Name: _________________________________________________________ Date: _________________________________ Period: __________
Algebra II – Unit 5 Assignments
Date
Assignment
Feb. 3 (Mon.) – A
Feb. 4 (Tues.) - B
5.1 Notes
5.1 Exercises (Due next class, Feb. 5/6)
5.1 Homework (Due next class, Feb. 5/6)
Feb. 5 (Wed.) – A
Feb. 6 (Thurs.) - B
5.2 Notes Part 1
5.2 Exercises Version 1 (Begin it, will be due Feb. 11/12)
5.2 Homework (Due next class, Feb. 7/10)
Quiz! 5.1 Exponent Properties
Feb. 7 (Fri.) – A
Feb. 10 (Mon.) - B
5.2 Notes Part 2
5.2 Exercises Version 1 (Finish it if not done already, due next class Feb. 11/12)
5.2 Exercises Version 2 (Begin it, will be due Feb. 13/14 )
Feb. 11 (Tues.) – A
Feb. 12 (Wed.) - B
5.2 Exercises Version 2 (Finish it, due next class Feb. 13/14
Feb. 13 (Thurs.) – A
Feb. 14 (Fri.) - B
5.3 Notes
5.3 Exercises (Due next class, Feb. 18/19)
5.3 Homework (Due next class, Feb. 18/19)
Feb. 18 (Tues.) – A
Feb. 19 (Wed.) - B
5.4 Notes
5.4 Exercises (Due next class, Feb. 20/21)
5.4 Homework (Due next class Feb. 20/21)
Quiz! 5.2 Operations with Radicals
Quiz! 5.3 Rational Exponents
Feb. 20 (Thurs.) - A
Feb. 21 (Fri.) - B
Unit 5 Review (Begin it, will be due Feb. 26/27)
Feb. 24 (Mon.) - A
Feb. 25 (Tues.) - B
Unit 5 Practice Test
Feb. 26 (Wed.) – A
Feb. 27 (Thurs.) - B
Unit 5 Test
Unit 5 Notebook Check
FEBRUARY - 2014
SUN
MON
TUE
WED
THU
FRI
SAT
1
2
3A
4B
5A
6B
7A
8
9
10B
11A
12B
13A
14B
15
16
17
18A
19B
20A
21B
22
23
24A
25B
26A
27B
28A
Name: _________________________________________________________ Date: _________________________________ Period: __________
Unit 5: Radicals and Exponents
5.1: Exponent Properties
Directions: Simplify each of the following expressions.
Leave no negative exponents in your final answer.
x8 ∙ x2
7xy 5 z 7 ∙ 8x 4 y 2
9x100 ∙ 5x100
1.
2.
3.
x4
5.
6.
7.
3. Write out what is happening at each of the steps to simplify:
−2
8𝑥 −2 𝑦 3 𝑧
32
−2
−2
1𝑥 𝑦 3 𝑧
4
−2
1𝑦 3 𝑧
4𝑥 2
2
4𝑥 2
1𝑦 3 𝑧
16𝑥 4
1𝑦 6 𝑧 2
xy
3
2x2 y4
z
4
3x4 y2
9xy
−5
8.
9.
10. x
11. 4x −2
x −2
y
12.
−1
x3 y4
13.
15.
5. Simplify this:
1.
2.
3.
4.
5.
3
3
3
4
125x 9
125y 2 z 4
216x 4 y 3
256s 7 t12
Step 2:
Step 3:
Step 4:
Step 5:
6.
7.
8.
9.
32𝑥 5 𝑦 4
64𝑥 7 𝑦 3
0
. Explain how you got your answer.
5
5
9 3+2 3
5 2x 2 + 2 3x 3
3 32a + 2 50a
14 3 xy − 3 3 xy
10. 200x 4 − x 72x 2
16.
11. 4 ∙ 6
17.
12. 9 2 ∙ 3 y
13. xy ∙ 4xy
3
3
14. 50x 2 z 5 ∙ 15y 3 z
3
3
15. 2xy 2 ∙ 4x 2 y 7
18.
19.
9x
2
xy
3x
3
18y2
3
5
4
6
5
−27
32x10
243x 5 y 8
128x 6 yz 9
243x 5 y15
6.
200 − 72
3
7. 9 x 2 + 8 x 4
3
3
8. 5 256 − 4
3
3
9. 4 5x 4 + x 625x
3
4
10. 2 8x + 5 8x
3
11. 4 ∙ 25
12. 4 2x ∙ 3 8x
3
13. 9 3 2y ∙ 3 y 2
3
3
14. −3 ∙ 9
4
15. x 2 y 5 ∙ 4 x 3 y11
16.
x
8
17.
128
8
3x5
18.
19.
3
3
20.
4
243k3
3k7
4x2
3
56y5
7y
24.
25.
2
8
x+2
14
7+ 2
x
8x2
81x8 y5
3x2 y
3
22. 4 − 2 3
3
23. 1+ 2
12y
20.
Part 2: Simplify
21. 1 − 5 2 + 5
3
3
1.
2.
3.
4.
5.
−2
5.2: Operations with Radicals
Part 1: Simplify
81x 4
Step 1:
8𝑥 3 𝑦 4 𝑧
32𝑥 5 𝑦
4. Explain what sort of expression would yield a negative exponent when you
tried to simplify it.
x5
−3
7x4 y5
14xy3
−1
8x2 y3
4x3 y5
14.
Homework Questions
1. If you multiply · you will get x10. List two possible combinations of
terms you could multiply to get x7.
2. If you multiply x5y2 · xy3 you will get x6y5. List one possible combination of
terms you could multiply together to get x2y3.
xy4
y2
9x2 y3 z
3xy
2x2
4x5
2
4.
x6
21. 6( 6 + 2)
22. (1 + 4 10)(2 − 10)
3− 10
5− 2
1− 3
24. 1+ 3
4
25. 10+ 2
23.
5.2: Operations with Radicals
Homework Questions
3
1. A student simplified the expression 27x 8 y 9 and got the answer 3x2y3. Explain what he did wrong.
2. In order for radical terms to be combined, they must have the same radicand and the same index. So
3
explain why 3 5 + 5 cannot be combined.
3. You have just solved a quadratic formula problem and ended up with the solution x =
−2±2𝑖 6
.
2
Explain
why this would then simplify to be x = −1 ± 1𝑖 6 and not x = −1 ± 1𝑖 3.
4. Find the conjugate of each of the following:
A. 6 + 3 2
B. x + 5
C. −1 + 2
D. 4 − 5 6
E. −3 − 2
8
5. To simplify 1−4𝑖 you would multiply the numerator and denominator by the complex conjugate, 1 + 4i.
8
To simplify 1−4
5
you would multiply the numerator and the denominator by the conjugate, 1 − 4 5.
Explain the difference between the two types of conjugates. How are the processes for simplifying alike in
this problem.
5.3: Rational Exponents
1-4: Rewrite each expression in radical form.
4
1
1. x 3
2. b 2
3. 2y
4
7
5-8: Rewrite each expression in exponential form.
2
5.
4. 2x 3
6.
x3
3
7.
x
3
2y 2
1
1
8.
5
x4
9-23: Simplify. Leave answers in exponential form with no negative exponents.
1
9. 273
10. −27
1
2
1
2
14. 2𝑦 ∙ 𝑦
−
19. 81
15. 3𝑎 𝑏
1
2
2
5
2
3
1
3
4
1
11. 814
3
12. (−1)5
1
2
16.
1
4
20. (2𝑥 )(6𝑥 )
1 4
16
17. 3𝑥
1
2
13. 𝑥 2 ∙ 𝑥 3
4𝑥
2
3
18. 𝑦
3
21.
8𝑥 5
1
22.
4𝑥
1
18𝑥 2
23.
3
20𝑥 2
9𝑥 4
Homework Questions
1. Explain what is happening at each step for simplifying the problem at
1
12𝑦 3
2. Invent an example of an expression that contains a rational exponent.
3. Choose one of the rules for rational exponents and explain what it
means in your own words (write at least 2 sentences).
4. Invent an expression that contains rational exponents (other than zero)
that would simplify to just 1.
5. When you are solving a problem that contains a rational exponent,
which do you like using more: radical form or exponential form? Give
two reasons to support why your chosen way is easier.
Question 1
1
12𝑦 3
1
4𝑦 2
1
4𝑦 2
−9
1
4𝑥 5
the right:
2
3
1
3𝑦 3
1
1𝑦 2
1 1
3𝑦 3−2
1
2 3
3𝑦 6−6
1
1
3𝑦 −6
1
3
1
1𝑦 2
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
5.4 Radical Equations
Directions: Solve and check for extraneous solutions.
1. 𝑥 − 2
1
3
4
2. 3𝑥 3 + 5 = 53
=5
1
6. (2𝑥 + 1)3 = −3
7. 2𝑥 − 5 = 7
4
11. 3𝑥 − 3 − 6 = 0 12. 4𝑥 3 − 4 = 5
3.
8.
3
2𝑥 + 1 = −3
4.
𝑥+1=x−1
5.
2𝑥 − 4 = 𝑥 − 2
9.
4𝑥 + 2 = 3𝑥 + 4
10. 2 𝑥 − 1 = 26 + 𝑥
13. 2𝑥 − 4 = −2
14. 2𝑥 + 1
1
3
𝑥+7 =𝑥−5
1
= (3𝑥 + 6)3 15. 7x − 6 − 5x + 2 = 0
Homework Questions
1. What operation is the inverse of square rooting? Of cube rooting? Of nth rooting?
2. How can you tell if a solution to a certain problem is extraneous?
3. If you have x raised to a rational exponent, what should you do to the problem to get x by itself? For
3
instance, how would you solve for x in the equation 𝑥 4 = 16?
Use the graphs below to answer the questions that follow.
𝑦= 𝑥
𝑦 = 𝑥+2
𝑦 = 𝑥+2
4. Compare and contrast the graphs for 𝑦 = 𝑥 and 𝑦 = 𝑥 + 2. What happens to the graph of the square root
of x when you add a two beneath the radical?
5. Compare and contrast the graphs for 𝑦 = 𝑥 and 𝑦 = 𝑥 + 2. What happens to the graph of the square root
of x when you add a two outside the radical?