This page maps the standards of NC Math 2 to the Brilliant lessons that teach them. Search by standard code or skill to find the closest match. A standard is listed only where Brilliant content fully or in part addresses the standard directly.
North Carolina teaches an integrated high school pathway rather than the Algebra 1 → Geometry → Algebra 2 sequence, so each of NC Math 1, 2, and 3 mixes algebra, functions, geometry, and statistics. This page covers NC Math 2 only; NC Math 1 and NC Math 3 have their own pages. Math 2 adds quadratics, congruence and similarity, right triangle trigonometry, and probability.
North Carolina writes its own codes, and they are not interchangeable with Common Core's even where the trailing part matches — NCDPI narrowed some standards, widened others, and folded several together. The codes below use dots throughout, so NCDPI's NC.M2.A-CED.1 appears here as NC.M2.A.CED.1.
Number and Quantity — The Real Number System (NC.M2.N-RN)
| NC standard | What the standard asks | Brilliant targeted skill |
|---|---|---|
| NC.M2.N.RN.1 | Explain how expressions with rational exponents can be rewritten as radical expressions. | Exponents and Radicals — Connecting fractional exponents to radicals Equations and Curves — Evaluating roots and inverse compositions |
| NC.M2.N.RN.2 | Rewrite expressions with radicals and rational exponents into equivalent expressions using the properties of exponents. | Exponents and Radicals — Adding and subtracting like square roots, Evaluating general fractional exponents, Evaluating unit fraction exponents, Multiplying square root expressions, Simplifying and combining unlike radicals Equations and Curves — Simplifying fractional exponents |
Number and Quantity — The Complex Number System (NC.M2.N-CN)
| NC standard | What the standard asks | Brilliant targeted skill |
|---|---|---|
| NC.M2.N.CN.1 | Know there is a complex number i such that i² = -1, and that every complex number has the form a + bi where a and b are real numbers. | Complex Numbers — Evaluating expressions with i, Evaluating real and imaginary parts, Simplifying powers of i |
Algebra — Seeing Structure in Expressions (NC.M2.A-SSE)
| NC standard | What the standard asks | Brilliant targeted skill |
|---|---|---|
| NC.M2.A.SSE.1.a | Identify and interpret parts of a quadratic, square root, inverse variation, or right triangle trigonometric expression, including terms, factors, coefficients, radicands, and exponents. | Quadratics — Understanding motion equations |
| NC.M2.A.SSE.3 | Write an equivalent form of a quadratic expression by completing the square, where a is an integer of a quadratic expression ax² + bx + c, to reveal the maximum or minimum value of the function the expression defines. | Quadratics — Completing the square, Converting to vertex form |
Algebra — Arithmetic with Polynomial and Rational Expressions (NC.M2.A-APR)
| NC standard | What the standard asks | Brilliant targeted skill |
|---|---|---|
| NC.M2.A.APR.1 | Extend the understanding that operations with polynomials are comparable to operations with integers by adding, subtracting, and multiplying polynomials. | Polynomials — Adding polynomials, Multiplying monomials, Multiplying polynomials, Subtracting polynomials, Working with multivariable polynomials |
Algebra — Creating Equations (NC.M2.A-CED)
| NC standard | What the standard asks | Brilliant targeted skill |
|---|---|---|
| NC.M2.A.CED.1 | Create equations and inequalities in one variable that represent quadratic, square root, inverse variation, and right triangle trigonometric relationships and use them to solve problems. | Quadratics — Finding when objects arrive |
Algebra — Reasoning with Equations and Inequalities (NC.M2.A-REI)
| NC standard | What the standard asks | Brilliant targeted skill |
|---|---|---|
| NC.M2.A.REI.4.a | Solve for all solutions of quadratic equations in one variable, understanding that the quadratic formula is the generalization of solving ax² + bx + c by using the process of completing the square. | Quadratics — Completing squares with fractions, Solving by completing the square, Using the quadratic formula |
| NC.M2.A.REI.4.b | Explain when quadratic equations will have non-real solutions and express complex solutions as a ± bi for real numbers a and b. | Quadratics — Classifying solution types, Determining number of solutions, Predicting whether a target is reached, Solving with imaginary numbers, Using the discriminant Complex Numbers — Solving equations with complex solutions |
Functions — Interpreting Functions (NC.M2.F-IF)
| NC standard | What the standard asks | Brilliant targeted skill |
|---|---|---|
| NC.M2.F.IF.2 | Extend the use of function notation to express the image of a geometric figure in the plane resulting from a translation, rotation by multiples of 90 degrees about the origin, reflection across an axis, or dilation as a function of its pre-image. | Coordinate Transformations — Computing 180-degree rotations, Computing axis reflections, Computing quarter-turn rotations, Translating with coordinates |
| NC.M2.F.IF.7 | Analyze quadratic, square root, and inverse variation functions by generating different representations, by hand in simple cases and using technology for more complicated cases, to show key features including domain and range; intercepts; intervals where the function is increasing, decreasing, positive, or negative; rate of change; maximums and minimums; symmetries; and end behavior. | Equations and Curves — Connecting transformations to domain and range, Finding domain and range after transformations Quadratics — Finding the axis of symmetry, Finding vertices using symmetry |
| NC.M2.F.IF.8 | Use equivalent expressions to reveal and explain different properties of a function by developing and using the process of completing the square to identify the zeros, extreme values, and symmetry in graphs and tables representing quadratic functions, and interpret these in terms of a context. | Quadratics — Finding maximum and minimum values, Finding the vertex |
Functions — Building Functions (NC.M2.F-BF)
| NC standard | What the standard asks | Brilliant targeted skill |
|---|---|---|
| NC.M2.F.BF.1 | Write a function that describes a relationship between two quantities by building quadratic functions with real solution(s) and inverse variation functions given a graph, a description of a relationship, or ordered pairs (including reading these from a table). | Visual Algebra — Breaking patterns into parts, Seeing squares inside patterns, Writing expressions as length times width Equations and Curves — Completing hyperbola equations, Finding equation parameters Quadratics — Writing equations for motion, Writing equations for real situations, Writing equations from graphs, Writing vertex form equations |
| NC.M2.F.BF.3 | Understand the effects on the graphical and tabular representations of a linear, quadratic, square root, or inverse variation function f of k · f(x), f(x) + k, and f(x + k) for specific values of k (both positive and negative). | Equations and Curves — Applying shifts and stretches, Combining multiple transformations, Shifting the square root graph, Transforming hyperbola graphs, Writing transformations from constraints Quadratics — Graphing parabolas from vertex form Introduction to Functions — Sliding Function Graphs |
Geometry — Congruence (NC.M2.G-CO)
| NC standard | What the standard asks | Brilliant targeted skill |
|---|---|---|
| NC.M2.G.CO.2 | Experiment with transformations in the plane: represent transformations in the plane; compare rigid motions that preserve distance and angle measure (translations, reflections, rotations) to transformations that do not preserve both (e.g. stretches, dilations); understand that rigid motions produce congruent figures while dilations produce similar figures. | Coordinate Transformations — Combining stretches with transformations, Stretching along an axis |
| NC.M2.G.CO.3 | Given a triangle, quadrilateral, or regular polygon, describe any reflection or rotation symmetry — actions that carry the figure onto itself — identifying the center and angle(s) of rotation symmetry and the line(s) of reflection symmetry. | Coordinate Transformations — Finding lines of symmetry, Finding rotational symmetry, Identifying types of symmetry |
| NC.M2.G.CO.5 | Given a geometric figure and a rigid motion, find the image of the figure; given a geometric figure and its image, specify a rigid motion or sequence of rigid motions that will transform the pre-image to its image. | Coordinate Transformations — Combining rotations, Combining rotations and translations, Combining translations, Computing diagonal reflections, Connecting reflections and rotations, Recognizing mirror images, Reflecting across any line, Reflecting across axes, Reversing reflections, Reversing rotations, Reversing translations, Rotating around any point, Rotating around the origin, Rotating by reflecting twice, Rotating clockwise, Sliding points and shapes, Translating by reflecting twice, Translating by rotating twice |
| NC.M2.G.CO.6 | Determine whether two figures are congruent by specifying a rigid motion or sequence of rigid motions that will transform one figure onto the other. | Coordinate Transformations — Proving congruence |
Geometry — Similarity, Right Triangles, and Trigonometry (NC.M2.G-SRT)
| NC standard | What the standard asks | Brilliant targeted skill |
|---|---|---|
| NC.M2.G.SRT.1 | Verify experimentally the properties of dilations with a given center and scale factor: (a) a line segment through the center of dilation and its image lie on the same line, and a segment not through the center is parallel to its image; (b) the length of the image of a segment equals the length of the segment times the scale factor; (c) the distance from the center of dilation to a point on the image equals the scale factor times the distance to the corresponding pre-image point; (d) dilations preserve angle measure. | Coordinate Transformations — Combining scaling and sliding, Scaling around any point, Scaling from the origin, Translating by scaling twice |
| NC.M2.G.SRT.2 | Understand similarity in terms of transformations: (a) determine whether two figures are similar by specifying a sequence of transformations that will transform one figure into the other; (b) use the properties of dilations to show that two triangles are similar when all corresponding pairs of sides are proportional and all corresponding pairs of angles are congruent. | Coordinate Transformations — Proving similarity |
| NC.M2.G.SRT.4 | Use similarity to solve problems and to prove theorems about triangles, and use theorems about triangles to prove relationships in geometric figures, including: a line parallel to one side of a triangle divides the other two sides proportionally and its converse; and the Pythagorean Theorem. | Geometry and Measurement — Find the scale factor and unknown lengths |
| NC.M2.G.SRT.8 | Use trigonometric ratios and the Pythagorean Theorem to solve problems involving right triangles in terms of a context. | Coordinate Geometry — Applying the Pythagorean theorem to areas, Finding side lengths with the Pythagorean theorem |
| NC.M2.G.SRT.12 | Develop properties of special right triangles (45-45-90 and 30-60-90) and use them to solve problems. | Trigonometric Functions — Finding special right triangle sides |
Statistics and Probability — Making Inferences and Justifying Conclusions (NC.M2.S-IC)
| NC standard | What the standard asks | Brilliant targeted skill |
|---|---|---|
| NC.M2.S.IC.2 | Use simulation to determine whether the experimental probability generated by sample data is consistent with the theoretical probability based on known information about the population. | Probability in Data — Estimating probabilities from past data |
Statistics and Probability — Conditional Probability and the Rules of Probability (NC.M2.S-CP)
| NC standard | What the standard asks | Brilliant targeted skill |
|---|---|---|
| NC.M2.S.CP.1 | Describe events as subsets of the outcomes in a sample space using characteristics of the outcomes, or as unions, intersections, and complements of other events. | Probability and Chance — Comparing the likelihood of outcomes, Counting outcomes across overlapping events, Counting possible outcomes, Finding the probability of both events, Finding the probability of either event, Finding the probability something won't happen, Using Venn diagrams |
| NC.M2.S.CP.3.b | Understand that event A is independent from event B if the probability of A does not change in response to the occurrence of B — that is, P(A|B) = P(A). | Predicting with Probability — Comparing a group to everyone Probability in Data — Identifying when events affect each other |
| NC.M2.S.CP.5 | Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. | Probability in Data — Estimating chances without data |
| NC.M2.S.CP.6 | Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in context. | Probability in Data — Finding conditional probabilities from data, Judging how often a rule fails Probability and Chance — Finding probability given a condition |
| NC.M2.S.CP.7 | Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in context. | Probability in Data — Adding probabilities of separate outcomes, Combining probabilities with a formula Predicting with Probability — Adding up probabilities to a threshold, Combining cases into one probability, Finding the chance of a range, Reading a probability plot |
| NC.M2.S.CP.8 | Apply the general Multiplication Rule P(A and B) = P(A)P(B|A) = P(B)P(A|B) and interpret the answer in context, including the case where A and B are independent: P(A and B) = P(A)P(B). | Predicting with Probability — Applying Bayes' theorem, Judging how much evidence matters Probability in Data — Combining probabilities across cases, Finding probabilities of multi-step outcomes, Finding probability of two related events, Updating probabilities with new evidence Probability and Chance — Finding probability of two unrelated events |
How this page is built
Every skill in the Brilliant math topics that reach North Carolina's high school mathematics is mapped to the single standard it aligns with most closely, using the North Carolina Standard Course of Study for Mathematics, adopted by the State Board of Education in June 2016, together with NCDPI's unpacking documents as the authority for what each standard requires and where its boundaries fall. Skills that build toward a standard without teaching its stated content are excluded, so a skill appears here only where it addresses the standard directly.
Each skill links to a lesson where it is practiced, and hovering a skill shows the description learners see for it. This page is regenerated from the mapping, so it reflects the current state rather than a fixed snapshot.
