CCAlg II.Unit-4-Assessment PDF

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UNIT #4 ASSESSMENT COMMON CORE ALGEBRA II Part I Questions 1. Which of the following is represents

(1) x

3

(2) x

3

2

(3) x

2

(4) x

2

1 x3

for all x  0 ?

3

 23

(1)

2. Given the graph of the exponential function y  a  b  shown below, which of the following statements must x

be true? In the exponential equation

(1) a  1 and b  5

, a is the y-intercept and b

is the growth factor. Since the y-intercept is above 5, the exponential function increases .

(2) a  5 and b  1

. Since

(3) a  1 and b  1 (4) a  5 and b  1

(2) 3. In the exponential function g  x   a  b  it is known that g  3  25 and g  7   3 . Which of the following is closest to the value of b? x

(1) 0.42

(3) 0.59

(2) 1.32

(4) 1.70

(3) 4. Which of the following is the solution to the equation shown below in terms of the unknown constant b? (1) 

4b 3

(2) x 

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b 4

3 (3) x  b 4

(4) x  

2 x b

1    9 

3

4x

3b 2

COMMON CORE ALGEBRA II, UNIT ASSESSMENTS – UNIT #4 – FORM B eM ATHINSTRUCTION™, RED HOOK, NY 12571, © 2018

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Answer Key - Unauthorized posting of key to any website is prohibited and a violation of copyright. 5. The level of water in a tank is decreasing such that its depth, d, can be modeled by d  18  .92  , where h represents the hours that the tank has been draining. Based on the model, which of the following represents the percent that the water level drops in the span of a single day? h

(1) 14%

(3) 72%

(2) 48%

(4) 86%

(4)

6. Which of the following will be the x-intercept of y  logb  x  k  based on the constants b and k? (1) x  k  1

(3) x  b k 1

(2) x  b  1

(4) x  k b  1

7. If the equation 5  2 

x

3

 a was solved for x in terms of a the result would be

3a 10

a (3) x  3log2    5

 a (2) x  log 3    10 

(4) x  5log 2  3a 

(1) x 

(1)

(3)

8. If Max places $525 in a savings account that earns a nominal 3.2% yearly interest compounded monthly, then which of the following is closest to the worth of this account after 3 years? (1) $577.40

(3) $577.82

(2) $577.67

(4) $577.90

(3)





9. The speed of a falling object can be modeled using the equation s  t   72 1  e .35t , where t is the number of seconds it has been falling and s is the speed in feet per second. Which of the following is closest to the number of seconds it will take for the object to reach a speed of 60 feet per second? (1) 4.93

(3) 5.48

(2) 5.12

(4) 6.02

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COMMON CORE ALGEBRA II, UNIT ASSESSMENTS – UNIT #4 – FORM B eM ATHINSTRUCTION™, RED HOOK, NY 12571, © 2018

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Answer Key - Unauthorized posting of key to any website is prohibited and a violation of copyright. PART II QUESTIONS: Answer all questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps and explain your reasoning. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. 2

10. Using properties of exponents, explain why 3 3 is equivalent to An exponent of

can be broken into

3

9.

. We can then use an

exponent law to convert into a power and a root as shown.

11. Myra is putting together a puzzle such that every 5 days she places one quarter of the remaining pieces into the puzzle. If she started with a 800 piece puzzle, how many pieces are left to be placed after 23 days? Show the work that leads to your answer.

12. Explain why the function y  log 2 x  4  doesn't have a y-intercept. The y-intercept of a function occurs when its input, or x-value, is equal to zero. But, doesn't exist because there is no real number that you can raise the base to in order to get -4.

PART III QUESTIONS: Answer all questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps and explain your reasoning. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. 13. An exponential function, f  x , passes through the points 2, 5  and 8, 20  . Determine the value of f  25  to the nearest integer. Only an algebraically based solution will receive full credit.

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COMMON CORE ALGEBRA II, UNIT ASSESSMENTS – UNIT #4 – FORM B eM ATHINSTRUCTION™, RED HOOK, NY 12571, © 2018

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Answer Key - Unauthorized posting of key to any website is prohibited and a violation of copyright. 14. The graph of y  logb  x  is shown below. (a) What is the value of b? Explain how you arrived at your answer.

The base of this logarithm, b, is 3. We can determine this because the point lies on the logarithm and

.

(b) The graph appears to pass through the point  9, 2  . Does it? Explain how you arrived at your answer. The point because

does lie on this graph since

.

PART IV QUESTION: Answer the question in this part. The question is worth 6 points. 15. The interest on a particular savings account is compounded continuously. The account initially had $2,200 deposited in it. The worth of the account after t-years can be calculated using the formula:

A  t   2200 e.05t (a) By what percent will the worth of the account increase per year? Round to the nearest hundredth of a percent.

(b) To the nearest tenth of a year, how long will it take for the worth of the account to triple?

(c) If another investment began with a principal of $2,500 and earned simplest interest of 3.8% applied once per year, which investment would be worth more after 10 years? Justify.

The second investment would be worth more after 10 years.

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COMMON CORE ALGEBRA II, UNIT ASSESSMENTS – UNIT #4 – FORM B eM ATHINSTRUCTION™, RED HOOK, NY 12571, © 2018

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