North CarolinaNorth Carolina Discrete Math Curriculum
Lessons and practice for every Discrete Math topic. Aligned to NC Standard courses of Study Math so North Carolina students can keep up and get ahead.
NC High School Discrete Math Curriculum | StudyPugHelp
ID | Standard | StudyPug Topic |
|---|---|---|
CC.HSS.CP.B.9 | Use permutations and combinations to compute probabilities of compound events and solve problems. |
CC.HSS.CP.A.1 | Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not"). |
CC.HSS.CP.A.2 | Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. |
CC.HSS.CP.A.3 | Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. |
CC.HSS.CP.A.5 | Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. |
CC.HSS.MD.A.1 | Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. |
CC.HSS.MD.A.2 | Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. |
CC.HSS.MD.A.3 | Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. |
CC.HSS.MD.B.7 | Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). |
CC.HSF.IF.A.1 | Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). |
CC.HSF.IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. |
CC.HSF.IF.A.3 | Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. |
CC.HSF.IF.B.5 | Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. |
CC.HSF.BF.A.2 | Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. |
CC.HSF.BF.B.4 | Find inverse functions. |
CC.HSF.LE.A.2 | Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). |
CC.HSA.SSE.B.4 | Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. |
CC.HSN.VM.C.6 | Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. |
CC.HSN.VM.C.9 | Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. |
CC.HSN.VM.C.10 | Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. |
CC.HSN.VM.C.11 | Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. |
CC.HSA.REI.C.8 | Represent a system of linear equations as a single matrix equation in a vector variable. |
CC.HSA.REI.C.9 | Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater). |
CC.HSS.ID.A.2 | Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. |
CC.HSS.ID.A.3 | Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). |
CC.HSS.IC.A.1 | Understand statistics as a process for making inferences about population parameters based on a random sample from that population. |
CC.HSS.IC.B.3 | Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. |
CC.HSS.IC.B.4 | Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. |
CC.HSN.VM.A.1 | Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes. |
CC.HSN.VM.A.2 | Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. |
CC.HSN.VM.B.4 | Add and subtract vectors. |
CC.HSN.VM.B.5 | Multiply a vector by a scalar. |
North Carolina Discrete Math: Topics and Skills
North Carolina high school Discrete Math draws from several branches of mathematics, giving students tools they'll use in statistics, computer science, and advanced math courses. The course follows the NC Standard Course of Study Math and covers four major areas: probability, functions and sequences, matrices, and statistics.
Probability and Counting
Students begin by learning how to count outcomes systematically using permutations and combinations, then apply these methods to calculate probabilities of compound events. Key concepts include:
- Describing sample spaces using set notation — unions, intersections, and complements
- Independent and dependent events
- Conditional probability: P(A|B) = P(A and B) / P(B)
- Two-way frequency tables and their use as sample spaces
- The general Multiplication Rule: P(A and B) = P(A)P(B|A)
These topics build a strong foundation for interpreting real-world data and making informed decisions using probability models.
Random Variables and Probability Distributions
Students learn to define random variables, graph probability distributions, and calculate expected values. Both theoretical and empirical probability distributions are developed. This includes analyzing decisions using probability — such as product testing scenarios or medical testing models — which connects math to real-life critical thinking.
Functions, Sequences, and Series
The functions unit reinforces core concepts students need for higher math:
- Function notation and evaluating functions for given inputs
- Domain, range, and interpreting graphs of functions
- Arithmetic and geometric sequences — recursive and explicit forms
- Inverse functions
- Constructing linear and exponential functions from graphs, tables, or input-output pairs
- Deriving and applying the formula for the sum of a finite geometric series
Matrices
Students explore matrices as tools for representing and manipulating data. Topics include:
- Matrix addition and multiplication
- Properties of matrix multiplication — associative and distributive, but not commutative
- The zero matrix, identity matrix, and determinants
- Matrix inverses and solving systems of linear equations using matrices
- Vectors as single-column matrices and matrix transformations of vectors
Statistics and Data Analysis
The statistics section prepares students to interpret and compare data sets critically:
- Comparing center (mean, median) and spread (IQR, standard deviation) across data sets
- Understanding the effect of outliers on data interpretation
- Computing and interpreting correlation coefficients
- Distinguishing correlation from causation
- Sample surveys, experiments, and observational studies
- Estimating population parameters and understanding margin of error
Vectors
Students are introduced to vectors as quantities with both magnitude and direction. Skills include representing vectors as directed line segments, finding vector components, adding and subtracting vectors, and multiplying a vector by a scalar.
How StudyPug Supports North Carolina Discrete Math Students
StudyPug provides lessons and practice problems for every topic in the North Carolina Discrete Math course. All content is aligned to the NC Standard Course of Study Math. Students can work through each topic at their own pace, revisit challenging concepts, and practice with problems similar to what they'll see in class.