Grade 9 Number & Quantity Practice ā€” Easy

Question 1 of 21Score 0/0Easy

Question 1 of 21: Which set contains ALL integers?

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Keep going: Read the lesson: The Real Number System
Answer key for parents & teachers (21 questions)
  1. Which set contains ALL integers? ā€” Integers and rationals. Every integer is also a rational number (p/q with q=1), so integers āŠ‚ rationals.
  2. Is 0.333... (repeating) rational or irrational? ā€” Rational, because it equals 1/3. 0.333... = 1/3, a ratio of two integers. Any repeating decimal is rational.
  3. Which of these is a NATURAL number? ā€” 5. Natural numbers are positive counting numbers: 1, 2, 3, ā€¦ 5 is the only natural number in this list.
  4. Ļ€ (pi) is best classified as: ā€” An irrational number. Ļ€ ā‰ˆ 3.14159ā€¦ is irrational ā€” its decimal expansion never terminates or repeats.
  5. Every whole number is also a(n): ā€” Integer. Whole numbers (0,1,2,ā€¦) are integers. Note: 0 is whole but not natural, so not every whole is natural.
  6. Which number is rational but NOT an integer? ā€” 3/4. 3/4 = 0.75, rational but not a whole number or integer. āˆš4=2 and āˆš25=5 are integers; āˆ’7 is an integer.
  7. The set of irrational numbers and the set of rational numbers are: ā€” Disjoint (no shared elements). No number can be both rational and irrational. They are completely disjoint and together they make up the real numbers.
  8. What does the exponent 1/2 mean? ā€” Take the square root. x^(1/2) = āˆšx. The denominator of a rational exponent is the root index.
  9. Evaluate 9^(1/2). ā€” 3. 9^(1/2) = āˆš9 = 3.
  10. Rewrite āˆ›x using rational exponent notation. ā€” x^(1/3). The nth root of x is x^(1/n). āˆ›x = x^(1/3).
  11. Evaluate 27^(1/3). ā€” 3. 27^(1/3) = āˆ›27 = 3 (since 3Ā³ = 27).
  12. In the expression x^(m/n), the numerator m represents: ā€” The power applied after taking the root. x^(m/n) = (āæāˆšx)^m. The denominator n is the root; the numerator m is the power.
  13. Evaluate 4^(3/2). ā€” 8. 4^(3/2) = (āˆš4)Ā³ = 2Ā³ = 8.
  14. Simplify x^(2/3) using radical notation. ā€” āˆ›(xĀ²). x^(2/3) = āˆ›(xĀ²). The denominator is the root (cube root), the numerator is the power (squared).
  15. What does i equal? ā€” āˆš(āˆ’1). The imaginary unit i is defined as i = āˆš(āˆ’1). It is not a real number.
  16. What is iĀ²? ā€” āˆ’1. iĀ² = (āˆš(āˆ’1))Ā² = āˆ’1. This is the fundamental property of the imaginary unit.
  17. Simplify āˆš(āˆ’9). ā€” 3i. āˆš(āˆ’9) = āˆš(9 Ā· (āˆ’1)) = āˆš9 Ā· āˆš(āˆ’1) = 3 Ā· i = 3i.
  18. What is iā“? ā€” 1. iā“ = (iĀ²)Ā² = (āˆ’1)Ā² = 1. The cycle of powers of i has period 4.
  19. What is iĀ³? ā€” āˆ’i. iĀ³ = iĀ² Ā· i = (āˆ’1) Ā· i = āˆ’i.
  20. Simplify āˆš(āˆ’25). ā€” 5i. āˆš(āˆ’25) = āˆš(25 Ā· (āˆ’1)) = 5i.
  21. To find i^n for large n, you: ā€” Divide n by 4 and use the remainder. Powers of i cycle with period 4: iĀ¹=i, iĀ²=āˆ’1, iĀ³=āˆ’i, iā“=1, then repeats. Remainder 0ā†’1, 1ā†’i, 2ā†’āˆ’1, 3ā†’āˆ’i.