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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 = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

3.2

Midpoint formula:

M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)

3.3

Gradient equation:

m = \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 - y_1 = m (x - x_1)

3.7

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

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

12.2

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

18.6

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

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

25.7

Arithmetic mean vs. Geometric mean

26. Limits and Derivatives

26.1

Finding limits from graphs

26.2

Definition of derivative

26.3

26.4

Slope and equation of tangent line

26.5

26.6

Derivative of trigonometric functions

26.7

Derivative of exponential functions

26.8

26.9

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

27.5

28. Integrals

28.1

Antiderivatives

28.2

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

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