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Unit 1 Study Guide TOPICS YOU NEED TO KNOW Good Luck to you _______________ Rational, irrational, integers, whole and real numbers Ordering of real numbers Simplifying square roots Finding a GCF (greatest common factor) and LCM (least common multiple) How to simplify positive and negative exponents Properties of exponents Finding roots (cube and 4th roots) Absolute Values Multiplying and dividing monomials Raising a monomial to a power Finding the root of a monomial Applying these topics to constructed responses MULTIPLE CHOICE: CIRCLE THE CORRECT ANSWER. (Show work) 1. Which set includes both rational and irrational numbers?
a.
! ! !"
, ,
! ! !! b. 0. 8, 0.52, 0.2121 …
c. { −5, −17, 8}
2. Which letter on the number line below shows the approximate location of
a. W
b. X
!"
, !
b. 21, 4. 3,
4. What is the simplified for of 252 ?
a. 6 36
b. 7 36
!"
!
c. 4. 3,
9,
d. Z
!"
!
,
21
c. 6 7
21,
!"
!
d. ,
, 4. 3
!"
!
, 4. 3, 21
d. 7 6
5. The expression 2 19𝑥 simplifies to 8 19. What must be the value of x?
a. 2
b. 4
c. 6
d. 16
6. What is the GCF of the expression 36𝑝! 𝑞 + 6𝑝! 𝑞! − 18𝑝! 𝑞! ?
a. 6𝑝! 𝑞
b. 3𝑝! 𝑞!
c. 36𝑝! 𝑞!
d. 90𝑝! 𝑞!
c. 12𝑘 !
d. 16𝑘 !
7. What is the LCM of 8𝑘 𝑎𝑛𝑑 12𝑘 ! ?
a. 2k
b. 24k2
10
2.9?
c. Y
3. Which list shows the following numbers in order from greatest to least?
a. 4. 3, 21,
8,
d.
Math Standards 8. What is the value of
Unit 1 Study Guide ! !
Good Luck to you _______________ ?
!
a. 3
!"#
b.
c.
!"
!"
!"#
d. !"#$
!"
9. Which expression is equivalent to 3!! ?
a.
!
! !!
10. What is the value of
!
!
!! ∙!! ∙!!
!!
!
!!
d. −3 ∙ −3 ∙ −3
?
!
a. !"
11. Simplify
c. −
b. −3!
!!
b. !"
c. −3
d. 81
b. 3!
c. 3!
d. 3!
c. −729
d.729
c. 2! ∙ 3!
d. 2!" ∙ 3!"
c. 32
d. 64
b. −17
c. 7
d. 17
b. 48𝑎! 𝑏 !
c. 48𝑎! 𝑏 !
d. 48𝑎! 𝑏!"
?
a. 3!
12. Find the value of −3!
!
?
a. −243
b. 243
13. Which expression is equivalent to 2! ∙ 3!
a. 6!"
14. What is the value of
b. 6!"
!
!
?
256?
a. 4
b. 16
15. What is the value of −12 − 5 ?
a. −7
16. Multiply 8𝑎𝑏 ! 6𝑎! 𝑏 ! .
a. 48𝑎! 𝑏 !
17. Divide this expression
a. 6𝑦 ! 𝑧 !
!"! ! ! !
!"! ! ! !
.
!! !
b. 6𝑦 ! 𝑧 !
c.
b. 9𝑎! 𝑏!"
c. 27𝑎! 𝑏 !
!!
d.
!! !
!!
18. Evaluate 3𝑎! 𝑏 ! ! .
a. 9𝑎! 𝑏 !
d. 27𝑎! 𝑏!"
Math Standards Unit 1 Study Guide 64𝑥 ! 𝑦!"
19. Evaluate
.
a. 8𝑥 ! 𝑦 !
20. Evaluate
!
Good Luck to you _______________ b. 8𝑥 ! 𝑦 !
c. 32𝑥 ! 𝑦 !
d. 32𝑥 ! 𝑦 !
b. 𝑥 ! 𝑦 ! 𝑧
c. 𝑥 ! 𝑦!" 𝑧 !
d. 𝑥 ! 𝑦!" 𝑧
𝑥 ! 𝑦 !" 𝑧 ! .
a. 𝑥 ! 𝑦 ! 𝑧 !
CONSTRUCTED RESPONSE. Please write in complete sentences and neatly. (Show work)
21. Consider a list of integers ordered on a number line.
a. What happens to the value of a negative rational number as its absolute value increases?
b. Give an example to support your answer to Part A.
22. The following expressions all use the same values for n, p, and q.
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2! ∙ 2! simplifies to 2!"
!!
!!
simplifies to 6!
3! ∙ 3!
!
simplifies to 3!
A. What is the value of the exponent n? Explain how you found your answer.
B. What is the value of the exponent p? Explain how you found your answer.
C. What is the value of the exponent q? Explain how you found your answer.