Algebra 2B Review Final Exam

Transcription

1 Algebra B Review Final Exam Multiple Choice Identify the choice that best completes the statement or answers the question.. x 0 x 5 = y m 4 Ê ˆ. Simplify. y m w Á 6y 4m w. 4. (5a ) 8c 4 d 8y 7m y m w (4cd) 45a b = 7 x x + 5 x x 5 6y 0m w 8y 0m w 0a 9b 7 c d 0a 9b 7 c d a 0a 6 9b 7 c d 9b 7 c d y 6y 4y = 4y y + 4y y 8y + 9 6y y 6y 9 y y 6y + 9 y

2 5. Which rational function best represents the graph below? f(x) = x + x f(x) = x + x + f(x) = x x f(x) = x x + 6. What are the equations of the vertical and horizontal asymptotes for? f(x) = (x + )(x ) x =, y = 0, x = x =, y = 0, x = x =, y = 0, x = x =, y = 0, x = 7. Which of the following is the best solution for the equation? 8 y y = y + y + no solution y = 5, y = y = 7, y = y = 5 8. What is the solution to the inequality? x x + + x > 4 x x > x < x < x > 9. x + 8 x + 4 = x + x 4 x + 4 x x 4 x 4 x + x + x + 4 x + 4

3 0. Pilar is graphing a parabola with a vertex of (, ) and x-intercepts of 4 and. Which of the following might be the equation of the parabola she is graphing? y = (x ) + y = (x + ) y = (x + ) + y = (x + ). What is the equation of the circle graphed below? (x ) + (y + ) = (x + ) + (y ) = (x ) + (y + ) = (x + ) + (y ) =. Which of the following is the graph of y = x + x 9?. What are the foci of 4(x + ) + 8(y ) =? (, 0) and (, 0) (, 5) and (, ) (0, ) and (0, ) (, ) and (, ) 4. x + y x + 8y + = 0 What is the standard form of the equation of the conic given above? (x + ) (y + ) (y + ) (x + ) = = (x ) (y + ) = (y + ) (x + ) =

4 5. Which of the following is the graph of (x ) 5 + (y + ) 9 =? 6. What is the common difference of the series below? What is the nth term in the arithmetic series below? n 6n + 6n 5(n + ) What is the sum of the first terms of the arithmetic series ? What is the 7st term of the arithmetic sequence whose first term is 7 and whose common difference is? none of the above 0. Which of the following series is neither arithmetic nor geometric?

5 . What is the kth term of the following geometric series? Ê 5 ˆ Ê Á 64 8(k ) 5 ˆ Á 5 8k Ê (40)8 (k ) 5 ˆ Á 64. What is the common ratio of the following series? (k ) 9 9. What is the 8th term of the geometric sequence whose first term is 5 and whose common ratio is? 5( 7 ) (5 8 ) 5( 8 ) (5 7 ) 4. What is the sum of the first 4 terms of ? 86,09, ,808 4,046,78 4,48, What is the sum of the first 50 terms of the geometric sequence ? È Ê [ (0.5) 50 ] 6 50 ˆ Á 4 ÎÍ È Ê 5 ˆ [ (0.5) Á 4 ] ÎÍ 6. What is the sum of the infinite geometric series ? An ice cream shop serves vanilla, strawberry, or chocolate ice cream. The ice cream can be served in a cup, sugar cone, or waffle cone. How many different combinations of flavor and serving method are possible? Abigail rolled a pair of six-sided number cubes numbered 6 on each side. What is the probability that the sum of the digits will be 7? 4 6 5

6 9. Justine s local flower shop sells small bouquets of roses, violets, lilies, tulips, daisies, carnations, and chrysanthemums. How many different large bouquets can she make using different small bouquets from the flower shop? Linda has 5 children. How many different ways can she seat her children on the back seat of her minivan? The seat has seat belts A bag contains 5 small yellow marbles, 8 large yellow marbles, small green marbles, and large green marbles. What is the probability of selecting a small marble from the bag? % 4 5% 7% 8%. A total of 5 freshmen, sophomores, and 9 seniors entered the school raffle. What is the probability that either a freshman or senior will win the raffle? Yumiko recorded the number of hours she watched television each day for a week in the chart below What is the variance of her data? Which expression represents f(g(x)) if f(x) = x + x and g(x) = x +? x + x + x + 7x + x + x + x + 4x + x 5. Which expression represents g(f(x)) if f(x) = 5x x and g(x) = x? (5x x) 8x x 5(x ) (x ) 5x 6 6x 4 6. If f(x) = 4x x and g(x) = x, which is an equivalent form of g(x) f(x)? x x x x x + x x + x 7. Which function is the inverse of f(x) = x? f (x) = x + f (x) = x f (x) = x f (x) = x 6

7 8. Which function is the inverse of f(x) = 7x 0? f (x) = 7 x + 0 f (x) = 7x 0 f (x) = 7 x f (x) = 7x Mrs. Jacobs wrote the equation x 0x + 5 x 5 = on the boar Which of the following statements is correct about the equation she wrote? The equation is true only when x = 6. The equation is always true. The equation is never true. The equation is always true, except when x = 5. Ê 40. A certain radioactive element decays over time according to the equation y = A ˆ 00, where A = the number of Á grams present initially and t = time in years. If 00 grams were initially present, how many grams will remain after 600 years? 0.8 gram 50 grams 5 grams 5000 grams 4. Which function represents exponential growth? f(x) = (4)x f(x) = x Ê ˆ Á 4 f(x) = 5(0.5) x f(x) = x Ê ˆ Á 4. What is the value of 6? The student enrollment, S, of a university was 475 students in 999. The enrollment has increased by exactly 0% per year. Which of the following equations expresses the university s student enrollment in terms of t, where t is the number of years since 999? S = 475(0.) t S = 0.(475) t S = 475(.) t S =.(475) t t 7

8 44. Given: y varies inversely as x, and y = 4 when x = 4. Write and graph the inverse variation function. y = x y = 4 x y = x y = 6 x 45. Simplify 0 x x. Identify any x-values for which the expression is undefine x + x 8 x 5 x + 4 The expression is undefined at x = 4. x 5 x + 4 The expression is undefined at x = and x = 4. x + 5 x + 4 The expression is undefined at x = and x = 4. x + 5 x + 4 The expression is undefined at x = 4. 8

9 46. Using the graph of f( x) = as a guide, describe the transformation and graph g ( x ) = +. x x Translate f( x) right units. Translate f( x) down units. Translate f( x) up units. Translate f( x) left units. 47. Identify the asymptotes, domain, and range of the function g(x) = x Vertical asymptote: x = 7 Domain: {x x 7} Horizontal asymptote: y = Range: {y y } Vertical asymptote: x = 7 Domain: {x x 7} Horizontal asymptote: y = Range: {y y } Vertical asymptote: x = 7 Vertical asymptote: x = 7 Domain: {x x 7} Horizontal asymptote: y = Range: {y y } Domain: {x x 7} Horizontal asymptote: y = Range: {y y } 9

10 48. Identify holes in the graph of f( x) = x + 8x +. Then graph. x + There is a hole in the graph at x = 6. There are no holes in the graph. There is a hole in the graph at x =. There is a hole in the graph at x =. 0

11 49. Graph the function f(x) = 4 x + 5, and identify its domain and range. The domain is the set of all real numbers. The range is also the set of real numbers. The domain is the set of all real numbers. The range is also the set of real numbers. The domain is the set of all real numbers. The range is also the set of real numbers. The domain is the set of all real numbers. The range is also the set of real numbers.

12 50. Using the graph of f( x) = x as a guide, describe the transformation and graph g( x) = 4 x. Stretch f vertically by a factor of 4 and translate it left units. Compress f horizontally by a factor of 4 and translate it up units. Stretch f vertically by a factor of 4 and translate it right units. Compress f horizontally by a factor of 4 and translate it down units.

13 5. Graph the inequality y x 5 5. Which equation can be used to find x? sin = x 7 tan = x 7 cot = 7 x cos = x 7

14 5. Find A to the nearest degree Rewrite 5π 4 radians in degree measure π Which angle is coterminal with a 400 angle in standard position? Find the exact value of cos θ if the terminal side of θ in standard position contains the point (6, 8) Which equation is graphed? y = sin θ y = sin θ y = cos θ y = cos θ 4

15 58. Find the amplitude of y = 6 cos 4θ. 4 6 π 59. Find the period of y = tan 5θ. 0π 5π π 5 π Which equation is graphed? y = sin (θ π 4 ) y = sin (θ + π 4 ) y = cos (θ π 4 ) y = cos (θ + π 4 ) 6. Find the phase shift of y = sin (θ π 4 ). π 4 4π π 4 4π 5

16 ID: A Algebra B Review Final Exam Answer Section MULTIPLE CHOICE. ANS: C STA: (Key)7.0. ANS: A STA: (Key)7.0. ANS: C STA: (Key) ANS: D STA: (Key) ANS: B STA: (Key) ANS: C STA: (Key) ANS: D STA: (Key) ANS: C STA: (Key) ANS: C STA: (Key) ANS: B STA: 6.0. ANS: D STA: 6.0. ANS: A STA: 6.0. ANS: D STA: ANS: A STA: ANS: C STA: ANS: B STA:.0 7. ANS: B STA:.0 8. ANS: D STA:.0 9. ANS: B STA:.0 0. ANS: A STA:.0. ANS: C STA:.0. ANS: D STA:.0. ANS: A STA:.0 4. ANS: D STA: (Key).0 5. ANS: C STA:.0 6. ANS: D STA:.0 7. ANS: B STA: (Key) ANS: C STA: (Key) ANS: A STA: (Key) ANS: D STA: (Key)8.0. ANS: C STA: PS.0. ANS: D STA: PS.0. ANS: B STA: PS ANS: C STA: ANS: A STA: ANS: B STA: ANS: D STA: ANS: B STA: ANS: A STA: (Key)5.0

17 ID: A 40. ANS: B STA: (Key).0 4. ANS: A STA: (Key).0 4. ANS: D STA: (Key).0 4. ANS: B STA: (Key) ANS: D 45. ANS: B STA: A ANS: B STA: MA ANS: D STA: MA ANS: B STA: MA ANS: C STA: A ANS: B STA: A ANS: C STA: A ANS: D 5. ANS: C 54. ANS: B 55. ANS: C 56. ANS: B 57. ANS: C 58. ANS: B 59. ANS: D 60. ANS: B 6. ANS: A