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

Yes. StudyPug covers every strand in Illinois high school Discrete Mathematics, including probability, matrix operations, and data analysis, so your child can find help on the exact topic assigned in class.

How long are the video lessons for Discrete Mathematics?

Most video lessons run between five and fifteen minutes, focusing on one concept at a time. Your child can pause, rewind, and rewatch as many times as needed before moving on to practice problems.

Is there an Illinois state test for high school Discrete Mathematics?

Illinois does not administer a dedicated state assessment specifically for Discrete Mathematics. The Illinois Assessment of Readiness covers math broadly, but Discrete Mathematics is not a separately tested course.

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Yes. StudyPug works on tablets, phones, and computers, so your child can study at home or on the go without needing to install anything extra.

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IL High School Discrete Math Curriculum

Give your student the support they need to keep up with Illinois high school Discrete Mathematics. Every strand from probability to matrices is covered with clear lessons and practice built around what Illinois schools teach.

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IL 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 Illinois Discrete Mathematics

Illinois high school Discrete Mathematics follows the Illinois Learning Standards, organized around probability, functions and sequences, matrices, statistics, and vectors. Students work through counting methods, conditional probability, random variables, matrix operations, data analysis, and vector arithmetic. StudyPug provides step-by-step lessons and practice problems for every strand so students can work at their own pace alongside class.

Strands covered: probability and counting, functions and sequences, matrices, statistics and data analysis, and vectors
Step-by-step lessons and worked examples for every topic
Practice problems with guided explanations aligned to Illinois Learning Standards
Support for STAAR-style reasoning across all discrete math strands

Curriculum topics by strand

Browse lessons and practice problems organized by strand and aligned to the Illinois Learning Standards for high school Discrete Mathematics.

Topic includes:

Practice

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StudyPug Topic

Illinois High School Discrete Mathematics Topics

Probability and Counting: Permutations, combinations, compound events, conditional probability, independence, two-way frequency tables, random variables, probability distributions, expected value, and decision analysis using probability concepts.
Functions and Sequences: Function notation, domain and range, inverse functions, arithmetic and geometric sequences defined recursively and explicitly, finite geometric series, and linear and exponential function construction.
Matrices: Matrix representation of data, matrix addition and multiplication, identity and zero matrices, determinants, multiplicative inverses, vectors as matrices, matrix transformations, and solving systems of linear equations using matrices.
Statistics and Data Analysis: Comparing center and spread across data sets, correlation coefficients, correlation versus causation, inference from random samples, sample surveys versus experiments, margin of error through simulation models.
Vectors: Vector quantities with magnitude and direction, component form, adding and subtracting vectors, and scalar multiplication.

How StudyPug Helps Illinois High School Discrete Mathematics Students

When a student gets stuck on conditional probability or matrix inverses, StudyPug lets them go back to the exact concept causing the problem. Each lesson breaks the topic into small steps, followed by practice problems with full explanations so students can check their reasoning before the next class.

Parents can track which strands their child has worked on, and students can move between topics freely - spending more time where they need it most and less time on material they have already mastered.

Aligned to Illinois High School Discrete Mathematics Curriculum

Every lesson and practice problem on StudyPug is built around the Illinois Learning Standards, so the content your child sees matches what their teacher is covering in class. From probability and counting methods through vectors and statistical inference, the sequence follows the structure Illinois schools use for Discrete Mathematics.

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Written by the StudyPug Math Team

Last updated June 5, 2026

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