Algebra Diagnostic Pre-Test

Algebra Diagnosti c Pre- Test 50 questions – 60 minutes Multiple Choice Use the answer “NOTA” (which stands for None Of The Above) if the answer is not listed 1. Evaluate 7m + 3 mn when m = 8 and n = 14 A) 84 2. B) 196 4. 5. B) 9 E) NOTA C) 75 D) 225 E) 135 (4x2y3)2 = A) 8x4y5 B) 16x4y5 D) 16x2y3 E) NOTA C) 4x4y6 (3x – 2)(4x + 1) = A)12x2 – 8x – 2 B) 12x2 + 5x – 2 D) 12x2 – 5x – 2 E) NOTA C) x2 – 5x – 2 (4xy2)-3 = A) – 64 x3 y6 D) – 6. D) 168 Simplify: 675 ÷ (6 + 9 ÷ 3) A) 15 3. C) 392 4 3 x y 6 B) 1 4x 3 y 6 C) 1 64 x 3 y 6 E) NOTA (x – 4)(x + 4) = A) x2 – 16 B) x2 + 16 D) x2 + 8x + 16 E) NOTA C) x2 – 8x + 16 7. Find the equation that best represents the following word problem: In a certain freshman class, the number of girls is 83 less than twice the number of boys (b). The total number of students in that freshman class is 259. How many boys and girls are in that class? A) b + 2b = 259 - 83 B) b + 2b – 83 = 259 C) b + 83 – 2b = 259 D) b + 2b = 259 E) NOTA 8. 9. Factor: 6x2 – 13x – 5 A) (6x + 5)(x – 1) B) (3x + 1)(2x – 5) C) (6x – 1)(x + 5) D) (2x – 1)(3x + 5) Which one of the following equals a negative number? A) B) C) D) E) 10. E) NOTA (-5) + 9 (-9) + 5 9+5 5 + (-9) + 4 9 – (-5) Solve the system of equations: 3x + 4y = 11 x – 2y = – 3 A) x = 1 y=2 3 B) x = -1 y = 4 C) x = 2 y=–3 D) x = 1 y=–2 E) NOTA 11. Factor: 25x2 – 16y2 A) (5x – 4y)2 D) (5x + 2y)(5x – 8y) B) 5 (5x – 4y) E) NOTA C) (5x + 4y)(5x – 4y) 12. Solve: 2x2 + 5x – 3 = 0 A) 3, 2 13. 3x + y = 10 If  x − 4 y = −1 A) 1 14. Solve: D) 3, 7 13 C) –2 D) C) 99 D) 96 B) 11 1 2 E) NOTA E) – 1 E) NOTA Solve: 3x + 17 – 5x = 12 – (6x + 3) B) 4 C) 0 D) – 4 E) NOTA You and three friends are eating a pizza with 12 pieces. Each person eats the same number of pieces. Let x represent the number of pieces each person eats. Which of the following equations is an algebraic model for the situation? A) 3x = 12 D) 17. 3 ,1 2 1 y + 28 = −5 3 A)2 16. C) then y = B) 3 A) –11 15. 1 2 B) –3, 1 x = 12 4 B) 1 x = 12 3 C) 4x = 12 E) NOTA (3x + 4)2 = A) 9x2 + 12x + 16 B) 9x2 + 16 D) E) 25x2 9x + 16 C) 9x2 + 24x + 16 18. Solve: 3x (x – 4)(3x + 5) = 0 A) 4, − 5 3 5 B) – 4, − , 3, 0 3 D) 4, –5, 0 19. 20. 21. 22. B) − 11 3 C) 4 3x2 + 11x = 4 D) 1 3 is E) NOTA Simplify: (3cd6)3(cd)4 A) 27c7d10 B) 27c7d13 D) 27c12d72 E) 27c7d22 C) 9c7d22 Simplify: (4c4 + 1) – (7c3 – 3) + (2c4 + 5c3) A) 6c4 + 2c3 – 4 B) 6c4 – 2c3 + 4 D) 2c4 – 2c3 – 2 E) 4c + 4 C) 6c4 – 2c3 – 2 The number ten is raised to a power between 0 and 1. The answer has to be between which two numbers? A) B) C) D) E) 23. E) NOTA One of the solutions of the equation: A) 0 5 C) − , 4, 0 3 0 and 1 1 and 10 10 and 100 but not 5 0 and 100 but not 50 – 10 and 0 Which of the following is the least? A) .27 B) 1 4 C) 3 8 D) 2 11 E) 11% 24. If x = 2 and y = −3, then −x y² = A) −36 25. B) −18 C) −12 D) 12 Which is closest to the distance between A and B on the number line? A B -4 A) -9 26. C) 13 4 D) 5 E) 12 Define p ~ q by the equation p ~ q = p2q3 – 3q. Then 2 ~ 3 = B) 27 C) 99 D) 117 E) 89 If 7x + 4 = -19 + 5x, then 2x – 14 equals A) 23 28. 0 B) -5 A) 108 27. E) 18 B) -23 C) -3 D) 16 E) NOTA Which of the following best describes the circled part of the statement? 7x + 9 = 40 A) B) C) D) E) 29. Coefficient Variable Term Expression Solution Solve for x: 5x – 10 = 2 – 2x + 10(x – 3) A) 6 B) 3 C) - 3 D) - 14 E) NOTA 30. Solve for r: A) A 31. B) t(A – p) 1 + tp pt D) 33. 34. C) A− p pt E) NOTA A− p One factor of 5x2 – 3x – 2 is A) 5x+2 32. A = p + prt B) 5x-2 C) x+1 D) 5x+1 E) 5x-1 Write the answer in proper scientific notation: (7 x 105) x (3 x 104) A) 21 x 109 B) 21 x 1020 D) 2.1 x 107 E) NOTA Factor: C) 2.1 x 108 8a2 − 17a + 2 A) (2a − 2)(4a − 1) B) a (8a − 17) + 2 D) (8a + 1)(a − 2) E) (8a − 1)(a − 2) C) (8a − 2)(a − 1) Find a possible middle term to make this polynomial factorable: x2 + ______ + 20 A) 12x 35. 2 B) 13x C) 7x D) 3x E) -10x 6 3 x y z 2 x y A) y4 2 = B) y4z3 C) z3 D) x y z E) y6z3 36. 37. (y² + 2y – 3) – (4y² – 5y – 2) = A) – 3y² – 9y + 5 B) – 3y² – 9y + 1 D) – 3y² + y – 5 E) – 3y² + 7y – 1 2 The solutions of the equation 2x − 6x − 8 = 0 are: A) −4 and 1 D) 38. C) – 3y² – y + 5 −1 2 B) 2, 4 and −1 C) −2 and 1 2 E) 5 3 E) −1 and 4 and 2 Find the x-coordinate of the system: 3x + 3y = 4 x – 3y = 1 A) 39. 6 5 B) 1 3 C) 1 D) 5 4 Find the slope of the line that passes through (4, 7) and (1, 3) A) −4 3 B) −3 4 C) 3 4 D) 4 3 E) 2 40. Find the slope and y-intercept of the line whose equation is 3 y =− x+4 2 A) slope = 2, y-int = 3 2 C) slope = 2, y-int = −3 E) slope = 3 , y-int = −2 2 3 B) slope = − , y-int = 4 2 D) slope = −2, y-int = 3 2 41. 42. 43. Find the equation of the line containing the point (−3, 5) and having slope: 4 A) y = 4x − 7 B) y = 4x D) y = 4x + 17 E) NOTA Solve: C) y = − 4x − 24 4x + 5 ≤ 3 + 6x A) x ≤ – 4 B) x ≥ 1 D) x ≥ – 4 E) x ≥ 4 C) x ≤ 4 Which of the following graphs represents the solution of 2x + 3 ≥ 1 A) B) C) D) E) -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 44. The solutions to x2 + 2x − 12 = − 12 are: A) 0, − 2 B) −4, 6 C) −6, 4 D) 12, 2 E) NOTA 45. 2 x 2 x A) D) 46. 47. − 5x = − 25 x B) 5 x E) x− 5 −x 5 C) x x − 25 x x +5 Which pair of lines represent graphs that are perpendicular? A) y = −3x + 7 y = –3x + 2 B) y = 5x + 5 y = 10x + 5 D) y = 9 x=5 E) y = x y=3 C) 2y = 4x − 16 y = 2x – 8 The graph of x – 4y + 8 = 0 crosses the y-axis at A) -8 B) -2 C) 0 D) 2 E) 8 48. Which equation is graphed to the right? A) x + y = 2 B) 2x – y = 3 D) 2 x − y = 5 E) 3x + y = 2 C) 2x + y = 3 49. What is the first step to solving this problem: 3x – 10 = 2(x + 3) A) add 10 to both sides of the equation B) subtract 3 from both sides of the equation C) distribute the 2 on the right side D) divide by 3 on both sides of the equation E) NOTA 50. A boy is mowing a rectangular lawn 40 ft. long and 30 ft. wide. He has cut all of it except for a rectangle that is 20 ft. long and 15 ft. wide. What fractional part of the lawn remains uncut? A) 1 4 B) 2 5 C) 3 125 D) 3 4 E) NOTA