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PreCalculus
Cumulative Test Review
Name _________________________
Date ____________________
For questions 1 to 5, use: f ( x)  x2  9; g ( x)  3x  1; h( x)   x  6  3
1. The domain of f(x) is:
a.
b.
c.
d.
( ,3)  (3, )
( , )
[0, )
( ,3]  [3, )
2. The Range of h(x) is:
a.
( ,3]  [3, )
d.
( , )
d.
neither
b.
c.
(,0]
(,3]
3. The value of f (5)  g ( 2) is:
a.
-1
b.
1
c.
9
d.
-9
4. The value of g  h(3) is:
a.
4
b.
c.
-17
d.
1
-97
5. Which of the following represents f 1 ( x) :
a.
x 3
b.
x2  9
c.
x2  9
6. If a function is a one-to-one function over a certain domain, then it passes the:
a.
HLT
b.
VLT
c.
HLT & VLT
d.
y-axis
7. Which of the following is the solution to e x 3  4 .
3  ln 4
ln 7
a.
b.
c.
e4  3
d.
ln 4  3
8. If f ( x )  log 2 ( x  2) , then f 1 ( x) 
a.
b.
2 x2
2x  2
d.
ln x  2
d.
0.81
c.
2x  1
9. The value of log 3 50 to the nearest hundredth is:
a.
1.22
b.
3.56
c.
2.18
For questions 10 to 12, a  2  i , b  3  4i , c  3i
10.
a – c2 =
a.
b.
7  i
5  2i
c.
2  2i
d.
11 i
11.
b
=
a
a.
3 4
  i
5 5
b.
6 2
 i
5 5
c.
2 11
  i
5 5
d.
16i  10
12.
a2 + b2 =
a.
4  20i
b.
4
c.
13  17i
d.
13  17i
d.
15
8
For questions 13 to 15, the terminal side for θ passes thru the point (8, -15).
15
7
8


13. tan θ =
a.
b.
c.
15
8
15
14. cos θ =
a.

8
15
b.
15
17
c.

8
17
d.
8
17
15. csc θ =
a.

15
17
b.
17
8
c.

8
17
d.

x2  4
x2  x  6
SA: y = x
b.
17
15
For questions 16 to 18, g ( x ) 
16. g(x) has: a.
17. g(x) has a y-intercept at
a.
(0,  2 )
b.
3
(0, -2)
18. g(x) has an x-intercept at
a.
(-3, 0)
b.
(2, 0)
HA: y = 1
c.
HA: y = 0
c.
(0, 2 )
3
d.
(0, 2)
c.
(-2, 0)
d.
(3, 0)
7
and tan C < 0, then sec C =
25
24
25

b.
c.
25
7
19. If sin C =
a.
d.

25
24
d.

25
7
no asymptotes
 14 
20. Give the exact value for cos

 3 
a.
-1
b.
0
c.

1
2
3
2
d.
21. The arc length formed by a 225° sector on a circle with radius 20cm:
a.
about 450 cm
b.
25 π cm
c.
5 π cm
d.
22. Solve the equation for x: log 3 (2 x  1)  4
a.
5
b.
81
c.
24
d.
41
23. Solve the equation for x: 3 log( x  1)  log 27
a.
3
b.
4
c.
9
d.
-3
 3 
24. Give the exact value for cot  

 2 
a.
-1
b.
undefined
0
d.
1
c.
about 320.6 cm
25. A ladder makes an angle of 36° with the ground, how long is the ladder if it reaches 18 ft up a wall?
a.
14.6 ft
b.
22.2 ft
c.
30.6 ft
d.
10.6 ft
26. What is the vertex of the quadratic function f ( x)  3x 2  6x  8 ?
a.
(2, 8)
b.
(1, 8)
c.
(-1, 11)
d.
(-2, 11)
Part II: Show all work
1. Given that $8,000 is invested at 7.5% per year
a.
Find the balance after 6 years of quarterly compounding.
b.
Find the balance after 6 years of continuous compounding.
c.
How long will it take for the money to triple, if compounded continuously?
2. Solve for x:
a.
3e-5x = 132
b.
ln x + ln (x – 2) = ln (x + 4)
3. The angle of elevation to the top of a building is 18°, the angle of elevation to an antenna at the top edge of
the building is 25°. If the angles are both measured 100 ft from the building, find the height of the antenna.
4. Given that f(x) = x4 – x3 + 3x2 – 9x – 54
a. Describe the end behavior of the function.
b. Is f(x) an even function, an odd function or neither? Explain your answer.
c. Write the completely factored form for the function.
5. Graph the following
a.

f ( x)  3  23
x 1
b.
f ( x) 
x2  x  1
x 2