Math 115 final exam fall, 2016

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Fall, 2016, V4.3

This is an open-book exam. You may refer to your text and other course materials as you work

on the exam, and you may use a calculator.  You must complete the exam individually.

Neither collaboration nor consultation with others is allowed.


Record your answers and work on the separate answer sheet provided.


There are 28 problems.

Problems #1–6 are Multiple Choice.

Problems #7–17 are Short Answer. (Work not required to be shown)

Problems #18–28 are Short Answer with work required to be shown.





1. Solve, and express the answer in interval notation:  | 3 – 8x | ≤ 21.


A.    (–∞, −9/4] ∪ [3, ∞)

B.     (–∞, –9/4]

C.     [–9/4, 3]

D.    [–9/4, ∞)



1. ______

2.  Which of the following polynomials has a graph which exhibits the end behavior of


downward to the left and downward to the right?

A.     f (x) = –6x5– x3– x2– 5

B.     f (x) = 8x3+ 6x2– x + 3


2. _______





f (x) = 5x6+ 7x2x

f (x) = –3x4 + 9x2– – 1



3. Express as an equivalent expression:   8 log y  + log 1 – log (x – 3)



3. ________


log 






   y +  



  x






-13log  8y + 4 − x


MATH 115 Precalculus


4. Determine the interval(s) on which the function is increasing.



A.     (− 4 / 3, 1)


B.     (−1,1) and (3,∞)


Fall, 2016, V4.3


4. ______



C.     (






11/ 3, ∞)


C.   f ( x) = −ex

D.     (  )     x    1

-40f   x  = e−   +

5. _____

Page 2 of 7


MATH 115 Precalculus


6. Which of the functions corresponds to the graph?





 A.  f (x) = cos(2x) + 2


B.  f (x) = 3 – sin x


C.   f (x) = sin x + 3


 D.   f (x) = 2 cos x + 1





7. Points (–7, 2) and (5, 6)  are endpoints of the diameter of a circle.


Fall, 2016, V4.3


6. ______



(a) What is the exact length of the diameter? (Simplify as much as possible)     Answer:  ________



 (b) What is the center of the circle?


(c) What is the equation of the circle?



Answer:  ____________


Answer:  ___________________________




8. Find the value of the logarithm: log

 Answer:  ____________

9.  Bill, a resident of Metropolis, pays Metropolis an annual tax of $55 plus 1.8% of his annual

income. If Bill paid $1,441 in tax, what was Bill’s income?

Answer:  _____________




Page 3 of 7


MATH 115 Precalculus


Fall, 2016, V4.3



10. A can of soda at 71° F. is placed in a refrigerator that maintains a constant temperature of 39°

F.  The temperature T of the soda t minutes after it is placed in the refrigerator is given by


T(t) = 39 + 32 e – 0.058 t


Find the temperature of the soda 20 minutes after it is placed in the refrigerator. (Round to the

nearest tenth of a degree.)

 Answer:  ________





11. Given the function




= 3 − 18   , find a formula for the inverse function.

  Answer:  __________________

12.   (a) State the reference angle associated with 300°.


 (b) Convert 300° to radians. Leave the answer in terms of ð.


13. Given y = 9 sin(8x – ð), state the


 (a)  period


(b)  phase shift


 Answer:  ________


 Answer:  ________

 Answer:  ________

 Answer:  ________

14. Solve the trigonometric equation   (cos x)(2cos x + 1)  = 0  in the interval [0, 360°).


    Answer:  _________________


15.   (a)    Find the exact value of  arccos  sin


(b)   Find the exact value of  arcsin  tan

16. For the parabola given by  (y + 5)2= 8(x – 2), find the following:


(a)  direction parabola opens (to the left, right, up, or down)

(b)  vertex


(c)  focus


Answer:  ________

Answer:  ________

 Answer:  ___________

Answer:  ___________


Answer:  ___________

Page 4 of 7


3x + 1

Fall, 2016, V4.3


17. Let


f (x) =


x − 2

   (a) State the domain.

(b) State the vertical asymptote(s).

(c) State the horizontal asymptote.

(d) Which of the following represents the graph of

f  x

(  )


3x + 1

x − 2


Answer:  _________________

Answer:  _________________

Answer:  _________________

Answer:  ______________





MATH 115 Precalculus

SHORT ANSWER, with work required to be shown, as indicated.


Fall, 2016, V4.3

(a) Find the composite function ( f o g)(x) and simplify. Show work.


(b) Find  (


f  o g   −   . Show work.


21. A projectile is launched from a platform 15 feet high with an initial velocity of 48 feet per second.

The height h of the projectile at t seconds after launch is given by  h = –16t2 + 48t + 15 feet.


(a) How many seconds after launch does the projectile attain maximum height?   Show work.


(b) What is the maximum height?    Show work.

22. Solve:

x − 6

x − 4





= 0 .  Show work.

23. Suppose that cos è  = 5/13 and that è  is a Quadrant IV angle.

(a) Find the exact value of sin è.

(b) Find the exact value of sin(2è ).

Show work.


Show work.


24.  Prove the identity   (sin x + cos x)2−  sin(2x) = 1

MATH 115 Precalculus


Fall, 2016, V4.3


25. From a point 48 feet from the base of a redwood tree, the angle of elevation to the top of the

tree is 52.3°. Find the height of the tree to the nearest tenth of a foot. Show work.

(sketch is not to scale)


26. For the triangle ABC, we are given that A = 46°, B = 64°, and c = 35.0.

Find the length of side a, rounded to the nearest tenth. Show work.

27. Let    = 〈10, –5〉 and     = 〈2, 4〉.


(b)   Calculate the dot product    ∙   .  Show work.


(c)    Determine the angle between    and   . Round the result to the nearest degree.  Show work.

28. An ellipse has the equation


= 1

(a) Is the major axis horizontal or vertical?

(b) Find the exact values of the foci of the ellipse. Show work.

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