PAT考试数学部分例题.doc

PAT考试数学部分例题PAT数学题型主要有： l Number and operations:数字和运算 l Algebra and functions：代数和函数 l Geometry and measurement：几何和测量 l Data analysis, statistics and probability:数据分析，统计和概率 做题策略： 关键是在于平时的数学题目的训练。要通过练习了解题型。一般能够讲高中所学的数学知识运用好就足以解决问题了。所以不用心理上存在畏惧。 做题的关键是能够阅读题目。在单词记忆的时候，要着重背一些数学名词等相关的词汇。 至于上面提到的4中类型的题目，需要在平时的训练中各个击破。在你看懂了题目要求以后，就按照高考的时候做数学题那么解决就行了。而PAT的数学远远没有高考题目那么复杂。1. Of the following, which is greater than ? A. 2/5 B. 4/7 C. 4/9 D. 5/11 E. 6/13 2. If an object travels at five feet per second, how many feet does it travel in one hour? A. 30 B. 300 C. 720 D. 1800 E. 18000 3. What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive? A. 90 B. 95 C. 100 D. 105 E. 110 4. A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long? A. 48 B. 32 C. 24 D. 18 E. 12 5. In a class of 78 students 41 are taking French, 22 are taking German and 9 students are taking both French and German. How many students are not enrolled in either course? A. 6 B. 15 C. 24 D. 33 E. 54 6. If f(x) = (x 50), what is the value of f(-5) ? A. 75 B. 25 C. 0 D. -25 E. -75 7. ( 2 - 3 ) = A. 5 - 26 B. 5 - 6 C. 1 - 26 D. 1 - 2 E. 1 8. Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip? A. 10 B. 8 C. 6 D. 4 E. 2 9. Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required? A. 10 B. 15 C. 20 D. 25 E. 30 10. Jos collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps? A. 5 : 1 B. 10 : 5 C. 15 : 2 D. 20 : 2 E. 25 : 2 11. A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle? A. 2.5 B. 3 C. 5 D. 4 E. 10 12. Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set? A. 4 B. 7 C. 8 D. 12 E. it cannot be determined from the information given. 13. If f(x) = (x + 2) / (x-2) for all integers except x=2, which of the following has the greatest value? A. f(-1) B. f(0) C. f(1) D. f(3) E. f(4) 14. If n 0, which of the following must be greater than n? (I) 2n (II) n (III) 2 - n A. I only B. II only C. I and II only D. II and III only E. None 15. After being dropped a certain ball always bounces back to 2/5 of the height of its previous bounce. After the first bounce it reaches a height of 125 inches. How high (in inches) will it reach after its fourth bounce? A. 20 B. 15 C. 8 D. 5 E. 3.2 16. n and p are integers greater than 1 ; 5n is the square of a number ; 75np is the cube of a number. The smallest value for n + p is A. 14 B. 18 C. 20 D. 30 E. 50 17. The distance from town A to town B is five miles. C is six miles from B. Which of the following could be the distance from A to C? (I) 11 (II) 1 (III) 7 A. I only B. II only C. I and II only D. II and III only E. I, II, or III 18. 5 percent of 55 = A. 0.05 B. 0.25 C. 0.5 D. 2.5 E. 25 19. If PQR = 1 , RST = 0 , and SPR = 0, which of the following must be zero? A. P B. Q C. R D. S E. T 20. -20 , -16 , -12 , -8 . In the sequence above, each term after the first is 4 greater than the preceding term. Which of the following could not be a term in the sequence? A. 0 B. 200 C. 440 D. 668 E. 762 (All terms in the sequence will be multiples of 4)21. If f(x) = x 3, where x is an integer, which of the following could be a value of f(x)? (I) 6 (II) 0 (III) -6 A. I only B. I and II only C. II and III only D. I and III only E. I, II and III 22. For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200? A. 48 B. 49 C. 50 D. 51 E. 52 23. In the following correctly worked addition sum, A,B,C and D represent different digits, and all the digits in the sum are different. What is the sum of A,B,C and D? A. 23 B. 22 C. 18 D. 16 E. 14 24. 12 litres of water a poured into an aquarium of dimensions 50cm length , 30cm breadth, and 40 cm height. How high (in cm) will the water rise? (1 litre = 1000cm) A. 6 B. 8 C. 10 D. 20 E. 40 25. Six years ago Anita was P times as old as Ben was. If Anita is now 17 years old, how old is Ben now in terms of P ? A. 11/P + 6 B. P/11 +6 C. 17 - P/6 D. 17/P E. 11.5P 26. If a = 12, then a4 = A. 144 B. 72 C. 36 D. 24 E. 16 27. If n is even, which of the following cannot be odd? (I) n + 3 (II) 3n (III) n - 1 A. I only B. II only C. III only D. I and II only E. I, II and III 28. One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle? (I) 24 (II) 20 (III) 5 A. I only B. II only C. III only D. II and III only E. I, II and III 29. A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 91 pounds? A. 12 B. 11 C. 10 D. 9 E. 8 30. A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube? A. 8p B. pq C. pq + 27 D. -p E. (p - q)6 31. What is the length of the line segment in the x-y plane with end points at (-2,-2) and (2,3)? A. 3 B. 31 C. 41 D. 7 E. 9 32. n is an integer chosen at random from the set 5, 7, 9, 11 p is chosen at random from the set 2, 6, 10, 14, 18 What is the probability that n + p = 23 ? A. 0.1 B. 0.2 C. 0.25 D. 0.3 E. 0.4 33. A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D? A. 0.75D B. 0.76D C. 0.765D D. 0.775D E. 0.805D 34. Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $324 per week. How much does she earn in dollars per hour? A. 11 B. 10 C. 9 D. 8 E. 7 35. ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all equal. What is the perimeter of the parallelogram? A. 12 B. 93 C. 9 D. 8 E. 33 36. If the product of 6 integers is negative, at most how many of the integers can be negative? A. 2 B. 3 C. 4 D. 5 E. 6 37. If a positive integer n, divided by 5 has a remainder 2, which of the following must be true? (I) n is odd (II) n + 1 cannot be a prime number (III) (n + 2) divided by 7 has remainder 2 A. none B. I only C. I and II only D. II and III only E. I, II and III 38. A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of the smaller cubes have paint on exactly 2 sides? A. 30 B. 24 C. 12 D. 8 E. 6 39. Line l contains the points (3,1) and (4,4). If line m is a different line, parallel to line l in the same coordinate plane, which of the following could be the equation of line m? A. y = 3x - 8 B. y = 1/3x - 3 C. y = -3x - 8 D. y = 3x + 1 E. y = -8x + 3 40. In the figure above the square has two sides which are tangent to the circle. If the area of the circle is 4a, what is the area of the square? A. 2a B. 4a C. 4a D. 16a E. 64a 41. A triangle has a perimeter 13. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side? A. 2 B. 4 C. 6 D. 8 E. 10 42. A machine puts c caps on bottles in m minutes. How many hours will it take to put caps on b bottles? A. 60bm/c B. bm/60c C. bc/60m D. 60b/cm E. b/60cm 43. Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water. The painter has by mistake added water so that he has 6 litres of paint which is half water and half paint. What must he add to make the proportions of the mixture correct? A. 1 litre paint B. 1 litre water C. litre water and one litre paint D. litre paint and one litre water E. litre paint 44. Which of the following can be used to illustrate that not all prime numbers are odd? A. 1 B. 2 C. 3 D. 4 E. 5 45. What is the greatest of 3 consecutive integers whose sum is 24 ? A. 6 B. 7 C. 8 D. 9 E. 10 46. Considering the positions on the number line above, which of the following could be a value for x? A. 5/3 B. 3/5 C. -2/5 D. -5/2 E. none 47. A piece of ribbon 4 yards long is used to make bows requiring 15 inches of ribbon for each. What is the maximum number of bows that can be made? A. 8 B. 9 C. 10 D. 11 E. 12 48. How many numbers between 200 and 400 begin or end with 3 ? A. 20 B. 60 C. 100 D. 110 E. 120 49. If f(3) = 15 and f(5) = 45, which of the following could be f(x)? A. 4x + 3 B. 2x 2x C. 2x - x D. 2x - 5 E. 5x 50. PQRS is a parallelogram and ST = TR. What is the ratio of the area of triangle QST to the area of the parallelogram? A. 1 : 2 B. 1 : 3 C. 1 : 4 D. 1 : 5 E. it cannot be determined 51. A picture is copied onto a sheet of paper 8.5 inches by 10 inches. A 1.5 inch margin is left all around. What area in square inches does the picture cover? A. 76 B. 65 C. 59.5 D. 49 E. 38.5 52. The table shows the results of a poll which asked drivers how many accidents they had had over the previous 5 years. What is the median number of accidents per driver? A. 0.5 B. 1 C. 1.5 D. 2 E. 4 53. If V = 12R / (r + R) , then R = A. Vr / (12 - V) B. Vr + V /12 C. Vr - 12 D. V / r - 12 E. V (r + 1) /12 54. The number 0.127 is how much greater than 1/8 ? A. B. 2/10 C. 1/50 D. 1/500 E. 2/500 55. Which of the following could not be the lengths of the sides of a right angled triangle? A. 3, 4, 5 B. 5, 12, 13 C. 8, 15, 17 D. 12, 15, 18 E. 9, 12, 15 56. Two equal circles are cut out of a rectangle of card of dimensions 16 by 8. The circles have the maximum diameter possible. What is the approximate area of the paper remaining after the circles have been cut out? A. 104 B. 78 C. 54 D. 27 E. 13 57. (a2-b2)/(a+b)=A. a + b + 1 B. a + b C. a - b D. ab E. it cannot be simplified further 58. x = y - (50/y), where x and y are both 0 If the value of y is doubled in the equation above, the value of x will A. decrease B. stay the same C. increase four fold D. double E. increase to more than double 59. Which of the following could be a solution of the equation x = 4x - 3 A. -1 B. -0.6 C. 0 D. 0.6 E. 1.5 60. The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is A. 720 B. 180 C. 75 D. 65 E. 60 61. 8. Jeff takes 20 minutes to jog around the race course one time, and 25 minutes to jog around a second time. What is his average speed in miles per hour for the whole jog if the course is 3 miles long? A. 6 B. 8 C. 10 D. 12 E. 14 62. A and B are equidistant from the line l. How many circles can be drawn with their centers on line l and that pass through both A and B? A. 1 B. 2 C. 3 D. 4 E. 10 63. A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet? A. 100xy B. 100y - x C. 100x - y D. 100y / x E. 100x / y 64. 3x + y = 19 , and x + 3y = 1. Find the value of 2x + 2y A. 20 B. 18 C. 11 D. 10 E. 5 65. The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 20 per cent. The two reductions together are equal to a single reduction of A. 45% B. 40% C. 35% D. 32.5% E. 30% 66. x and y are integers ; x + y 6 ; What is the smallest possible value of x - y ? A. 1 B. 2 C. 4 D. -2 E. -4 67. If x5y4z2 0 , which of the following must be true? I xy 0 II yz 0 III xz 0 A. I B. II C. III D. I and II E. None 68. BCD is a line segment and Angle BAC = Angle ACB ; Angle ACD = ? A. 140 B. 100 C. 120 D. 60 E. it cannot be determined from the information given 69. Which of the following integers is in the solution set of 1 3x 0 , which of the following must be true? I n 1 II n - n 0 A. I only B. II only C. III only D. I and II only E. none 78. If the slope of a line is and the y-intercept is 3, what is the x-intercept of the same line? A. 6 B. 3/2 C. 0 D. -2/3 E. -6 79. 6 people meet for a business lunch. Each person shakes hands once with each other person present. How many handshakes take place? A. 30 B. 21 C. 18 D. 15 E. 10 80. If x - y = 55, and x - y = 11, then y = A. 8 B. 5 C. 3 D. -8 E. -3 81. 9. In a sports club with 30 members, 17 play badminton and 19 play tennis and 2 do not play either. How many members play both badminton and tennis? A. 7 B. 8 C. 9 D. 10 E. 1182. Rectangle ABCD has a perimeter of 26. The half circle with diameter AD has an area of 8. What is the perimeter of the part of the figure that is not shaded? A. 26 + 4 B. 18 + 8 C. 18 + 4 D. 14 + 4 E. 14 + 2 83. Courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is $1.55 ? A. 1155 B. 1145 C. 1040 D. 950 E. 259 84. AB and DE are parallel. Angle BAC = 30 , angle CDE = 50. What is the measure of angle ACD ? A. 100 B. 90 C. 80 D. 70 E. cannot be determined from the information 85. If x / y is an integer, which of the following statements must be true? A. both x and y are integers B. x is an integer C. either x or y is negative D. y / x is an integer E. x = ny where n is an integer 86. What is the average of four tenths and five thousandths? A. 25002 B. 2502 C. 0.225 D. 0.2025 E. 0.02025 87. What is the simplified result of following the steps above in order? (1) add 5y to 2x (2) multiply the sum by 3 (3) subtract x + y from the product A. 5x + 14y B. 5x + 16y C. 5x + 5y D. 6x + 4y E. 3x + 12y 88. If the equation of a line p in the coordinate plane is y = 3x + 2, what is the equation of line q which is a reflection of line p in the x-axis? A. y = -3x + 2 B. y = -3x - 2 C. y = 3x - 2 D. y = -1/3x 5 E. y = -1/3x + 5 89. If y x = y2x for all positive integers, then (3 4) 2 = A. 38 B. 312 C. 316 D. 324 E. 332 Explanation: The strange sign tells us what operation to carry out on x and y Carry out the same procedure on 3 and 4 first. So 38 is the result. Now carry out the procedure on 38 and 2. So (38)4 is the result, which is equivalent to 332 90. The first term in a sequence is 1 and the second term is 5. From the third term on each term is the average (arithmetic mean) of all preceding terms. What is the 25th term in the sequence? A. 2.5 B. 3 C. 5 D. 25 E. 50 91. (3x + 2) (2x - 5) = ax + kx + n . What is the value of a - n + k ? A. 5 B. 8 C. 9 D. 10 E. 11 92. A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following could not be the length of the fence in feet? (12 inches = 1 foot) A. 17 B. 28 C. 35 D. 39 E. 50 Explanation: The fence will consist of one more post than there are chains. (e.g. P-c-P-c-P). Therefore, a total length has to be a multiple of the length of the chain plus one post (5.5) plus one post extra.We have length = (5.5n + 0.5), where n can be any positive whole number. If n= 3, length =17; if n= 5, length = 28, etc.but there is no whole number that can give 35. hence C is the correct answer. 93. A circular logo is enlarged to fit the lid of a jar. The new diameter is 50 per cent larger than the original. By what percentage has the area of the logo increased? A. 50 B. 80 C. 100 D. 125 E. 250 94. n denotes the number obtained when n is rounded to the nearest tenth. For example 4.31 = 4.3 0.089 - 1.135 = A.