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Complete Math 30-1 Help

Get better in Math 30-1 with step-by-step walkthroughs, practice, exam tips, and more!

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Math 30-1 Topics

Factoring Polynomials

Factor by taking out the greatest common factor

Factor by grouping

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

Factoring trinomials of greater degree

Factoring difference of cubes

Factoring sum of cubes

Quadratic Functions

Introduction to quadratic functions

Transformations of quadratic functions

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

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

Completing the square

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Functions

Function notation

Operations with functions

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Composite functions

Inverse functions

One to one functions

Difference quotient: applications of functions

Transformations of Functions

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

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

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

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

Combining transformations of functions

Polynomial Functions

What is a polynomial function?

Polynomial long division

Polynomial synthetic division

Remainder theorem

Factor theorem

Rational zero theorem

Characteristics of polynomial graphs

Multiplicities of polynomials

Imaginary zeros of polynomials

Determining the equation of a polynomial function

Applications of polynomial functions

Solving polynomial inequalities

Fundamental theorem of algebra

Descartes' rule of signs

Radical Functions

Basic radical functions

Transformations of radical functions

Square root of a function

Solving radical equations

Rational Functions

What is a rational function?

Point of discontinuity

Vertical asymptote

Horizontal asymptote

Slant asymptote

Graphs of rational functions

Solving rational equations

Solving rational inequalities

Exponential Functions

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

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

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

Exponents: Negative exponents

Exponents: Zero exponent: a^0 = 1

Exponents: Rational exponents

Solving exponential equations using exponent rules

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

Logarithmic Functions

What is a logarithm?

Converting from logarithmic form to exponential form

Evaluating logarithms without a calculator

Common logarithms

Natural log: ln

Evaluating logarithms using change-of-base formula

Converting from exponential form to logarithmic form

Solving exponential equations with logarithms

Product rule of logarithms

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

Evaluating logarithms using logarithm rules

Solving logarithmic equations

Graphing logarithmic functions

Finding a logarithmic function given its graph

Applications of Exponential and Logarithmic Functions

Exponential growth and decay by a factor

Exponential decay: Half-life

Exponential growth and decay by percentage

Finance: Compound interest

Continuous growth and decay

Logarithmic scale: Richter scale (earthquake)

Logarithmic scale: pH scale

Logarithmic scale: dB scale

Finance: Future value and present value

Trigonometric Ratios and Angle Measure

Angle in standard position

Coterminal angles

Reference angle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

Unit circle

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

Graphing Trigonometric Functions

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

Cotangent graph: y = cot x

Secant graph: y = sec x

Cosecant graph: y = csc x

Graphing transformations of trigonometric functions

Determining trigonometric functions given their graphs

Applications of Trigonometric Functions

Ferris wheel trig problems

Tides and water depth trig problems

Spring (simple harmonic motion) trig problems

Trigonometric Identities

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Cofunction identities

Double-angle identities

Solving Trigonometric Equations

Solving first degree trigonometric equations

Determining non-permissible values for trig expressions

Solving second degree trigonometric equations

Solving trigonometric equations involving multiple angles

Solving trigonometric equations using pythagorean identities

Solving trigonometric equations using sum and difference identities

Solving trigonometric equations using double-angle identities

Permutations and Combinations

Fundamental counting principle

Factorial notation

Path counting problems

Permutation vs. Combination

Permutations

Combinations

Problems involving both permutations and combinations

Pascal's triangle

Binomial theorem

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