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Year 12 Maths Topics

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1. Linear Equations

1.1

Introduction to linear equations

1.2

Introduction to nonlinear equations

1.3

Special case of linear equations: Horizontal lines

1.4

Special case of linear equations: Vertical lines

1.5

Parallel line equation

1.6

Perpendicular line equation

1.7

Combination of both parallel and perpendicular line equations

1.8

Applications of linear equations

2. Linear Inequalities

2.1

Express linear inequalities graphically and algebraically

2.2

Solving one-step linear inequalities

2.3

Solving multi-step linear inequalities

2.4

Compound inequalities

3. Inequalities in Two Variables

3.1

Graphing linear inequalities in two variables

3.2

Graphing simultaneous linear inequalities

3.3

Graphing quadratic inequalities in two variables

3.4

Graphing simultaneous quadratic inequalities

3.5

Applications of inequalities

3.6

What is linear programming?

3.7

Linear programming word problems

4. Introduction to Relations and Functions

4.1

Relationship between two variables

4.2

Understand relations between x- and y-intercepts

4.3

Domain and range of a function

4.4

Identifying functions

4.5

Function notation

5. Linear Functions

5.1

Distance formula:

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

5.2

Midpoint formula:

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

5.3

Gradient equation:

m = \frac{y_2-y_1}{x_2- x_1}

5.4

Gradient intercept form: y = mx + b

5.5

General form: Ax + By + C = 0

5.6

Gradient-point form:

y - y_1 = m (x - x_1)

5.7

5.8

Graphing linear functions using table of values

5.9

Graphing linear functions using x- and y-intercepts

5.10

Graphing from gradient-intercept form y=mx+b

5.11

Graphing linear functions using a single point and gradient

5.12

Word problems of graphing linear functions

5.13

Parallel and perpendicular lines in linear functions

5.14

Applications of linear relations

6. Absolute Value Functions

6.1

Absolute value functions

6.2

Solving absolute value equations

6.3

Solving absolute value inequalities

7. Solving Simultaneous Equations

7.1

Determining number of solutions to linear equations

7.2

Solving simultaneous equations by graphing

7.3

Solving simultaneous equations by elimination

7.4

Solving simultaneous equations by substitution

7.5

Money related questions in linear equations

7.6

Unknown number related questions in linear equations

7.7

Distance and time related questions in linear equations

7.8

Rectangular shape related questions in linear equations

7.9

Simultaneous linear-quadratic equations

8. Factorising Polynomial Expressions

8.1

Common factors of polynomials

8.2

Factorising polynomials by grouping

8.3

Solving polynomials with the unknown "b" from x^2 + bx + c

8.4

Solving polynomials with the unknown "c" from x^2 + bx + c

8.5

Factorising polynomials: x^2 + bx + c

8.6

Applications of polynomials: x^2 + bx + c

8.7

Solving polynomials with the unknown "b" from

ax^2 + bx + c

8.8

Factorising polynomials:

ax^2 + bx + c

8.9

Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

8.10

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

8.11

Evaluating polynomials

8.12

Using algebra tiles to factorise polynomials

8.13

Solving polynomial equations

8.14

Word problems of polynomials

9. Quadratic Functions

9.1

Characteristics of quadratic functions

9.2

Transformations of quadratic functions

9.3

Quadratic function in general form: y = ax^2 + bx + c

9.4

Quadratic function in vertex form: y = a(x-p)^2 + q

9.5

Completing the square

9.6

Converting from general to vertex form by completing the square

9.7

Shortcut: Vertex formula

9.8

Graphing parabolas for given quadratic functions

9.9

Finding the quadratic functions for given parabolas

9.10

Applications of quadratic functions

10. Quadratic Equations and Inequalities

10.1

Solving quadratic equations by factoring

10.2

Solving quadratic equations by completing the square

10.3

Using quadratic formula to solve quadratic equations

10.4

Nature of roots of quadratic equations: The discriminant

10.5

Applications of quadratic equations

10.6

Solving quadratic inequalities

11. Polynomial Functions

11.1

What is a polynomial function?

11.2

Polynomial long division

11.3

Polynomial synthetic division

11.4

Remainder theorem

11.5

11.6

Rational zero theorem

11.7

Characteristics of polynomial graphs

11.8

Multiplicities of polynomials

11.9

Imaginary zeros of polynomials

11.10

Determining the equation of a polynomial function

11.11

Applications of polynomial functions

11.12

Solving polynomial inequalities

11.13

Solving polynomial equations by iteration

11.14

Fundamental theorem of algebra

11.15

Descartes' rule of signs

12. Surds

12.1

Operations with surds

12.2

Conversion between entire radicals and mixed surds

12.3

Adding and subtracting surds

12.4

Multiplying surds

12.5

Solving surd equations

13. Laws of indices

13.1

Product rule of exponents

13.2

Quotient rule of exponents

13.3

Power of a product rule

13.4

Power of a quotient rule

13.5

Power of a power rule

13.6

Negative exponent rule

13.7

Combining the exponent rules

13.8

13.9

Convert between radicals and rational exponents

13.10

Solving for exponents

14. Algebraic Fractions

14.1

Simplifying algebraic fractions and restrictions

14.2

Adding and subtracting algebraic fractions

14.3

Multiplying algebraic fractions

14.4

Dividing algebraic fractions

14.5

Solving equations with algebraic fractions

14.6

Applications of equations with algebraic fractions

14.7

Simplifying complex fractions

14.8

Partial fraction decomposition

15. Functions

15.1

Function notation

15.2

Operations with functions

15.3

Adding functions

15.4

Subtracting functions

15.5

Multiplying functions

15.6

Dividing functions

15.7

Composite functions

15.8

Inequalities of combined functions

15.9

Inverse functions

15.10

One to one functions

15.11

Difference quotient: applications of functions

16. Transformations of Functions

16.1

Transformations of functions: Horizontal translations

16.2

Transformations of functions: Vertical translations

16.3

Reflection across the y-axis: y = f(-x)

16.4

Reflection across the x-axis: y = -f(x)

16.5

Transformations of functions: Horizontal stretches

16.6

Transformations of functions: Vertical stretches

16.7

Combining transformations of functions

16.8

Even and odd functions

17. Reciprocal functions

17.1

Graphing reciprocals of linear functions

17.2

Graphing reciprocals of quadratic functions

18. Exponential Functions

18.1

Exponents: Product rule (a^x)(a^y) = a^(x+y)

18.2

Exponents: Division rule (a^x / a^y) = a^(x-y)

18.3

Exponents: Power rule (a^x)^y = a^(x * y)

18.4

Exponents: Negative exponents

18.5

Exponents: Zero exponent: a^0 = 1

18.6

Exponents: Rational exponents

18.7

Solving exponential equations using exponent rules

18.8

Graphing exponential functions

18.9

Graphing transformations of exponential functions

18.10

Finding an exponential function given its graph

19. Logarithmic Functions

19.1

What is a logarithm?

19.2

Converting from logarithmic form to exponential form

19.3

Evaluating logarithms without a calculator

19.4

Common logarithms

19.5

Natural log: ln

19.6

Evaluating logarithms using change-of-base formula

19.7

Converting from exponential form to logarithmic form

19.8

Solving exponential equations with logarithms

19.9

Product rule of logarithms

19.10

Quotient rule of logarithms

19.11

Combining product rule and quotient rule in logarithms

19.12

Evaluating logarithms using logarithm rules

19.13

Solving logarithmic equations

19.14

Graphing logarithmic functions

19.15

Finding a logarithmic function given its graph

20. Applications of Exponential and Logarithmic Functions

20.1

Exponential growth and decay by a factor

20.2

Exponential decay: Half-life

20.3

Exponential growth and decay by percentage

20.4

Finance: Compound interest

20.5

Continuous growth and decay

20.6

Logarithmic scale: Richter scale (earthquake)

20.7

Logarithmic scale: pH scale

20.8

Logarithmic scale: dB scale

20.9

Finance: Future value and present value

21. Circles and Parabolas

21.1

Angles in a circle

21.2

Chord properties

21.3

Tangent properties

21.4

Circles and circumference

21.5

Arcs of a circle

21.6

Areas and sectors of circles

21.7

Inscribed quadrilaterlas in circles

21.8

Central and inscribed angles in circles

21.9

Circles in coordinate plane

21.10

22. Introduction to Trigonometry

22.1

Use sine ratio to calculate angles and side (Sin =

\frac{o}{h}

22.2

Use cosine ratio to calculate angles and side (Cos =

\frac{a}{h}

22.3

Use tangent ratio to calculate angles and side (Tan =

\frac{o}{a}

22.4

Combination of SohCahToa questions

22.5

Solving expressions using 45-45-90 special right triangles

22.6

Solving expressions using 30-60-90 special right triangles

22.7

Word problems relating ladder in trigonometry

22.8

Word problems relating guy wire in trigonometry

22.9

Other word problems relating angles in trigonometry

23. Trigonometry

23.1

Angle in standard position

23.2

Coterminal angles

23.3

Reference angle

23.4

Find the exact value of trigonometric ratios

23.5

ASTC rule in trigonometry (All Students Take Calculus)

23.6

23.7

Converting between degrees and radians

23.8

Trigonometric ratios of angles in radians

23.9

Radian measure and arc length

24. Sine Rule and Cosine Rule

24.1

24.2

24.3

Applications of the sine rule and cosine rule

25. Bearings

25.1

Introduction to bearings

25.2

Bearings and direction word problems

25.3

Angle of elevation and depression

26. Graphing Trigonometric Functions

26.1

Sine graph: y = sin x

26.2

Cosine graph: y = cos x

26.3

Tangent graph: y = tan x

26.4

Cotangent graph: y = cot x

26.5

Secant graph: y = sec x

26.6

Cosecant graph: y = csc x

26.7

Graphing transformations of trigonometric functions

26.8

Determining trigonometric functions given their graphs

27. Trigonometric Identities

27.1

Quotient identities and reciprocal identities

27.2

Pythagorean identities

27.3

Sum and difference identities

27.4

Cofunction identities

27.5

Double-angle identities

28. Sequences and Series

28.1

Arithmetic sequences

28.2

Arithmetic series

28.3

Geometric sequences

28.4

Geometric series

28.5

Infinite geometric series

28.6

28.7

Arithmetic mean vs. Geometric mean

29. Set Theory

29.1

29.2

Set builder notation

29.3

Intersection and union of 2 sets

29.4

Intersection and union of 3 sets

30. Probability

30.1

Determining probabilities using tree diagrams and tables

30.2

Probability of independent events

30.3

Finding probabilities using two-way frequency tables

30.4

Probability with Venn diagrams

31. Permutations and Combinations

31.1

Fundamental counting principle

31.2

Factorial notation

31.3

Path counting problems

31.4

Permutation vs. Combination

31.5

31.6

31.7

Problems involving both permutations and combinations

31.8

Pascal's triangle

31.9

Binomial theorem

32. Statistics

32.1

Median and mode

32.2

32.3

Range and outliers

32.4

Application of averages

32.5

Influencing factors in data collection

32.6

Data collection

33. Data and Graphs

33.1

Reading and drawing bar graphs

33.2

Reading and drawing histograms

33.3

Reading and drawing line graphs

33.4

Box-and-whisker plots and scatter plots

33.5

Stem-and-leaf plots

33.6

Reading and drawing Venn diagrams

34. Parametric Equations and Polar Coordinates

34.1

Defining curves with parametric equations

34.2

Polar coordinates

35. Limits

35.1

Finding limits from graphs

35.2

35.3

Finding limits algebraically - direct substitution

35.4

Finding limits algebraically - when direct substitution is not possible

35.5

Infinite limits - vertical asymptotes

35.6

Limits at infinity - horizontal asymptotes

35.7

Intermediate value theorem

35.8

Squeeze theorem

36. Differentiation

36.1

Definition of derivative

36.2

36.3

Slope and equation of tangent line

36.4

36.5

Derivative of trigonometric functions

36.6

Derivative of exponential functions

36.7

36.8

36.9

Implicit differentiation

36.10

Derivative of inverse trigonometric functions

36.11

Derivative of logarithmic functions

36.12

Higher order derivatives

36.13

Critical number & maximum and minimum values

37. Integration

37.1

Antiderivatives

37.2

37.3

Definite integral

37.4

Fundamental theorem of calculus

38. Integration Applications

38.1

Areas between curves

38.2

Volumes of solids with known cross-sections

38.3

Volumes of solids of revolution - Disc method

38.4

Volumes of solids of revolution - Shell method

38.5

Average value of a function

38.6

38Chapters

289Topics

1841Videos

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