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Mathematical Proofs: Introduction and Basic Techniques

This worksheet introduces fundamental concepts and techniques in mathematical proofs, suitable for Grade 10 students.

Grade 10 Math AlgebraMathematical Proofs
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Includes

Multiple ChoiceFill in the BlanksTrue / FalseShort Answer3 Custom

Standards

CCSS.MATH.CONTENT.HSG.CO.C.9CCSS.MATH.CONTENT.HSG.CO.C.10CCSS.MATH.CONTENT.HSG.CO.C.11

Topics

mathproofsgeometryalgebralogic
9 sections · Free to use · Printable
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Mathematical Proofs: Introduction and Basic Techniques

Name:

Date:

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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. Which of the following is a statement that has been proven to be true?

a

Conjecture

b

Axiom

c

Theorem

d

Hypothesis

2. A mathematical proof is a   argument that demonstrates a statement is true.

3. The starting points of a proof, which are accepted without proof, are called  .

4. A counterexample is sufficient to prove a statement true.

T

True

F

False

5. State the Law of Detachment.

6. Prove the following statement using a direct proof:

If n is an even integer, then n² is an even integer.

7. Prove the following statement using proof by contrapositive:

If n² is an odd integer, then n is an odd integer.

8. Consider the statement: "If it is raining, then the ground is wet."

a) Write the converse of the statement.

b) Write the inverse of the statement.

c) Write the contrapositive of the statement.