VirginiaVirginia Discrete Mathematics Curriculum
Lessons and practice for every Discrete Mathematics topic. Aligned to Virginia Mathematics Standards of Learning for high school students.
Virginia Discrete Mathematics 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. |
Virginia Discrete Mathematics: Full Course Overview
Discrete Mathematics is a high school course in Virginia that brings together topics from probability, algebra, statistics, and linear algebra. Aligned to Virginia's Mathematics Standards of Learning (SOL), this course prepares students for college mathematics and careers in STEM, data science, and computer science.
Probability and Statistics
A major portion of Discrete Mathematics focuses on probability. Virginia students learn to use permutations and combinations to count outcomes and calculate probabilities of compound events. From there, students explore:
- Sample spaces and events (unions, intersections, complements)
- Independent and dependent events
- Conditional probability using P(A and B)/P(B)
- Two-way frequency tables and their use in identifying independence
- The general Multiplication Rule: P(A and B) = P(A)P(B|A)
StudyPug has practice problems for every one of these probability standards, with worked examples that walk through each step clearly.
Random Variables and Probability Distributions
Students define random variables, build probability distributions, and calculate expected value. They work with both theoretical and empirical probability distributions, then apply probability concepts to real-world decisions — such as product testing and medical testing scenarios.
Functions and Sequences
Discrete Mathematics revisits and extends function concepts. Virginia students work with:
- Function notation and domain/range relationships
- Sequences as functions, including recursive definitions
- Arithmetic and geometric sequences — both recursive and explicit formulas
- Inverse functions
- Linear and exponential functions from graphs, tables, and descriptions
- The formula for the sum of a finite geometric series
Matrices and Linear Systems
Matrix operations are a core component of this course. Students learn to represent data with matrices, perform matrix multiplication, and understand properties like the associative and distributive laws. Key topics include:
- Matrix addition and multiplication
- Identity and zero matrices; determinants and inverses
- Multiplying vectors by matrices as transformations
- Representing systems of linear equations as matrix equations
- Solving systems using inverse matrices (with technology for 3×3 or larger)
Data Analysis and Inference
Students interpret data distributions by comparing center and spread across data sets. They compute and interpret correlation coefficients, distinguish between correlation and causation, and understand the role of random sampling in statistical inference. Topics also include margin of error and the differences between surveys, experiments, and observational studies.
Vectors
The course concludes with an introduction to vectors. Students represent vector quantities using directed line segments, find vector components, add and subtract vectors, and multiply vectors by scalars. These skills connect matrix transformations to geometric reasoning.
How StudyPug Helps Virginia Discrete Math Students
StudyPug covers every topic in Virginia's Discrete Mathematics course with step-by-step lessons and practice problems. Whether your student is stuck on conditional probability, matrix inverses, or geometric series, they can find the exact topic and work through it at their own pace. StudyPug is accessible on any device and available anytime — making it easy to keep up with class or get ahead.