NC Math 2 (North Carolina SCOS)

Number and Quantity – The Real Number System (N-RN)

• Extend the properties of exponents to rational exponents
• NC.M2.N-RN.1 Explain how expressions with rational exponents can be rewritten as radicals.
• NC.M2.N-RN.2 Rewrite expressions with radicals and rational exponents using properties of exponents.
• Use properties of rational and irrational numbers
• NC.M2.N-RN.3 Explain why sums and products of rationals are rational and what happens when irrationals are combined.

Number and Quantity – The Complex Number System (N-CN)

• Defining complex numbers
• NC.M2.N-CN.1 Know that i² = −1 and that complex numbers have the form a + bi.

Algebra – Seeing Structure in Expressions (A-SSE)

• Interpret the structure of expressions
• NC.M2.A-SSE.1 Interpret expressions that represent a quantity in terms of its context.
• NC.M2.A-SSE.1a Identify and interpret parts of quadratic, square root, inverse variation, or right-triangle trigonometric expressions.
• NC.M2.A-SSE.1b Interpret parts of quadratic and square root expressions made of several parts as single entities.
• Write expressions in equivalent forms to solve problems
• NC.M2.A-SSE.3 Complete the square in a quadratic expression to reveal its maximum or minimum.

Algebra – Arithmetic with Polynomials and Rational Expressions (A-APR)

• Perform arithmetic operations on polynomials
• NC.M2.A-APR.1 Add, subtract, and multiply polynomials by analogy with integers.

Algebra – Creating Equations (A-CED)

• Create equations that describe numbers or relationships
• NC.M2.A-CED.1 Create and solve one-variable equations and inequalities for quadratic, radical, inverse variation, and trigonometric relationships.
• NC.M2.A-CED.2 Create and graph two-variable equations for quadratic, square root, and inverse variation relationships.
• NC.M2.A-CED.3 Create systems of linear, quadratic, square root, and inverse variation equations to model situations.

Algebra – Reasoning with Equations and Inequalities (A-REI)

• Understand solving equations as a process of reasoning and explain the reasoning
• NC.M2.A-REI.1 Justify the method and each step when solving quadratic, square root, and inverse variation equations.
• NC.M2.A-REI.2 Solve and interpret inverse variation and square root equations from contexts, explaining extraneous solutions.
• Solve equations and inequalities in one variable
• NC.M2.A-REI.4 Solve quadratic equations in one variable and find all solutions.
• NC.M2.A-REI.4a Understand the quadratic formula as a generalization of completing the square.
• NC.M2.A-REI.4b Explain when quadratics have non-real solutions and write them as a ± bi.
• Solve systems of equations
• NC.M2.A-REI.7 Solve systems of a linear and a quadratic equation with tables, graphs, and algebra and interpret in context.
• Represent and solve equations and inequalities graphically
• NC.M2.A-REI.11 Approximate solutions of f(x) = g(x) from graphs where the functions include square root and inverse variation.

Functions – Interpreting Functions (F-IF)

• Understand the concept of a function and use function notation
• NC.M2.F-IF.1 Extend the function concept to geometric transformations whose domain and range are sets of points.
• NC.M2.F-IF.2 Use function notation for images of points under translations, rotations, reflections, and dilations.
• Interpret functions that arise in applications in terms of the context
• NC.M2.F-IF.4 Interpret key features in context: domain, range, rate of change, symmetries, and end behavior.
• Analyze functions using different representations
• NC.M2.F-IF.7 Analyze quadratic, square root, and inverse variation functions in different representations to show key features.
• NC.M2.F-IF.8 Use completing the square to find zeros, extreme values, and symmetry of quadratics and interpret them.
• NC.M2.F-IF.9 Compare key features of two linear, quadratic, square root, or inverse variation functions given in different ways.

Functions – Building Functions (F-BF)

• Build a function that models a relationship between two quantities
• NC.M2.F-BF.1 Write quadratic functions with real solutions and inverse variation functions from graphs, descriptions, or points.
• Build new functions from existing functions
• NC.M2.F-BF.3 Understand how k·f(x), f(x) + k, and f(x + k) change graphs and tables.

Geometry – Congruence (G-CO)

• Experiment with transformations in the plane
• NC.M2.G-CO.2 Represent transformations and compare rigid motions with transformations that do not keep distance, such as dilations.
• NC.M2.G-CO.3 Describe reflection and rotation symmetries of triangles, quadrilaterals, and regular polygons.
• NC.M2.G-CO.4 Verify experimentally the properties of rotations, reflections, and translations.
• NC.M2.G-CO.5 Find the image of a figure under a rigid motion, or the motions that map one figure onto another.
• Understand congruence in terms of rigid motions
• NC.M2.G-CO.6 Decide whether figures are congruent by giving a sequence of rigid motions.
• NC.M2.G-CO.7 Use rigid motions to show triangles are congruent when corresponding sides and angles match.
• NC.M2.G-CO.8 Justify the ASA, SAS, and SSS criteria and use congruence criteria, including HL, to decide congruence.
• Prove geometric theorems
• NC.M2.G-CO.9 Prove theorems about lines and angles, such as vertical angles and parallel lines cut by a transversal.
• NC.M2.G-CO.10 Prove theorems about triangles, such as angle sums, exterior angles, isosceles base angles, and midsegments.

Geometry – Similarity, Right Triangles, and Trigonometry (G-SRT)

• Understand similarity in terms of similarity transformations
• NC.M2.G-SRT.1 Verify experimentally the properties of dilations with a given center and scale factor.
• NC.M2.G-SRT.1a Show that lines through the center are unchanged and other lines map to parallel lines.
• NC.M2.G-SRT.1b Show that image lengths equal original lengths times the scale factor.
• NC.M2.G-SRT.1c Show that distances from the center scale by the scale factor.
• NC.M2.G-SRT.1d Show that dilations preserve angle measure.
• NC.M2.G-SRT.2 Understand similarity in terms of similarity transformations.
• NC.M2.G-SRT.2a Decide whether figures are similar by giving a sequence of transformations.
• NC.M2.G-SRT.2b Use dilations to show triangles are similar when sides are proportional and angles congruent.
• NC.M2.G-SRT.3 Use transformations to justify the AA criterion for similar triangles.
• Prove theorems involving similarity
• NC.M2.G-SRT.4 Use similarity to solve problems and prove triangle theorems, including the side-splitter and Pythagorean theorems.
• Define trigonometric ratios and solve problems involving right triangles
• NC.M2.G-SRT.6 Verify that side ratios in similar right triangles depend only on the angle and define the trigonometric ratios.
• NC.M2.G-SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right-triangle problems in context.
• NC.M2.G-SRT.12 Develop properties of 45°-45°-90° and 30°-60°-90° triangles and use them to solve problems.

Statistics – Making Inferences and Justifying Conclusions (S-IC)

• Understand and evaluate random processes underlying statistical experiments
• NC.M2.S-IC.2 Use simulation to check whether experimental probability from samples matches theoretical probability.

Statistics – Conditional Probability and the Rules of Probability (S-CP)

• Understand independence and conditional probability and use them to interpret data
• NC.M2.S-CP.1 Describe events as subsets of a sample space using unions, intersections, and complements.
• NC.M2.S-CP.3 Develop and understand independence and conditional probability.
• NC.M2.S-CP.3a Use two-way tables to understand P(A|B) as the fraction of B's outcomes that are also in A.
• NC.M2.S-CP.3b Understand that A and B are independent when P(A|B) = P(A).
• NC.M2.S-CP.4 Build two-way frequency tables to find conditional, joint, and marginal probabilities and test independence.
• NC.M2.S-CP.5 Explain conditional probability and independence in everyday language and situations.
• Use the rules of probability to compute probabilities of compound events
• NC.M2.S-CP.6 Find the conditional probability of A given B and interpret it in context.
• NC.M2.S-CP.7 Apply the Addition Rule and interpret the result in context.
• NC.M2.S-CP.8 Apply the general Multiplication Rule, including for independent events, and interpret the result.