Algebra II H Semester 2 Practice Exam B

Algebra II H Semester 2 Practice Exam B DRAFT

2 1. Find the solution set of 7x- x + 1 = 0 . 2 7. Let p( x) =1 - x and q( x) = x - 2 x .

镲禳1- 3i 3 1 + 3 i 3 Find q( p( x)) . A. 睚 , 铪镲 14 14 8. Which is the inverse of the function 镲禳1- 3 3 1 + 3 3 B. 睚 , y= x - 2 for x 2 ? 铪镲 14 14 1 y = 镲禳1-i 29 1 + i 29 A. , x ≥ 0 C. 睚 , x - 2 铪镲 14 14 B. y= x + 2 , x ≥ 0

镲禳1- 29 1 + 29 2 D. 睚 , C. y= - x - 2 , x ≥ 0 铪镲 14 14 D. y= x2 + 2 , x ≥ 0

2. Write the expression 4 2 5 12 in 16x y z 9. The graph below is the function exponential notation. y= k x .

3 y 3. Simplify 164 .

A. 2 10 B. 4 C. 8 5 D. 12

2 2 4. Let f( x) = - x 3 and g( x) = x 3 . Find 5 10 x ( f- g)( x) .

5. Given k( x) = x - 4 and s( x) = 4 x2 , What is the value of k? k2� s 1 what is ( ) ( ) ? 1 A. k = 5 A. –80 B. –8 B. k = 5 C. 32 C. k = 5 D. 640 D. k = 25

2008–2009 1 GO ON Clark County School District Revised 07/22/2009 Algebra II H Semester 2 Practice Exam B DRAFT 13. 10. Solve for x: 23 x + 3 - 2 = 3

A. x = 5 9 B. x = 2 119 C. x = 2 101 D. x = 8

11. To compete in a sailboat race, a boat must satisfy the rule

l+1.25 s - 10 3 d = 24 骣2 , 琪桫3

where l is the length of the boat (in meters), s is the area of the sails (in square meters), and d is the volume of water displaced by the boat (in cubic meters).

A boat has a length of 21 meters and sail area of 400 square meters. What is its displacement?

1+ 2i 12. Simplify the expression where 2- 3i i = -1 .

8 1 A. + i 7 7 4 7 B. - + i 13 13 8 C. + i 7 D. –4 + 7i

2008–2009 2 GO ON Clark County School District Revised 07/22/2009 Algebra II H Semester 2 Practice Exam B DRAFT

D. y 14. What graph represents the function 8 y=log( x - 4) ?

A. y 8 -8 8 x

-8 8 x

B. y 8

-8 8 x

C. y 8

-8 8 x

x 骣1 15. Sketch the graph of y = 2 琪 . 21. Solve for y: 桫3 1- 2logy = 3 16. Simplify the expression 2log6- log4 . A. y = 0.01 9 A. log B. y = 0.1 4 C. y = 1 B. log3 D. y = 10 C. log8 22. The relationship between an log9 D. earthquake’s moment magnitude M and its energy released E (in ergs) is 17. Which equation is equivalent to approximately defined by the function:

y = log3 4 ? M=0.3ln E + 1.2 A. 3y = 4 Find the amount of energy released by a B. 4y = 3 magnitude 8.1 earthquake. C. y = 34 23. What is the minimum or maximum of D. y = 43 the quadratic function p( x) = -3 + 6 x - x2 ? 18. What is the solution of the equation 2 A. p( x) = -30 log3 ( x ) = 4 ? B. p( x) = -3 A. x = ±8 B. x = ±9 C. p( x) = 2 C. x = 64 D. p( x) = 6 A. x = 81 24. The value of z varies jointly with x and 19. Solve for k: e-k = 5 y. If z = 4 when x = 1 and y = 12, what is the value of z when x = 5 and y = –6?

20. A. –90 B. –10 C. 2 D. 8

4 3 5 25. Sketch the graph of y = . 30. What is the solution set of + = 2 x - 2 x x + 2 ? 26. Which best describes all asymptotes of A. {3, –1} x - 1 the function y = ? x - 2 B. {0, 4} 禳1 A. x = 1, x = 2 C. 睚铪2 B. x = 1, y = 1 D. {–1} C. x = 2, y = 0 D. x = 2, y = 1 31. The equation

1 1 1 27. Which expression is equivalent to = + x2+8 x + 16 x 2 - 4 f d d ? i o x+2 x2 + 6 x + 8 describes the relationship between the 3( x - 4) focal length f of a thin lens, the distance A. d an object is from the lens, and the 2 o distance di the image is from the lens. x - 2 B. x + 2 A lens has a focal length of 6 centimeters. How far is an object ( x+4)( x - 2) from a lens when its image is three times C. x + 2 as far away? ( x+4)( x - 2)2 D. 32. Given the system of linear equations ( x + 2)2 2x+ 7 y = 3 28. Solve for x: x+4 y = - 8

3 3 1 find the solution to the system using - = matrices by: 2x x 2 轾x A. x = –3 (1) writing in the form = A-1 B , 犏y B. x = 1 臌 C. x = 2 (2) then computing A-1 , D. x = 3 轾x (3) and finally computing 犏 . 臌y 29.

33. Identify and graph the conic section: 40. Graph the function:

2 2 ( x+1) +( y - 3) = 4 1, if 0�x 1 2, if 1�x 2 f( x ) = 34. Identify and graph the conic section: 3, if 2�x 3 4, if 3�x 4 2 2 ( x+3) ( y + 2) + = 1 5 49 16 2 41. Expand the expression (k + 1) . n=1 35. Identify and graph the conic section: A. 1+ 4 + 9 + 16 + 25 2 2 9x- 4 - 4 y + 2 = 36 ( ) ( ) B. 2+ 5 + 10 + 17 + 26 C. 4+ 9 + 16 + 25 + 36 36. Identify and graph the conic section: D. 5+ 10 + 17 + 26 + 37 x= 2 y2 42. What is the series 0+ 3 + 6 + 9 + 12 + 37. What type of conic section is when written in summation notation? represented by the graph of x2-2 x - y 2 + 4 y - 4 = 0 ? 43. What equation is the sum of the first 15 terms in the series 2 + 5 + 8 + 11 + …? A. circle 14 B. ellipse A. S =轾2� 2 - ( 14 1) 3 15 2 臌 C. hyperbola 15 D. parabola B. S =轾2� 2 - ( 14 1) 3 15 2 臌 38. Which is the equation of a parabola? 15 C. S15 =臌轾2� 2 - ( 15 1) 3 2 2 A. y-16 x = 0 16 2 2 x y D. S15 =臌轾2� 2 - ( 16 1) 3 B. - = 1 2 25 25

2 C. x2 +( y -2) = 81

2 2 D. 16( x+ 4) + 4( y + 2) = 64

44. A box of paper clips begins with 270 50. Postal codes in Canada consist of three clips. A person takes one-third of the letters and three digits, in an alternating clips and passes the box to a second pattern, beginning with a letter. For person who takes one-third of the example, T1J4A5. remaining clips. Another person then takes one third of the remaining clips. Any digit is allowed in the 2nd, 4th, and 6th How many clips remain when a fourth places. The letters D, F, I, O, Q, and U person receives the box? are not allowed in the 1st, 3rd, or 5th places. Additionally, the letters W and A. 10 Z are not allowed in the 1st place. B. 80 How many possible Canadian postal C. 90 codes exist? D. 120 A. 18鬃 202 10 3 45. What is the sum of the infinite geometric B. 203 10 3 1 2 4 series + + + ? C. 3 3 3 15 75 26 10 D. 28鬃 302 36 3 46. Write the formula of an arithmetic

sequence when t1 = 2 and t5 = 82 . 51. Three students are chosen at random from a group of five. How many 47. Which is a formula of the geometric different combinations of three students sequence 0.04, 0.2, 1, 5, …? are possible?

n-2 A. 10 A. tn = 5 B. 20 B. t = 5n-3 n C. 60 3-n C. tn = 5 D. 120 t = 55-n D. n 4 52. What is the expanded form of (2x- y) 48. Write a recursive rule for the sequence ? 1, 2, 5, 14, 41, 122, … 53. What is the coefficient of x2 y in the 3 49. expansion of (2x+ 3 y) ?

A. 12 B. 18 C. 36

2008–2009 7 GO ON Clark County School District Revised 07/22/2009 Algebra II H Semester 2 Practice Exam B DRAFT D. 54

54. A group of students consists of 60. What are the domain and range of the x 3 freshmen, 4 sophomores, 5 juniors, 骣1 and 2 seniors. If two students are function f( x) =琪 + 3 ? 2 chosen at random from the group, what 桫 is the probability that neither student is A. Domain: x 0 a junior? Range: y > 0 55. Which measure(s) of central tendency B. Domain: x 0 are generally affected by outliers? Range: y > 3 C. Domain: all real numbers 56. The list below shows the low Range: y > 0 temperatures for a North Dakota city over a 10-day period. D. Domain: all real numbers Range: y > 3 11, 17, 17, 12, 1, 2, 18, 17, 26, 28 61. What are the domain and range of the Create a box-plot that represents the data. function f( x) =3log( x - 1) ?

57. What is the domain of the function 62. What are the horizontal asymptotes of f( x) =3 x - 4 + 5 ? the logistic growth function 2 f( x) = -3 x ? A. {x| x 4} 1+ 4e

B. {x| x 4} 63. Sketch the logistic growth function 2 C. x| x 0 f( x) = -3 x . { } 1+ 4e D. {x| x } 64. What is the local maximum of the x2 +6 x + 9 58. What is the range of the function function f( x) = ? x + 1 x f( x) = + 2? 3 A. (-3, 0)

A. f( x) 0 B. (-2, - 1) 2 B. f( x) C. (0, 9) 3 D. (1, 8) C. f( x) 2 D. all real numbers

65. What are the approximate local minima of the function below? y 8

-6 -4 -2 2 4 6 x -2

66. What is the first step in a proof by mathematical induction?

67. What is assumed in the second step in a proof by mathematical induction?

2008–2009 10 Clark County School District Revised 07/22/2009 Algebra II H Semester 2 Practice Exam B Free Response DRAFT

3 1. Use the function f( x) =3( x - 2) to answer the questions below.

A. What are the domain and range of f( x) ?

A. Derive f-1 ( x) .

B. Sketch the graph of y= f-1 ( x) on the same set of axes.

C. If g( x) =2 x + 1, find f( g( x)) .

2. The value A of an investment earning I percent annual interest compounded quarterly can be 4t 骣 I modeled by the function A( t) = A0 琪1 + , where A0 is the initial value of the investment and t is 桫 4 the length of the investment in years.

D. The amount $3000 is deposited into an investment earning 8% annual interest. What is the value of the investment after 10 years? (Leave your answer as an expression; do not complete the computation.)

E. Write an equation for t( A) , the time required for an investment to reach a value of A.

F. Using your answer from Part B, how much time will a $1000 investment need to be an account earning 10% interest to double its value? (Leave your answer as an expression; do not complete the computation.)

2008–2009 1 GO ON Clark County School District Revised 07/22/2009 Algebra II H Semester 2 Practice Exam B Free Response DRAFT 4 2 68. Use the functions f( x) = and g( x) = to answer the questions below. x + 2 x - 3

A. Let h( x) = f( x) + g( x) . Find h( x) .

B. Solve h( x) = 0 .

C. Sketch the graph of y= h( x) on the grid provided. Be certain to note any asymptotes and intercepts on the graph.

2008–2009 2 Clark County School District Revised 07/22/2009