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Math II

Math II

Real and complex numbers, polynomials, quadratics, proof, circles, trigonometry, and probability.

73 objectives
Objective 120 A-APR.1

Add, subtract, and multiply polynomials; understand polynomial closure under these operations.

Objective 121 A-CED.1

Create and solve one-variable equations and inequalities, including absolute-value, linear, quadratic, simple rational, and exponential cases.

Objective 122 A-CED.2

Create equations in two or more variables and graph them with appropriate labels and scales.

Objective 123 A-CED.4

Rearrange formulas to isolate a chosen quantity, including formulas with quadratic terms.

Objective 124 A-REI.4.a

Complete the square to transform quadratics and derive the quadratic formula.

Objective 125 A-REI.4.b

Solve quadratics by inspection, square roots, completing the square, formula, and factoring; express complex solutions.

Objective 126 A-REI.7

Solve simple linear-quadratic systems algebraically and graphically.

Objective 127 A-SSE.1.a

Interpret terms, factors, and coefficients in quadratic and exponential expressions.

Objective 128 A-SSE.1.b

Interpret quadratic/exponential expressions by treating sub-expressions as meaningful units.

Objective 129 A-SSE.2

Use expression structure to identify useful rewrites, such as difference-of-squares factoring.

Objective 130 A-SSE.3.a

Factor quadratics to reveal zeros of the function they define.

Objective 131 A-SSE.3.b

Complete the square to reveal maximum or minimum values of quadratic functions.

Objective 132 A-SSE.3.c

Use exponent properties to transform exponential expressions and interpret growth/decay rates.

Objective 133 F-BF.1.a

Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.

Objective 134 F-BF.1.b

Combine standard function types arithmetically to create models.

Objective 135 F-BF.3

Analyze transformations of quadratic and absolute-value functions and identify even/odd functions.

Objective 136 F-BF.4.a

Find inverse functions by solving f(x)=c for simple invertible functions and writing inverse expressions.

Objective 137 F-IF.4

Interpret key graph/table features of quadratic models in context.

Objective 138 F-IF.5

Relate the domain of a quadratic function to its graph and situation.

Objective 139 F-IF.6

Calculate, estimate, and interpret average rate of change for quadratic functions.

Objective 140 F-IF.7.a

Graph linear and quadratic functions and identify intercepts, maxima, and minima.

Objective 141 F-IF.7.b

Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions, showing key features by hand in simple cases and with technology when the functions are more complicated.

Objective 142 F-IF.8.a

Use factoring and completing the square to reveal zeros, extrema, and symmetry of quadratics.

Objective 143 F-IF.8.b

Use exponent properties to interpret exponential expressions, including percent growth and decay.

Objective 144 F-IF.9

Compare function properties across representations, especially quadratic comparisons.

Objective 145 F-LE.3

Compare growth of exponential, linear, quadratic, and other polynomial models using graphs/tables.

Objective 146 F-LE.6

Apply quadratic functions to physical situations such as projectile motion under gravity.

Objective 147 F-TF.8

Prove and use sin^2(theta)+cos^2(theta)=1 to find trig values with quadrant information.

Objective 148 G-C.1

Prove that all circles are similar.

Objective 149 G-C.2

Analyze relationships among inscribed angles, central angles, circumscribed angles, radii, chords, diameters, and tangents.

Objective 150 G-C.3

Construct inscribed/circumscribed circles of triangles and prove angle properties of cyclic quadrilaterals.

Objective 151 G-C.4

Construct a tangent line from an external point to a circle.

Objective 152 G-C.5

Derive arc length and sector area formulas using similarity; define radians and convert degrees/radians.

Objective 153 G-CO.10

Prove triangle theorems including angle sum, isosceles base angles, midsegment theorem, and medians concurrence.

Objective 154 G-CO.11

Prove parallelogram theorems and their converses, including diagonal and rectangle results.

Objective 155 G-CO.9

Prove theorems about lines and angles: vertical angles, parallel-line angle relationships, and perpendicular bisectors.

Objective 156 G-GMD.1

Explain circumference, area, and volume formulas using informal arguments such as dissection, Cavalieri, and limits.

Objective 157 G-GMD.3

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Objective 158 G-GMD.5

Apply scale factors to length, area, and volume using k, k^2, and k^3 relationships.

Objective 159 G-GMD.6

Use triangle angle-side relationships and triangle inequality in mathematical and real-world problems.

Objective 160 G-GPE.1

Derive the equation of a circle from center/radius and complete the square to identify center/radius.

Objective 161 G-GPE.2

Derive the equation of a parabola from a focus and directrix.

Objective 162 G-GPE.4

Use coordinates to prove simple geometric theorems, including simple circle theorems.

Objective 163 G-GPE.6

Find the point that partitions a directed segment between two points in a given ratio.

Objective 164 G-SRT.1.a

Verify that dilations send non-center-passing lines to parallel lines and leave center-passing lines unchanged.

Objective 165 G-SRT.1.b

Verify that dilations scale line segments by the dilation scale factor.

Objective 166 G-SRT.2

Use similarity transformations to decide similarity and explain angle equality and side proportionality in triangles.

Objective 167 G-SRT.3

Use similarity transformations to establish the AA similarity criterion.

Objective 168 G-SRT.4

Prove triangle-similarity theorems, including proportional segments and the Pythagorean Theorem via similarity.

Objective 169 G-SRT.5

Use triangle congruence and similarity criteria to solve problems and prove geometric relationships.

Objective 170 G-SRT.6

Define trigonometric ratios for acute angles using right-triangle similarity.

Objective 171 G-SRT.7

Explain and use the complementary-angle relationship between sine and cosine.

Objective 172 G-SRT.8

Use trig ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Objective 173 G-SRT.8.1

Derive and use trig ratios for 30-60-90 and 45-45-90 special right triangles.

Objective 174 N-CN.1

Understand i as a number with i^2=-1 and represent complex numbers as a+bi.

Objective 175 N-CN.2

Add, subtract, and multiply complex numbers using i^2=-1 and algebraic properties.

Objective 176 N-CN.7

Solve real-coefficient quadratic equations that have complex solutions.

Objective 177 N-CN.8

Extend polynomial identities to complex numbers, such as factoring sums of squares over the complex numbers.

Objective 178 N-CN.9

Know the Fundamental Theorem of Algebra and verify it for quadratic polynomials.

Objective 179 N-RN.1

Explain rational exponents as extensions of integer exponent rules and as radical notation.

Objective 180 N-RN.2

Rewrite expressions with radicals and rational exponents using exponent properties.

Objective 181 N-RN.3

Explain closure properties of rational numbers and irrational results from rational/irrational sums and products.

Objective 182 S-CP.1

Describe events as subsets of a sample space using unions, intersections, and complements.

Objective 183 S-CP.2

Determine event independence using P(A and B)=P(A)P(B).

Objective 184 S-CP.3

Understand conditional probability and connect independence to unchanged conditional probabilities.

Objective 185 S-CP.4

Construct and interpret two-way frequency tables as sample spaces for independence and conditional probability.

Objective 186 S-CP.5

Explain conditional probability and independence in everyday language and situations.

Objective 187 S-CP.6

Compute conditional probability as the fraction of one event's outcomes that also belong to another event.

Objective 188 S-CP.7

Apply and interpret the Addition Rule P(A or B)=P(A)+P(B)-P(A and B).

Objective 189 S-CP.8

Apply and interpret the general Multiplication Rule with conditional probability.

Objective 190 S-CP.9

Use permutations and combinations to compute probabilities of compound events and solve problems.

Objective 191 S-MD.6

Use probability to make fair decisions, such as lotteries or random selection.

Objective 192 S-MD.7

Analyze decisions and strategies with probability concepts in applied settings.