1
Final Exam
Math 1103, Fall 2012
1. Find the slope and y-intercept of the line that is parallel to 2๐ฅ + 3๐ฆ = 5 and passes through the point (1,โ1) a. ๐๐๐๐๐ = !
!;๐ฆ โ ๐๐๐ก๐๐๐๐๐๐ก = !
!
b. ๐๐๐๐๐ = โ !
!;๐ฆ โ ๐๐๐ก๐๐๐๐๐๐ก = !
!
c. ๐๐๐๐๐ = โ !
!;๐ฆ โ ๐๐๐ก๐๐๐๐๐๐ก = โ !
!
d. ๐๐๐๐๐ = โ !
!;๐ฆ โ ๐๐๐ก๐๐๐๐๐๐ก = !
!
e. None of the above
2. Find the domain of the function ๐ ๐ฅ = !
!!!!!!
a. (โโ,โ) b. ๐ฅ โ 1 c. ๐ฅ โ โ2 d. ๐ฅ โ 2,โ1 e. ๐ฅ โ โ2,1
3. If the point โ2,1 is on the graph of ๐(๐ฅ) and ๐(๐ฅ) is known to be odd, what other point must be on the graph of ๐(๐ฅ) a. โ2,โ1 b. 2,โ1 c. โ2,1 d. 1,โ1 e. 0,โ1
2
4. Find the value of ๐ 2 โ ๐(0), if
๐ ๐ฅ = 2โ ๐ฅ, ๐ฅ < 1 ๐ฅ! โ ๐ฅ + 1, ๐ฅ โฅ 1
a. 3 b. โ1 c. 2 d. 0 e. 1
5. If ๐ ๐ฅ = !!+ 1 and ๐ ๐ฅ = !
!โ 1, find ๐๐ (๐ฅ).
a. !
!!โ 1
b. 1
c. 1โ ๐ฅ
d. !
!!!
e. 0
6. The length of a rectangle is 5 units longer than twice its width. Assuming that the width of the rectangle is w and the area is ๐ด, find the area as a function of the width. a. ๐ด ๐ค = ๐ค! + 5๐ค b. ๐ด ๐ค = 2๐ค! + 5 c. ๐ด ๐ค = 2๐ค! โ 5๐ค d. ๐ด ๐ค = 2๐ค! + 5๐ค e. None of the above
3
7. 1000 dollars grows to 1 million dollars after 60 years in a bank. If interest is compounded continuously, what is the rate of interest per year? a. 1.83% b. 11.51% c. 28.13% d. 3.84% e. 0.12%
8. Find the sum of all the zeros of the polynomial ๐ ๐ฅ = ๐ฅ! + 2๐ฅ! โ 5๐ฅ โ 6 a. โ5
b. โ2
c. 0
d. 2
e. 6
9. The graph of ๐ฆ = (๐ฅ โ 4)! + 5 can be obtained by the transformation of ๐ ๐ฅ = ๐ฅ!.
Which of the following transformations must be used? I. Move 5 units down. II. Move 5 units up. III. Move 4 units down. IV. Move 4 units left V. Move 4 units right.
a. V, then II b. IV, then II c. III, then I d. II, then III e. III, then II
4
10. Which of the following functions represents the inverse of the function ๐ ๐ฅ = 3๐! . a. ๐ ๐ฅ = 3๐!! b. ๐ ๐ฅ = !
!!!
c. ๐ ๐ฅ = ln (!!)
d. ๐ ๐ฅ = !!ln (๐ฅ)
e. ๐ ๐ฅ = log (!!)
11. The vertex of the parabola ๐ ๐ฅ = 2๐ฅ! โ 4๐ฅ + 7 is a. โ1 , 13 b. 1 , 7 c. 2 , 5 d. โ1 , 5 e. 1 , 5
12. Find the horizontal asymptote (HA) and vertical asymptote (VA) of
๐ ๐ฅ =๐ฅ! โ 4๐ฅ(๐ฅ + 2)
a. HA: ๐ฆ = 1 VA: ๐ฅ = 0, ๐ฅ = โ2
b. HA: ๐ฆ = 0 VA: ๐ฅ = 0, ๐ฅ = โ2 c. HA: ๐ฆ = 1 VA: ๐ฅ = 0 d. HA: ๐ฆ = 0 VA: ๐ฅ = 0 e. HA: None VA: ๐ฅ = 0, ๐ฅ = โ2
5
13. Find the oblique asymptote of
๐ ๐ฅ =๐ฅ! + 1๐ฅ โ 1
a. ๐ฆ = 1 b. ๐ฆ = ๐ฅ โ 1 c. ๐ฆ = ๐ฅ! + 1 d. ๐ฆ = ๐ฅ + 1 e. ๐ฆ = 0
14. If ๐ ๐ฅ = !! and ๐ ๐ฅ = 1โ !
! , find (๐ โ ๐)(๐ฅ)
a. 1 b. 1โ ๐ฅ c. โ1+ !
!!
d. !
!โ !
!!
e. 0
15. What are all the possible rational roots of ๐ ๐ฅ = 6๐ฅ! โ ๐ฅ! โ 4๐ฅ! โ ๐ฅ โ 2? a. ยฑ1,ยฑ2,ยฑ3,ยฑ6,ยฑ !
!,ยฑ !
!
b. ยฑ1,ยฑ2,ยฑ !!,ยฑ !
!,ยฑ !
!,ยฑ !
!
c. โ !!, !!
d. โ1, !!
e. None of the above
6
16. Which of the following intervals represents the solution set to the inequality
!!!!!!
> 3 a. โ4,โ b. โโ,โ !"
!
c. โ !"!,โ4
d. (โ4,1) e. โโ, 3)
17. Which of the following statements are true? I. (ln ๐ฅ)! = 2 ln ๐ฅ II. log! 3๐ฅ! = 4 log!(3๐ฅ) III. log ๐ฅ โ ๐ฆ = !"#!
!"#!
IV. log!!!= 2โ log! 4
V. ln ๐ฅ! = 2 ln ๐ฅ a. I and II only b. I, II, and III only c. I and III only d. IV and V only e. I and IV only
18. Solve ๐๐๐(๐ฅ โ 1)+ ๐๐๐(๐ฅ + 1) = 0 a. ๐ฅ = 2 b. ๐ฅ = โ1, ๐ฅ = 1 c. ๐ฅ =1 d. ๐ฅ = โ 2, ๐ฅ = 2 e. ๐ฅ = 2
7
19. Solve the equation 2!!! = 16! a. ๐ฅ = 0 b. ๐ฅ = 1 c. ๐ฅ = 2 d. ๐ฅ = 3 e. ๐ฅ = !
!
20. Convert the equation 3!! = !! to logarithmic form
a. log!(
!!) = โ2
b. log!(โ2) =!!
c. log!!(!!) = 3
d. log!!(3) = โ2
e. log!!(โ2) = 3
21. Find the range of the function ๐ ๐ฅ = 5 sin[2(๐ฅ + !!)]โ 4
a. [โ1,1]
b. [โ !!, !!]
c. [โ1,9]
d. [โ9,1]
e. None of the above.
8
22. Suppose that sin๐ = !! and ๐ is in Quadrant 2. Evaluate cos๐
a. !!!"
b. !
!"
c. โ !"!
d. !"!
e. !"!
23. Find the quadrant in which the terminal side of ๐ = 4 ๐๐๐๐๐๐๐ is located a. One b. Two c. Three d. Four e. None of the above.
24. Find ! !!! !!(!)!
if ๐ ๐ฅ = ๐ฅ! + 2๐ฅ โ 1 a. โ + 6 b. 2 c. 2+ โ d. โ! + 2โ โ 1 e. 1
9
25. Find the exact value of ๐๐๐ก!!(โ1).
a. โ !!
b. !!
c. !!!
d. โ !!!
e. None of the above.
26. Find the inverse of the function ๐ ๐ฅ = sin(!!), where โ !
!๐ โค ๐ฅ โค !
!๐,
a. ๐!! ๐ฅ = !!"#(!!)
b. ๐!! ๐ฅ = csc(5๐ฅ)
c. ๐!! ๐ฅ = !!sin!!(๐ฅ)
d. ๐!! ๐ฅ = 5sin!!(๐ฅ)
e. ๐!! ๐ฅ = sin!!( !!!)
27. By using sum or difference formulas, cos(!!โ ๐ฅ) can be written as
a. โ cos ๐ฅ
b. sin ๐ฅ c. cos ๐ฅ d. โ sin ๐ฅ e. None of the above
10
28. Which of the following is an expression for cos(2๐ผ) a. 1+ 2cos !(๐ผ) b. โ1+ 2cos! ๐ผ c. 1โ cos !(๐ผ) d. โ1โ cos !(๐ผ) e. 2cos(๐ผ)
29. A 41 meter guy wire is attached to the top of a 34.6 meter antenna and to a point on the ground. What angle, in degrees, does the guy wire make with the ground?
a. 1ยฐ
b. 57.55ยฐ
c. 37.65ยฐ
d. 45ยฐ
e. None of the above.
30. Find an angle ๐ between 0โ and 360โ that is coterminal with โ790โ a. ๐ = 90ยฐ b. ๐ = 70ยฐ c. ๐ = โ70ยฐ d. ๐ = 290ยฐ e. None of the above
11
31. The general solution of the equation cos (2๐) = 1 is
a. ๐๐, where ๐ is an integer b. 0 c. 2๐๐, where ๐ is an integer d. !
!+ 2๐๐ , where ๐ is an integer
e. !!!+ 2๐๐, where ๐ is an integer
32. Simplify sec ๐ฅ โ sec ๐ฅ . sin! ๐ฅ
a. 1 b. sec ๐ฅ c. sin! ๐ฅ d. cos! ๐ฅ e. cos ๐ฅ
33. Find the length of the side ๐ in the triangle ๐ด๐ต๐ถ where ๐ = 3, ๐ = 3 and โ ๐ด๐ถ๐ต = 120ยฐ
(Note the figure is not drawn to scale)
a. 27
b. 27
c. 18 โ 9 3
d. 18 + 9 3
e. 10
12
34. For what values of ๐ฅ in the interval [โ2๐, 2๐] does the graph of ๐ฆ = cot(2๐ฅ) have a vertical asymptote? (Angles are measured in radians)
a. โ2,โ1, 0, 1, 2
b. โ2๐,โ !!!,โ๐,โ !
!, 0, !
!,๐, !!
!, 2๐
c. โ2๐,โ๐, 0,๐, 2๐
d. โ !!!, !!!
e. โ2๐, 0, 2๐
35. In the figure below, โ ๐ถ = 125ยฐ ,๐ด๐ต = 8.6 ๐๐๐โ๐๐ , and ๐ด๐ถ = 5.7 ๐๐๐โ๐๐ . Find โ ๐ต in degrees.
(Note the figure is not drawn to scale)
a. โ ๐ต = 29.8ยฐ b. โ ๐ต = 32.9ยฐ c. โ ๐ต = 35.7ยฐ d. โ ๐ต = 38.2ยฐ e. โ ๐ต = 30.6ยฐ
Top Related