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Ch 8: Michigan Merit Exam - Math: Mathematical Reasoning

About This Chapter

The short video lessons and quizzes in this chapter about mathematical reasoning will provide you with the knowledge and practice you need to answer similar questions on the Michigan Merit Exam.

Michigan Merit Exam - Math: Mathematical Reasoning

In this chapter, you can watch short but fun video lessons that will remind you of the meanings of statistical arguments and critical thinking. End of the lesson quizzes will evaluate your comprehension of math principles. The mixture of video lessons and quizzes will help you be able to provide the right answers to Michigan Merit Exam questions based on the following:

  • Deductive and inductive reasoning
  • How statistical and logical arguments differ
  • Critical thinking in math
  • Math principles and problem solving
  • Definitions of the axiomatic system, direct proofs, and geometric proofs
  • Proof by contradiction

Use the Timeline to go back and forth between sections in the video lessons. If you get any of your quiz questions incorrect, you can go to the specific parts of the video lessons that address the answers. Our instructors will be happy to answer any of your questions about the lessons.

8 Lessons in Chapter 8: Michigan Merit Exam - Math: Mathematical Reasoning
Test your knowledge with a 30-question chapter practice test
Reasoning in Mathematics: Inductive and Deductive Reasoning

1. Reasoning in Mathematics: Inductive and Deductive Reasoning

Many people think that deductive and inductive reasoning are the same thing. It is assumed these words are synonymous. They are not. This lesson reveals the reality of these two types of reasoning.

The Differences Between Statistical & Logical Arguments

2. The Differences Between Statistical & Logical Arguments

Logical arguments and statistical arguments are both important, rigorous ways in which premises can support conclusions; however, there are several important differences, which we'll discuss in this lesson.

Critical Thinking and Logic in Mathematics

3. Critical Thinking and Logic in Mathematics

Logic has its own unique language and way of defining what is true and false. Watch this video lesson to learn how you can critically think in the language of logic while working with math.

Mathematical Principles for Problem Solving

4. Mathematical Principles for Problem Solving

Solving problems is not just a simple, straightforward process. There are a few principles that can help you as you approach any problem solving scenarios. This lesson covers those principles with examples.

The Axiomatic System: Definition & Properties

5. The Axiomatic System: Definition & Properties

Learn what kinds of things are included in an axiomatic system in this video lesson. Also learn why consistency, independence, and completeness are important in axiomatic systems.

Direct Proofs: Definition and Applications

6. Direct Proofs: Definition and Applications

In math, we can't explain that something is true just because. That's not enough. In this lesson, we'll learn to prove things using one of our most straightforward tools, the direct proof.

Geometric Proofs: Definition and Format

7. Geometric Proofs: Definition and Format

Do you have something to prove? Can you explain why? In this lesson, we'll learn all about geometric proofs, including the parts that comprise a proof.

Proof by Contradiction: Definition & Examples

8. Proof by Contradiction: Definition & Examples

One of several different ways to prove a statement in mathematics is proof by contradiction. Learn the definition of this method and observe how it is applied to proving a statement's truth value through examples and exploration.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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Other Chapters

Other chapters within the Michigan Merit Exam - Math: Test Prep & Practice course

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