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Math 30-1 Topics

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1. Factoring Polynomials

1.1

Factor by taking out the greatest common factor

1.2

Factor by grouping

1.3

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

1.4

Factoring trinomials of greater degree

1.5

Factoring difference of cubes

1.6

Factoring sum of cubes

2. Quadratic Functions

2.1

Introduction to quadratic functions

2.2

Transformations of quadratic functions

2.3

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

2.4

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

2.5

Completing the square

2.6

Converting from general to vertex form by completing the square

2.7

Shortcut: Vertex formula

2.8

Graphing quadratic functions: General form VS. Vertex form

2.9

Finding the quadratic functions for given parabolas

2.10

Applications of quadratic functions

3. Functions

3.1

Function notation

3.2

Operations with functions

3.3

Adding functions

3.4

Subtracting functions

3.5

Multiplying functions

3.6

Dividing functions

3.7

Composite functions

3.8

Inverse functions

3.9

One to one functions

3.10

Difference quotient: applications of functions

4. Transformations of Functions

4.1

Transformations of functions: Horizontal translations

4.2

Transformations of functions: Vertical translations

4.3

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

4.4

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

4.5

Transformations of functions: Horizontal stretches

4.6

Transformations of functions: Vertical stretches

4.7

Combining transformations of functions

5. Polynomial Functions

5.1

What is a polynomial function?

5.2

Polynomial long division

5.3

Polynomial synthetic division

5.4

Remainder theorem

5.5

5.6

Rational zero theorem

5.7

Characteristics of polynomial graphs

5.8

Multiplicities of polynomials

5.9

Imaginary zeros of polynomials

5.10

Determining the equation of a polynomial function

5.11

Applications of polynomial functions

5.12

Solving polynomial inequalities

5.13

Fundamental theorem of algebra

5.14

Descartes' rule of signs

6. Radical Functions

6.1

Basic radical functions

6.2

Transformations of radical functions

6.3

Square root of a function

6.4

Solving radical equations

7. Rational Functions

7.1

What is a rational function?

7.2

Point of discontinuity

7.3

Vertical asymptote

7.4

Horizontal asymptote

7.5

Slant asymptote

7.6

Graphs of rational functions

7.7

Solving rational equations

7.8

Solving rational inequalities

8. Exponential Functions

8.1

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

8.2

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

8.3

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

8.4

Exponents: Negative exponents

8.5

Exponents: Zero exponent: a^0 = 1

8.6

Exponents: Rational exponents

8.7

Solving exponential equations using exponent rules

8.8

Graphing exponential functions

8.9

Graphing transformations of exponential functions

8.10

Finding an exponential function given its graph

9. Logarithmic Functions

9.1

What is a logarithm?

9.2

Converting from logarithmic form to exponential form

9.3

Evaluating logarithms without a calculator

9.4

Common logarithms

9.5

Natural log: ln

9.6

Evaluating logarithms using change-of-base formula

9.7

Converting from exponential form to logarithmic form

9.8

Solving exponential equations with logarithms

9.9

Product rule of logarithms

9.10

Quotient rule of logarithms

9.11

Combining product rule and quotient rule in logarithms

9.12

Evaluating logarithms using logarithm rules

9.13

Solving logarithmic equations

9.14

Graphing logarithmic functions

9.15

Finding a logarithmic function given its graph

10. Applications of Exponential and Logarithmic Functions

10.1

Exponential growth and decay by a factor

10.2

Exponential decay: Half-life

10.3

Exponential growth and decay by percentage

10.4

Finance: Compound interest

10.5

Continuous growth and decay

10.6

Logarithmic scale: Richter scale (earthquake)

10.7

Logarithmic scale: pH scale

10.8

Logarithmic scale: dB scale

10.9

Finance: Future value and present value

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. Graphing Trigonometric Functions

12.1

Sine graph: y = sin x

12.2

Cosine graph: y = cos x

12.3

Tangent graph: y = tan x

12.4

Cotangent graph: y = cot x

12.5

Secant graph: y = sec x

12.6

Cosecant graph: y = csc x

12.7

Graphing transformations of trigonometric functions

12.8

Determining trigonometric functions given their graphs

13. Applications of Trigonometric Functions

13.1

Ferris wheel trig problems

13.2

Tides and water depth trig problems

13.3

Spring (simple harmonic motion) trig problems

14. Trigonometric Identities

14.1

Quotient identities and reciprocal identities

14.2

Pythagorean identities

14.3

Sum and difference identities

14.4

Cofunction identities

14.5

Double-angle identities

15. Solving Trigonometric Equations

15.1

Solving first degree trigonometric equations

15.2

Determining non-permissible values for trig expressions

15.3

Solving second degree trigonometric equations

15.4

Solving trigonometric equations involving multiple angles

15.5

Solving trigonometric equations using pythagorean identities

15.6

Solving trigonometric equations using sum and difference identities

15.7

Solving trigonometric equations using double-angle identities

16. Permutations and Combinations

16.1

Fundamental counting principle

16.2

Factorial notation

16.3

Path counting problems

16.4

Permutation vs. Combination

16.5

16.6

16.7

Problems involving both permutations and combinations

16.8

Pascal's triangle

16.9

Binomial theorem

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