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Exam ReviewExam ReviewChapters 2-6Chapters 2-6
1.1. Find the exact value of Find the exact value of sin 240°sin 240°
a) ½a) ½
b) -½b) -½
c) c)
d) d)
3
2
2.2. Find the exact value of the Find the exact value of the
arccos (-1/2)arccos (-1/2)
a) 120°a) 120°
b) - 60°b) - 60°
c) - 30°c) - 30°
d) 150°d) 150°
3.3. Write the equation for the Write the equation for the graph below:graph below:
a)a)
b) b)
c)c)
d) d)
4.4. Solve:Solve:
a) x = -4, 7a) x = -4, 7
b) x = -7, 4b) x = -7, 4
c) x = 4, 7c) x = 4, 7
d) x = -4, -7d) x = -4, -7
2 28 2x x x
5.5. DivideDivide
by x + 1.by x + 1.
a) a)
b)b)
c)c)
d)d)
3 22 13 24 6x x x
6.6. Find the inverseFind the inverse
a)a)
b) b)
c)c)
d)d)
3( ) 2
4f x x
7.7. Find the domain:Find the domain:
a)a) (-∞, -5) U (4,∞)(-∞, -5) U (4,∞)
b)b) (- 5, 4)(- 5, 4)
c)c) (-∞, -4) U (5, ∞)(-∞, -4) U (5, ∞)
d)d) (-4, 5)(-4, 5)
23log 20y x x
8.8. Solve for x:Solve for x:
a) x = - 6, 1a) x = - 6, 1
b) x = - 1, 6b) x = - 1, 6
c) x = - 2, 3c) x = - 2, 3
d) x = - 3, 2d) x = - 3, 2
2 52 64x x
9.9. Simplify:Simplify:
a) sin a) sin ββ
b) - sin b) - sin ββ
c) cos c) cos ββ
d) - cos d) - cos ββ
2sin1
1 cos
10.10. What is the What is the asymptote for the graph ofasymptote for the graph of
y = - log(x+3)?y = - log(x+3)?
a) x = - 3a) x = - 3 c) x = 0c) x = 0
b) x = 3b) x = 3 d) y = 0d) y = 0
11.11. Find the exact value ofFind the exact value of
a) a) c) c)
b)b) d)d)
1 3tan
3
12.12. Find the exact value Find the exact value ofof
a) a) b) -1b) -1
c) c) d) d)
5sin
4
13.13. Convert 200° to Convert 200° to
radians.radians.
a) a) b) b)
c) c) d) d)
14.14. Solve:Solve:
a) x = 6a) x = 6 b) x = 9b) x = 9
c) x = -2c) x = -2 c) x = 2/3c) x = 2/3
2 2log 3 2 log 5 4x x
15.15. Find the exact value ofFind the exact value of
cos 70°cos 70°
sin(-20°)sin(-20°)
a)a)11 b) -1b) -1
c) 0c) 0 d) cot 50°d) cot 50°
16.16. Graph:Graph:
a)a) b) b)
c)c) d) d)
1y x
17.17. Find the exact value Find the exact value ofof
a) a) b) b)
c) 0c) 0 d) d) ππ
1 5cos tan
4
18.18. Find the domain:Find the domain:
a) (2, ∞)a) (2, ∞) b) x ≠ 6, -3b) x ≠ 6, -3
c) x ≠ 6c) x ≠ 6 d) (-∞, 2)d) (-∞, 2)
2 3 18( )
2
x xf x
x
19.19. Evaluate:Evaluate:
a) 1/5a) 1/5 b) 5b) 5
c) 1c) 1 d) -1d) -1
5 5log 6 log 30
20.20. Simplify:Simplify:
a) a) b) b)
c) c) d) 2d) 2
sec sin
csc cos
21.21. Simplify:Simplify:
a) a)
b) b)
c) c)
d) d)
28 42
22.22. Find the arc length of Find the arc length of a circle with a radius of 4 a circle with a radius of 4 feet and a central angle of feet and a central angle of 210°.210°.
a) a) b)b)
c)c) d)d)
23.23. Find all the zeros of Find all the zeros of the function:the function:
a)a) b)b)
c)c) d)d)
4 3 26 11 12 18x x x x
24.24. Graph:Graph:
a)a) b)b)
c)c) d)d)
tan 22
y x
25.25. Find the exact value Find the exact value of cos 105°.of cos 105°.
a)a) b)b)
c)c) d)d)
26.26. What is the x-What is the x-intercept intercept of 4x + 3y of 4x + 3y = 12?= 12?
a) x = 3a) x = 3
b) (0, 4)b) (0, 4)
c) (-3, 0)c) (-3, 0)
d) (3, 0)d) (3, 0)
27.27. What is the period of What is the period of
y = 4 csc 3x ?y = 4 csc 3x ?
a)a) b)b)
c)c) d)d)
28.28. Solve:Solve:
a)a) b)b)
c)c) d)d)
24 6 2x x
29.29. Find the exact value Find the exact value of of cos110°sec110°. cos110°sec110°.
a) -1a) -1
b) 0b) 0
c) 1c) 1
d) cot 110°d) cot 110°
30.30. Factor:Factor:
a) primea) prime
b)b)
c)c)
d)d)
3 125m
31.31. Find all the zeros:Find all the zeros:
a)a) b) b)
c)c) d) d)
4 3 22 7 7 3 0x x x x
32.32. Evaluate:Evaluate:
a)a)
b) b)
c)c)
d)d)
2 38
27
33.33.
Given ( )
and ( ) 2 3,
find ( )( ).
f x x
g x x
g g x
a) 4x - 9 b) 4x - 6
c) 4x + 9 d) 4x + 6
34.34. Expand:Expand:
a)a)
b)b)
c)c)
d)d)
3
2log5
x
x
35.35. Find the domain:Find the domain:
a)a) (-∞, ∞)(-∞, ∞) b) (0, ∞)b) (0, ∞)
c)c) (-∞, 0)(-∞, 0) d) (2, ∞)d) (2, ∞)
3 2xy e
36.36. What is the What is the asymptote asymptote for for y = ln y = ln (x+4) – 1 (x+4) – 1 ? ?
a) y = 0a) y = 0 b) y = - 1b) y = - 1
c) x = 0c) x = 0 d) x = - 4d) x = - 4
37.37. Graph:Graph:
a)a) b) b)
c)c) d) d)
2 2xy
38.38. What is the What is the remainder whenremainder when is divided by is divided by
a)a) 77 b) -13b) -13
c)c) -29-29 d) -9d) -9
3 24 5x x 2 ?x
39.39.
a)a) b) b)
c)c) d) d)
Given ( ) 2
and ( ) 1 2 ,
find ( ( )).
f x x
g x x
g f x
40.40. How much money will How much money will you have after 5 years if you you have after 5 years if you invest $500 in a money invest $500 in a money market that pays 8% interest market that pays 8% interest compounded quarterly?compounded quarterly?
a) $19,168.80a) $19,168.80 b) $742.97b) $742.97
c) $27,299.10c) $27,299.10 d) $745.91d) $745.91
41.41. Where are the asymptotes Where are the asymptotes in the graph in the graph y = 2 sec (x – y = 2 sec (x – ππ) ) ??
a) At multiples of a) At multiples of ππ
b) At multiples of b) At multiples of ππ/2/2
c) At odd multiples of c) At odd multiples of ππ
d) At odd multiples of d) At odd multiples of ππ/2/2
42.42. Find a polynomial Find a polynomial f(x)f(x) of of degree 4 whose coefficients degree 4 whose coefficients are real numbers and whose are real numbers and whose zeros are 3, -1, and 2 + zeros are 3, -1, and 2 + ii..
a)a)
b)b)
c)c)
d)d)
43.43. Find the exact value ofFind the exact value of
a)a) b)b)
c)c) d) d)
1 3csc sin
7
44.44. Evaluate: Evaluate: ln 1ln 1
a) 0a) 0
b) b) ee
c) -1c) -1
d) d) -e-e
45.45. Find the vertex and the Find the vertex and the axis of symmetry:axis of symmetry:
a) (2, -3) x = 2a) (2, -3) x = 2
b) (-2, -3) x = -2b) (-2, -3) x = -2
c) (2, 3) x = 2c) (2, 3) x = 2
d) (-2, 3) x = -2d) (-2, 3) x = -2
2( ) 2 8 5f x x x
46.46. Find the cot Find the cot θθ if cos if cos ΘΘ = - .8 and = - .8 and ππ/2 < /2 < ΘΘ < < ππ . .
a)a) 3/53/5 b)b) -3/4-3/4
c) 5/3c) 5/3 d) -4/3d) -4/3
47.47. What is the phase shift What is the phase shift of the graph of of the graph of y = y = 2sin(3x+2sin(3x+ππ))??
a) left a) left ππ/3/3 b) right b) right ππ/3/3
c) left c) left ππ d) right d) right ππ
48.48. Evaluate:Evaluate:
a)a)UndefinedUndefined
b)b)00
c)c)-1-1
d)d)11
2 25 5tan sec
6 6
49.49. Graph: y = - |x+1|Graph: y = - |x+1|
a)a) b) b)
c)c) d) d)
50.50. Find the exact value ofFind the exact value of
a)a) b)b)
c)c) d)d)
1 3cos cos
5