North Carolina · NCDPISyllabus
Maths syllabus, dot point by dot point
Every dot point in the North Carolina Mathssyllabus, with a focused answer for each one. Click any dot point for a worked explainer, past exam questions, and links to related dot points. Written by Claude Opus 4.8, Anthropic's latest AI.
Coordinate Geometry and Reasoning
Module overview →- How do you use coordinates to prove a figure is a particular shape?Use coordinates to prove simple geometric facts about triangles and quadrilaterals using slope and distance (NC.M1.G-GPE.4).11 min answer →
- How do you find the distance between two points, and why does the formula come from the Pythagorean theorem?Use the distance formula to find the length of a segment and apply it to coordinate problems (NC.M1.G-GPE.4).10 min answer →
- How do you find the midpoint of a segment, and how is it used in coordinate problems?Find the midpoint of a segment and apply it to coordinate problems and figures (NC.M1.G-GPE.6, G-GPE.4).9 min answer →
- How do slopes tell you whether two lines are parallel or perpendicular?Use slope criteria to determine whether lines are parallel, perpendicular, or neither, and write equations of such lines (NC.M1.G-GPE.5).10 min answer →
- How do you find the point that divides a segment in a given ratio?Find the point on a directed line segment that partitions it in a given ratio (NC.M1.G-GPE.6).10 min answer →
Descriptive Statistics
Module overview →- How do you compare two data sets using measures of center and spread?Use statistics appropriate to the shape of the distribution to compare center and spread of two or more data sets (NC.M1.S-ID.2).10 min answer →
- What does the correlation coefficient measure, and why does correlation not imply causation?Use the correlation coefficient to describe the strength and direction of a linear relationship and distinguish correlation from causation (NC.M1.S-ID.8, S-ID.6c).10 min answer →
- How do you represent a single data set and describe the shape of its distribution?Represent data with dot plots, histograms, and box plots, and interpret the shape of a distribution (NC.M1.S-ID.1, S-ID.3).10 min answer →
- How do you fit a linear model to two-variable data and interpret its slope and intercept?Represent two quantitative variables on a scatter plot, fit a linear model, and interpret slope and intercept in context (NC.M1.S-ID.6, S-ID.7).11 min answer →
- How do you read a two-way frequency table and compute joint, marginal, and conditional relative frequencies?Summarize two-variable categorical data in two-way tables and interpret joint, marginal, and conditional relative frequencies (NC.M1.S-ID.5).11 min answer →
Expressions and Operations
Module overview →- How do you factor a quadratic expression, and how does the factored form reveal the zeros?Factor quadratic expressions including common factor, trinomials, and difference of squares, and use the factored form to reveal zeros (NC.M1.A-SSE.3).11 min answer →
- How do you read the parts of an algebraic expression and explain what each part means in a real context?Interpret the parts of a linear, exponential, or quadratic expression (terms, factors, coefficients, exponents) and interpret a multi-part expression as a combination of entities (NC.M1.A-SSE.1a, A-SSE.1b).10 min answer →
- How do you add, subtract, and multiply polynomials, and why do they behave like the integers?Understand that polynomials are closed under addition, subtraction, and multiplication, and perform these operations (NC.M1.A-APR.1).10 min answer →
- How does a rational exponent relate to a radical, and how do you rewrite expressions using the properties of exponents?Explain how rational exponents extend the integer-exponent properties and rewrite expressions with radicals and rational exponents (NC.M1.N-RN.1, N-RN.2).11 min answer →
- When is a sum or product of numbers rational, and when is it irrational?Explain why sums and products of rational and irrational numbers are rational or irrational (NC.M1.N-RN.3).9 min answer →
- How can you use the structure of an expression to rewrite it in an equivalent, more useful form?Use the structure of an expression to identify ways to rewrite it, and write an equivalent factored form of a quadratic to reveal zeros (NC.M1.A-SSE.2, A-SSE.3).10 min answer →
Functions and Exponential Models
Module overview →- What is the average rate of change of a function over an interval, and how do you compute it?Calculate and interpret the average rate of change of a function over an interval from a graph or table (NC.M1.F-IF.6).10 min answer →
- How do linear, quadratic, and exponential functions differ, and why does exponential growth eventually win?Compare linear, quadratic, and exponential functions across representations and observe that exponential growth eventually exceeds the others (NC.M1.F-LE.3, F-IF.9).11 min answer →
- How do exponential functions model growth and decay, and how do you read their parameters?Construct and interpret exponential functions for growth and decay, and interpret their parameters in context (NC.M1.F-LE.1, F-LE.2, F-LE.5).11 min answer →
- What makes a relation a function, and how do you use function notation, domain, and range?Define a function, use function notation to evaluate, and relate domain and range to a graph and context (NC.M1.F-IF.1, F-IF.2, F-IF.5).11 min answer →
- How do you read the key features of a graph and interpret them in context?Interpret key features of graphs and tables (intercepts, increasing/decreasing, maxima/minima, end behavior) for linear, quadratic, and exponential functions (NC.M1.F-IF.4).11 min answer →
- How do you write arithmetic and geometric sequences recursively and explicitly?Recognize sequences as functions and write arithmetic and geometric sequences both recursively and explicitly (NC.M1.F-IF.3, F-BF.2).11 min answer →
- How do you solve a quadratic equation, and how do you choose a method?Solve quadratic equations by inspection, square roots, factoring, and the quadratic formula, writing exact solutions (NC.M1.A-REI.4a).11 min answer →
Linear Equations and Functions
Module overview →- How do you turn a real situation into an equation or inequality you can solve?Create linear, quadratic, and exponential equations and inequalities in one or two variables to model and solve problems (NC.M1.A-CED.1, A-CED.2).11 min answer →
- How do you graph a linear equation, and how do you read its intercepts and slope from the graph?Graph linear equations in two variables and identify slope and intercepts, labeling axes and scale (NC.M1.A-CED.2, F-IF.4).10 min answer →
- How do you rearrange a formula to solve for a different variable?Rearrange formulas and literal equations to isolate a specified variable (NC.M1.A-CED.4).9 min answer →
- How do you find slope, and how do you write the equation of a line from the information given?Find slope and write linear functions in slope-intercept and point-slope form from a graph, a description, or two points (NC.M1.F-LE.2, F-BF.1a).11 min answer →
- How do you solve a linear equation in one variable, and how does each step follow from the properties of equality?Solve linear equations in one variable, including those with letter coefficients, and justify each step from the properties of equality (NC.M1.A-REI.1, A-REI.3).10 min answer →
- How do you solve a linear inequality, and when does the inequality sign flip?Solve linear inequalities in one variable and represent the solution on a number line, applying the sign-flip rule for negatives (NC.M1.A-REI.3).10 min answer →
Systems of Equations and Inequalities
Module overview →- Why does replacing one equation with a combination of the two keep the same solution?Prove that replacing one equation in a system with the sum of it and a multiple of the other produces an equivalent system (NC.M1.A-REI.5).9 min answer →
- How do you graph a linear inequality in two variables, and what does the shaded region mean?Graph a linear inequality in two variables as a half-plane with the correct boundary line and shading (NC.M1.A-REI, A-CED.3).10 min answer →
- How do you turn a real situation with two conditions into a system and interpret the solution?Model situations with systems of equations or inequalities, represent constraints, and interpret solutions as viable or non-viable (NC.M1.A-CED.3, A-REI.6).11 min answer →
- How do you solve a system of two linear equations using substitution or elimination?Solve systems of two linear equations in two variables algebraically by substitution and elimination (NC.M1.A-REI.6).11 min answer →
- How does the intersection of two graphs give the solution of a system or equation?Solve systems by graphing and explain why the x-coordinates of intersections of y = f(x) and y = g(x) solve f(x) = g(x) (NC.M1.A-REI.11, A-REI.6).10 min answer →