Algebra 1 Regents Comprehensive Exam

Algebra 1 Regents Comprehensive Exam Instructions Answer all questions. Show all work. Calculators may be used unless otherwise noted. Part I: Multiple Choice (1–20) 1. What is the solution to the equation 3x − 7 = 2x + 5? 2. Which graph represents a linear function? 3. Solve the inequality: 4x − 5 < 3x + 2 4. What is the slope of the line passing through (2, −3) and (6, 1)? ( y = 2x + 3 5. Solve: y = −x + 6 6. Simplify: 23 · 24 7. Simplify the expression: (x3 y 2 )2 8. What is the solution to x2 + 4x + 3 = 0? 9. Factor completely: x2 − 9 10. Solve using the quadratic formula: x2 − 6x + 1 = 0 √ 11. What is the value of 72 in simplest radical form? 12. Find the distance between the points (3, 4) and (7, 1) 13. The graph of y = x2 − 4x + 3 opens: 14. Which is a solution to the equation |2x − 5| = 9? 15. Identify the vertex of the function y = (x − 2)2 − 4 16. Which sequence is arithmetic? 17. Which function represents exponential decay? 1 Name: Algebra 1 Regents Exam 18. What is the mean of the data: 5, 10, 15, 20, 25? 19. A transformation maps f (x) = x2 to g(x) = (x − 2)2 + 3. What is the transformation? 20. What is the solution to the system of equations: ( 2x + 3y = 12 x−y =1 Page 2 Name: Algebra 1 Regents Exam Part II: Short Response (21–35) 21. Graph the inequality y > −2x + 3 22. Factor: x2 + 2x − 35 √ √ 23. Simplify: 50 − 18 24. Expand and simplify: 3(x − 4)2 − 5 25. Find the equation of a line through (4, 2) with slope −3 26. If f (x) = 3x2 − 6x + 5, find g(x) = f (x − 2) + 1 27. Is the relation {(1, 2), (2, 3), (3, 4), (1, 5)} a function? 28. Find the IQR of: 12, 17, 23, 28, 30, 35, 41 29. If f (x) = x2 + 1, g(x) = x − 3, find (f ◦ g)(2) 30. Solve: x2 ≤ 16 31. A ball’s height is h(t) = −16t2 + 32t + 5. What is the max height? 32. Solve: 3x2 = 27 33. A triangle has legs x and x + 1, hypotenuse 5. Find x. 34. A rectangle has area x2 + 5x − 6 and width x − 1. Find length. 35. Find the distance between (2, −1) and (5, 3) Page 3 Name: Algebra 1 Regents Exam Part III: Constructed Response (36–42) 36. A town’s population is 50,000 and grows 4% per year. Model this with an exponential function. 37. Write a quadratic with zeros x = −2 and x = 5 38. Find the vertex and axis of symmetry of y = −2x2 + 8x − 5 39. Solve algebraically: 2x x+1 =3 40. A square and rectangle have same area. Square side is x, rectangle sides x + 2, x − 1. Find x. 41. A student earns $12/hr tutoring and $8/hr babysitting. Write a system to earn at least $100. 42. Solve: (x − 3)2 = 16 Page 4 Name: Algebra 1 Regents Exam Part IV: Extended Response (43–50) 43. A rocket’s height: h(t) = −5t2 + 20t + 80. When does it hit the ground? 44. Find the mean, median, mode of: 55, 65, 70, 70, 80, 85, 90, 95, 100 45. A parabola has vertex (1, −2), passes through (3, 6). Find its equation. 46. Analyze f (x) = 12 (x + 4)2 − 3: vertex, axis, direction, domain, range 47. A cylinder has radius r, height 2r. Find volume in terms of r and when r = 3 48. A quadratic relationship is modeled by a table. Use regression to model and predict value. √ 49. Prove 2 is irrational. 50. A cell population doubles every 3 hours. Starts at 200. How many after 12 hours? Page 5 Name: Algebra 1 Regents Exam Answer Key Part I: Multiple Choice 1. (B) x = 12 2. (A) Line with constant slope 3. (A) x < 7 4. (D) Slope = 1 5. (A) x = 1, y = 5 6. (C) 27 = 128 7. (B) x6 y 4 8. (D) x = −1, x = −3 9. (C) (x − 3)(x + 3) √ 10. (A) x = 3 ± 8 √ 11. (D) 6 2 12. (B) Distance = 5 13. (A) Opens upward 14. (B) x = 7, x = −2 15. (C) Vertex (2, −4) 16. (A) 3, 7, 11, 15 17. (C) f (x) = a(1 − r)x 18. (B) Mean = 15 19. (D) Right 2, Up 3 20. (B) x = 3, y = 2 Page 6 Name: Algebra 1 Regents Exam Part II: Short Response 21. Graph: dashed line, shaded above 22. (x + 7)(x − 5) √ 23. 2 2 24. 3x2 − 24x + 43 25. y = −3x + 14 26. g(x) = 3(x − 6)2 − 2 27. Not a function 28. IQR = 35 − 17 = 18 29. 2 30. x ∈ [−4, 4] 31. Max height = 21 32. x = ±3 33. x = 3 34. x + 6 35. Distance = 5 Part III: Constructed Response 36. P (t) = 50000(1.04)t 37. f (x) = (x + 2)(x − 5) 38. AOS: x = 2, Vertex: (2, 3) 39. x = 3 40. x = 3 41. 12x + 8y ≥ 100 42. x = 7, x = −1 Page 7 Name: Algebra 1 Regents Exam Part IV: Extended Response 43. t = 8 44. Mean = 80.6, Median = 80, Mode = 70 45. y = 2(x − 1)2 − 2 46. Vertex (–4, –3); Opens up; Domain: R; Range: y ≥ −3 47. Volume = 2πr3 ; r = 3: V = 54π 48. Regression required; varies 49. Not rational: no fraction of integers 50. 200 · 24 = 3200 Page 8