Sure! Here’s a unit test on rational and irrational numbers. This test includes a variety of question types, including multiple choice, short answer, and problems that require explanations.
Rational and Irrational Numbers Unit Test
Name: _________________________
Date: _________________________
Part 1: Multiple Choice (1 point each)
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Which of the following is a rational number? a) \( \sqrt{2} \)
b) \( \frac{1}{3} \)
c) \( \pi \)
d) \( e \) -
Which number is irrational? a) -1
b) 0
c) \( \sqrt{9} \)
d) \( \sqrt{5} \) -
The sum of two rational numbers is: a) Always rational
b) Always irrational
c) Sometimes rational, sometimes irrational
d) None of the above -
Which of the following intervals contains only irrational numbers? a) \( (0, 1) \)
b) \( (1, 2) \)
c) \( (\sqrt{2}, \sqrt{3}) \)
d) \( (3, \sqrt{5}) \)
Part 2: Short Answer (2 points each)
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Provide an example of a rational number and explain why it is rational.
Answer: _________________________________________________________
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Provide an example of an irrational number and explain why it is irrational.
Answer: _________________________________________________________
-
Explain the difference between rational and irrational numbers.
Answer: _________________________________________________________
Part 3: Problems (3 points each)
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Determine whether the following numbers are rational or irrational:
a) \( -\frac{7}{2} \)
b) \( 0.3333... \) (repeating)
c) \( \frac{22}{7} \)
d) \( \sqrt{16} \)
e) \( \sqrt{3} \)Answers:
a) _______________
b) _______________
c) _______________
d) _______________
e) _______________ -
If a rational number is expressed as a decimal, can it be a non-terminating decimal? Explain your answer.
Answer: _________________________________________________________
-
If you add an irrational number to a rational number, what type of number do you get? Justify your answer with an example.
Answer: _________________________________________________________
Part 4: True or False (1 point each)
- Every whole number is a rational number. (True/False)
- The number \( \frac{0}{10} \) is irrational. (True/False)
- The product of two irrational numbers is always irrational. (True/False)
Scoring Guide:
- Part 1: 4 points total
- Part 2: 6 points total
- Part 3: 15 points total
- Part 4: 3 points total
Total Points: 28
Instructions for Grading:
- Correct answers in Part 1 and Part 4 receive full points; partial credit may be given for explanations if needed.
- For Parts 2 and 3, evaluate based on the completeness and correctness of the explanations and examples provided.
Feel free to modify any part of the test to better suit your needs!