North Carolina · NCDPIQ&A
MathsQ&A by dot point
A short Q&A bank for every North Carolina Maths syllabus dot point. Each question and answer is drawn directly from our worked dot-point page, so you can scan key concepts before opening the long-form answer.
Coordinate Geometry and Reasoning
- Use coordinates to prove simple geometric facts about triangles and quadrilaterals using slope and distance (NC.M1.G-GPE.4).2Q&A pairs
- Use the distance formula to find the length of a segment and apply it to coordinate problems (NC.M1.G-GPE.4).3Q&A pairs
- Find the midpoint of a segment and apply it to coordinate problems and figures (NC.M1.G-GPE.6, G-GPE.4).2Q&A pairs
- Use slope criteria to determine whether lines are parallel, perpendicular, or neither, and write equations of such lines (NC.M1.G-GPE.5).2Q&A pairs
- Find the point on a directed line segment that partitions it in a given ratio (NC.M1.G-GPE.6).2Q&A pairs
Descriptive Statistics
- 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).2Q&A pairs
- 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).2Q&A pairs
- Represent data with dot plots, histograms, and box plots, and interpret the shape of a distribution (NC.M1.S-ID.1, S-ID.3).2Q&A pairs
- 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).2Q&A pairs
- Summarize two-variable categorical data in two-way tables and interpret joint, marginal, and conditional relative frequencies (NC.M1.S-ID.5).2Q&A pairs
Expressions and Operations
- Factor quadratic expressions including common factor, trinomials, and difference of squares, and use the factored form to reveal zeros (NC.M1.A-SSE.3).3Q&A pairs
- 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).2Q&A pairs
- Understand that polynomials are closed under addition, subtraction, and multiplication, and perform these operations (NC.M1.A-APR.1).2Q&A pairs
- 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).2Q&A pairs
- Explain why sums and products of rational and irrational numbers are rational or irrational (NC.M1.N-RN.3).2Q&A pairs
- 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).2Q&A pairs
Functions and Exponential Models
- Calculate and interpret the average rate of change of a function over an interval from a graph or table (NC.M1.F-IF.6).2Q&A pairs
- 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).2Q&A pairs
- 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).2Q&A pairs
- 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).2Q&A pairs
- 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).2Q&A pairs
- Recognize sequences as functions and write arithmetic and geometric sequences both recursively and explicitly (NC.M1.F-IF.3, F-BF.2).2Q&A pairs
- Solve quadratic equations by inspection, square roots, factoring, and the quadratic formula, writing exact solutions (NC.M1.A-REI.4a).4Q&A pairs
Linear Equations and Functions
- 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).3Q&A pairs
- Graph linear equations in two variables and identify slope and intercepts, labeling axes and scale (NC.M1.A-CED.2, F-IF.4).2Q&A pairs
- Rearrange formulas and literal equations to isolate a specified variable (NC.M1.A-CED.4).2Q&A pairs
- 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).2Q&A pairs
- 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).3Q&A pairs
- 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).4Q&A pairs
Systems of Equations and Inequalities
- 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).2Q&A pairs
- 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).2Q&A pairs
- 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).2Q&A pairs
- Solve systems of two linear equations in two variables algebraically by substitution and elimination (NC.M1.A-REI.6).3Q&A pairs
- 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).2Q&A pairs