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Algebra II 2010–2011 Semester 1 Exam — Released 1. To which sets of numbers does –5 belong? 4. What is the value of x when (A) real numbers, whole numbers (B) real numbers, rational numbers, integers, whole numbers 16 3 7 x ? 5 2 10 (C) real numbers, rational numbers, integers (A) 5 16 (D) real numbers, irrational numbers (B) 1 4 2. Evaluate 5 2a 3b when a b 2 . 1 and 2 (C) 1 4 (D) 4 (A) 35 5. Solve the formula for r, where V, r, and h are positive real numbers. (B) 1 (C) 25 V r 2h (D) 29 (A) r 3. Which is a simplified form of the expression 2 x 5 3 x 4 ? V h (B) r V h (A) x 2 (C) r (B) x 1 (C) x 17 V h (D) r V h (D) x 22 6. Solve for y: 2 x y 5x 3 y 4 x 1 7 (A) y x 2 2 1 1 (B) y x 2 2 1 (C) y x 2 2 (D) y 2010–2011 Clark County School District 1 Revised 08/02/2011 3 x2 2 GO ON Algebra II 2010–2011 Semester 1 Exam — Released 7. What is the solution set of 2 x 12 8 ? (A) 2, 10 (B) 2 (C) 2 (D) 2, 2 10. Which graph is NOT a function? (A) 8. Which expresses all of the solutions for the compound inequality? 7 3x 2 13 (B) (A) x 3 or x 5 (B) 3 x 5 (C) x 3 and x 5 (D) no solution 9. A television repairman charges a $55 service charge for each visit and $40 per hour for labor. Let C represent the total cost of the repairman’s visit and h represent the number of hours in the visit. (C) Which is a model for the total cost of the repairman’s visit? (A) C 55h 40 (B) C 55h 40 (C) C 40h 55 (D) (D) C 40h 55 2010–2011 Clark County School District 2 Revised 08/02/2011 GO ON Algebra II 2010–2011 Semester 1 Exam — Released 11. What is the domain of the relation? 14. Use the graph. 5, 3 , 2, 1 , 6, 4 (A) 5, 2, 6 (B) 6, 2, 5 (C) 4, 3, 1 (D) 1, 3, 4 12. Which is the equation of a line that passes through the points 1, 1 and 3, 5 ? (A) y 2 x 1 What is the slope of the line? (B) y 2 x 1 (C) y 2 x 3 1 1 (D) y x 2 2 13. Which equation represents the relation? x −3 y −14 −1 −8 1 −2 3 4 5 10 (A) y 3x 2 (B) y 1 7 x 3 3 (C) y 7 x 3 3 (A) 5 3 (B) 3 5 (C) 3 5 (D) 5 3 15. At 1:00 p.m. an airplane is at an altitude of 30,000 ft. At 3:00 p.m. the airplane is at an altitude of 18,000 ft. What is the average rate of change of the altitude of the airplane? (A) 24, 000 ft per hour (D) y 3 x 5 (B) 6, 000 ft per hour (C) 4, 000 ft per hour (D) 6,000 ft per hour 2010–2011 Clark County School District 3 Revised 08/02/2011 GO ON Algebra II 2010–2011 Semester 1 Exam — Released 16. Classify the relationship between the lines 1 y x 5 and 4 x y 3 . 4 17. Which graph represents the equation y x 2 3? (A) The lines are parallel. (A) (B) The lines are perpendicular. (C) The lines coincide. (D) None of these (B) (C) (D) 2010–2011 Clark County School District 4 Revised 08/02/2011 GO ON Algebra II 2010–2011 Semester 1 Exam — Released 18. The cost c of placing an advertisement in the newspaper varies directly with the number of lines n. The cost of an advertisement with 12 lines was $84. How many lines would an advertisement have that costs $56? 19. Which graph represents the piecewise function? 3x 1, x 1 f x x 2, x 1 (A) (A) 7 (B) 8 (C) 9 (D) 10 (B) (C) (D) 2010–2011 Clark County School District 5 Revised 08/02/2011 GO ON Algebra II 2010–2011 Semester 1 Exam — Released 20. The equations of two lines are given. 23. Which graph shows the solution to the system of inequalities? 1 y x 4 3 y 2 x 5 y x2 4 x 3 y 13 What is the x-coordinate of the point of intersection of the two lines? (A) (A) x = −5 (B) x = −7 (C) x = −11 (D) x = −15 21. What is the y-coordinate of the solution of the system of equations? (B) x y 8 2 x 5 y 31 (A) y = −5 (B) y = −3 (C) y = 3 (D) y = 5 (C) 22. What is the z-coordinate of the solution of the system of equations? x 2 y 5 z 1 2 x y z 2 3x 4 y 4 z 14 (A) z = –2 (B) z = –1 (D) (C) z = 1 (D) z = 2 2010–2011 Clark County School District 6 Revised 08/02/2011 GO ON Algebra II 2010–2011 Semester 1 Exam — Released 24. An artist opens a business of selling handpainted greeting cards. Her start-up cost is $40 for paint and brushes. She buys plain cards for $3 per box, and will sell the painted cards for $5 per box. How many boxes must the artist sell for her income to equal her expenses? 25. A carpenter produces c chairs and t tables under the following constraints: 2c 3t 30 c 0 c t 12 t 0 The constraints are illustrated in the graph. (A) 5 boxes (B) 8 boxes (C) 10 boxes (D) 20 boxes The objective function maximizing the carpenter’s profit is P 40c 30t . How many tables and chairs should the carpenter make to maximize profit? (A) 12 chairs, 0 tables (B) 0 chairs, 10 tables (C) 4 chairs, 10 tables (D) 6 chairs, 6 tables 2010–2011 Clark County School District 7 Revised 08/02/2011 GO ON Algebra II 2010–2011 Semester 1 Exam — Released 26. The tables show the deposit amounts d and withdrawal amounts w of a bank customer’s checking and savings accounts. Checking Account Week d w 1 450 200 2 350 350 3 475 325 4 500 475 27. Determine the values of x and y that make the equation true. 11 4 6 7 x 3 3 y 8 6 9 12 17 Savings Account Week d w 1 1000 500 2 1200 1100 3 1500 1200 4 1000 1000 (A) x = 11, y = –4 (B) x = –5, y = 2 (C) x = 5, y = –6 Which could be used to find the total weekly deposits and withdrawals for the two accounts? 450 350 (A) 475 500 1000 200 500 1200 350 1100 1500 325 1200 1000 475 1000 450 350 (B) 475 500 200 1000 500 350 1200 1100 325 1500 1200 475 1000 1000 (D) x = 17, y = –2 28. What is the product AB? 1 0 1 3 A , B 2 4 2 1 1 3 (A) 6 2 7 12 (B) 4 4 0 3 (C) 4 5 1450 700 1550 1450 (C) 1975 1525 1500 1475 1 0 (D) 4 4 650 1500 700 2300 (D) 800 2700 975 2000 3 4 29. What is the determinant of ? 2 5 (A) −23 (B) −22 (C) −7 (D) −4 2010–2011 Clark County School District 8 Revised 08/02/2011 GO ON Algebra II 2010–2011 Semester 1 Exam — Released 30. A linear system is written as a matrix equation: 31. What graph represents 2 f x x 2 1 ? 4 11 x 6 1 3 y 1 (A) Solve the matrix equation for x. (A) x 9 (B) x 2 (C) x 7 (D) x 35 (B) (C) (D) 2010–2011 Clark County School District 9 Revised 08/02/2011 GO ON Algebra II 2010–2011 Semester 1 Exam — Released 32. What are the solutions of the quadratic equation x 2 10 x 24 ? 35. What is the solution set of the equation 2 x 2 7 25 ? (A) x 4, x 6 (A) 4, 4 (B) x 6, x 4 (B) 3, 3 (C) 3 (D) 4 (C) x 2, x 12 (D) x 12, x 2 33. What is the solution set of the quadratic equation x 2 6 x 4 0 ? (A) (B) (C) (D) 6 3 6 3 36. Using the discriminant, how many real and imaginary solutions are there for the equation 2 x 2 3x 7 0 ? 5, 3 5 13, 6 13 13, 3 13 5, 6 5 (A) 2 real solutions, no imaginary solutions (B) no real solutions, 2 imaginary solutions (C) 1 real solution, 1 imaginary solution (D) no real solutions, 1 imaginary solution 34. What value of c makes the left side of the equation a perfect square trinomial? 37. What is the solution set of x 2 4 x 20 0 ? x2 6x c 0 (A) 4 8i, 4 8i (C) −3 (B) 4 4i, 4 4i (D) −9 (C) 2 4i, 2 4i (D) 2 4i, 2 4i (A) 36 (B) 9 38. What is the product 1 3i 2 3i ? (A) 7 3i (B) 11 3i (C) 3 (D) 11 2010–2011 Clark County School District 10 Revised 08/02/2011 GO ON Algebra II 2010–2011 Semester 1 Exam — Released 39. What graph represents the quadratic inequality? 40. Use the formula below, where h is the height (in feet) of a falling object after t seconds and h0 is the object’s initial height (in feet). y x2 2 x 3 h 16t 2 h0 (A) A rock falls from the edge of a cliff 256 feet above the ground. How much time does it take for the rock to reach the ground? (Note: h 0 when the rock reaches the ground.) (A) 1 second 4 (B) 3 seconds (B) (C) 4 seconds (D) 5 seconds (C) (D) 2010–2011 Clark County School District 11 Revised 08/02/2011 GO ON Algebra II 2010–2011 Semester 1 Exam — Released 42. What graph represents the polynomial function y x 4 3x3 3x 2 ? 41. What graph represents the polynomial function f x x 3 x 1 x 4 ? (A) (A) (B) (B) (C) (C) (D) (D) 2010–2011 Clark County School District 12 Revised 08/02/2011 GO ON Algebra II 2010–2011 Semester 1 Exam — Released 43. Which polynomial represents the product x3 3 x2 4 ? 46. What is the set of all real zeros of the polynomial function f x x3 2 x 2 4 x 8 ? (A) x5 4 x3 3x 2 12 (B) x 5 12 (A) 4, 2 (C) x 6 4 x 4 3x3 12 (B) 2, 2 (D) x 6 7 (C) 2 (D) 2, 4, 8 44. What is the solution set of the equation x 4 3x 2 4 0 ? (A) 2, 2 (B) 2i, 2i (C) i, i, 2, 2 (D) 2, 1, 1, 2 47. According to the Fundamental Theorem of Algebra, how many zeros does the function have? f x 3x4 2x3 x 5 (A) 2 (B) 3 (C) 4 45. What are the zeros of the polynomial function represented by this graph? (D) 5 48. What is x3 x 2 4 x 4 divided by x 2 ? (A) x 2 x 1 (B) x 2 x 8 (C) x 2 3 x 2 (D) x 2 x 2 (A) 3, 1, 2, 6 (B) 3, 1, 2 (C) 2, 1, 3, 6 (D) 2, 1, 3 2010–2011 Clark County School District 13 Revised 08/02/2011 GO ON Algebra II 2010–2011 Semester 1 Exam — Released 49. Which describes the end behavior of the graph of f x x4 3x2 15 as x ? (A) f x (B) f x (C) f x 15 (D) f x 1 50. What function represents the graph? (A) f x x3 2x2 3x 4 (B) f x x4 5x3 2 x2 5x 4 (C) f x x3 5x2 3x 4 (D) f x x4 5x3 4x2 5x 4 2010–2011 Clark County School District 14 Revised 08/02/2011 GO ON Algebra II 2010–2011 Semester 1 Exam — Released Free Response 1. This question obsolete as of 2011–2012. See new test specifications and practice questions. 2. This question obsolete as of 2011–2012. See new test specifications and practice questions. 3. This question obsolete as of 2011–2012. See new test specifications and practice questions. 2010–2011 Clark County School District 1 Revised 08/02/2011 GO ON

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