All work must be shown, or you will not receive credit. Students are not allowed to ask for help on the day the problem set is due.

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Adv Alg/Precalculus Problem Sets 4th Term

READ THE DIRECTIONS CAREFULLY!



Problem sets are designed to review concepts taught in previous courses as well as

those taught in this class. Problem sets must be taken seriously and emphasis should

be on the process to answer each question and not necessarily the answer itself.



Problems are due according to the schedule below.



All work must be shown, or you will not receive credit.



Students are not allowed to ask for help on the day the problem set is due.



Work must be shown in order to receive credit. No exceptions. Even if the

majority of the work was done on the calculator, you still must show all steps.



Late problem sets will be penalized 1 point for every day (not class period) it is late.

If you are absent on the due date, it is your responsibility to get me your problem set

on your first day back to school to avoid the penalty.

Packet

Due at the BEGINNING of class on or before the class date:

1 4/9 or 4/10

2 4/23 or 4/24

3 5/7 or 5/8

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Adv Alg/Precal 4th Term PS #4 1

Adv Alg/Precalculus (4th term) Early ______ Name ___________________

Problem Set #4 Due: 5/21 or 5/22 Period ______

Directions: This problem set is a study guide for the final exam and should be approached as such. It should be worked without a calculator, if possible. Show all work for full credit. Place answers in the appropriate blanks.

1) Evaluate: 3ln 5

7 ln 6 2 ln 7 1) _______

(a) –3.8222 (b) –2.6559 (c) 0.5582 (d) –11.6058 (e) None of these

2) Find the domain of the function: f x( ) 3log(5x 2). 2) _______ (a) ( , ) (b) 1,

3 (c)

2 ,

5 (d) (0.064, ) (e) None of these

3) Evaluate: ln e1 x 3) _______

(a) e1 x (b) e (c) 1 x (d) ln(1 x) (e) None of these

4) Simplify: ln 5e3 4) _______

(a) 3 ln 5 (b) 3ln 5 (c) 3 3ln 5 (d) 5e3 (e) None of these

5) Use the change of base formula to identify the expression 5) _______ that is equivalent to log 10₃ .

(a) ln 3 ln10 (b) 10 log 3 (c) 10 ln 3 (d) 1

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6) Write as a sum, difference, or multiple of logarithms:

3 2 log_b x y

w . 6) _______

(a) 3 2

x y w (b) 1log 1log 2 log

3 b x 2 b y b w

(c) 3log 2 log 1log 2 b x b y bw (d) 3log 2 log 1 log 2 x y w

(e) None of these

7) Solve for x: log 8_x 3 7) _______

(a) 2 (b) 512 (c) 1

2 (d) –2 (e) None of these

8) Simplify: 2 ln(x 1)

e 8) _______

(a) 2

(x 1) (b) 2(x 1) (c) 2

ln( 1)

e x (d) x 1 (e) None of these

9) Solve for x: 21 x 3x 9) _______ (a) ln 2 ln 6 (b) 1 ln 3 (c) 2 ln

3 (d) ln 3 ln 2 (e) None of these

10) Solve for x: log(7 x) log(3x 2) 1 10) _______

(a) 19 31 (b) 13 31 (c) 27 29 (d) 9

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11) Find the number of years required for a $2000 investment 11) _______ to triple at a 9.5% interest rate compounded continuously.

(a) 12.6 (b) 13.7 (c) 11.6 (d) 15.1 (e) None of these

12) Solve for t: e 0.0097t 12. 12) _______

(a) –256.1759 (b) –1237.1134 (c) 16,778,844.47 (d) –2.5886 (e) None of these

13) Determine the principal, P, that must be invested at a 13) _______ rate of 7.5% interest compounded quarterly so that the

balance, B, in 20 years will be $35,000.

(a) $2333.33 (b) $14,000.00 (c) $9635.17 (d) $7918.78 (e) None of these

14) An initial deposit of $2800 is made in a savings account 14) _______ for which the interest is compounded continuously. The

balance will triple in eight years. What is the annual rate of interest for this account?

(a) 6.9% (b) 13.7% (c) 11.6% (d) 9.9% (e) None of these

15) Solve for x: 16 27x 5 15) _______

(a) 0.1143 (b) –0.3010 (c) 13

7 (d)

9

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1) Given a triangle with a 112, b 130, and A 56 , find c. 1) _______ (a) 103.2 (b) 98.1 (c) 42.2 and 98.1 (d) 42.2 and 103.2 (e) No solution

2) A television antenna sits on the roof. Two 72-foot support wires are 2 _______ positioned on opposite sides of the antenna. The angle of elevation

each makes with the ground is 26 . How far apart are the ends of the two guy wires? (a) 24.9 feet (b) 21.5 feet (c) 112.1 feet (d) 129.4 feet (e) None of these

3) Given a triangle with a 17, b 39, and c 50, find A. 3) _______ (a) 16.88 (b) 73.12 (c) 163.12 (d) 106.88 (e) None of these

5) Use Heron’s formula to find the area of the triangle with 5) _______

41.6, 54.2, and 47.1

a b c .

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6) A trigonometry class wants to determine the length of a pond near 6) _______ the school (shown below). From point A, they measure the distance

to each end of the pond and the angle between these sides. What is the approximate length of the pond?

(a) 352 feet (b) 289 feet (c) 407 feet (d) 331 feet (e) None of these

7) The domain of f x( ) 3 ex is: 7) _______

(a) (3, ) (b) 0, (c) ( , ) (d) ( ,3) (e) None of these

8) The range of f x( ) 1 e x is: 8) _______

(a) ( , ) (b) (0, ) (c) ( 1, ) (d) (1, ) (e) None of these

9) $3500 is invested at a rate of 4.5% compounded continuously. 9) _______ What is the balance at the end of 10 years?

(a) $315,059.96 (b) $5472.45 (c) $5221.39 (d) $5489.09 (e) None of these

10) Determine the amount of money that should be invested at 10) _______ a rate of 6.5% compounded monthly to produce a final

balance of $15,000 in 20 years.

(a) $4102.34 (b) $5216.07 (c) $2458.83 (d) $14,056.14 (e) None of these

78°

215 ft 300 ft

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1) Find the x- and y-intercepts: y x2 3x 4 1) _______

(a) (0, 4), ( 4, 0), (1, 0) (b) (0, 4), (4, 0), ( 1, 0)

(c) (0, 4), ( 4, 0), (0,1) (d) (4, 0), (0, 4), ( 1, 0)

(e) None of these

2) Find the minimum point on the graph of f x( ) x2 4x 14 2) _______ (a) (2, 18) (b) (–2, 18) (c) (–2, 26) (d) (2, 10) (e) None of these

3) The perimeter of a rectangle is 300 feet. What is the width of the rectangle 3) _______ of maximum area?

(a) 100 feet (b) 50 feet (c) 75 feet (d) 60 feet (e) None of these

4) Divide: 4 3 2 (3x 2x 3x 1) (x 1) 4) _______ (a) 3 2 2 3 5₂ 2 1 x x x x (b) 2 2 5 4 3 2 3 1 x x x x (c) 3 2 2 4 ₂5 1 x x x x (d) 2 2 4 5 3 1 1 x x x x

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5) Find all the real zeros of the polynomial function: g t( ) t3 3t2 16t 48 5) _______ (a) –3 (b) 3 (c) –4, –3, 4 (d) –3, 4 (e) None of these

6) Use synthetic division to find f( 2): f x( ) 4x3 3x 10 6) _______ (a) 20 (b) –20 (c) 36 (d) –28 (e) None of these

7) Simplify the rational function:

5 1 ( ) 1 x f x x 7) _______ (a) 4 x (b) 4 3 2 x x x x (c) 4 3 2 1 x x x x (d) 4 3 2 1 x x x x

(e) None of these

8) Write as a product of linear factors: f x( ) x4 3x2 28 8) _______ (a) (x2 4)(x2 7) (b) (x 2 )(i x 2 )(i x 7)(x 7)

(c) (x 2 )(i x 2 )(i x 7)(x 7) (d) (x 2 )(i x 2 )(i x 7)(x 7)

(e) None of these

9) Find the vertical, horizontal, and oblique asymptotes: ( ) ₂ 2

2 3 x f x x x 9) VA: _________ HA: _________ OA: _________

10) Find a fourth degree polynomial that has zeros: 1, –3, 2i 10) _______

(a) 4 3 2 2 8 12 x x x x (b) 4 3 2 2 7 8 12 x x x x (c) x4 2x3 x2 8x 12 (d) x4 2x3 7x2 8x 12

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Simplify. 1) (4x y5 3)(3x y2 3) 2) 5m0n4 1) _________________ 2) _________________ 3) ₂ ₄ 3 3 20 5 b a b a  4)

 

2 3 3 6a b  3) _________________ 4) _________________ Evaluate each radical expression.

5) 3 27  6) 3 644 5) ________________ 6) ________________ 7) 3



₆₄



4 ₈₎ 5 3 1 32 7) ________________ 8) ________________ Rewrite each expression in simplified exponential form. Use positive exponents.

9)            ₄_x12 ₂_x32 ₁₀₎ 3 2 3 4 6 27         z y x 9) ________________ 10) ________________