Unit Summary 4
Class : Algebra 1 Honors
Unit 4: Exponents and Radicals – Chapter 9
I. Big Ideas:
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Students will understand how to simplify and evaluate monomial expressions and formulas.
Students will understand that exponents and radicals are inverses of each other.
Students will understand that relationships can be described for mathematical situations that have
numbers repeat in predictable ways.
Students will be able to use graphs and tables to distinguish between linear and nonlinear functions.
Students will understand that real world applications involving growth can be modeled using a linear
growth model or an exponential growth model.
II. Topics that will be covered:
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III.
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Multiplication properties of exponents
Division properties of exponents
Negative and zero exponents
Scientific notation
Simplifying radicals
Rationalizing
Exponential growth
Exponential decay
Graphing exponential functions
Essential Questions:
What is simplest form?
How is the power rule related to the product rule?
What does a negative exponent mean?
What does it really mean to “cancel” when simplifying fractions?
Where can I use scientific notation and radicals in the real-world?
How are exponential functions different from linear functions?
What happens with the exponents when the same bases are multiplied or divided?
IV.
Sample questions to answer by the end of the unit:
Write all answers in simplest form.
1. 2x2(3x2 – 5x – 12)
2. 12x(3x – 5) – 6x(2x – 4)
3. 12x2 – 24x – 8
4x
4. (2x3y7)4
5. (10xy)3(4x3y)2
6. 12x2y9
18x7y4
Determine whether each number is written in scientific notation. If it is not, write it in scientific
notation.
7. 950 x 105
8. 72.35 x 109
9. 1.6 x 107
10. 0.26 x 10-13
Write each expression so that all exponents are positive.
11. b-4g3d-5
12. x-4y8g-2
x-3y16g7
13. -83(8-5)
14. (3x2y-5)-2
Solve for g.
15. g2 = 36
16. 2g = 1
17. 2g = ½
18. 2g = 0.25
Identify each function as exponential growth or exponential decay then find the percent of increase or
decrease for each function.
19. y = 105  0.53x
20. y = 856  1.07x
21. y = 3112  2.49x
22. y = 4  0.19x
23. y = 10,000  0.48x
24. y = 21  0.34x
Write an exponential function to model each situation.
25. 5,000,000,000 initial population
3.5% annual decrease
8 years
26. $2400 purchase
10% loss in value each year
9 years
27. $500 initial market value
13.2% annual increase
17 years
Simplify each radical.
28. 6√7 - 2√28
29. 5(√20 + √80)
30. √54 - 2√6
31. √96 *√25
32. 84
121
33. 100
169
* Question 32 and 33 should have a radical sign over the entire fraction.
Add, subtract, or multiply as indicated. Leave answers in scientific notation.
34. 5.1 x 106 + 4.5 x 105 =
35. 8.1 x 108 – 6.7 x 107 =
36. 2.3 x 103  3.6 x 107 =
37. 6.77 x 1012 + 5.4 x 109 =