Created 2015

NAME __________________________________________

ALGEBRA 2 REVIEW/MATH ANALYSIS AND TRIG PREVIEW

Follow the directions for each problem. Show your work, you may need to do the work on a

separate piece of paper. Circle the best answer for each problem.

1) Which of the following is not a function?

a) (1,1), (2, 2), (3,5), (4,10), (5,15) b) 13 13 17 17(17, ), ( ,17), (13, ), ( ,13)

4 4 4 4

c) (1, 2), ( 2, 0), ( 1, 2), (1,3) d) 2 3 3 2( 3, ), ( 2, ), ( , 5), (5, )

5 5 2 5

2) Simplify: 3- 3

2 + 3

3 5 3 9 5a) 9 5 3 b) c) d) 9 5

7 7

3) Simplify completely: 3 4 524 9x y xy

2 9 2 4 2 3 2 3a) 3x 24y b) 6x y 6y c) 6x y 6 d) 3x y 24

4) Simplify: 10 3 75 2 13i i i

) 5 15 ) 5 11 ) 5 11 ) 5 15a i b i c i d i

5) Solve: 23 12 0x

a) 4 b) i2 c) i4 d) 2

6) Factors of 2 218 21 9a ab b are :

)(6 9 )(3 2 )a a b a b ) 3(2 3 )(3 )b a b a b

)(2 3 )(3 )c a b a b ) 3(2 3 )(3 )d a b a b

7) Factors of 3 27x are:

)( 3)( 3)( 3)a x x x 2)( 3)( 9)b x x

2)( 3)( 6 9)c x x x 2)( 3)( 3 9)d x x x

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8) Solve for a: 2 9 0a a

a) {9, 0} b) {9, -9} c) {-3 , 3} d) {0, 3, -3}

9) Solve for x: 2 8 6x x

a) {8, 1} b) {4, -2} c) {-2, -4} d) {2, 4}

10) Solve the following equation.

2

1

2

2x 3 1 0

3 3 17 3) , 1 ) ) )

4 4 2

17 17

x

a b c d

11) Find the product of (3 5 )(2 8 )x y x y

2 2 2 2

2 2 2 2

) 6 34 40 ) 6 14 40

) 6 40 ) 5 4 13

a x xy y b x xy y

c x xy y d x xy y

12) Find the quotient when you divide 3 23 4 12 16 2x x x by x

2 2 2) 3 2 16 ) 3 2 16 ) 3 10 8 ) 3 8a x x b x x c x x d x

13) Write the equation of the line that passes through the point (-3, 2) and is parallel to the

line 2x – 3y =4.

a) 2x – 3y = 0 b) 2x + 3y + 12 = 0 c) 2x – 3y +12 = 0 d) y = 2 4

3 3x

14) Determine the value of k so that the line through the given points will have the

slope m:

(4, k), (-1, 3k); m = 4

a) -6 b) -10 c) 6 d) 10

15) Solve: 2 3 4 0x x

a) 1, b) ( , 1) (4, ) c) ( , 4) ( 1, ) d) 1,4

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16) Which of the following correctly describes the vertex for the quadratic expression

2( ) 6 8 :

)(17, 3); minimum b) (-3,-17); maximum

c) (17,3); maximum d) (-3,-17); minimum

f x x x

a

17) Simplify: 9 16

a) -12 b) 12 c) -12i d) 12i

18) Simplify: 4 2

7

i

i

a) 15 9

24

i b)

15 9

25

i c)

13 9

25

i d)

13 9

24

i

19) If 1

log 38

n , then n =

a) 512 b) -2 c) 3 d) 2

20) If log( 3) log( 7) log3x x , then x

a) no solution b) 5 c) -12 d) 12

21) If 4x-1 = 8x, then x =

a) 1 b) log 2 c) -2 d) -1

22) Simplify: 2

2 3 12

1 3 2 3x x x x

a) 2

3

2 3x x b)

2

21

2 3

x

x x

c)

1

1x d)

1

1x

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23) Solve: 3 3

21 1

x

x x

a) -1 b) 1 c) No Solution d) 7

2

24) Perform the operation and express in simplest form. 2 24 6

5 10 10 20

x x x

x x

a) 2 2

3

x

x

b)

2

2

2 3 2

50 2

x x x

x

c)

12

3

x

x d) 2

25) Find the solution set for the system of equations: 5x2 = 30 – y2

9x2 – y2 = - 16

a) {(1,5)} b) {(1,5),(-1,-5)}

c) {(1,5),(-1,-5),(-1,3)} d) {(1,5),(1,-5),(-1,5),(-1,-5)}

26) The value of the sum 4

2

2k

k

is

a) 54 b) 81 c) 29 d) 9

27) If the terminal ray of an angle in standard position passes through the point

)1,3( , find the cosine of this angle.

a) –1 b) 2

1 c) 3 d)

2

3 e) None of these

28) In right triangle ABC in which the right angle is at C, if b = 32.6 and mA = 53, find c to

the nearest tenth.

a) 40.8 b) 26.0 c) 19.6 d) 54.2 e) None of these

29) Given 4

sin7

A , find the Atan if the terminal side of A is in quadrant II.

a) 33

334 b)

4

33 c)

4

65 d)

4

33 e) None of these

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30) Identify the period of the function y = 1

cos 24

.

a) 2 b) c) 1

4 d)

1

2 e) None of these

31) Simplify: 2 3 4

4 3 1

42x y z

x y z

a) 6 3

9

42y z

x b)

6 3

1

42x z c)

6

6 3

42y

x z d)

6

8 342

y

x z

32) Find the distance between P(8,-4) and Q(1,8).

a) 89 b) 193 c) 19 d) 13

33) Simplify and rationalize the denominator 5

12

5 5 53 3 2) ) ) )

12 12 6 4

60a b c d

34) Which of the following is not a zero/root of 4 3 2( ) 7 11 7 12f x x x x x ?

) 1 ) 3 ) 3 ) 1a x b x c x d x

35) Which of the following intervals represents the solution set of -3x > 6 or 6x – 3 ≥ 9?

) ( , ) ) ( , 2) [2, ) ) 2, ) ( , 2)a b or c d

36) Find ( )(4)g fo when 3

( ) 1f x x and ( ) 5 3g x x

a) 4914 b) 322 c) 66 d) 1105

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37) Determine the quadrant in which the terminal side of 7

5

lies.

a) I b) II c) III d) IV

38.) Evaluate 5

sin4

a) 2

2 b)

2

2

c)

3

2 d)

3

2

39) Evaluate 11

tan6

a) 3

3

b)

3

3 c) 3 d) 3

40) Find the reference angle for 52

45

a) 45

b)

10

45

c)

45

d)

7

45

41) Simplify the expression sin secx x

a) cot x b) csc x c) tan x d) sec x

42) Simplify the expression cot secxx

a) cot x b) csc x c) tan x d) sec x

43) Find all solutions of 22sin sin 1 0x x on the interval 0,2

a) 7 11

,6 6

x

b) 5 7 11

, , ,6 6 6 6

x

c) 7 11

, ,6 6 2

x

d) 7 11 3

, , ,6 6 2 2

x

44) Find all solutions of tan 3 0x

a) 2 5

,3 3

b)

2𝜋

3+ 𝜋𝑛, 𝑛 ∈ Ζ c)

5𝜋

6+ 𝜋𝑛, 𝑛 ∈ Ζ d)

𝜋

3+ 𝜋𝑛, 𝑛 ∈ Ζ

45) Find the complement of 4

5

a) 5

b)

6

5

c)

5

d) does not exist

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I. MATCHING: For each question in Column A choose the best answer from Column B.

COLUMN A COLUMN B

______ 46) 222 ryx A. Point-slope form of a line

______ 47) 12

2

2

2

b

y

a

x B. Equation of an ellipse with center at origin

______ 48) 2 2

2 21

x y

a b C. Definition of slope

______ 49) 2 1

2 1

y ym

x x

D) Equation of a circle with center at origin

______ 50) 1 1y y m x x E) Equation of a hyperbola with center at origin

Open Ended Questions

51) Find the dimensions of a rectangle with minimum perimeter if its area is 200 square

meters. Find the least perimeter. (Hint: Use your graphing calculator to graph the

function to find the minimum values). Round answers three decimal places and give

exact values.

Created 2015

52) From the top of a 100-ft tall building a man observes a car moving towards the building.

If the angle of depression of the car changes from 22 o to 46 o during the period of

observation, how far does the car travel?

53) A total of $12,000 is invested at an annual interest rate of 3%. Find the balance after 5

years if the interest is compounded (a) quarterly and (b) continuously.

54) Given the following function, 2

2

9( )

2 3

xf x

x x

find the following (a) the y intercept

(b) the x intercept(s) and (c) the domain and (d) the range.

22o

46o 100 .ft

x d

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55) Sketch the graph of the quadratic function 2( ) 2 3f x x x

Must plot 5 points including, the vertex, and all

Intercepts.

56) Graph two periods of the function 1

( ) 3sin2

f x

Period: _______________ amp: ______________

Include 5 points on one cycle (initial, first quarter, middle, third quarter and end)

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Solutions

1. C 2. A 3. B

4. C 5. B 6. B

7. D 8. A 9. D

10. C 11. B 12. C

13. C 14. B 15. D

16. D 17. A 18. C

19. D 20. D 21. C

22. B 23. C 24. A

25. D 26. C 27. D

28. D 29. A 30. B

31. C 32. B 33. C

34. B 35. B 36. B

37. C 38. B 39. A

40. D 41. C 42. B

43. C 44. B 45. D

46. D 47. E 48. B

49. C 50. A

51. 14.142l meters, 14.142w meters, 56.569P meters

Exact answers : 10 2l meters, 10 2w meters , P= 40 2 meters

52. x= 150.940 feet

53. a. $13,934.21 b. $13,942.01

54. a. (0,3), b. (-3,0) c. ( , 1) 1,3 3, d. ,1 1,

55.

56. period = 4 , amp=3

Created 2015