ARITHMETIC. Suggested time 40 minutes 35 Questions

Transcription

1 ARITHMETIC Suggested time 40 minutes 5 Questions Directions: In this section solve each problem Then decide which is the best of the choices given What is 7589 rounded to the nearest hundredth? (A) 76 (B) 7 (C) 7 (D) = (A) 4 (B) 8 9 (C) (D) = (A) 5 (B) 6 (C) 5 (D) is between (A) 4 and 6 (B) 6 and 8 (C) 60 and 80 (D) 600 and of 48 is 4 (A) 6 (B) 6 (C) 8 (D) = (A) 89 (B) 0 (C) 98 (D) 7 Beth makes fruit punch by adding cups of fruit juice to every 5 liters of soda If she uses 5 liters of soda, how many cups of juice should she use? (A) 9 (B) (C) (D) is closest to 008 (A) (B) 0 (C) 00 (D) = (A) (B) 5 8 (C) 4 8 (D) 0 If the average of 5 numbers is 50, what is their sum? (A) 0 (B) 5 (C) 55 (D) = (A) (B) 5 (C) (D) 5 8 = (A) 4 (B) 4 4 (C) 4 (D) 40 57

2 7 0 = (A) 005 (B) 05 (C) 86 (D) = (A) (B) 4 (C) (D) 7 5 If 0 percent of a number is 40, then 5 percent of that number is (A) 4 (B) 0 (C) 6 (D) 00 6 A clock that gains 0 seconds every hour will gain how many minutes in a day? (A) 4 (B) 8 (C) 6 (D) = (A) 8 5 (B) 5 (C) 5 (D) 5 8 Figure Tax Allocation in Frazier Township 8 According to the graph above, if the township collected a total of $,600,000 in taxes, what amount was set aside for the emergency fund? (A) $900,000 (B) $44,000 (C) $90,000 (D) $4, , 60 5 = (A) 7 5 (B) 7 5 (C) 70 5 (D) If eight furlongs measures 0 rods, how many furlongs are in a measure of 600 rods? (A) 6 (B) 0 (C) 5 (D) 40 A theater was sold out for 85 percent of its performances last season Once the theater was sold out for 5 performances in a row

3 From the information above, which of the following can be determined? (A) The total number of performances last season that were sold out (B) The number of performances last season that were not sold out (C) The percent of the performances last season that were not sold out (D) The percent of the performances sold out in a row Three people who work full time are to work together on a project, but their total time in the project is to be equivalent to that of only one person working full time If one of the people is budgeted for of his time to the project and a second person 4 of her time, what part of the third worker s time should be budgeted to this project? (A) (B) 5 (C) 4 7 (D) 4 5 percent of 40 is closest to (A) 5 (B) 40 (C) 50 (D) is closest to (A) 500 (B) 600 (C) 5, 000 (D) 6, In year X the population of a certain city was reported to be 50,00, which represented 8 percent of the state s population According to these figures, what was the approximate population of the state in year X? (A) 40, 000 (B) 50, 000 (C) 60, 000 (D) 790, Which of the following is greater than 00 and less than 050? (A) 8 (B) 5 (C) 5 (D) How many fifths are there in 8? (A) 40 (B) 4 (C) 56 (D) If N equals 04, then N is approximately 0 (A) 4 (B) 4 (C) 5 (D) 06 9 If pik = 0 jums and dim = 5 jums, what is the ratio of the value of 5 piks to 4 dims? (A) : (B) : 5 (C) 5 : (D) 5 : 4 0 On two tests, a student scored 85 and 9, respectively What score must the student achieve on a third test in order to have an average score of 90 for the tests? (A) 89 (B) 90 (C) 9 (D) 95

4 4 Which of the following is closest to 4000? (A) 0 (B) 60 (C) 400 (D) 000 A rectangular recreation area 0 meters long and 5 meters wide is to be marked off by putting a rope around it The length of the shortest rope that can be used is about how many meters? (A) 5 (B) 70 (C) 05 (D) is closest to which of the following? 0 (A) 0074 (B) 074 (C) 74 (D) 74 4 Which of the following shows a way to change 5 to an equivalent fraction? (A) (B) 5 5 (C) 5 + (D) is closest to 8 (A) 6 (B) 6 (C) 7 (D) 7

5 5 ELEMENTARY ALGEBRA Suggested time 40 minutes 5 Questions Directions: In this section solve each problem Then decide which is the best of the choices given Which of the following is greater than 6? (A) 7 (B) 6 (C) (D) 9 5(x + ) = (A) 5x + (B) 5x + 5 (C) 5x + 8 (D) x + 5 (7) = 7 (A) (B) 4 (C) 0 (D) 4 x 6y 5x + y = (A) 7x 5y (B) 7x 7y (C) 7x 5y (D) 7 5y ( 5 8 ) 8 (A) (B) 0 (C) 7 8 (D) If c =, then 4c + 5c = (A) 5 (B) 7 (C) 9 (D) 7 7 Which of the following numbers is least? (A) 4 (B) (C) 0 (D) 4 8 6x 6 = (A) 8x 4 (B) 8x (C) 6x 4 (D) 6x 9 If x 5 = 7, then x = (A) (B) (C) 6 (D) 6 0 (x )(x + ) = (A) x 9 (B) 4x 9 (C) 4x + 9 (D) 4x 6x 9 5x x (A) 5x (B) 5x (C) x (D) 5 x

6 6 (x y) (A) 6x 6 y (B) 8x 5 y (C) 8x 6 y (D) 9x 6 y On Monday, Dave drove exactly m miles On Tuesday, he drove fewer miles than he drove on Monday Which of the following expressions represents the total number of miles Dave drove on both days? (A) m (B) m (C) m (D) m 4 x (5x 4) = (A) 8x 4 (B) x 4 (C) x + 4 (D) x 5 If 4x = 7x, then x = (A) (B) (C) (D) 6 Of the following, which is a factor of 4x x + 4x? (A) x (B) 4x (C) 8x (D) x 7 4x 9y = (A) (4x + y)(4x y) (B) (x + y)(x y) (C) (4x 9y)(x + y) (D) (x y) 8 Which if the following is an equation of the graph above? (A) y = x (B) y = (C) x = (D) x = 9 If 5 x + = 0, then x = (A) 6 5 (B) 8 (C) 4 5 (D) x 4 y = (A) 4y 4x x + y (B) 4y 4x xy (C) 4 xy (D) 0 (a b) = (A) a 4ab + 4b (B) a ab + 4b (C) a + 4b (D) a 4b

7 7 All the following points are on the graph of y = x +, EXCEPT (A) (, 5) (B) (, 4) (C) (0, ) (D) (, 6) (A) 6rs ( ) ( ) s 0r 5r 6s = (B) r s (C) s x + y = 5 x y = 4 For the system of equations above, what is the value of x? (D) s 50r (A) 4 (B) 6 (C) 7 (D) 9 5 Given x = 5 + 6, y = 5 + 6, and z = 5 + 6, which one of the following is true about the numbers x, y, and z? (A) x = y (B) y = z (C) x = y = z (D) x < y 6 Which of the following is a factor of x 5x 6? (A) x (B) x (C) x 6 (D) x 7 The equation N = 5 could be used to represent which of the following sentences? (A) less than half a number N equals 5 (B) Half a number N less than equals 5 (C) A number N minus divided by equals 5 (D) Two times a number N minus equals 5 8 If 8 is of a number N, then N = 4 (A) 6 (B) (C) (D) 4 9 If x y =, and x = y, then x = (A) 4 (B) 8 (C) 6 (D) 0 0 Kim earns x dollars per hour for the first 40 hours she works in a week and over 40 If she worked 5 hours last week, how much, in dollars, did she earn? times as much for each hour (A) 5x (B) 40 + x (C) 5x + x (D) 58x

8 8 Which of the following is a factor of a 7a + 0? (A) a 0 (B) a 4 (C) a + 4 (D) a = + x (A) x (B) 0 x + (C) 0x x + (D) 0 + x In a certain school there were 5 more seniors than juniors In one marking period, percent of the juniors and 0 percent of the seniors were on the honor roll If the total of juniors and seniors on the honor roll was 7, how many seniors were there in the school in that marking period? (A) 80 (B) 75 (C) 55 (D) 8 4 (A) 4 8 x + 5 x + = (B) (x + )(x + ) (C) x + (x + )(x + ) (D) x 7 (x + )(x + ) 5 If x a = b, then x = (A) (a + b) (B) a + b (C) b + a (D) b + a

9 9 Directions: In this section solve each problem Then decide which is the best of the choices given x 0x + = COLLEGE LEVEL MATHEMATICS Suggested time 50 minutes 5 Questions (A) (x )(x 4) (B) [(x )] (C) (x )(x ) (D) (x + 6)(x ) (E) (x 5)(x ) Where defined, 8x y 8 z 6x y 4 z = (A) xy 4 (B) xy (C) xy4 (D) xy (E) y4 x Which of the following shaded regions is the graph of the region described by x and 0 y? (A) y (B) y x x (C) y (D) y x x (E) y x

10 0 4 The figure above is a portion of the graph of which of the following equations? (A) y = sin x (B) y = cos x (C) y = sin x (D) y = csc x (E) y = tan x 5 Which of the following can be factored in the form (x + h), where h is an integer? (A) x + (B) x + 9 (C) x + 6x + (D) x + 6x + 6 (E) x + 6x Where defined, ( x + x 6 x + ) ( ) x + x = 4 (A) 0 (B) (C) x x (D) x+ x+ (E) x+ x+ 7 Where defined, (A) cos θ sin θ tan θ = 8 If 4(x ) + 5 = 6 (x + 5), then x = (B) sin θ cos θ (C) sec θ (D) cos θ (E) csc θ (A) 9 4 (B) 4 9 (C) 4 9 (D) 4 5 (E) For what values of x is x + 5 = 5? (A) 5 only (B) 8 only (C) 5 and 5 (D) 0 and 5 (E) 5 and 0 0 What is the sum of the roots of the equation (x + )(x )(x ) = 0? (A) 6 (B) 4 (C) 5 (D) 4 (E) 6 If x < 0, then x +x = (A) x (B) x (C) x (D) x (E) x

11 If sin 50 = x, then which one of the following is true? (A) 0 < x < (B) < x < (C) < x < (D) < x < (E) < x < If the equation of the linear function in the figure is y = mx + b, then m = (A) r (B) r s (C) r s (D) s r (E) s r 4 If a = a + and a = 4a +, then in terms of a, a + a + a = (A) 7a + 7 (B) a + 7 (C) 0a + 6 (D) a + 6 (E) a For what real numbers x is x 4x + 49 negative? (A) 7 < x < 7 (B) x < 7 or x > 7 (C) x = 7 or x = 7 (D) 0 < x < 4 (E) For no x 6 An equation of the line in the figure above is (A) y = x + (B) y = x (C) y = x + (D) y = x + (E) y = x + 7 If log 5 x =, then x =

12 (A) 5 (B) 5 (C) 5 (D) 5 (E) 5 8 What is the amplitude of y = 5 sin 4x (A) 4 (B) π 4 (C) 5 4 (D) 5 (E) 5 9 If f (x) = 4x + and g(x) = x, then f (g(x)) = 4 (A) x (B) x (C) 8x + 8x + 4 x y P(x, y) θ (, 0) x (D) 7x (E) (4x + )(x ) 4 0 In the figure above, if the coordinates of point P on the unit circle are (x, y), then sin θ = (A) x y (B) y (C) x (D) y (E) x y 4x y 4x In the square in the figure above, the area of the unshaded region is (A) (4x y)(4x y) (B) 6x + y (C) 4x(4x y) y(4x + y) (D) 4x(4x + y) + y(4x + y) (E) (4x + y)(4x y)

13 { y = x + y = x What values of x satisfy the system of equations above? (A) and (B) and (C) and (D) 4 and (E) 4 and Which one of the following could represent the graph of y = x + c? (A) (B) (C) (D) (E) 4 csc π = (A) (B) (C) (D) (E) 5 If f (x) = x 4, then f (x) = (A) f (x ) (B) f (x) (C) 0 (D) f (x) (E) f (x + ) 6 n=4 n = (A) 7 (B) 0 (C) 60 (D) 66 (E)! 4! 7 8( )(4 4 ) = (A) 4 9 (B) 6 (C) 7 4 (D) 7 (E) 9

14 4 8 Which of the following could be an equation of the graph shown in the figure above? (A) y = (x ) + 5 (B) y = (x ) 5 (C) y = (x + ) 5 (D) y = x 5 (E) y = x log = (A) 5 (B) (C) (D) 5 (E) 5 0 If the domain D of the function f is the set of all real numbers x for which f (x) = 4 x is a real number, then D = (A) {x x or x } (B) {x x < or x > } (C) {x x } (D) {x x } (E) {x < x < } i + i = (A) 7 i (B) i (C) 7 i (D) 5 i (E) i If f (x) = f (x + h) f (x), x 0, then x h (A) h x(x + h) (B) h x(x + h) is (C) (D) x(x + h) (E) x(x + h) What is the solution set cos x = sin x, where 0 x π? (A) { π} (B) { π} (C) { π 6, 4π } (D) { π 6, 7π 6 } (E) { π 6, 5π 6, 7π 6, π } 6 4 If f (x) = 6x, and f denotes the inverse of f, then f () = (A) 4 (B) 0 (C) 0 (D) 4 (E) undefined 5 If is a double root of the equation ax + bx + cx + d = 0, which of the following could NOT be a factor of the left member of the equation? (A) x 4x + 4 (B) x 5x + 6 (C) x 6x + 9 (D) x + x (E) x 9