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Math III

Math III

Polynomial and rational expressions, advanced functions, trigonometry, geometric modeling, and statistical inference.

55 objectives
Objective 193 A-APR.1

Add, subtract, and multiply polynomials beyond quadratic cases.

Objective 194 A-APR.2

Apply the Remainder Theorem to connect p(a), remainders, and factors x-a.

Objective 195 A-APR.3

Identify zeros from factorizations and use them to sketch polynomial graphs.

Objective 196 A-APR.4

Prove polynomial identities and use them to solve or describe numerical relationships.

Objective 197 A-APR.5

Apply the Binomial Theorem for expanding (x+y)^n using Pascal's Triangle or combinatorial reasoning.

Objective 198 A-APR.6

Rewrite rational expressions using inspection, polynomial division, or technology.

Objective 199 A-APR.7

Add, subtract, multiply, and divide rational expressions as a closed system like rational numbers.

Objective 200 A-CED.1

Create and solve one-variable equations and inequalities from contexts using all studied expression types, including simple root functions.

Objective 201 A-CED.2

Create equations in two or more variables, graph them, and interpret relationships with labels and scales.

Objective 202 A-CED.3

Represent constraints and systems, then interpret viable and non-viable solutions in modeling contexts.

Objective 203 A-CED.4

Rearrange formulas to highlight a chosen quantity across the expression types studied.

Objective 204 A-REI.11

Solve f(x)=g(x) approximately using intersections of polynomial, rational, radical, absolute-value, exponential, and logarithmic graphs.

Objective 205 A-REI.2

Solve simple rational and radical equations and identify extraneous solutions.

Objective 206 A-SSE.1.a

Interpret terms, factors, and coefficients in polynomial and rational expressions.

Objective 207 A-SSE.1.b

Interpret complex polynomial/rational expressions by treating parts as single units.

Objective 208 A-SSE.2

Use expression structure to find useful rewrites.

Objective 209 A-SSE.4

Derive and use the finite geometric series formula to solve problems such as mortgage-payment models.

Objective 210 F-BF.1.b

Combine studied function types arithmetically to build models.

Objective 211 F-BF.3

Analyze graph transformations across radical, rational, exponential, logarithmic, and other functions; recognize even and odd functions.

Objective 212 F-BF.4.a

Find inverse functions for simple invertible functions, including rational examples.

Objective 213 F-IF.4

Interpret key features of rational, square-root, cube-root, and other function models in context.

Objective 214 F-IF.5

Relate a function's domain to its equation, graph, and context, especially when model choice matters.

Objective 215 F-IF.6

Calculate, estimate, and interpret average rate of change for advanced function types.

Objective 216 F-IF.7.b

Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions.

Objective 217 F-IF.7.c

Graph polynomial functions using zeros, factorizations, and end behavior.

Objective 218 F-IF.7.e

Graph exponential, logarithmic, and trigonometric functions with key features.

Objective 219 F-IF.8

Rewrite functions in equivalent forms to reveal and explain useful properties.

Objective 220 F-IF.9

Compare functions represented algebraically, graphically, numerically, or verbally.

Objective 221 F-LE.4

Use logarithms to solve exponential equations of the form ab^(ct)=d and evaluate with technology.

Objective 222 F-LE.4.1

Prove simple logarithm laws.

Objective 223 F-LE.4.2

Use the definition of logarithms to translate among logarithms in any base.

Objective 224 F-LE.4.3

Use logarithm properties to simplify numeric logarithmic expressions and estimate values.

Objective 225 F-TF.1

Understand radian measure as arc length on the unit circle.

Objective 226 F-TF.2

Use the unit circle to extend trig functions to all real-number radian measures.

Objective 227 F-TF.2.1

Graph all six basic trigonometric functions.

Objective 228 F-TF.5

Choose trig functions to model periodic phenomena using amplitude, frequency, and midline.

Objective 229 G-GMD.4

Identify cross-sections of 3D objects and solids generated by rotating 2D objects.

Objective 230 G-GPE.3.1

Complete the square for general quadratic conic equations; identify and graph circles, ellipses, parabolas, or hyperbolas.

Objective 231 G-MG.1

Use geometric shapes, measurements, and properties to describe real-world objects.

Objective 232 G-MG.2

Apply density concepts based on area and volume in modeling situations.

Objective 233 G-MG.3

Use geometric methods to solve design problems under constraints such as cost, space, or ratios.

Objective 234 G-SRT.10

Prove the Laws of Sines and Cosines and use them to solve problems.

Objective 235 G-SRT.11

Apply the Laws of Sines and Cosines to find unknown measurements in right and non-right triangles.

Objective 236 G-SRT.9

Derive the triangle area formula A=1/2ab sin(C) using an auxiliary altitude.

Objective 237 N-CN.8

Extend polynomial identities to complex numbers for higher-degree polynomial work.

Objective 238 N-CN.9

Know the Fundamental Theorem of Algebra and connect it to polynomial roots.

Objective 239 S-IC.1

Understand statistics as inference about population parameters from random samples.

Objective 240 S-IC.2

Use simulation to decide whether data are consistent with a proposed model.

Objective 241 S-IC.3

Distinguish sample surveys, experiments, and observational studies; explain randomization in each.

Objective 242 S-IC.4

Use sample data to estimate population means/proportions and develop margins of error using simulation.

Objective 243 S-IC.5

Use randomized-experiment data and simulations to compare treatments and judge significance.

Objective 244 S-IC.6

Evaluate reports based on data.

Objective 245 S-ID.4

Use mean and standard deviation to fit normal distributions and estimate population percentages with technology.

Objective 246 S-MD.6

Use probabilities to make fair decisions in more complex settings.

Objective 247 S-MD.7

Analyze decisions and strategies using probability concepts in more complex settings.