CaliforniaCalifornia Mathematics III Curriculum
Video lessons and practice for every Mathematics III topic. Aligned to California Common Core State Standards for high school math. Get help anytime.
California Mathematics III Curriculum | StudyPugHelp
ID | Standard | StudyPug Topic |
|---|---|---|
CA.M3.N.CN.8 | Extend polynomial identities to complex numbers |
CA.M3.N.CN.9 | Know the Fundamental Theorem of Algebra |
CA.M3.A.SSE.1 | Interpret expressions |
CA.M3.A.SSE.2 | Use structure of expressions |
CA.M3.A.SSE.4 | Derive formula for finite geometric series |
CA.M3.A.APR.1 | Perform operations on polynomials |
CA.M3.A.APR.2 | Know and apply the Remainder Theorem |
CA.M3.A.APR.3 | Identify zeros of polynomials |
CA.M3.A.APR.4 | Prove polynomial identities |
CA.M3.A.APR.5 | Know and apply the Binomial Theorem |
CA.M3.A.APR.6 | Rewrite simple rational expressions |
CA.M3.A.APR.7 | Understand rational expressions as a system |
CA.M3.A.CED.1 | Create equations and inequalities in one variable |
CA.M3.A.CED.2 | Create equations in two or more variables |
CA.M3.A.CED.3 | Represent constraints by equations or inequalities |
CA.M3.A.CED.4 | Rearrange formulas |
CA.M3.A.REI.2 | Solve simple rational and radical equations |
CA.M3.A.REI.11 | Explain why x-coordinates of intersection points are solutions |
CA.M3.F.IF.4 | Interpret key features of graphs and tables |
CA.M3.F.IF.5 | Relate domain of a function to its graph |
CA.M3.F.IF.6 | Calculate and interpret average rate of change |
CA.M3.F.IF.7 | Graph functions |
CA.M3.F.IF.8 | Write functions in different but equivalent forms |
CA.M3.F.IF.9 | Compare properties of two functions |
CA.M3.F.BF.1 | Write a function that describes a relationship |
CA.M3.F.BF.3 | Identify effect of replacing f(x) by transformations |
CA.M3.F.BF.4 | Find inverse functions |
CA.M3.F.LE.4 | Express solutions as logarithms |
CA.M3.F.LE.4.1 | Prove simple laws of logarithms |
CA.M3.F.LE.4.2 | Use definition to translate between logarithms in any base |
CA.M3.F.LE.4.3 | Use properties of logarithms to simplify and identify values |
CA.M3.F.TF.1 | Understand radian measure of an angle |
CA.M3.F.TF.2 | Explain extension of trigonometric functions to all real numbers |
CA.M3.F.TF.2.1 | Graph all 6 basic trigonometric functions |
CA.M3.F.TF.5 | Choose trigonometric functions to model periodic phenomena |
CA.M3.G.SRT.9 | Derive A = (1/2)ab sin(C) for triangle area |
CA.M3.G.SRT.10 | Prove Laws of Sines and Cosines |
CA.M3.G.SRT.11 | Apply Laws of Sines and Cosines |
CA.M3.G.GPE.3.1 | Put conic equations into standard form |
CA.M3.G.GMD.4 | Identify shapes of cross-sections |
CA.M3.G.MG.1 | Use geometric shapes to describe objects |
CA.M3.S.ID.4 | Use normal distribution to estimate population percentages |
CA.M3.S.IC.1 | Understand statistics as a process for making inferences |
CA.M3.S.IC.2 | Decide if a model is consistent with results |
CA.M3.S.IC.3 | Recognize differences among statistical studies |
CA.M3.S.IC.4 | Use sample data to estimate population parameters |
CA.M3.S.IC.5 | Use data to compare two treatments |
CA.M3.S.IC.6 | Evaluate reports based on data |
CA.M3.S.MD.6 | Use probabilities to make fair decisions |
CA.M3.S.MD.7 | Analyze decisions using probability concepts |
Mathematics III Topics for California High School Students
Mathematics III is the third course in California's high school math sequence. It brings together advanced algebra, functions, geometry, and statistics into one rigorous course. StudyPug covers every topic aligned to California Common Core State Standards so students always know they are studying the right material.
Algebra and Functions in Mathematics III
Students extend their algebra skills to include complex numbers, the Fundamental Theorem of Algebra, and polynomial identities. The course also covers the Binomial Theorem, rational expressions, and creating equations with one or more variables. Function topics include graphing, transformations, inverse functions, and average rate of change.
- Extend polynomial identities to complex numbers
- Know and apply the Remainder Theorem
- Identify zeros of polynomials and their graphs
- Rewrite simple rational expressions
- Find inverse functions and express solutions as logarithms
Logarithms and Exponential Functions
Mathematics III introduces the laws of logarithms, radian measure, and how to translate between logarithms in any base. Students use properties of logarithms to simplify expressions and solve equations, building the foundation needed for calculus.
Trigonometry in Mathematics III
Students graph all six basic trigonometric functions, choose trig functions to model periodic phenomena, and prove the Laws of Sines and Cosines. They also derive the formula for triangle area using A = (1/2)ab sin(C) and apply these laws to real-world problems.
- Understand radian measure of an angle
- Graph all 6 basic trigonometric functions
- Prove and apply the Laws of Sines and Cosines
- Choose trigonometric functions to model periodic phenomena
Geometry: Conic Sections and Modeling
The geometry strand covers putting conic equations into standard form, identifying cross-sections of three-dimensional figures, and applying geometric methods to solve design problems. Students also apply concepts of density in real-world modeling contexts.
Statistics and Probability
Mathematics III covers the normal distribution, statistical inference, comparing two treatments using data, and evaluating reports based on data. Probability topics include using probabilities to make fair decisions and analyzing decisions using probability concepts.
- Use normal distribution to estimate population percentages
- Recognize differences among observational studies, experiments, and surveys
- Use sample data to estimate population parameters
- Use probabilities to make fair decisions
- Analyze decisions using probability concepts
California Assessment: CAASPP and Smarter Balanced
California measures high school math achievement through the CAASPP/Smarter Balanced assessment administered in Grade 11. Mathematics III content directly prepares students for this test. StudyPug's practice problems and video lessons help students build the skills and confidence they need before test day.