exponent: a^0 = 1
20.6 Indices: Rational exponents
20.7 Combining laws of indices
20.8 Scientific notation
20.9 Convert between radicals and rational exponents
20.10 Solving for indices

21. Exponential Functions

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

22. Applications of Exponential Functions

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

23. Logarithmic Functions

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

24. Applications of Logarithmic Functions

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

25. Sequences and Series

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

26. Limits and Derivatives

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

27. Derivative Applications

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

28. Integrals

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

29. Integration Applications

29.1 Areas between curves

30. Normal Distribution and Z-score

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

31. Discrete Probabilities

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

32. Confidence Intervals

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

32 Chapters · 214 Topics · 1317 Videos

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