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Year 12 Maths 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. 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. 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 gradient-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. Factorising

4.1

Factorise by taking out the greatest common factor

4.2

Factorise by grouping

4.3

Factorising difference of squares: x^2 - y^2

4.4

Factorising trinomials:

ax^2 + bx + c

5. Quadratic Functions

5.1

Characteristics of 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 parabolas for given quadratic functions

5.9

Finding the quadratic functions for given parabolas

5.10

Applications of quadratic functions

6. Quadratic Equations and Inequalities

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

6.6

Solving quadratic 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

8. Simultaneous Equations (Advanced)

8.1

Simultaneous linear equations

8.2

Simultaneous linear-quadratic equations

8.3

Simultaneous quadratic-quadratic equations

8.4

Solving 3 variable simultaneous equations by substitution

8.5

Solving 3 variable simultaneous equations by elimination

8.6

Solving 3 variable simultaneous equations with no or infinite solutions

8.7

Word problems relating 3 variable simultaneous equations

9. Inequalities in two variables (Advanced)

9.1

Graphing linear inequalities in two variables

9.2

Graphing simultaneous linear inequalities

9.3

Graphing quadratic inequalities in two variables

9.4

Graphing simultaneous quadratic inequalities

9.5

Applications of inequalities

9.6

What is linear programming?

9.7

Linear programming word problems

10. Imaginary and Complex Numbers

10.1

Introduction to imaginary numbers

10.2

Complex numbers and complex planes

10.3

Adding and subtracting complex numbers

10.4

Complex conjugates

10.5

Multiplying and dividing complex numbers

10.6

Distance and midpoint of complex numbers

10.7

Angle and absolute value of complex numbers

10.8

Polar form of complex numbers

10.9

Operations on complex numbers in polar form

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

Fundamental theorem of algebra

11.14

Descartes' rule of signs

12. Radicals

12.1

Operations with radicals

12.2

Conversion between entire radicals and mixed radicals

12.3

Adding and subtracting radicals

12.4

Multiplying radicals

12.5

Solving radical equations

13. Exponents

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

Scientific notation

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. Reciprocal Functions

15.1

Graphing reciprocals of linear functions

15.2

Graphing reciprocals of quadratic functions

16. Rational Functions

16.1

What is a rational function?

16.2

Point of discontinuity

16.3

Vertical asymptote

16.4

Horizontal asymptote

16.5

Slant asymptote

16.6

Graphs of rational functions

16.7

Solving rational inequalities

17. Operations of Functions

17.1

Function notation

17.2

Operations with functions

17.3

Adding functions

17.4

Subtracting functions

17.5

Multiplying functions

17.6

Dividing functions

17.7

Composite functions

17.8

Inequalities of combined functions

17.9

Inverse functions

17.10

One to one functions

17.11

Difference quotient: applications of functions

18. Transformations of Functions

18.1

Transformations of functions: Horizontal translations

18.2

Transformations of functions: Vertical translations

18.3

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

18.4

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

18.5

Transformations of functions: Horizontal stretches

18.6

Transformations of functions: Vertical stretches

18.7

Combining transformations of functions

18.8

Even and odd functions

19. Exponential Functions

19.1

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

19.2

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

19.3

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

19.4

Exponents: Negative exponents

19.5

Exponents: Zero exponent: a^0 = 1

19.6

Exponents: Rational exponents

19.7

Graphing exponential functions

19.8

Graphing transformations of exponential functions

19.9

Finding an exponential function given its graph

20. Logarithmic Functions

20.1

What is a logarithm?

20.2

Converting from logarithmic form to exponential form

20.3

Evaluating logarithms without a calculator

20.4

Common logarithms

20.5

Natural log: ln

20.6

Evaluating logarithms using change-of-base formula

20.7

Converting from exponential form to logarithmic form

20.8

Solving exponential equations with logarithms

20.9

Product rule of logarithms

20.10

Quotient rule of logarithms

20.11

Combining product rule and quotient rule in logarithms

20.12

Evaluating logarithms using logarithm rules

20.13

Solving logarithmic equations

20.14

Graphing logarithmic functions

20.15

Finding a logarithmic function given its graph

21. Applications of Exponential and Logarithmic Functions

21.1

Exponential growth and decay by a factor

21.2

Exponential decay: Half-life

21.3

Exponential growth and decay by percentage

21.4

Finance: Compound interest

21.5

Continuous growth and decay

21.6

Logarithmic scale: Richter scale (earthquake)

21.7

Logarithmic scale: pH scale

21.8

Logarithmic scale: dB scale

21.9

Finance: Future value and present value

22. Introduction to Trigonometry

22.1

Use sine ratio to calculate angles and sides (Sin =

\frac{o}{h}

22.2

Use cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

22.3

Use tangent ratio to calculate angles and sides (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. Trigonometric Ratios and Angle Measure

23.1

23.2

Coterminal angles

23.3

Reference angles

23.4

Find the exact value of trigonometric ratios

23.5

ASTC rule in trigonometry (All Students Take Calculus)

23.6

23.7

23.8

23.9

Applications of the sine law and cosine law

24. Bearings

24.1

Introduction to bearings

24.2

Bearings and direction word problems

24.3

Angle of elevation and depression

25. Graphing Trigonometric Functions

25.1

Sine graph: y = sin x

25.2

Cosine graph: y = cos x

25.3

Tangent graph: y = tan x

25.4

Cotangent graph: y = cot x

25.5

Secant graph: y = sec x

25.6

Cosecant graph: y = csc x

25.7

Graphing transformations of trigonometric functions

25.8

Determining trigonometric functions given their graphs

26. Trigonometric Identities

26.1

Quotient identities and reciprocal identities

26.2

Pythagorean identities

26.3

Sum and difference identities

26.4

Cofunction identities

26.5

Double-angle identities

27. Conics

27.1

Conics - Parabola

27.2

Conics - Ellipse

27.3

Conics - Circle

27.4

Conics - Hyperbola

28. Surface Area and Volume

28.1

Surface area and volume of prisms

28.2

Surface area and volume of pyramids

28.3

Surface area and volume of cylinders

28.4

Surface area and volume of cones

28.5

Surface area and volume of spheres

29. Sequences and Series

29.1

Arithmetic sequences

29.2

Arithmetic series

29.3

Geometric sequences

29.4

Geometric series

29.5

Infinite geometric series

29.6

29.7

Arithmetic mean vs. Geometric mean

30. Probability

30.1

Determining probabilities using tree diagrams and tables

30.2

Probability of independent events

30.3

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

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

33.7

Frequency tables and dot plots

33Chapters

245Topics

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