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Mathematics III

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Mathematics III Help: Master Concepts FastHelp

ID	Standard	StudyPug Topic
CA.M3.N.CN.8	Extend polynomial identities to complex numbers	Polar form of complex numbers Introduction to imaginary numbers Complex numbers and complex planes Adding and subtracting complex numbers Complex conjugates Multiplying and dividing complex numbers Distance and midpoint of complex numbers Angle and absolute value of complex numbers Operations on complex numbers in polar form

CA.M3.N.CN.9

Know the Fundamental Theorem of Algebra

Fundamental theorem of algebra

CA.M3.A.SSE.1

Interpret expressions

Polynomial functions

Evaluating algebraic expressions

Solving literal equations

CA.M3.A.SSE.2

Use structure of expressions

Factor by taking out the greatest common factor

Factoring polynomials by grouping

Solving polynomials with unknown coefficients

Solving polynomials with unknown constant terms

Factoring polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

Solving polynomials with the unknown

Factoring polynomials: ax^2 + bx + c

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

CA.M3.A.SSE.4

Derive formula for finite geometric series

Infinite geometric series

Geometric series

CA.M3.A.APR.1

Perform operations on polynomials

Polynomial long division

Adding and subtracting polynomials

Multiplying polynomials by monomials

Solving linear equations using multiplication and division

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving linear equations with variables on both sides

Solving one - step equations: x + a = b

CA.M3.A.APR.2

Know and apply the Remainder Theorem

Remainder theorem

CA.M3.A.APR.3

Identify zeros of polynomials

Rational zero theorem

Multiplicities of polynomials

Imaginary zeros of polynomials

CA.M3.A.APR.4

Prove polynomial identities

Determining the equation of a polynomial function

CA.M3.A.APR.5

Know and apply the Binomial Theorem

Binomial theorem

Pascal's triangle

CA.M3.A.APR.6

Rewrite simple rational expressions

Simplifying rational expressions and restrictions

Polynomial synthetic division

CA.M3.A.APR.7

Understand rational expressions as a system

Partial fraction decomposition

Adding and subtracting rational expressions

Multiplying rational expressions

Dividing rational expressions

CA.M3.A.CED.1

Create equations and inequalities in one variable

Solving polynomial inequalities

Absolute value functions

Solving absolute value equations

Solving absolute value inequalities

CA.M3.A.CED.2

Create equations in two or more variables

Applications of rational equations

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Parallel and perpendicular lines in linear functions

Applications of linear relations

CA.M3.A.CED.3

Represent constraints by equations or inequalities

Applications of inequalities

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Graphing systems of linear inequalities

CA.M3.A.CED.4

Rearrange formulas

Converting from general to vertex form by completing the square

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

CA.M3.A.REI.2

Solve simple rational and radical equations

Solving rational equations

Solving radical equations

CA.M3.A.REI.11

Explain why x-coordinates of intersection points are solutions

System of linear-quadratic equations

Solving systems of linear equations by graphing

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

Solving 3 variable systems of equations by substitution

Solving 3 variable systems of equations by elimination

Word problems relating 3 variable systems of equations

Solving 3 variable systems of equations (no solution, infinite solutions)

CA.M3.F.IF.4

Interpret key features of graphs and tables

Characteristics of polynomial graphs

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

CA.M3.F.IF.5

Relate domain of a function to its graph

Point of discontinuity

CA.M3.F.IF.6

Calculate and interpret average rate of change

Difference quotient: applications of functions

Rate of change

CA.M3.F.IF.7

Graph functions

Graphs of rational functions

CA.M3.F.IF.8

Write functions in different but equivalent forms

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Operations with functions

CA.M3.F.IF.9

Compare properties of two functions

Applications of polynomial functions

Inequalities of combined functions

CA.M3.F.BF.1

Write a function that describes a relationship

Function notation (advanced)

One to one functions

CA.M3.F.BF.3

Identify effect of replacing f(x) by transformations

Transformations of quadratic functions

Combining 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

CA.M3.F.BF.4

Find inverse functions

Inverse functions

CA.M3.F.LE.4

Express solutions as logarithms

Solving exponential equations with logarithms

Solving logarithmic equations

What is a logarithm?

Evaluating logarithms without a calculator

Natural log: ln

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

CA.M3.F.LE.4.1

Prove simple laws of logarithms

Product rule of logarithms

CA.M3.F.LE.4.2

Use definition to translate between logarithms in any base

Evaluating logarithms using change-of-base formula

CA.M3.F.LE.4.3

Use properties of logarithms to simplify and identify values

Evaluating logarithms using logarithm rules

CA.M3.F.TF.1

Understand radian measure of an angle

Reference angle

Converting between degrees and radians

CA.M3.F.TF.2

Explain extension of trigonometric functions to all real numbers

Unit circle

CA.M3.F.TF.2.1

Graph all 6 basic trigonometric functions

Secant graph: y = sec x

CA.M3.F.TF.5

Choose trigonometric functions to model periodic phenomena

Determining trigonometric functions given their graphs

CA.M3.G.SRT.9

Derive A = (1/2)ab sin(C) for triangle area

Area of triangles: 1/2 a*b sin(C)

CA.M3.G.SRT.10

Prove Laws of Sines and Cosines

Law of sines

Law of cosines

CA.M3.G.SRT.11

Apply Laws of Sines and Cosines

Applications of the sine law and cosine law

CA.M3.G.GPE.3.1

Put conic equations into standard form

CA.M3.G.GMD.4

Identify shapes of cross-sections

Surface area of 3-dimensional shapes

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface area of cylinders

CA.M3.G.MG.1

Use geometric shapes to describe objects

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

CA.M3.S.ID.4

Use normal distribution to estimate population percentages

Introduction to normal distribution

Normal distribution and continuous random variable

Z-scores and random continuous variables

CA.M3.S.IC.1

Understand statistics as a process for making inferences

Point estimates

CA.M3.S.IC.2

Decide if a model is consistent with results

Confidence levels and critical values

CA.M3.S.IC.3

Recognize differences among statistical studies

Margin of error

CA.M3.S.IC.4

Use sample data to estimate population parameters

Making a confidence interval

CA.M3.S.IC.5

Use data to compare two treatments

Confidence intervals to estimate population mean

CA.M3.S.IC.6

Evaluate reports based on data

Student's t-distribution

CA.M3.S.MD.6

Use probabilities to make fair decisions

Probability of independent events

Addition rule for

Multiplication rule for

Conditional probability

Probability involving permutations and combinations

CA.M3.S.MD.7

Analyze decisions using probability concepts

Comparing experimental and theoretical probability

Probability distribution - histogram, mean, variance & standard deviation

Binomial distribution

Mean and standard deviation of binomial distribution

Complete California Mathematics III Coverage

Mathematics III Lessons

155

Video Explanations

884

Practice Problems

1601

California Standards

100% Aligned

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Complete Math III curriculum with video lessons on polynomials, complex numbers, trigonometry, logarithms, statistics, and probability. Includes practice problems, step-by-step solutions, and progress tracking for every topic.

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