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