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Discrete Mathematics

South Carolina Discrete Mathematics Curriculum

Video lessons and practice for every Discrete Math topic. Aligned to SC College Career Ready Standards for South Carolina high school students.

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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.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.5

Multiply a vector by a scalar.

South Carolina Discrete Mathematics Curriculum

Discrete Mathematics is a high school course in South Carolina that covers a wide range of topics, including probability, combinatorics, matrix operations, functions, sequences, and vector quantities. All content on StudyPug aligns to SC College Career Ready Standards, so South Carolina students can follow along with exactly what their teacher is covering in class.

Probability and Statistics

Students learn to use permutations and combinations to compute probabilities of compound events. Topics include independent and conditional probability, two-way frequency tables, random variables, expected value, and probability distributions. These skills are essential for data analysis and real-world decision-making.

  • Permutations and combinations for compound events
  • Independent events and conditional probability
  • Two-way frequency tables and sample spaces
  • Random variables and expected value
  • Empirical and theoretical probability distributions

Functions and Sequences

This section covers the definition and notation of functions, domain and range, and how sequences relate to functions. Students write arithmetic and geometric sequences recursively and explicitly, find inverse functions, and derive the formula for the sum of a finite geometric series.

  • Function notation and evaluation
  • Domain and range of functions
  • Arithmetic and geometric sequences
  • Inverse functions
  • Sum of a finite geometric series

Matrices

Students use matrices to represent and manipulate data, including payoffs and network relationships. They explore matrix multiplication, identity and zero matrices, determinants, and matrix inverses. Students also apply matrices to solve systems of linear equations.

  • Matrix addition and multiplication
  • Identity and zero matrices
  • Determinants and multiplicative inverses
  • Matrix transformations of vectors
  • Solving systems of linear equations with matrices

Data Analysis and Vectors

Students compare data distributions using center and spread, interpret correlation coefficients, and distinguish between correlation and causation. The vector unit covers magnitude, direction, components, addition, subtraction, and scalar multiplication.

  • Center and spread of data distributions
  • Correlation coefficient and linear fit
  • Correlation vs. causation
  • Vector quantities and directed line segments
  • Adding, subtracting, and scaling vectors