Discrete Math Worksheets | Sets, Logic, Counting and Graphs with Answer Key

Discrete math worksheets for high school

These discrete math worksheets are a 12 page packet with 80 questions on the basics of discrete mathematics. The worksheet is marked for grades 9 to 12.

It covers set theory, propositional logic, counting, graph theory, sequences and probability. Each topic has its own section, so a teacher can start anywhere.

Teachers who need discrete mathematics fundamentals practice for a high school elective, a math club or an early college course will find six sections here, and the discrete math with answer key lists the reasoning behind every answer.

What’s on the pages

The worksheet has six sections, and each one has its own heading and short directions.

• Set theory: 15 multiple choice questions, such as the cardinality of a set, De Morgan’s Law for the complement of a union, and unions with subsets.
• Propositional logic: 15 true or false statements, such as logical equivalence by truth table, tautologies and the contrapositive of an implication.
• Combinatorics and counting: 15 fill in the blank questions that use a Number Bank, such as the permutation P(6, 2) and the factorials 6! and 4!.
• Graph theory basics: 15 multiple choice questions, such as the Handshaking Lemma, Euler’s formula for planar graphs and what a connected graph with no cycles is called.
• Probability and sequences: 10 multiple choice questions, such as the type of sequence 3, 9, 27, 81 and the constants in arithmetic and geometric sequences.
• Advanced logic and sets: 10 true or false statements, such as the union of a set and its complement and the cardinality of a power set.

The language is formal but the numbers are small, so students concentrate on the ideas instead of long calculations.

Students who want set theory and logic worksheets will find the first two sections ready for that use, and the graph theory basics worksheet pages in the fourth section are a quick way to introduce vertices, edges and cycles. The discrete math worksheets are written as practice rather than as a full textbook, so they pair with any lesson.

The same discrete math worksheets can be used again by a teacher who wants to check progress, because the sections stand alone and keep the same format.

What’s in the download

• Student worksheet: 12 pages
• Answer key: 17 pages, with a short explanation after each answer
• Answer sheet: 4 pages
• Lesson plan: 2 pages

The four parts add up to 35 pages, and everything comes as PDF.

How to use these discrete math worksheets

The lesson plan is set for 90 minutes. Its objectives are set operations such as union, intersection and complement, truth values of propositions with AND, OR, NOT and implications, permutations, combinations and factorials, and the key parts of graphs such as vertices and edges.

The materials list a scientific calculator for the counting questions, so students can check factorials and permutations.

You can use the packet in order, as a short course, or section by section as a review. The set theory and logic sections fit together, and the counting and graph sections suit a second week.

Many students meet these ideas for the first time in a discrete math course. The explanations in the key help them see why De Morgan’s Law or Euler’s formula gives the answer it does.

The answer sheet keeps the worksheet clean for reuse, so a teacher can run the same practice with another group.

Where it fits

Use it for a discrete math unit, an enrichment group, a math club, test preparation or independent study. Homeschool families can use it as a first look at the topics before a full course.

Take a look at the preview pages before you buy, so you can see the worksheet, the answer key and the answer sheet.

For more practice, browse the math worksheets, the wider set of printable worksheets or the whole shop.

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