Download HAT - Parkway C-2

HAT
2nd Semester Final Review
1. Simplify: 8
a) -4

2
3
b) 8
c)-8
d)
2. Simplify the radical expression:
a)
2q 4 2q 7
n n4
b)
36
83
b)
4. Solve:
a) x =
1
5
e) -
1
4
32q11n 8
2q 2 4 2q 3
2q 4 2q 3
c)
n
n2
3. Rationalize the demonimator:
a)
4
1
4
d)
16q8 4 2q 3
n8
e) NOT
6
9 2
54  6 2
79
c)
54  6 2
79
d)
54  6 2
83
e) NOT
8
6x

 2
3x  1 3x  1
b) x = 
1
3
c) x =
5
3
d) x =
5. Perform the multiplication and simplify:
1
3
e) NOT
p 2  36
p4
 2
2
p  7 p  12 7 p  43 p  6
a)
p6
p  6, 4
( p  3)(7 p  1)
b)
p6
p  6, 4
( p  3)(7 p  1)
c)
p6
p  6, 4
( p  3)(7 p  1)
d)
p6
p  6, 4
( p  3)(7 p  1)
e) NOT
6. Perform the division and simplify:
6r 2  19r  3
r 3
 2
2
2r  13r  7 2r  9r  4
a)
(6r  1)(r  4)
1
r  3,
r 7
2
b)
(6r  1)( r  4)
1
r  3, 
r7
2
c)
(6r  1)(r  4)
1
r  3,
r 7
2
d)
(6r  1)(r  4)
1
r  3,
r7
2
7. Perform the subtraction and simplify:
a)
9x 1
5 x
b)
9x 1
x5
9x
1

x5 5 x
c)
9x 1
x5
8. Determine the domain of the function f ( x) 
a)
b)
c)
d)
e)
e) NOT
d)
9x 1
x5
e) NOT
2
( x  1) 2
All Reals except x = -2 and 1
All Reals except x = 1
All Reals except x = -2 and -1
All Reals except x = 2 and 1
All Reals
9. Find the vertical asymptote(s): f ( x) 
a) x = -2, x = 5
b) y = 1
1
( x  2)( x  5)
c) y = 0
d) y = 1, y = 0
x 1
10. Find the horizontal asymptote(s): f ( x)  2
x 9
a) y = 1
b) y = 0
c) x = 1
d) x = 1
e) NOT
2
7
x4
d) x = 0
11. Find the horizontal asymptote(s): f ( x) 
a) x = 4
b) y = 0
c) y = 7
e) NOT
e) NOT
x3  1
x2  4
b) all reals except x = 2
12. Find the domain: f ( x) 
a) all reals
c) all reals except x = 1
d) all reals except x = 1, 2
e) NOT
13. Find the real zeros of f: f ( x) 
6x  3
x2 1
a)
1
2
b)
1
2
c) 1
14. Find the intercepts of: f ( x) 
a) (0, -2), (14, 0)
d) (14, 0) (0,
7
)
2
15. Graph: f ( x) 
1
, 1
2
e) NOT
x  14
2x  7
b) (-14, 0) (
e) NOT
x2  2 x  2
2x 1
d)
1
, 0)
2
c) (14, 0) (0,
1
)
2
x3  7 x 2  1
x2  1
c) y = x – 8
16. Find the slant asymptote of: f ( x) 
a) y = 1
b) y = x + 7
 1 
17. Evaluate: log 3  
 27 
1
1
a)
b)
3
3
d) y = x + 1
c) -3
d) 3
e) NOT
c) -3
d) 3
e) NOT
18. Evaluate: ln 3 e
a)
1
3
b)
1
3
19. Evaluate log a 18 , given that log a 2  0.2789, log a 3  0.4421
a) 1.1631
b) 0.2466
c) 0.0349
d) 1.4420
d) NOT
2
3
e) NOT
20. Solve for x: 27 x  81
a)
3
4
b)
1
3
c)
4
3
d)
21. Solve for : ln (7 – x) + ln (3x + 5) = ln ( 24x)
a)
6
11
b)
7
3
c)
7
, 5
3
d)
6
,5
11
e) NOT
e) NOT
22. Graph: f ( x)  log 2 ( x  1)  3
23. Graph: f ( x)  3x  2  1
24. Determine the quadrant in which the terminal side of an angle of 215 lies.
a) I
b) II
c) III
d) IV
e) It is quadrantal
11
30
49
d)
15
25. Give the reference angle for  
a)
4
15
b)
7
30
c)
11
30
26. Give the exact value of sec
a) 2
b)
3
2
c)
27. Graph: f ( x)  2 cos
e) NOT
7
4
3
3
d)
2
2
e) NOT
3x
2
28. Evaluate: arcsin 0
a)

2
b) 
c) 0
29. Evaluate sin(arctan
a)
8
3
b)
a)
2
1  cos x

2
e) NOT
3
)
8
73
8
30. Add and simplify:
d)
c)
1

1  cos x
b) 0
3 55
55
3 73
73
e) NOT
d) 2 csc ² x
e) NOT
d)
1
1  cos x
c) 2 cot x csc x
31. Simplify: sec4 x  sec 2 x  2
a) 2 tan 4 x
b) (sec2 x  2)(tan 2 x)
d) tan² x + 2
e) NOT
c) 2 tan² x
32. Find all solutions in the interval [0, 2 ): sin 2x = 0
a) 0, 
b) 0,

2
, ,
3
2
c)
 3
2
,
2
d)
 3 5 7
4
,
4
,
4
,
4
e) NOT
33. Given triangle with A = 47º, B = 63º, and c = 123, find a.
a) 88.6
b) 95.7
c) 82.6
d) 112.1
e) NOT
34. Given triangle with A = 74º, a = 59.2, and c = 60.3, find the two possible values of B.
a) 78.3º, 101. 7º
b) 4.3 º, 27.7 º
c) 73.7 º, 106.3º
d) 32.3º, 0.3º
e) NOT
35. Given triangle with a = 19, b = 4, c = 22, find C.
a) 117.4º
b) 132.1º
c) 87.2º
d) 99.7º
e) NOT
36. You throw your gum into the street and watch as a car runs over it and the gum gets
stuck in the tire. You watch the gum as it goes round and round, making one revolution
every 3 seconds. You estimate the tire is 36 inches in diameter. Being incredibly bored
that day, you would like to find the formula of the path of the gum so that you can tell
anyone who asks where the gum is given the time it has traveled. Which of the following
would be that formula:
a) f(x) = 18 cos
d) f(x) = 18 sin
2
+18
3
2
+18
3
b) f(x) = -18 sin
e) NOT
2
+18
3
c) f(x) = -18 cos
2
+18
3
ANSWERS:
1. D
2. B
3. B
4. A
5. B
6. D
7. D
8. B
9. A
10. A
11. B
12. E
13. A
14. A
15.
16.
17.
18.
19.
20.
21.
B
C
B
A
C
B
22.
23.
24. C
25. C
26. A
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
C
D
D
B
B
B
B
E
C