Subset II Part 2: Mathematics
27. If the number 360 is written as a product of its prime factors in the form a3b2c, what is the numerical value of a + b + c? A. 10 B. 16 C. 17 D. 22
A
42. Use the diagram on page 21 to answer the question that follows. To find the length of a lake, surveyors measure the distances shown suchthat ΔABC and ΔARS are similar. If RS = 3 km, AS = 4 km, and SC = 2 km, what is BC, the length of the lake? A. 4.5 km B. 5 km C. 6 km D. 8 km
A
43. Triangle ABC is isosceles. Angle B has a measure of 120°. What is the measure of angle A? A. 30° B. 45° C. 60° D. 120°
A
50. Use the table below to answer the question that follows. Jan. - Feb. - Mar. - Apr. - May - June 28° - 29° - 38° - 44° - 58° - 73° July - Aug. - Sept. - Oct. - Nov. - Dec. 78° - 77° - 72° - 63° - 47° - 35° The table above gives the mean temperatures for each month of the year. What is the range in mean temperatures during this year? A. 50° B. 52.5° C. 53.0° D. 53.5°
A
28. Use the diagram below to answer the question that follows. 5/8 + 1/6 + 3/7 What is the sum of the shaded areas in the three circles above if each circle represents one unit? A. 1 9/21 B. 1 15/42 C. 1 37/168 D. 1 205/336
C
31. Use the number line below to answer the question that follows. < 0 - 1/8 - 2/8 - 3/8 - 4/8 - P - Q - 7/8 - 1 > Which of the following numbers can be represented on the number line between points P and Q? A. 17/37 B. 26/43 C. 39/59 D. 57/71
C
34. Which of the following illustrates the operation 1 1/2 divided by 1/4? A. Sean has 1 1/2 pounds of popcorn. He wants to divide it equally into 4 bags. How many pounds should he put into each bag? B. A trip to the beach is usually a 1 1/2-hour drive. Repairs to the freeway have increased the travel time by 1/4. How long will the trip take? C. Maria has 1 1/2 yards of rope. She wants to divide it into 1/4-yard lengths. How many pieces of rope will she have? D. The perimeter of a rectangular field is 1 1/2 miles. The field is 1/4 mile wide. How long is the field?
C
37. Use the table below to answer the question that follows. Radius - Area 0.0 - 0 1.0 - 3.14 2.0 - 12.57 3.0 - 28.31 4.0 - 50.29 The table gives the area of several circles of different radii. Which of the following graphs best represents the data in the table? A. (Radius, Area) - straight diagonal line from 0,0 to 10,5 B. (Radius, Area) - curved (top left quarter of an oval like) line from 0,0 to 10,7.5 C. (Radius, Area) - curved (bottom right quarter of an oval like) from 0,0 to 5,10 D. (Radius, Area) - curved upside down u line from 0,0 to 10,0
C
41. Use the equation below to answer the question that follows. 3n + 2(n - 4) = n + 15 Which of the following equations could occur as a step in solving the equation above for n? A. 4n = 19 B. 4n = 7 C. 4n = 23 D. 6n = 7
C
45. Use the diagram on page 23 to answer the question that follows. The figure above is rolled up and folded to make a cylinder of volume 10 cm^3. Which of the following statements about the figure must be true? A. The area of the rectangular section, AR, is 10 cm^2. B. The length of the rectangle, LR, is 5 cm^2. C. The area of each circular section, A1 and A2, is 5 cm^2. D. The sum of the areas of the circular sections, A1 + A2, equals 5 cm^2.
C
46. Given that figure ABCD is a parallelogram, what are the coordinates of point C? A (2,2) B (6,2) C ( , ) D (4,4) A. (4, 8) B. (6, 4) C. (8, 4) D. (12, 4)
C
47. Use the diagram below to answer the question that follows. A regular hexagon is made from equilateral triangle ABC by cutting along the dotted lines and removing the three smaller triangles. If triangle ABC has a perimeter of 18, what is the perimeter of the hexagon? A. 6 square root of 3 B. 9 C. 12 D. 15
C
48. The scale on a map is 1 inch = 15 miles. On the same map, the distance between Belmont and Smithville is 13 inches. Which of the following is the best estimate of how long it will take to drive from Belmont to Smithville at an average speed of 60 miles per hour? A. 2 hours 8 minutes B. 2 hours 14 minutes C. 3 hours 15 minutes D. 4 hours 0 minutes
C
51. The range of hourly wages for 15 employees of a small company starts at $7.50 and ends at $21.40. If only one worker receives the median wage of $8.90, how many workers receive a higher hourly wage? A. 5 B. 6 C. 7 D. 8
C
52. Each of the numbers from 4 to 24 inclusive is written on a separate piece of paper and placed in a bag. If one of these pieces of paper is randomly selected from the bag, what is the probability that the number on it will be a prime number? A. 2/7 B. 3/10 C. 1/3 D. 7/20
C
29. Use the problem below to answer the question that follows. For a bake sale, Marianne has baked p chocolate chip cookies and Jeffrey has baked q peanut butter cookies. They want to package their cookies separately so that each bag has the same number of cookies. How many cookies could they put in each bag? Which of the following methods could be used to find all the solutions to this problem? A. Find the divisors of p + q. B. Find the common factors of p and q. C. Find the prime factors of p • q. D. Find the common multiples of p and q.
B
30. What value does the 2 represent in the number 2.1 x 10^-3? A. 2/10,000 B. 2/1,000 C. 2/100 D. 2/10
B
32. In a town with a population of 4800 people, 8% of the population is evenly distributed in grades 1-6. Approximately how many students are in grade 4? A) 55 B) 64 C) 77 D) 96
B
33. Use the numbers below to answer the question that follows. 212 206 246 238 231 216 224 To estimate the sum of the numbers given above, Riley first rounds each number to the nearest ten and then adds the rounded values. By how much will Riley's estimate differ from the actual sum? A) 3 B) 7 C) 33 D) 73
B
39. Use the graph below to answer the question that follows. A (0,3) B (4,3) C (4,1) D (3,-3) E (2,-1) Point E is on a line with a slope of 2 in the x-y plane. Which of the following points is also on the line? A. Point A B. Point B C. Point C D. Point D
B
44. Use the diagram on page 22 to answer the question that follows. AC | line (main road) = 8 km AB | line (west road) = 6 km. BC | line (cross road) = _ km. The Δ is a right triangle. Main Road and West Road are perpendicular and intersect at point A. Cross Road intersects Main Road 8 km from point A and intersects West Road 6 km from point A. What is CB, the length of Cross Road? A. square root of 28 km B. 10 km C. 14 km D. 28 km
B
49. In some countries, area is measured in pings. If the area of a rectangular piece of land that measures 22 feet × 27 feet is 33 pings, how many square feet is equal to one ping? A. 6 B. 18 C. 26.9 D. 40.5
B
35. Pat is baking a cake. The recipe calls for of 2 1/4 cups of flour per 1/2 pound of butter. If Pat uses 3 cups of flour, how much butter should be used to keep the proportion of ingredients equal? A. 1/6 pound B. 1/4 pound C. 3/8 pound D. 2/3 pound
D
36. The problem below shows steps in finding the product of two two- digit numbers using this standard multiplication algorithm. The missing digits in the problem are represented by the symbol _. _9 x 36 = 29_ + _4_ _ = _ _ _ _ A. 1 B. 4 C. 6 D. 7
D
38. Grapefruits in a supermarket display are stacked in the shape of a pyramid. Each layer of the stack is square. The bottom layer is a square with 5 grapefruits on each side. The side of each successive layer is made shorter by one grapefruit. What is the total number of grapefruits that can be stacked? A. 15 B. 35 C. 54 D. 55
D
40. A repair person charges a $30 fixed charge plus $45 per hour for time spent working. What is the total bill for a job that requires n hours of work? A. ($30 + $45)n B. $15n + $30 C. $30n + $45 D. $45n + $30
D