DIRECTIONS: Solve each problem, choose the correct answer, and then fill in the corresponding oval on your answer document. ACT Math Homework Math 1 60 Minutes 60 Questions Note: Unless otherwise stated, all of the following should be assumed. Do not linger over problems that take too much time. Solve as many as you can; then return to the others in the time you have left for this test. You are permitted to use a calculator on this test. You may use your calculator for any problem you choose, but some of the problems may best be done without using a calculator. 1. Illustrative figures are NOT necessarily drawn to scale.. Geometric figures lie in a plane. 3. The word line indicates a straight line. 4. The word average indicates arithmetic mean. 1. What is the median in the following sequence of numbers? 40, 11, 13, 11, 1, 5, 5, 30, 31, 10 A. 11 B. 13 C. 15 D. 17 E. 19. The width of a square is increased by inches and the length by 3 to give a rectangle. If each side of the original square was n inches long, what is the area of the rectangle in terms of n? F. 6n G. n + 3n H. 6n J. n + 5n + 6 K. n + 6n + 5 1
3. If a= 4 and b= 3 - what is a b 3? -1 3 5 A. 53 38-50 67 B. -3 4-14 1 C. -1 6-6 1 D. -53-38 50-67 E. 1 36 36 1 4. In the triangle below, side x is equal to what value? F. 7 x G. 8 6 H. 10 J. 1 K. 13 8 5. 3 ½ + 8 3 /5 6 ¾ =? A. 1 7 /0 B. 3 7 /0 C. 4 4 /0 D. 5 7 /0 E. 8 17 /0
6. If x > 0, and x x = 6, what is x? F. -3 G. - H. 0 J. K. 3 7. (10 a ) (10 b )= (10 c ), what is d in terms of a, b and c (10 d* ) (where d* indicates d )? A. (c/ab) 1/ B. (c-a-b) 1/ C. (c-ab) 1/ D. (a+b-c) 1/ E. (c/(a+b)) 1/ 8. What is the graph of the linear inequality 35 > -x + 5? F. -15 G. -15 H. -0 J. -15 K. -0 9. If f (x) = x + 3x and g(x) = x 3 + x 3x +, what is g (f(x)), when x = -? A. 110 B. 86 C. -18 D. -0 E. -4 3
10. A microbiologist was studying the reproduction of a specific bacterium. Using the graph below, determine the time span during which the bacterium has the greatest increase in colonies. Bacterial Growth 100000 1000000 # of Bacteria 800000 600000 400000 00000 0 1 3 4 5 6 7 8 9 10 11 1 Hours F. 11-1 hours G. 10-11 hours H. 9-10 hours J. 7-8 hours K. 6-7 hours 11. Simplify 640 : A. 8 10 B. 16 C. 6 10 D. 1 E. 4 10 1. If x + y = 9 and y = 1 /, what is the value of x? F. 6.5 G. 7 H. 7.5 J. 8 K. 8.5 4
13. 3x 3 + 9x = 30x, find the zeros of this polynomial equation. A. 0, -5, B., 5 C. 0 D. -5, -, 0 E. None of the above 14. Which of the following are equal to a for any real number a? I. a II. ( a) III. a F. I only G. II only H. III only J. I and II only K. I, II, and III 15. If there are 5 cards in a deck, what is the probability of the second card obtained from a deck of cards being a jack of hearts if the first card was not replaced nor was it the jack of hearts? A. 4 5 B. 3 5 C. 5 D. 1 51 E. 1 53 16. What is the sixth term in the arithmetic sequence 10, 7, 4? F. -5 G. -6 H. -8 J. -15 K. -0 5
17. Which of the following is the simplified form of 5x +10xy+5y +5? A. 5xy(x++y+5) B. 5(x +xy+y +5) C. 5(x +xy+y+5) D. 5(x+y+5) E. 5x +10xy+5y+5 18. What would be the next number in the sequence 3, 4, 6, 9, 13, 18.? F. 1 G. 3 H. 4 J. 5 K. 6 19. In a classroom, the original ratio of boys to girls is 3:1. If two more girls register to take the class and one boy drops out of the class, what is the new number of girls in the class if the original total number of students was 100? A. 75 B. 74 C. 35 D. 8 E. 7 0. - -7 + (- -8 ) + 3 3 =? F. 585 G. 19 H. 143 J. 1 K. -567 6
1. Given sin θ = 0.5 and cos θ = ( 3), what does tan θ equal? A. 3 3 B. C. 3 D. 3 E. 4 3. ( 3 x) x can also be written as? F. x /3 G. x 3/4 H. x 4/3 J. x 4 K. x 8/3 3. The speed of one boat exceeds three times the speed of another by 5 mph. If s mph is the speed of the slower boat, which of the following expresses the speed, in miles per hour, of the faster boat? A. 3s + 75 B. 3s + 5 C. s + 75 D. s + 5 E. s + 1.5 4. Evaluate f(x) = x 3 + 3x -, when x = -3. F. 38 G. 16 H. -0 J. -38 K. -4 7
5. A circle has circumference equal to 10π. What is the area of the circle? A. 5 π B. 10 π C. 5π D. 50 π E. 100 π 6. The midpoint of the line with endpoints at α (-1, ) and β (3, ) is equal to which value? F. (1, -) G. (, 1) H. (, ) J. (1, ) K. (0, 0) 7. What is the slope of the line given by the equation 4x + 3y = -1? A. 3 B. 4 C. -3/4 D. -4/3 E. -4 8. If f(x) = x -5 and g(x) = x 5, what value(s) of x would make f(x)=g(x) F. 0 ± 300 6 G. 0 ± 40 6 H. 0 ± 300 10 J. 30 or 10 K. Cannot be determined 8
9. A circle has its center at the origin. A point P on the circumference of the circle has coordinates (0, 7). If P travels 70 from its original position, what are the new coordinates of P? A. (7, 0) B. (0, 7) C. (0, -7) D. (7, 7) E. (-7, -7) 30. A rectangle has an area of 35 in, if the width is 5 in what is the length? F. 30 G. 10 H. 7 J. 5 K. 4 31. A reception hall can accommodate p people. When setting up for a reception, how many tables (t) would they need if each table has room for c chairs? A. p c B. p t C. p c D. c p E. p c 3. What is ( 100 x 3 x ( 3) x 4 ) F. 4,400 G. 10,00 H. 1,400 J. 6,00 K. 3,400 8 /3 9
33. If - is subtracted from 3-18, the difference is? A. 11 B. 11i C. -7i D. -11 E. 7i 34. If f(x) = 4x -1 and g(x) = x + 1, what is g(f(x))? 4 F. -x + 1 G. x H. -x J. x - 1 K. x + 35. What is the result when (x + )(x - 5) is subtracted from (3x + )(x - 5)? A. x(5x - 14) B. x(5x - 8) C. x(8-5x) D. 5x - 8x E. 5x - 8x - 0 10
36. What is the square of the complex number (i - )? F. -1i G. -8i H. -8i + 8 J. -4i - 4 K. 8i - 4 37. In the x-y plane there exists two points X (-, -5) and Y (5, 1), what are the coordinates of the midpoint of line segment XY? A. (-, 3/) B. (-7/, -3) C. (3/, -) D. (7/, -) E. (-3/, ) 38. x + 7 = 10, what is x? F. 18 G. 17 H. 4 J. 3 K. 11
39. What is the mean of the following sequence of numbers: 11, 13, 0, 11, 100, 100, 100, 33, 13? (Round to the nearest tenth) A. 100. B. 6.4 C. 11.6 D. 5.8 E. 44.6 40. What is the domain of f(x) when f(x) = 8 - x? x - 3 F. x < 3; 3 < x 8 G. x > 3; x < 3 H. x 8 J. x < 3; 3 < x < 8 K. x > 3; x < 8 41. The painted area beneath a basketball hoop (see diagram below) needs to be repainted. Approximately what area needs to be painted? 10 ft 15 ft A. 8 ft B. 10 ft C. 196 ft D. 189 ft E. 154 ft 1
4. Simplify: log 7 1 + log 7 7 - log 7 1 = 7 F. 10 G. 7 H. 1 J. 0 K. 43. Simplify: 5 x + 10 30 A. 15 x 0 B. 15 < x > 0 C. 35 x 40 D. 15 x 0 E. 35 x 40 44. Marcy would like to receive a final grade of at least a 90 in her math course. If her final grade is the average of her five test scores, and she has taken four tests so far, receiving scores of 9, 93, 83, and 89, she must score at least what on the fifth test to achieve her goal? F. 95 G. 94 H. 93 J. 9 K. 89 45. A rectangular soccer field that measures 10yd by 75yd needs to be covered with a tarp prior to inclement weather. In order to cover the entire field, what would the area of the tarp have to be? A. 9000 yd B. 7500 yd C. 5000 yd D. 195 yd E. 45 yd 46. If ƒ(x) = -3x + 1, then f(-) =? F. 4 G. 1 H. 6 J. 0 K. -4 13
47. If 9 x = 3 3x+1, what is the value of x? A. 81 B. 7 C. 9 D. 3 E. 1 48. If f(x) = x + x and g(x) = -x + 1, what is the value of f(g(x))? F. x + 4x + 3 G. x - 4x + 3 H. x + 3 J. x - 3x K. x 49. What is the sine of 105º? [Note: sin (α + β) = sinαcosβ + sinβcosα] A. 3 B. 3 + C. 6 + 4 D. 3 E. 1/ 50. If a + b = 8 and (a-b) =9, what is the value of ab? F. 3 G. 1 H. 1/ J. 0 K. -1/ 14
51. Two congruent right isosceles triangles overlap so that they share one leg (see diagram). If the length of one leg is 6, what is the area of the shaded region? A. 4 B. 9 C. 18 D. 18 E. 7 6 5. Which of the following is equivalent to (a + bi)? F. a + b G. a + abi + b H. a + abi J. a + abi - b K. a - b 53. If 4x+3 = 16, what is x? A. 1 B. 1 4 C. 1 D. E. 4 54. 3 + 5 x - 6 3 =? F. 101 G. 83.33 H. 1 J. 16 K. 1 15
55. In triangle ABC angle BCA = x, angle BAC = x, and angle ABC = 3x. If side AC = 10, what is the perimeter of the triangle? A. 15 + 5 3 B. 10 + 5 3 C. 30 D. 15 + 10 3 E. 0 56. If (x + y) = 64, and xy = 8, what is the value of x + y? F. 48 G. 5 H. 64 J. 68 K. 7 57. If a 4 =, then 4(9a 4 ) =? 3 A. 18 B. 54 C. 108 D. 140 E. 144 58. In triangle ABC below, what is the degree measure of angle A rounded to the nearest whole number? F. 78 G. 7 H. 64 J. 8 K. 1 A 10 B C 16
59. What is 0% of 50% of x? A..01x B..05x C..1x D..7x E. x 60. In the x-y plane, a circle has its center at the origin. If the diameter of the circle is 8, what are the coordinates of the circle s x and y intercepts? F. x-intercepts: (8,0) & (-8,0), y-intercepts: (0,8) & (0,-8) G. x-intercepts: (4,0) & (-4,0), y-intercepts: (0,4) & (0,-4) H. x-intercepts: (6,0) & (-6,0), y-intercepts: (0,6) & (0,-6) J. x-intercepts: (,0) & (-,0), y-intercepts: (0,) & (0,-) K. x-intercepts: (10,0) & (-10,0), y-intercepts: (0,10) & (0,-10) 17