EOC NC Math 1 and NC Math 3 Achievement Level Descriptors

Level 5

Students at Level 5 demonstrate comprehensive understanding of grade level content standards, are on track for career and college, and are prepared for advanced content at the next grade/course.

Level 5 students can:

• Analyze and interpret how changing the parameters of the expression impacts the contextual situation;
• Use factoring to reveal solutions and zeros of quadratic equations, and analyze the relationship between the factors, zeros, and solution of a quadratic equation;
• Add and subtract quadratic and linear expressions, and multiply linear expressions, given a contextual situation;
• Compare zeros and solutions given an equation, table, or graph of a quadratic equation;
• Create, solve, and analyze problems that require creating linear, quadratic, or exponential equations and inequalities in one or two variables in context;
• Justify why replacing one equation in a system of linear equations with the sum of that equation and a multiple of the other produces a system with the same solutions;
• Create and compare explicit and recursive forms of arithmetic and geometric sequences;
• Compare key features of two different linear, exponential, or quadratic functions, given different representations;
• Use coordinates to compute perimeters and areas of polygons, and verify when a set of points produces a particular type of polygon in context;
• Determine and justify which representation best fits the data using residuals;
• Determine and justify which function best illustrates the data (linear/exponential).

Level 4

Students at Level 4 demonstrate a thorough understanding of grade level content standards and are on track for career and college.

Level 4 students can:

• Rewrite algebraic expressions in two or more variables with integer exponents using any combination of exponent properties;
• Interpret expressions and parts of expressions in terms of a context;
• Use factoring to reveal solutions and zeros of quadratic equations in the form ax2 + bx + c, where |a| ≠ 1;
• Add and subtract quadratic and linear expressions, and multiply linear expressions;
• Determine the solutions of a quadratic equation not given in factored form;
• Model situations by creating systems of linear equations or inequalities;
• Solve formulas for a quantity of interest;
• Use mathematical reasoning to justify all steps in solving linear and quadratic equations;
• Solve quadratic equations in one variable by taking square roots and factoring;
• Solve systems of equations using tables, graphs, and algebraic methods, and interpret the solutions;

• Graph the solutions to a linear inequality or a system of linear inequalities on a coordinate plane;
• Use the domain and range of a relation to determine whether the relation is or is not a function;
• Evaluate functions for inputs in the domain and interpret statements that use function notation in terms of a context;
• Recognize that arithmetic sequences have a range which is a subset of the range of a linear function and geometric sequences have a range which is a subset of the range of an exponential function;
• Interpret functions and key features of representations of functions in terms of a context;
• Calculate and interpret the average rate of change of a function over a specified interval;
• Analyze linear, exponential, and quadratic functions to show and identify key features;
• Compare key features of two of the same functions, given different representations;
• Build linear and exponential equations from a mathematical or real-world context, including combining two functions;
• Represent situations with recursive and explicit forms of arithmetic and geometric sequences, and translate between the two forms;
• Identify situations that can be modeled by linear and exponential functions, and justify the choice of function type to model the situation;
• Interpret the parameters of linear and exponential functions in terms of a context;
• Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, and verify when a set of points produces a particular type of triangle or quadrilateral;
• Use coordinates to determine whether two lines are parallel or perpendicular, and find the equation of parallel or perpendicular lines when given a line and a point not on the line;
• Use coordinates to find the midpoint and endpoints of line segments;
• Represent data with histograms and box plots using technology, and interpret the data in context;
• Compare the center and spread of different data sets, and interpret differences in shape, center, and spread in context;
• Represent data on a scatterplot, and describe the relationship between the variables;
• Fit a function to the appropriate model (linear/exponential) given a data set, and use fitted function to solve problems;
• Interpret the rate of change and intercept of a linear model, and interpolate and extrapolate to predict values;
• Analyze the relationship between two variables using correlation coefficients and residuals;
• Distinguish between association and causation.

Level 3

Students at Level 3 demonstrate sufficient understanding of grade level content standards though some support may be needed to engage with content at the next grade/course.

• Rewrite algebraic expressions in two or more variables with integer exponents using one property of exponents;
• Interpret expressions in terms of a context;
• Use factoring, the quadratic equation, and graphing to reveal solutions and zeros of quadratic equations;
• Add and subtract quadratic and linear expressions;
• Determine the solutions of a quadratic equation given an equation in factored form;
• Create and solve linear, quadratic, or exponential equations and inequalities in one variable;
• Create and graph linear, quadratic, or exponential equations in two variables;
• Identify graphs of systems of equations that model a context;
• Use mathematical reasoning to justify all steps in solving linear equations;
• Solve linear equations and inequalities in one variable;
• Solve quadratic equations in one variable by taking square roots;
• Solve systems of equations using tables and graphs, and interpret the solutions;
• Justify how the graph of a two-variable equation represents the set of all solutions to the equation;
• Graph the solutions to a linear inequality on a coordinate plane;
• Identify the domain and range of a function;
• Evaluate functions for inputs in the domain;
• Recognize recursively and explicitly defined sequences as functions with a domain that is a subset of the integers;
• Interpret representations of functions in terms of a context;
• Calculate the average rate of change of any function over a specified interval;
• Analyze linear and exponential equations to show and identify key features;
• Compare key features of two exponential or quadratic functions given the same type of representation;
• Build linear and exponential equations from a mathematical or real-world context;
• Represent situations with recursive and explicit forms of arithmetic sequences;
• Identify situations that can be modeled by linear or exponential functions;
• Interpret the parameters of linear functions in terms of a context;
• Use coordinates to compute perimeters of polygons and areas of triangles and rectangles;
• Use coordinates to determine whether two lines are parallel or perpendicular;
• Use coordinates to find the midpoint of line segments;
• Represent data with histograms and box plots using technology;
• Compare the center and spread of different data sets;
• Examine the effects of extreme data points on shape, center, and/or spread;
• Represent data on a scatterplot;
• Fit a function to the appropriate model (linear/exponential) given a data set;
• Interpret the rate of change and intercept of a linear model, and interpolate to predict values;
• Analyze the relationship between two variables using correlation coefficients.

Not Proficient students can:

• Rewrite algebraic expressions in one variable with whole-number exponents using one property of exponents;
• Identify parts of expressions;
• Determine the zeros of a quadratic given a quadratic in factored form;
• Add and subtract linear expressions;
• Determine the zeros of a quadratic equation by looking at a graph;
• Use linear equations and inequalities to solve problems;
• Solve linear equations in one variable;
• Solve systems of equations using tables and graphs;
• Understand that the graph of a two-variable equation represents the set of all solutions to the equation;
• Calculate the average rate of change of a linear function;
• Compare key features of two linear functions, given the same type of representation;
• Identify situations that can be modeled by linear functions;
• Determine the distance between two points on a line;
• Identify components of histograms and box plots; 
• Calculate the mean and median of a data set;
• Identify extreme data points informally;
• Informally, find the line of best fit.

Level 5

Students at Level 5 demonstrate comprehensive understanding of grade level content standards, are on track for career and college, and are prepared for advanced content at the next grade/course.

Level 5 students can:

• Apply the fundamental theorem of Algebra to justify the number and types of solutions for polynomial functions;
• Rewrite piecewise, absolute value, polynomial, exponential, and rational expressions to interpret terms, factors, coefficients, and exponents in context;
• Apply the relationship among factors of polynomial expressions, solutions of polynomial equations, and zeros of polynomial functions using the remainder theorem;
• Rewrite rational expressions requiring more than one arithmetic operation;
• Analyze noncontinuous functions to identify key features;
• Justify the effect of replacing f(x) with kf(x), f(x) + k, f(x + k), and f(kx);
• Justify why two functions are inverses;
• Use different centers of triangles in contextual situations;
• Construct a proof of a theorem about parallelograms in different formats;
• Construct a proof of a theorem about circles in different formats (flow chart, t-chart, paragraph);
• Interpret the radian measure of an angle as a unitless measure and use linear measures to find angle measures;
• Recognize any equation of a circle, and find the center and radius and other points on the circle;
• Apply geometric concepts to model and solve design and optimization modeling problems;
• Determine how changes in sample size or population parameters can affect the margin of error and differences between distinct populations;
• Make appropriate judgments on the context of graphical displays of data.

Level 4

Students at Level 4 demonstrate a thorough understanding of grade level content standards and are on track for career and college.

Level 4 students can:

• Determine the number and potential types of solutions for polynomial functions;
• Interpret piecewise, absolute value, polynomial, exponential, and rational expressions and parts of these expressions in terms of a context;
• Use equivalent forms of exponential expressions to reveal rates based on different intervals of the domain;
• Apply the remainder theorem;
• Rewrite simple rational expressions in different forms;
• Divide rational expressions;

• Solve problems that require creating absolute value, polynomial, exponential, and rational equations and inequalities in one variable. Justify solution methods and steps of the solving process; 
• Create and graph absolute value, polynomial, and exponential equations in two variables;
• Create and graph rational equations in two variables;
• Represent contextual situations by creating a system of equations, and approximate solutions using technology;
• Use mathematical reasoning to justify all steps in solving equations;
• Solve and interpret one-variable rational equations, and explain extraneous solutions;
• Understand trigonometric ratios as functions of angle measure;
• Interpret statements that use function notation in terms of a context;
• Interpret functions and key features, including periodicity or discontinuities, given various representations in context;
• Analyze continuous piecewise functions to identify key features;
• Compare key features of two different functions given with different representations;
• Build polynomial and exponential functions with real solutions from a mathematical or real- world context, including combining standard function types with arithmetic;
• Recognize the effect of replacing f(x) with kf(x), f(x) + k, f(x + k), and f(kx);
• Find the inverse function for linear, quadratic, and exponential equations;
• Compare end behavior of functions, and show that a quantity increasing exponentially eventually exceeds a quantity increasing as a polynomial function;
• Use logarithms to express solutions to equations, and evaluate logarithms using technology;
• Interpret the relationship between sine and cosine and radian measure of an angle;
• Verify properties of the centers of triangles;
• Complete a proof of theorems about parallelograms;
• Complete a proof of theorems about circles;
• Interpret the relationship between arc length and central angle measure as the radian measure of an angle;
• Find arc lengths and areas of sectors of circles in contextual problems;
• Find the center and radius of a circle given in standard form;
• Use volume formulas to solve multistep problems in context;
• Identify cross sections of three-dimensional objects and three-dimensional objects formed by rotating two-dimensional objects;
• Apply geometric concepts to model and solve contextual problems;
• Identify when to use sample surveys, experiments, and observational studies and how randomization applies in each;
• Use simulations to estimate margins of error and to analyze differences between samples from distinct populations;
• Identify sources of data, designs of studies, and the ways data are graphically displayed in articles and websites.

Level 3

Level 3 students can:

• Determine the number of solutions for polynomial functions;
• Interpret piecewise, absolute value, polynomial, exponential, and rational expression in terms of a context;
• Write equivalent expressions for piecewise, absolute value, polynomial (degree 3 or higher), and rational expressions (with linear denominator);
• Determine factors of polynomial expressions, solutions of polynomial equations, and zeros of polynomial functions;
• Rewrite simple rational expressions in different forms where the simplified form has a remainder of zero;
• Add and subtract rational expressions with linear denominators;
• Multiply rational expressions;
• Create absolute value, polynomial, exponential, and rational equations and inequalities in one variable;
• Create and graph absolute value and exponential equations in two variables;
• Create systems of equations and inequalities that model a context;
• Use mathematical reasoning to justify all steps in solving absolute value, polynomial, and exponential equations;
• Solve and interpret one-variable rational equations;
• Approximate solutions using graphing technology or a table of values;
• Evaluate piecewise functions for inputs in the domain;
• Interpret key features of functions given various representations in context;
• Analyze absolute value, polynomial, exponential, and trigonometric functions to identify key features;
• Compare key features of two functions of the same type given with different representations;
• Build polynomial and exponential functions with real solutions from a mathematical or real- world context;
• Recognize the effect of replacing f(x) with kf(x), f(x) + k, and f(x + k) for absolute value, polynomial, exponential, and trigonometric functions;
• Find the inverse function for a linear or quadratic equation;
• Compare end behavior of different function types;
• Evaluate logarithms using technology;
• Find radian measure;
• Interpret the parameters of a sine function;
• Interpret key features of the function in terms of a context;
• Find the centers of triangles;
• Provide statements or reasons to complete parallelogram proofs;
• Solve problems about parallelograms and other two-dimensional figures;
• Provide statements or reasons to complete circle proofs;
• Solve problems about circles;