Will this help with my child's high school Discrete Math homework?

Yes. StudyPug covers every strand in NC Discrete Math - from conditional probability and expected value to matrix operations and statistical inference - so students can get unstuck on homework topics quickly with worked examples and practice problems.

How long are the video lessons for Discrete Math?

Most video lessons run between 5 and 15 minutes, keeping concepts focused and digestible. Students can pause, rewind, and rewatch at any time, making it easy to review a tricky topic like the Multiplication Rule or matrix inverses at their own pace.

Is there a state test for high school Discrete Math in North Carolina?

Discrete Math is not a designated NC EOC assessment course. Students in NC are assessed through NC EOG and NC EOC tests in designated grades and courses; Discrete Math is typically taken as an elective outside those tested courses, so no dedicated state exam applies.

Can my child use StudyPug on a tablet or phone?

Yes. StudyPug works on tablets, phones, and desktop computers, so your child can practice probability distributions, review matrix operations, or watch a lesson on geometric sequences from any device, at school or at home.

Can I try StudyPug before paying?

Yes. StudyPug offers free sample lessons so you can explore the content before committing. If you subscribe and decide it is not the right fit, there is a 30-day money-back guarantee - no risk to getting started.

NC High School Discrete Math Curriculum

Give your high schooler the support they need to succeed in Discrete Math. Our lessons follow the NC Standard Course of Study, covering probability, matrices, functions, sequences, and data analysis.

NC High School Discrete Math Curriculum

IDStandardStudyPug Topic

CC.HSS.CP.B.9Use permutations and combinations to compute probabilities of compound events and solve problems.
- Permutations
- Combinations
- Probability involving permutations and combinations
CC.HSS.CP.A.1Describe 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").
- Introduction to probability
- Organizing outcomes
- Introduction to probability
- Set notation
- Set builder notation
- Intersection and union of 2 sets
- Intersection and union of 3 sets
CC.HSS.CP.A.2Understand 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.
- Probability of independent events
- Multiplication rule for
- Probability of independent events
CC.HSS.CP.A.3Understand 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.
- Conditional probability
CC.HSS.CP.A.5Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
- Comparing experimental and theoretical probability
CC.HSS.MD.A.1Define 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.
- Probability distribution - histogram, mean, variance & standard deviation
CC.HSS.MD.A.2Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
- Properties of expectation
CC.HSS.MD.A.3Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
- Binomial distribution
- Mean and standard deviation of binomial distribution
CC.HSS.MD.B.7Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
- Type 1 and type 2 errors
CC.HSF.IF.A.1Understand 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).
- Domain and range of a function
- Function notation (advanced)
- Identifying functions
CC.HSF.IF.A.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
- Function notation
- Difference quotient: applications of functions
CC.HSF.IF.A.3Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
- Greatest common factors (GCF)
- Introduction to sequences
- Sigma notation
CC.HSF.IF.B.5Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
- Point of discontinuity
- Even and odd functions
CC.HSF.BF.A.2Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
- Arithmetic sequences
- Geometric sequences
- Arithmetic series
- Geometric series
- Infinite geometric series
CC.HSF.BF.B.4Find inverse functions.
- Finding the quadratic functions for given parabolas
- Inverse functions
CC.HSF.LE.A.2Construct 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).
- Graphing linear functions using table of values
CC.HSA.SSE.B.4Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
- Geometric series
- Factor by taking out the greatest common factor
- Factor by grouping
- Factoring difference of squares: $x^2 - y^2$
CC.HSN.VM.C.6Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
- Notation of matrices
- Adding and subtracting matrices
CC.HSN.VM.C.9Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
- Properties of matrix multiplication
CC.HSN.VM.C.10Understand 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.
- Zero matrix
- Identity matrix
- The determinant of a 2 x 2 matrix
- The determinant of a 3 x 3 matrix (General & Shortcut Method)
- The Inverse of a 2 x 2 matrix
CC.HSN.VM.C.11Multiply 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.
- Transforming vectors with matrices
- Transforming shapes with matrices
CC.HSA.REI.C.8Represent a system of linear equations as a single matrix equation in a vector variable.
- Representing a linear system as a matrix
- Notation of matrices
- Adding and subtracting matrices
- Scalar multiplication of matrices
CC.HSA.REI.C.9Find 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).
- The Inverse of a 2 x 2 matrix
- Solving linear systems using 2 x 2 inverse matrices
- Matrix multiplication
- The three types of matrix row operations
CC.HSS.ID.A.2Use 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.
- Median and mode
- Mean
- Range and outliers
- Center of a data set: mean, median, mode
- Spread of a data set - standard deviation & variance
CC.HSS.ID.A.3Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
- Application of averages
- Shapes of distributions
CC.HSS.IC.A.1Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
- Sampling methods
CC.HSS.IC.B.3Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
- Census and bias
CC.HSS.IC.B.4Use 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.
- Margin of error
- Confidence intervals to estimate population mean
- Making a confidence interval
CC.HSN.VM.A.1Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes.
- Use sine ratio to calculate angles and sides (Sin = o / h)
- Introduction to vectors
- Magnitude of a vector
- Direction angle of a vector
CC.HSN.VM.A.2Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
- Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- Scalar multiplication of vectors
- Equivalent vectors
CC.HSN.VM.B.4Add and subtract vectors.
- Slope equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- Adding and subtracting vectors in component form
- Operations on vectors in magnitude and direction form
CC.HSN.VM.B.5Multiply a vector by a scalar.
- Slope intercept form: y = mx + b
- Unit vector

Discrete Math

About High School North Carolina Discrete Math

North Carolina's Discrete Math course follows the NC Standard Course of Study, organized around probability and statistics, functions and sequences, matrix algebra, and vector quantities. Students work through conditional probability, random variables and expected value, matrix operations and transformations, arithmetic and geometric sequences, data distributions, correlation, and inferential statistics. StudyPug provides video lessons, step-by-step worked examples, and practice problems aligned to every strand in this course.

Strands: probability and statistics, functions and sequences, matrix algebra, and vectors and data analysis
Video lessons and step-by-step worked examples for every topic
Practice problems with instant feedback aligned to NC Standard Course of Study
Study tools available on desktop, tablet, and phone anytime

Curriculum topics by strand

Find lessons and practice for every Discrete Math topic, organized by strand and aligned to the NC Standard Course of Study.

Topic includes:

Practice

Video

Quiz

Standard

StudyPug Topic

NC High School Discrete Math Topics

Probability and Counting: Permutations, combinations, compound event probabilities, sample spaces, unions, intersections, and complements of events.
Conditional Probability and Independence: Independent events, conditional probability P(A|B), the general Multiplication Rule, two-way frequency tables, and everyday applications of probability concepts.
Random Variables and Probability Distributions: Defining random variables, graphing probability distributions, calculating expected value from theoretical and empirical data, and analyzing decisions using probability.
Functions and Sequences: Function notation, domain and range, arithmetic and geometric sequences defined recursively and explicitly, inverse functions, linear and exponential functions, and the sum of finite geometric series.
Matrix Algebra: Representing data with matrices, matrix multiplication properties, identity and zero matrices, determinants, matrix inverses, vector-matrix multiplication, and solving systems of linear equations using matrices.
Statistics and Data Analysis: Comparing center and spread across data sets, interpreting outliers, correlation coefficients, distinguishing correlation from causation, sampling methods, margin of error, and population inference.
Vectors: Vector quantities, magnitude and direction, components of vectors, adding and subtracting vectors, and scalar multiplication.

How StudyPug Helps NC High School Discrete Math Students

When a student hits a wall on conditional probability or gets confused by matrix inverses, StudyPug provides clear video lessons that break each concept into manageable steps. Practice problems with instant feedback let students check their understanding right away, and step-by-step video solutions show exactly where reasoning went wrong - so confusion turns into confidence rather than frustration.

Every lesson is available on demand, meaning students can revisit the expected value formula before a test or work through geometric sequences on a weekend without waiting for class. The content is organized strand by strand, matching the structure of the NC Standard Course of Study so nothing studied on StudyPug is out of place in a North Carolina Discrete Math classroom.

Aligned to NC High School Discrete Math Curriculum

StudyPug's Discrete Math content is built to match the NC Standard Course of Study for high school mathematics. Each lesson maps to the specific skills students are expected to develop in North Carolina - from applying the Multiplication Rule and interpreting correlation coefficients to working with matrix transformations and constructing probability distributions - so what students practice on StudyPug directly supports what they are learning in class.

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Written by the StudyPug Math Team

Last updated June 5, 2026

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