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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., , 2, 2, Factor: 25x – 16y, , A) (5x – 4y)2, D) (5x + 2y)(5x – 8y), , B) 5 (5x – 4y), E) NOTA, , C) (5x + 4y)(5x – 4y)
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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, , 2, (3x + 4) =, , A) 9x2 + 12x + 16, , B) 9x2 + 16, , D), , E) 25x2, , 9x + 16, , C) 9x2 + 24x + 16
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18., , Solve: 3x (x – 4)(3x + 5) = 0, A) 4, −, , 5, 3, , 5, B) – 4, − , 3, 0, 3, , D) 4, –5, 0, , 19., , E) NOTA, , One of the solutions of the equation:, B) −, , A) 0, , 5, C) − , 4, 0, 3, , 11, 3, , C) 4, , 3x2 + 11x = 4, D), , 1, 3, , is, E) NOTA, , 20. Simplify: (3cd6)3(cd)4, A) 27c7d10, , B) 27c7d13, , 12 72, D) 27c d, , 21., , C) 9c7d22, , E) 27c7d22, , Simplify: (4c4 + 1) – (7c3 – 3) + (2c4 + 5c3), A) 6c4 + 2c3 – 4, , B) 6c4 – 2c3 + 4, , 4, 3, D) 2c – 2c – 2, , E) 4c + 4, , C) 6c4 – 2c3 – 2, , 22. 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., , 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%
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24. If x = 2 and y = −3, then −x y² =, A) −36, 25., , B) −18, , C) −12, , D) 12, , E) 18, , Which is closest to the distance between A and B on the number, line?, A, , B, -4, , A) -9, , 0, , B) -5, , C) 13, , 4, , D) 5, , E) 12, , 26. Define p ~ q by the equation p ~ q = p2q3 – 3q. Then 2 ~ 3 =, A) 108, , B) 27, , C) 99, , D) 117, , E) 89, , 27. If 7x + 4 = -19 + 5x, then 2x – 14 equals, A) 23, , B) -23, , C) -3, , D) 16, , E) NOTA, , 28. Which of the following best describes the circled part of the, statement?, 7x + 9 = 40, A), B), C), D), E), , Coefficient, Variable, Term, Expression, Solution, , 29. Solve for x:, 5x – 10 = 2 – 2x + 10(x – 3), A) 6, , B) 3, , C) - 3, , D) - 14, , E) NOTA
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36., , 37., , (y² + 2y – 3) – (4y² – 5y – 2) =, A) – 3y² – 9y + 5, , B) – 3y² – 9y + 1, , D) – 3y² + y – 5, , E) – 3y² + 7y – 1, , C) – 3y² – y + 5, , The solutions of the equation 2x2 − 6x − 8 = 0 are:, A) −4 and 1, D), , B) 2, 4 and −1, , −1, and 2, 2, , C) −2 and, , 1, 2, , E), , 5, 3, , E) −1 and 4, , 38. 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
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41., , 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, , 42. Solve:, , C) y = − 4x − 24, , 4x + 5 ≤ 3 + 6x, , A) x ≤ – 4, , B) x ≥ 1, , D) x ≥ – 4, , E) x ≥ 4, , C) x ≤ 4, , 43. 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
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45., , x 2 − 5x, =, x 2 − 25, x, A), 5, x, D), x−5, , −x, 5, x, E), x+5, , B), , C), , x, x − 25, , 46. 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, , 47. 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
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Answers for, Algebra, Diagnostic, Pretest, , 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, , C, C, E, D, C, A, B, B, B, A, C, B, A, E, E, C, C, C, D, E, B, B, E, B, C, , 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, , C, E, D, A, C, A, E, E, A, B, E, E, D, D, B, D, B, B, A, E, D, D, B, C, A
