Name________________________ Date ________

Day 1 HW: Exponent Rules

Complete the 5 review questions and then choose 20 POINTS worth of new material. Mix and match as YOU NEED to feel confident with this material.

I. REVIEW – complete all of these (2 pt each)

1. 3 2 3 12x− + + = − 2. 2 75x − >

3. (1 pt) Explain the similarities and differences between solving linear equations/inequalities and absolute value equations/inequalities. II. PRACTICE – Simplify each expression. Assume all variables are positive (1 pt. each)

1. 52 • 54

2. 2

2

4

32

⎟⎟⎠

⎞⎜⎜⎝

⎛ 3.

5

21 −

⎟⎠⎞⎜

⎝⎛

4. (4 • 3)4

5. (3-3)2

6. 3 5( )xy −

7. ⎟⎟⎠

⎞⎜⎜⎝

⎛−7

4

yy

8. ))(( 5324 −− zyzy 9.

10. 2

2

93

−yx

11. !!!!!

!!!!!!!!

12. 65

85

−

−

yxyx

( )−3 5 2 4fg h

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III. MORE PRACTICE – 2 pts each

Rewrite the following as two different expressions using the product rule:

19. x7

20. z9

IV. REACH FOR THE STARS! – 3 pts each Represent the following as an expression of exponents using AT LEAST THREE exponent rules.

21.

4

3

16cd

⎛ ⎞⎜ ⎟⎝ ⎠

22. – 9x10y6

13. 2

4

32⎟⎟⎠

⎞⎜⎜⎝

⎛−dc

14. 15.

16. )5)(3( 4375 −− yxyx

17. yxyxxy

4

1264

9)2)(3( −

18.

38 3

7 5

248x yx y

−⎛ ⎞⎜ ⎟⎝ ⎠

69

2

3

2 3

2

xy

y xx

⋅− 4

8

3

2

3 2

1

xy

y xx

⋅− −

−

Name________________________ Date ________

Day 2 HW: Rational Exponents, Simplifying Square Roots, and the Imaginary Number “i”

Complete the 5 review questions and then choose 20 POINTS worth of new material. Mix and match as YOU NEED to feel confident with this material. I. REVIEW – complete all of these (2 pt each)

1. 743

>+x 2. 1 4 73x + >

3. Explain how #1 and #2 are different? How did this affect the process of solving the inequality? II. PRACTICE – 1 point each Simplify each expression. Assume all variables are positive.

4. ! 51/2 i53/2 5. ! (4 i3)2/3

6. !(32/3)5/2 7. !

93/592/5

After simplifying the expressions above, translate the exponential form to radical form: 4.) 5.) 6.) 7.)

Simplify using the product rule. Assume all variables are positive. 8. 72 9. 24𝑎!𝑏!𝑐! 10. 216𝑥!𝑦! 11. −144 Simplify the following 12. i! 13. i!" 14. i!"# 15. i!" 16. i!"

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Add or subtract the following 17. 213 + 184 18. 273122 − 19. 32502 − + 23

II. MORE PRACTICE – 2 points each Simplify. Rationalize the denominators if needed.

20. 21

21. 45

22. 32

23. 3 3   ∙   12

24.  3 3   ∙   −12 25. !!!

!"!!

26. !"

!" 27. −6   ∙  2 2

III. REACH FOR THE STARS! – 3 pts each

28. !"!!

!" 29. !"!!

!"!

30. What is the difference between #28 and #29?

Name________________________ Date ________

Day 3 HW: Solving by Square Root Method I. REVIEW – complete all of these (1 pt each) Simplify completely.

1. 75 2. −75

3. 4+ 40 4. −121+ −81

5. Explain the difference between your answers in problems 1 and 2. If these were solutions to a quadratic equation, how would their differences affect the graph of the function?

II. PRACTICE – 2 points each Determine all solutions to the quadratic function using the square root method. 6. y = 4x2 + 2 7. y = x2 + 4 8. y = x2 – 1 9. y = x2 – 9 10. y = x2 + 1 11. y = x2 – 16

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II. PRACTICE – 3 points each Determine all solutions to the quadratic function using the square root method. 12. (x – 3)2 + 8 = 12 13. – (x+2)2 – 6 = -42 14. 3(x+1)2 + 8 = -4 15. -2(x)2 + 6 = 50 16. (x+5)2 – 10 = -131 17. 5(x – 6)2 – 12 = -66 IV. REACH FOR THE STARS! – 4 pts each 18. Create a quadratic function that has solutions of x = 4 and x = -4. HINT: The square root of what number would have solutions of x = 4 and x = -4 19. One person at the top of a waterfall that is 90 feet tall dumps into the water. The distance from the person to the water can be modeled by the equation h = -16t2 + s, where h is the height from the water, t is the time in seconds, and s is the initial height from the water in feet. How long will it take for the person to reach the water? Round your answer to the nearest tenth of a second.

Name________________________ Date ________

Day 4 HW: Operations with Complex Numbers Complete the 5 review questions and then choose 20 POINTS worth of new material. Mix and match as YOU NEED to feel confident with this material. I. REVIEW – complete all of these (1 pt each) 1. 3(y – 3) – (4 – y) = 2(y – 1) 2. Evaluate 52 3. Evaluate -52

4. Evaluate x2 when x=-5

5. Multiply (x + 5)2 II. PRACTICE – 1 pt each Solve the equation over the Complex Numbers. 6. x2 = -49 7. x2 = -25 8. x2 = -50 9. x2 + 121 = 0 Simplify the expressions 10. (3 – 2i) + (1 + 4i) 11. (5 + i) – (3 – 5i) 12. i – (5 + 6i) 13. 2i(4 + i) 14. 4i(3 - 2i)

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III. MORE PRACTICE – 2 pts each Simplify the expression without a calculator. Rationalize if needed. 16. 2i – (2 + 3i) + (1 – 8i) 17. -3i(-5 – 3i) 18. (4 – 2i)(2 – 3i) 19. 2(4i – 3) – (8 + i) 20. !

! 21. !"!  !  !

!!

Solve the following equations over the Complex Numbers. 22. x2 = 2x2 + 4 23. 3x2 + 40 = -x2 - 56 24. 2(x2 – 1) = -14 25. (x – 3)2 = -16 IV. REACH FOR THE STARS! – 3 pts each Simplify the following. Rationalize if needed. 28. 𝟑𝒊!𝟐

𝒊!𝟔 29. 𝟒𝒊!𝟐

𝟐𝒊!𝟑