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

Yes. StudyPug covers every strand in the Virginia SOL Discrete Mathematics course, including probability, matrices, functions, and statistics, so your child can find the exact topic they are stuck on, watch a worked example, and then try practice problems to check their understanding.

How long are the video lessons for Discrete Mathematics?

Most video lessons run between five and fifteen minutes and focus on one concept at a time, such as conditional probability or matrix multiplication, so students can watch the relevant lesson without sitting through unrelated material.

Is there a Virginia state test for high school Discrete Mathematics?

Virginia's Standards of Learning assessments for mathematics are tied to specific courses such as Algebra I, Geometry, and Algebra II. Discrete Mathematics does not have its own separate SOL end-of-course test, so there is no standalone state exam for this course.

Can my child use StudyPug on a tablet or phone?

Yes. StudyPug works on smartphones, tablets, laptops, and desktop computers through any modern browser, so your child can practice Discrete Mathematics topics at home, at school, or on the go without needing to install anything.

Can I try StudyPug before paying?

Yes. StudyPug offers free sample lessons so you can explore the Discrete Mathematics content before committing, and every paid plan is backed by a 30-day money-back guarantee if you decide it is not the right fit.

VA High School Discrete Math Curriculum

Give your student a clear path through Virginia's Discrete Mathematics course, with lessons and practice covering probability, matrices, functions, and data analysis built around what their class actually teaches.

VA 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 Mathematics

About High School Virginia Discrete Mathematics

Virginia's high school mathematics courses follow the Virginia Standards of Learning (SOL), organized around connected strands of content and reasoning. Discrete Mathematics works through probability and counting methods, conditional probability and independence, random variables and expected value, functions and sequences, matrix operations, statistical reasoning, and vector quantities. StudyPug provides video lessons, worked examples, and practice problems aligned to each of these strands so students can work at their own pace alongside class.

Strands: probability and counting, conditional probability, random variables, functions and sequences, matrices, statistics and data analysis, and vectors
Video lessons with step-by-step explanations for every topic
Practice problems with instant feedback for each strand
Content aligned to the Virginia Standards of Learning (SOL) for Discrete Mathematics

Curriculum topics by strand

Browse lessons and practice problems organized by strand and aligned to the Virginia Standards of Learning (SOL) for high school Discrete Mathematics.

Topic includes:

Practice

Video

Quiz

Standard

StudyPug Topic

VA High School Discrete Mathematics Topics

Probability and Counting: Permutations, combinations, compound event probabilities, and strategies for solving counting problems.
Conditional Probability and Independence: Sample spaces as sets, unions and intersections, the Multiplication Rule, two-way frequency tables, and interpreting independence in everyday situations.
Random Variables and Expected Value: Defining random variables, graphing probability distributions, and calculating and interpreting expected value from both theoretical and empirical models.
Functions and Sequences: Function notation, domain and range, arithmetic and geometric sequences written recursively and explicitly, inverse functions, linear and exponential function construction, and the sum of a finite geometric series.
Matrices: Matrix representation of data, matrix multiplication properties, identity and zero matrices, determinants, vector-matrix multiplication, and solving systems of linear equations using inverse matrices.
Statistics and Data Analysis: Comparing center and spread of data sets, correlation coefficients, distinguishing correlation from causation, sample surveys versus experiments, and estimating population parameters with margins of error.
Vectors: Magnitude and direction, finding vector components, adding and subtracting vectors, and multiplying a vector by a scalar.

How StudyPug Helps Virginia High School Discrete Mathematics Students

When a student gets stuck on a topic like conditional probability or matrix inverses, StudyPug lets them go back to the specific concept, watch a focused video lesson, and then work through practice problems with instant feedback. Each lesson is built around the steps a student needs to follow, not just the final answer, so the reasoning behind the method is always clear.

Because the content is organized by strand and aligned to the Virginia Standards of Learning, students can move directly to whichever part of the Discrete Mathematics course their class is working on without searching through unrelated material.

Aligned to Virginia High School Discrete Mathematics Curriculum

Every lesson and practice problem in StudyPug's Discrete Mathematics course is matched to the Virginia Standards of Learning (SOL), covering probability and counting, conditional probability, random variables, functions and sequences, matrices, statistical reasoning, and vectors in the same way Virginia schools teach them, so what students practice on StudyPug directly supports what they are doing in class.

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Written by the StudyPug Math Team

Last updated June 5, 2026

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