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