SAT 数学教程全解析

1、 SAT免费在线做题测评网SAT 数学教程全解析I. 解题技巧训练1 The units digit of 23333 is how much less than the hundredths digit of (A) 1 (B) 2 (C) 3 (D) 4 (E) 5备考SAT下载Satonline手机APP2. What is the units digit of 1597365?3. Bob has a pile of poker chips that he wants to arrange in even stacks. If he stacks the

2、m in piles of 10, he has 4 chips left over. If he stacks them in piles of 8, he has 2 chips left over. If Bob finally decides to stack the chips in only 2 stacks, how many chips could be in each stack?A. 14 B. 17 C. 18 D. 24 E. 344. If x and y are two different integers and the product 35xy is the s

3、quare of an integer, which of the following could be equal to xy?A. 5 B.70 C. 105 D. 140 E. 3505. If x2=y3 and (x-y)2=2x, then y could equal (A) 64 (B) 16 (C) 8 (D) 4 (E) 26. For positive integers p, t, x and y, if px=ty and x-y=3, which of the following CANNOT equal t?A. 1 B. 2 C. 4 D. 9 E. 257. If

4、 3t-36s+9 and t-5s2, what are all possible values of x that satisfy the equation above?A. x0, B. 0x1 C.0x2 D.1x2II. 算术 对应知识点训练1. 代数题(1). Karl bought x bags of red marbles for y dollars per bag, and z bag of blue marbles for 3y dollars per bag. If he bought twice as many bags of blue marbles as red m

5、arbles, then in terms of y, what was the average cost, in dollars, per bag of marbles? (A) (B) (C) 3x-y (D) 2y (E) 6y(2) At this bake sale, Mr. Right sold 30% of his pies to one friend. Mr. Right then sold 60% of the remaining pies to another friend. What percent of his original number of pies did M

6、r. Right have left?(A) 10% (B) 18% (C) 28% (D) 36% (E) 40%(3) At a track meet, 2/5 of the first-place finishers attended Southport High School, and 1/2 of them were girls. If 2/9 of the first-place finishers who did NOT attend Southport High School were girls, what fractional part of the total numbe

7、r of first-place finishers were boys?(A) 1/9 (B) 2/15 (C) 7/18 (D) 3/5 (E) 2/32. 中位数（4）Number of siblings per student in a preschool classNumber of siblingsNumber of Students03162231The table above shows how many students in a class of 12 preschoolers had 0,1,2, or 3 siblings. Later, a new student j

8、oined the class, and the average (arithmetic mean) number of siblings per student became equal to the median number of siblings per student. How many siblings did the new student have?A. 0 B. 1 C. 2 D. 3 E. 4（5）In a set of eleven different numbers, which of the following CANNOT affect the value of t

9、he median?A. Doubling each numberB. Increasing each number by 10C. Increasing the smallest number onlyD. Decreasing the largest number onlyE. Increasing the largest number only （6）. The least and greatest numbers in a list of 7 real numbers are 2 and 20, respectively. The median of the list is 6, an

10、d the number 3 occurs most often in the list. Which of the following could be the average (arithmetic mean) of the numbers in the list?I. 7 II. 8.5 III. 10A. I only B. I and II only C. I and III only D. II and III only E. I, II and III3. 集合部分(6) Set F consist of all of the prime numbers from 1 to 20

11、 inclusive, and set G consist of all of the odd numbers from 1 to 20 inclusive. If f is the number of values in set F, g is the number of values of in Set G, and j is the number of values in FG, which of the following gives the correct value of f(j-g)?A. 4 B. 8 C. 10 D. 11 E. 18(7) Set X has x membe

12、rs and set Y has y members. Set Z consists of all members that are in either Set X or Set Y with the exception of the k common members (k0). Which of the following represents the number of members in set Z?A. x+y+k B. x+y-k C. x+y+2k D. x+y-2k E. 2x+2y-2k(8) Of the 240 campers at a summer camp, 5/6

13、could swim, if 1/3 of the campers took climbing lessons, what was the least possible number of campers taking climbing lessons who could swim?A. 20 B.40 C. 80 D.120 E. 200(9) Set F consist of all of the prime numbers from 1 to 20 inclusive, and set G consist of all of the odd numbers from 1 to 20 in

14、clusive. If f is the number of values in set F, g is the number of values of in Set G, and j is the number of values in FG, which of the following gives the correct value of f(j-g)?A. 4 B. 8 C. 10 D. 11 E. 184. 排列组合题(10)Mr. Jones must choose 4 of the following 5 flavors of jellybean: apple, berry, c

15、oconut, kumquat, and lemon, How many different combinations of flavors can Mr. Jones choose?（11） If the 5 cards shown above are placed in a row so that is never at either end, how many different arrangements are possible?（12） As shown above, a certain design is to be painted using 2 different colors

16、. If 5 different colors are available for the design, how many differently painted designs are possible?A. 10 B. 20 C. 25 D. 60 E. 120（13）In the integer 3589 the digits are all different and increase from left to right. How many integers between 4000 and 5000 have digits that are all different and t

17、hat increased from left to right?（14）. On the map above, X represents a theater, Y represents Chriss house, and Z represents Peters house. Chris walks from his house to Peters house without passing the theater and then walks with Peter to the theater and then walks without walking by his own house a

18、gain. How many different routs can Chris take?（15）In a certain game, 8 cards are randomly placed face-down on a table. The cards are numbered from 1 to 4 with exactly 2 cards having each number. If a player turns over two of the cards, what is the probability that the cards will have the same number

19、?（16）The Acme Plumbing Company will send a team of 3 plumbers to work on a certain job. The company has 4 experienced plumbers and 4 trainees. If a team consists of 1 experienced plumber and 2 trainees, how many different such teams are possible?（17）If p, r, m, n, t and s are six different prime num

20、bers greater than 2, and n=p*r*s*m*n*t, how many positive factors, including 1 and n, does n have?5.数列部分(14) The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are in this set? A. 25 B. 26 C.50 D. 51 E. 52(15) 1,2,2,3,3,3,4,4,4,4.All posi

21、tive integers appear in the sequence above, and each positive integer k appears in the sequence k times. In the sequence, each term after the first is greater than or equal to each of the terms before it. If the integer 12 first appears in the sequence as the nth term, what is the value of n?(16) Th

22、e first term of a sequence of numbers is 2. Subsequently, every even term in the sequence is found by subtracting 3 from the previous term, and every odd term in the sequence is found by adding 7 to the previous term. What is the difference between 77th and 79th terms of this sequence?A. 11 B. 7 C.

23、4 D. 3 E. 26.应用题(16) A positive integer is said to be “tri-factorable” if it is the product of three consecutive integers. How many positive integers less than 1000 are tri-factorable?(17) Tom and Alison are both salespeople. Toms weekly compensation consists of $300 plus 20 percent of his sale. Ali

24、sons weekly compensation consists of $200 plus 25 percent of her sales. If they both had the same amount of sales and the same compensation for a particular week, what was that compensation, in dollars? (Disregard dollar sign when gridding your answer)(18) To celebrate a colleagues graduation, the m

25、 coworkers in an office agreed to contribute equally to a catered lunch that costs a total of y dollars. If p of the coworkers fail to contribute, which of the following represents the additional amount, in dollars, that each of the remaining coworkers must contribute to pay for the lunch?A. B. C. D

26、. E. (19) In a certain store, the regular price of a refrigerator is $600. How much money is saved by buying this refrigerator at 20 percent off the regular price rather than buying it on sale at 10 percent off the regular price with an additional discount of 10 percent off the sale price?(A) $6 (B)

27、 $12 (C) $24 (D) $54 (E) $607.整除，最小公倍数，余数问题(20) When a is divided by 7, the remainder is 4. When b is divided by 3, the remainder is 2. If 0a24 and 2b8, which of the following could have a remainder of 0 when divided by(A) (B) (C) a-b (D) a+b (E) ab(21) The alarm of Clock A rings every 4 minutes, th

28、e alarm of Clock B rings every 6 minutes, and the alarm of Clock C rings every 7 minutes. If the alarms of all three clocks ring at 12:00 noon, the next time at which all the alarms will ring at exactly the same time isA. 12:28 P.M. B. 12:56 P.M. C. 1:24 P.M. D. 1:36 P.M. E. 2:48 P.M. (22) If a, b,

29、and c are distinct positive integers, and 10% of abc is 5, then a+b could equalA. 1 B. 3 C. 5 D. 6 E. 25(23) On 5 math tests, Gloria had an average score of 86. If all test scores are integers, what is the lowest average score average score Gloria can receive on the remaining 3 tests if she wants to

30、 finish the semester with an average score of 90 or higher? A. 90 B. 92 C. 94 D. 96 E. 97(24) If is the cube of an integer greater than 1, and k2=y, what is the least possible value of y? A. 1 B. 2 C. 4 D. 6 E. 27III 代数问题(1) The height of the steam burst of a certain geyser varies with the length of

31、 time since the previous steam burst. The longer the time since the last burst, the greater the height of the steam burst. If t is the time in hours since the previous steam burst and H is the height in meters of the steam burst, which of the following could express the relationship of t and H?A H(t

32、)= (t-7) B. H(t)= C. H(t)=2-(t-7) D. H(t)= 7-2t E. H(t)= （2） 4) The above graph could represent which of the following inequalities?A. y B. y0, what is the value of a?(15) (x-8)(x-k)= x2-5kx+mIn the equation above, k and m are constants. If the equation is true for all value of x, what is the value

33、of m?A. 8 B. 16 C. 24 D. 32 E. 40(16) A certain function f has the property that f(x+y)=f(x)+f(y) for all values of x and y. which of the following statements must be true when a=b?I. f(a+b)= 2f(a) II. f(a+b)=f(a)2 III. f(a)+f(b)=f(2a)A. None B. I only C. I and III only D. II and III only E. I, II a

34、nd III（17）. The shaded region in the figure above is bounded by the x-axis, the line x=4, and the graph of y=f(x). if the point (a, b) lies in the shaded region, which of the following must be true?I. a4 II. ba III. bf(a)(A) I only(B) III only(C) I and II only(D) I and III only(E) I, and II and III（

35、18）The figure above shows the graphs of y=x2 and y=a-x2 for some constant a. if the length of PQ is equal to 6, what is the value of a? A. 6 B. 9 C. 12 D. 15 E. 18（19）In the figure above, ABCD is a rectangle. Points A and C lie on the graph of y=px3, where p is a constant,. If the area of ABCD is 4,

36、 what is the value of p?IV 几何部分（1）Each of the small squares in the figure above has an area of 4. If the shortest side of the triangle is equal in length to 2 sides of a small square, what is the area of the shaded triangle?A. 160 B. 40 C. 24 D. 20 E. 16（2）. In the figure above, a shaded polygon whi

37、ch has equal sides and angles is partially covered with a sheet of blank paper. If x+y=80, how many sides does the polygon have?A. 10 B. 9 C. 8 D. 7 E. 6（3）The area of rectangle ABCD is 96, and AD=2/3(AB). Points X and Y are midpoints of AD and BC, respectively. If the 4 shaded triangles are isoscel

38、es, what is the perimeter of the unshaded hexagon? A. 16 B.8+6 C. 24 D. 8+16 E. 16+24（4）In the figure above, what is the value of c in terms of a and b?A. a+3b-180 B. 2a+2b-180 C. 180-a-b D. 360-a-b E. 360-2a-3b（5） The figure above shows an arrangement of 10 squares, each with side of length k inche

39、s. The perimeter of the figure is p inches. The area of the figure is a square inches. If p=a, what is the value of k?（6）. One end of an 80-inch-long paper strip is shown in the figure above. The notched edge, shown in bold, was formed by removing an equilateral triangle from the end of each 4-inch

40、length on one edge of the paper strip. What is the total length, in inches, of the bold notched edge on the 80-inch paper strip?（7）. At a beach, a rectangular swimming area with dimensions x and y meters and a total area of 4000 square meters is marked off on three sides with rope, as shown above, a

41、nd bounded on the fourth side by the beach. Additionally, rope is used to divide the area into three smaller rectangular sections. In terms of y, what is the total length, in meters, of the rope that is need both to bound the three sides of the area and to divide it into sections?A. y+ 4000/y B. y+1

42、6000/y C. y+16000/(3y) D. 3y+ 8000/(3y) E. 3y+ 16000/(3y)（8） If a triangle ABC has AB=7 and BC=7, then the difference between the greatest and least possible integer values of AC is A. 11 B. 12 C. 13 D. 14 E. 15（9）In a triangle PQR, the length of side QR is 12 and the length of side PR is 20. What i

43、s the greatest possible integer length of side PQ?A. 9 B. 16 C. 25 D. 27 E. 31（10）. In the figure above, arc SBT is one quarter of a circle with center R and radius 6. If the length plus the width of rectangle ABCR is 8, then the perimeter of the shaded region isA. 8+3 B. 10+3 C. 14+ 3 D. 1+6 E. 12+

44、6（11） In the figure above, QR is the arc of a circle with center P. If the length of the arc QR is 6,what is the area of sector PQR?A. 108 B. 72 C. 54 D. 36 E. 9（12）. The figure above consists of two circles that have the same center. If the shaded area is 64 square inches and the smaller circle has

45、 a radius of 6 inches, what is the radius, in inches, of the larger circle?（13）. The figure above shows part of a circle whose circumference is 45. If arcs of length 2 and length b continue to alternate around the entire circle so that there are 18 arcs of each length, what is the degree measure of

46、each of the arcs of length b?A. 40 B. 60 C. 100 D. 160 E. 20o（14）In a certain machine, a gear makes 12 revolutions per minute. If the circumference of the gear is 3 inches, approximately how many feet will the gear turn in an hour?A. 6782 B. 565 C. 113 D. 108 E. 9（15）In the xy-coordinate plane, the graph of x=y2-4 intersects line l at (0, p) and (5, t). what is the greatest possible value of the slope of