ACT Diagnostic Review #1

Transcription

1 Name Date Score ACT Diagnostic Review #1 1. Gabe biked a total of kilometers over the course of his morning and afternoon bike rides. If he biked a distance of in the afternoon? kilometers in the morning, how many kilometers did he bike D. E. 2. The acidity of an acid-base solution is found by dividing the volume of acid, in ml, by the sum of the volumes of acid and base. If there are 16.2 ml of acid and 5.8 ml of base, what is the acidity of the solution to the nearest percent? 3% 26% 58% D. 74% E. 36% 3. During the first three months of the year, a car salesman has grossed total monthly sales of $125,000, $95,000 and $112,000. If he wants to increase his average monthly sales to $120,000 by the end of the first four months of the year, what do his sales need to be in the fourth and final month? $111,000 $129,000 $120,000 D. $148,000 E. $333,000

2 4. A professional DJ plays music for parties. He charges $100 for use of his equipment and charges an additional $30 per hour to play music. Which of the following expressions represents the cost, in dollars, of having the DJ play for h hours at a party? 40h 30h h D. 40h E. 30h 5. D. E. 6. If 5x + 2 = 3x - 8, then x =? D. -1 E The figure below shows quadrilateral VXYZ. What is the measure of V + Y? D. 161 E. 180

3 8. If, then d =? D. E. 9. If a 3 2 matrix and a 2 1 matrix are multiplied together, what are the dimensions of the product? 3 1 matrix Matrices of different dimensions cannot be multiplied. 2 2 matrix D. 3 2 matrix E. 1 3 matrix 10. Which of the following sets of three numbers could be the side lengths of a triangle? 3, 3, 6 3, 6, 9 3,, 3 D. 3,, 3 E. 3, 3, If 13 trinkets cost $8.45, how much does 1 trinket cost? $1.30 $0.45 $0.85 D. $0.65 E. $0.60

4 12. The height, h feet, a circus performer reaches when shot out of a cannon is modeled by h(t) = -2(t) t, where t is the length of time, in seconds, that the circus performer spends in the air. According to this model, what is the shortest possible length of time, in seconds, it takes the performer to reach a height of 16 feet? D. 2 E In the standard (x, y) coordinate plane, what is the distance between the points (16, -12) and (19, -8)? D. 15 E All runners who are serious about the sport monitor their dietary intake. Mary does not monitor her dietary intake. Timothy is a serious runner. Which of the following must be true? Timothy monitors his dietary intake. Mary is a serious runner. Mary is a runner, but not a serious one. D. Timothy does not monitor his dietary intake. E. Timothy is a better runner than Mary. 15. What is the least common denominator when adding D. 336 E. 48

5 16. The graph below shows the number of gyms in five cities, to the nearest hundred gyms. According to the graph below, what fraction of the gyms are located in city A and city C? D. E. 17. Which of the following inequalities defines the solution set for the inequality -7-4a > 97? a < -26 a > -20 a > -26 D. -26 < a < -20 E. a < If Anne works each week next year, she will earn a salary of $42,120 at her job. Next year, she is allowed to take as many weeks of vacation as she'd like, but only a maximum of two of those weeks will be vacation with pay. Assuming she earns the same amount each week, what is the maximum salary Anne could earn next year if she takes 8 weeks of vacation? (Hint: there are 52 weeks in one year) $6,480 $40,289 $35,640 D. $4,860 E. $37, Sara has three transportation options to get from city A to city B, five options to get from city B to city C and two options to get from city C to city D. How many distinct routes are available for Sara to travel from city A to city D if she has to pass through each city along the way? D. 60 E. 10

6 20. There are 10 chocolate bars, 20 mints, 30 boxes of raisins, 60 lollipops and 80 pieces of gum in the piñata. If, after the piñata is broken, one piece of candy is randomly chosen, what is the probability that the piece of candy chosen will NOT be gum? D. E. 21. The solution set of is the set of all real numbers x such that: x > 26 x > 44 x > 16 D. x > 7 E. x > What is the slope-intercept form of -9x + y + 2 = 0? y = -3x + y = 27x - 6 y = 3x - D. y = 27x - 2 E. y = -27x In the diagram below, BD = DE, points A, B and E are collinear, quadrilateral CABD is a trapezoid and the ratio of BED to EDB is 4:1. What is the measure of BDC? D. 20 E. 60

7 24. If (x - 5) is a factor of 3x 2-13x + d, what is the value of d? D. 5 E Which of the following is a value of x that satisfies log x 27 = -3? 3 9 D. -9 E In a company of 250 employees, the average salary for non-executive positions is $60,000, while the average salary for executive positions is $90,000. The ratio of non-executive to executive positions is 3:2. What is the average salary for the entire company? $72,000 $180,000 $75,000 D. $39,600 E. $120, If p and q are positive integers such that the greatest common factor of p 2 q 2 and p 3 q 4 is 36, and if p > q, which of the following could equal q? D. 5 E. 4

8 28. A circle in the standard (x, y) coordinate plane is tangent to both the x- and y-axes at 9. Which of the following is an equation of the circle? x 2 + y 2 = 81 (x + 9) 2 + (y + 9) 2 = 81 (x - 9) 2 + (y - 9) 2 = 9 D. (x - 9) 2 + (y - 9) 2 = 81 E. x 2 + y 2 = Which of the following expressions is equivalent to (7x - 11xy)3xy 2? -12x 2 y 2-9x 2 y 2 21x 2 y 2-33x 2 y 3 D. 21xy 2-33x 2 y 2 E. -12xy 30. For right triangle XYZ shown below, what is cos Z? D. E. 31. In the diagram above, ABC is an equilateral triangle, CD = DE and FC = CG. If ACD = 62, points F, C and D are collinear, and points A, C and G are collinear, what is the value of a + b? D. 123 E. 120

9 32. Which of the following is equivalent to (-3a 3 b 6 ) 5? -243a 8 b 30-15a 15 b 30-15a 8 b 11 D. -243a 15 b 11 E. -243a 15 b If x = 4t - 8 and y = 7 - t, which of the following expresses y in terms of x? y = y = y = D. y = E. y = 34. Point B is the center of the circle below and points A and C are on the circle. If ABC is 45, what percent of the circumference of the entire circle is? 25% 12.5% 50% D. 37.5% E. 62.5% 35. ABC has an area of 48, chord BC = 12, and point A is the center of the larger circle. If point A is on the perimeter of the smaller circle, what is the difference in the area of the larger circle and the area of the smaller circle? D. 48 E. Cannot be determined from the information given

10 36. If x 2 = 625 and y 3 = -8, which of the following could be the value of x - y? D. 25 E A retail dance store classifies its stock into four categories: Ballet, Ballroom, Jazz, and Tap. Each day, the store notes the number of shoes, leggings and clothing items sold in each category. Shown below are the matrices for Monday's and Tuesday's sales: Monday Category Shoes Leggings Clothing Items Ballet Ballroom Jazz Tap Which of the following matrices represents the combined sales for Monday and Tuesday? Tuesday Category Shoes Leggings Clothing Items Ballet Ballroom Jazz Tap D. E.

11 38. To which of the following can be simplified? D. E. 39. The price of a guitar increased by 30% from 2006 to 2007 and then decreased by 20% from 2007 to By what percent did the price of the guitar increase from 2006 to 2008? D. 30 E Which of the following degree measures is equivalent to 2.25 radians? D E Square ABCD is reflected across the y-axis to have the image A'B'C'D' in the standard (x, y) coordinate plane; thus, A reflects to A'. The coordinates of point A are (f, g). What are the coordinates of point A'? (-f, -g) Cannot be determined from the information given (-f, g) D. (f, -g) E. (f, g)

12 42. In the diagram above, ACFD is a rectangle, B is the midpoint of AC, BE is perpendicular to AC, AC is twice as long as AD and AE = 10. What is the perimeter of AEC? D. 30 E After the tree is chopped down, its top lands on the edge of the riverbank with a 15% slope (that is, for every 100 feet of horizontal distance covered, the tree has a height of 15 feet). The horizontal distance from the base of the tree to the base of the riverbank is 35 feet. What is the length of the tree? feet feet 5.25 feet D feet E feet D. 11 E Highway 892 loops around the city to form a circle with a 4-mile radius. David drives along the highway far enough to form a 45 angle between his starting point, E, the center of the circle formed by the highway, O, and his ending point, S. What distance has David traveled?

13 46. A circle is inscribed within a square of area 81, as shown below. What is the sum of the lengths of the segments connecting the corner of each square to the circle? 47. The curve y = 3x 2-600x + 30,000 is shown above for 0 < x < 200. The line segment connecting A(0, 30,000) and B(100, 0) is also shown above in the standard (x, y) coordinate plane. What is the y-coordinate for the point on the curve with an x-coordinate of 50? 15, ,000 D. 7,500 E. 10, The length of the curve connecting A and B is longer than the segment connecting A and Approximately how long is AB in coordinate units? 31,000 30, ,000 D. 3,000 E. 30,100

14 49. What is the approximate area under the curve that is bound by the curve, the y-axis, and the x- axis? Greater than 1,500,000 square units because the curve lies under A 1,500,000 square units Less than 1,500,000 square units because the curve lies under A D. Greater than 1,500,000 square units because the curve lies over A E. Less than 1,500,000 square units because the curve lies over A 50. Which of the following quadratic equations has solutions x = 4c and x = 12d? x 2 - x(3cd) - 48cd = 0 x 2 + x(8cd) - 3cd = 0 x 2 + x(4c + 12d) + 48cd = 0 D. x 2 - x(4c + 12d) - 48cd = 0 E. x 2 - x(4c + 12d) + 48cd = The volume of the larger cylinder is four times that of the smaller cylinder. What is the ratio of the height of the larger cylinder to that of the smaller cylinder if the radii of the cylinders are equal? 1:2 4:1 1:4 D. 2:1 E. 16:1

15 53. If f(x) = x 2 + 9, then f(x + p) =? x 2 + 2xp + p x 2 p + p 2 x 2 + p 2 D. x 2 + p + 9 E. x 2 + 2xp + p Henry started with a score of 53 on his first French test. His goal was to increase his score by 3.5 points on each successive test. If Henry met, but did not exceed his goal, what was his combined score on all tests after 15 tests? ,162.5 D E Square XYZV is reflected across the x-axis and is then rotated 90 clock-wise about its center to have the image X'Y'Z'V' in the standard (x, y) coordinate plane. If the square has an area of 16, a center at (4, 4), and the coordinates of point X are (2, 6), what are the coordinates of point X'? (6, -6) (2, -6) (6, 6) D. (2, -2) E. (6, -2)

16 57. Which of the following is the graph of the function f(x) defined below? 58. Susie wants to buy a new flat screen television. She researches the difference between a 32- inch television and a 24-inch television. Televisions are measured by their diagonal length (NOT by their lengths or widths), and the aspect ratio (length to width) of all flat screen televisions is 16:9. What is the approximate length, to the nearest whole inch, of the longer side of a 32-inch television? D. 30 E. 21

17 59. Susie wants to buy a new flat screen television. She researches the difference between a 32- inch television and a 24-inch television. Televisions are measured by their diagonal length (NOT by their lengths or widths), and the aspect ratio (length to width) of all flat screen televisions is 16:9. What is the approximate difference in length between the shorter sides of both televisions? D E. 4.25