exam review chapters 2-6. 1. find the exact value of sin 240° a) ½ b) -½ c)d)

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


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


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


a) a) b) b)

c) c) d) 2d) 2

sec sin

csc cos


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


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


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)


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


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)


a)a) b)b)

c)c) d)d)

1 3cos cos

5

exam review chapters 2-6. 1. find the exact value of sin 240° a) ½ b) -½ c)d)

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