1、GRE（ QUANTITATIVE）综合模拟试卷 21及答案与解析 1 An antiques dealer bought c antique chairs for a total of x dollars. The dealer sold each chair for y dollars. (a)Write an algebraic expression for the profit, P, earned from buying and selling the chairs. (b)Write an algebraic expression for the profit per chair.
2、 2 In the coordinate system below, find the following.(a)Coordinates of point Q(b)Lengths of PQ, QR, and PR(c)Perimeter of PQR(d)Area of PQR(e)Slope, y-intercept, and equation of the line passing through points P and R 3 In the xy-plane, find the following. (a)Slope and y-intercept of the line with
3、equation 2y + x = 6 (b)Equation of the line passing through the point(3,2)with y-intercept 1 (c)The y-intercept of a line with slope 3 that passes through the point(-2,1) (d)The x-intercepts of the graphs in(a),(b), and(c) 4 For the parabola y = x2 -4x-12 in the xy-plane, find the following. (a)The
4、x- intercepts (b)The y-intercept (c)Coordinates of the vertex 5 For the circle(x- 1)2 +(y+ 1)2= 20 in the xy-plane, find the following. (a)Coordinates of the center (b)Radius (c)Area 6 For each of the following functions, give the domain and a description of the graph y =f(x)in the xy-plane, includi
5、ng its shape, and the x- and y-intercepts.(a)f(x)= -4(b)f(x)= 100 - 900x(c)f(x)= 5-(x + 20)2(d)f(x)= (e)f(x)= x+ x 7 What is the sum of the measures of the interior angles of a decagon(10-sided polygon)? 8 If the decagon in exercise 4 is regular, what is the measure of each interior angle? 9 The len
6、gths of two sides of an isosceles triangle are 15 and 22, respectively. What are the possible values of the perimeter? 10 Triangles PQR and XYZ are similar. If PQ = 6, PR = 4, and XY = 9, what is the length of side XZ? 11 Six hundred applicants for several post office jobs were rated on a scale from
7、 1 to 50 points. The ratings had a mean of 32.5 points and a standard deviation of 7.1 points. How many standard deviations above or below the mean is a rating of 48 points? A rating of 30 points? A rating of 20 points? 12 Suppose that a computer password consists of four characters such that the fi
8、rst character is one of the 10 digits from 0 to 9 and each of the next 3 characters is any one of the uppercase letters from the 26 letters of the English alphabet. How many different passwords are possible? 13 How many different five-digit positive integers can be formed using the digits 1, 2, 3,4,
9、 5,6, and 7 if none of the digits can occur more than once in the integer? 14 Suppose you want to select a 3-person committee from a group of 9 students. How many ways are there to do this? 15 Consider an experiment with events A, B, and C for which P(A)= 0.23, P(B)= 0.40, and P(C)= 0.85. Suppose th
10、at events A and B are mutually exclusive and events B and C are independent. What are the probabilities P(A or B)and P(B or C)? 16 Suppose that there is a 6-sided die that is weighted in such a way that each time the die is rolled, the probabilities of rolling any of the numbers from 1 to 5 are all
11、equal, but the probability of rolling a 6 is twice the probability of rolling a 1. When you roll the die once, the 6 outcomes are not equally likely. What are the probabilities of the 6 outcomes? 17 Suppose that you roll the weighted 6-sided die from example 4.4.5 twice. What is the probability that
12、 the first roll will be an odd number and the second roll will be an even number? 18 A box contains 5 orange disks, 4 red disks, and 1 blue disk. You are to select two disks at random and without replacement from the box. What is the probability that the first disk you select will be red and the sec
13、ond disk you select will be orange? 19 The daily temperatures, in degrees Fahrenheit, for 10 days in May were 61, 62, 65,65, 65, 68, 74, 74, 75, and 77. (a)Find the mean, median, mode, and range of the temperatures. (b)If each day had been 7 degrees warmer, what would have been the mean, median, mod
14、e, and range of those 10 temperatures? 20 The numbers of passengers on 9 airline flights were 22, 33, 21, 28,22, 31,44, 50, and 19. The standard deviation of these 9 numbers is approximately equal to 10.2. (a)Find the mean, median, mode, range, and interquartile range of the 9 numbers. (b)If each fl
15、ight had had 3 times as many passengers, what would have been the mean, median, mode, range, interquartile range, and standard deviation of the 9 numbers? (c)If each flight had had 2 fewer passengers, what would have been the interquartile range and standard deviation of the 9 numbers? 21 A group of
16、 20 values has a mean of 85 and a median of 80. A different group of 30 values has a mean of 75 and a median of 72. (a)What is the mean of the 50 values? (b)What is the median of the 50 values? 22 In how many different ways can the letters in the word STUDY be ordered? 23 Martha invited 4 friends to
17、 go with her to the movies. There are 120 different ways in which they can sit together in a row of 5 seats, one person per seat. In how many of those ways is Martha sitting in the middle seat? 24 How many 3-digit positive integers are odd and do not contain the digit 5? 25 From a box of 10 lightbul
18、bs, you are to remove 4. How many different sets of 4 lightbulbs could you remove? 26 A talent contest has 8 contestants. Judges must award prizes for first, second, and third places, with no ties. (a)In how many different ways can the judges award the 3 prizes? (b)How many different groups of 3 peo
19、ple can get prizes? 27 If an integer is randomly selected from all positive 2-digit integers, what is the probability that the integer chosen has (a)a 4 in the tens place? (b)at least one 4 in the tens place or the units place? (c)no 4 in either place? 28 In a box of 10 electrical parts, 2 are defec
20、tive. (a)If you choose one part at random from the box, what is the probability that it is not defective? (b)If you choose two parts at random from the box, without replacement, what is the probability that both are defective? 29 Let A, B, C, and D be events for which P(A or B)= 0.6, P(A)= 0.2, P(C
21、or D)= 0.6, and P(C)= 0.5. The events A and B are mutually exclusive, and the events C and D are independent. (a)Find P(B) (b)Find P(D) 30 Lin and Mark each attempt independently to decode a message. If the probability that Lin will decode the message is 0.80 and the probability that Mark will decod
22、e the message is 0.70, find the probability that (a)both will decode the message (b)at least one of them will decode the message (c)neither of them will decode the message 31 Lines l and m below are parallel. Find the values of x and y. 32 In the figure below, AC = BC. Find the values of x and y. 33
23、 In the figure below, what is the relationship between x, y, and z? 34 What are the lengths of sides NO and OP in triangle NOP below? 35 In the figure below, AB = BC = CD. If the area of triangle CDE is 42, what is the area of triangle ADG? 36 In rectangle ABCD below, AB = 5, AF=7, and FD = 3. Find
24、the following.(a)Area of ABCD(b)Area of triangle AEF(c)Length of BD(d)Perimeter of ABCD 37 In parallelogram ABCD below, find the following.(a)Area of ABCD(b)Perimeter of ABCD(c)Length of diagonal BD 38 The circle with center O below has radius 4. Find the following.(a)Circumference of the circle(b)L
25、ength of arc ABC(c)Area of the shaded region 39 The figure below shows two concentric circles, each with center O. Given that the larger circle has radius 12 and the smaller circle has radius 7, find the following.(a)Circumference of the larger circle(b)Area of the smaller circle(c)Area of the shade
26、d region 40 For the rectangular solid below, find the following.(a)Surface area of the solid(b)Length of diagonal AB 41 If W is a random variable that is normally distributed with a mean of 5 and a standard deviation of 2, what is P(W 5)? Approximately what is P(3 5 corresponds to exactly half of th
27、e area under the normal distribution. So P(W 5)= 1/2. For the event 3 W 7, note that since the standard deviation of the distribution is 2, the values 3 and 7 are one standard deviation below and above the mean, respectively. Since about two-thirds of the area is within one standard deviation of the
28、 mean, P(3 W 7)is approximately 2/3. For the event W -1, note that -1 is 3 standard deviations below the mean. Since the graph makes it fairly clear that the area of the region under the normal curve to the left of-1 is much less than 5 percent of all of the area, the best of the four estimates give
29、n for P(W-1)is 0.01. The standard normal distribution is a normal distribution with a mean of 0 and standard deviation equal to 1. To transform a normal distribution with a mean of m and a standard deviation of d to a standard normal distribution, you standardize the values(as explained below exampl
30、e 4.2.9); that is, you subtract m from any observed value of the normal distribution and then divide the result by d. Very precise values for probabilities associated with normal distributions can be computed using calculators, computers, or statistical tables for the standard normal distribution. F
31、or example, more precise values for P(3 W 7)and P(W -1)are 0.683 and 0.0013. Such calculations are beyond the scope of this review. 42 【正确答案】 230 42 percent I 【试题解析】 (a)According to the table, in 2003,1 percent of the total number of complaints concerned credit. Therefore, the number of complaints c
32、oncerning credit is equal to 1 percent of 22,998. By converting 1 percent to its decimal equivalent, you obtain that the number of complaints in 2003 is equal to(0.01)(22,998), or about 230.(b)The decrease in the total number of complaints from 2003 to 2004 was 22,998 - 13,278, or 9,720. Therefore,
33、the percent decrease was( )(100%), or approximately 42 percent.(c)Since 20.0 + 18.3 + 13.1 and 22.1 + 21.8 + 11.3 are both greater than 50, statement I is true. For statement II, the percent of special passenger accommodation complaints did remain the same from 2003 to 2004, but the number of such c
34、omplaints decreased because the total number of complaints decreased. Thus, statement II is false. For statement III, the percents shown in the table for flight problems do in fact increase by more than 2 percentage points, but the bases of the percents are different. The total number of complaints
35、in 2004 was much lower than the total number of complaints in 2003, and clearly 20 percent of 22,998 is greater than 22.1 percent of 13,278. So, the number of flight problem complaints actually decreased from 2003 to 2004, and statement III is false. 43 【正确答案】 4 to 1 $765 million 【试题解析】 (a)The ratio
36、 of the value of sensitized goods to the value of still-picture equipment is equal to the ratio of the corresponding percents shown because the percents have the same base, which is the total value. Therefore, the ratio is 47 to 12, or approximately 4 to 1.(b)The value of office copiers produced in
37、1971 was 0.25 times $3,980 million, or $995 million. Therefore, if the corresponding value in 1970 was x million dollars, then 1.3x= 995 million. Solving for x yields x = 765, so the value of office copiers produced in 1970 was approximately $765 million. 44 【正确答案】 five 70 percent 【试题解析】 (a)The numb
38、er of bicyclists who had both a training index less than 50 units and a finishing time less than 4.5 hours is equal to the number of points on the graph to the left of 50 and below 4.5. Since there are five data points that are both to the left of 50 units and below 4.5 hours, the correct answer is
39、five. (b)The 10 lowest data points represent the 10 fastest bicyclists. Of these 10 data points, 3 points are to the right of 90 units, so the number of points to the left of 90 units is 7, which represents 70 percent of the 10 fastest bicyclists. 45 【正确答案】 23 178 72 【试题解析】 In the Venn diagram, the
40、rectangular region represents the set of all travelers surveyed; the two circular regions represent the two sets of travelers to Africa and Asia, respectively; and the shaded region represents the subset of those who have traveled to both continents. (a)The set described here is represented by the p
41、art of the left circle that is not shaded. This description suggests that the answer can be found by taking the shaded part away from the first circle in effect, subtracting the 70 from the 93, to get 23 travelers who have traveled to Africa but not to Asia. (b)The set described here is represented
42、by that part of the rectangle that is in at least one of the two circles. This description suggests adding the two numbers 93 and 155. But the 70 travelers who have traveled to both continents would be counted twice in the sum 93 + 155. To correct the double counting, subtract 70 from the sum so tha
43、t these 70 travelers are counted only once: 93 + 155-70=178 (c)The set described here is represented by the part of the rectangle that is not in either circle. Let N be the number of these travelers. Note that the entire rectangular region has two main nonoverlapping parts: the part outside the circ
44、les and the part inside the circles. The first part represents N travelers and the second part represents 93 + 155 - 70 = 178 travelers(from question(b). Therefore, 250 = N+178 and solving for N yields N= 250 -178 = 72 46 【正确答案】 mean = 2.03, median = 1 47 【正确答案】 (a)range = 41, Q1= 114, Q2= 118, Q3= 126, interquartile range =12 (b)40 measurements 48 【正确答案】 (a)21/40(b)7/10(c)9/40 49 【正确答案】 (a)1,440(b)0.15 50 【正确答案】 (a)1998(b)19% 51 【正确答案】 (a)Three(b)9 to 14, or 9/14(c)I, II, and III 52 【正确答案】 (a)$17,550(b)Miscellaneous
