【小站教育】SAT数学难题汇总及答案

1、SAT数学难题汇总及答案xA2表示x的平方，=!表示不等于。pi表示圆周 率类型 1 ：20. 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) 5214. Exactly 4 actors try out for the 4 parts in a play. If each actor can perform any one part

2、 and no one will perform more than one part, how many different assignments of actors are possible16. Set X has x members 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 (k > 0). Which of the following represents

3、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 - 2k20. There are 75 more women than men enrolled in Linden College. If there are n menenrolled, then, in terms of n, what percent of those enrolled are men(A)-% 2刀十75© I 10)(2 75)(D)，喋 n r 75INVENTO

4、RY OF CLOCKS AND FREQUENCY OF CHIMESNumberof ClocksChimes n Times on the nth HourChimes Once on the HourChimes Once on the Half HourType A10Type 85Type C317. A merchant sells three types of clocks that chime as indicated by the check marksin the table above. What is the total number of chimes of the

5、 inventory of clocks inthe 90-minute period from 7:15 to8:4518. If the 5 cards shown above are placed in a row so many different arrangements are possiblethatis never at eithe end, how20. When 15 is divided by the positive integer k, the remainder is 3. For how many different values of k is this tru

6、e(A) One(B) Two(C) Three(D) Four(E) FiveI !11-11b+1|0117. On the number line above, there are 9 equal intervals between 0 and 1. What is the value of x19. If a, b. c, and f are four nonzero numbers, then all of the following proportions are equivalentEXCEPT (A)a/f=b/c(B)f/c=b/a(C) c/a=f/b(D)a/c=b/f(

7、E)af/bc=1what is the value of ab/18. If a and b are positive integers and(A)6(B) 12(C) 18(D) 24(E) 36of theexperienced16. After the first term, each term in a sequence is3 greater than1/3preceding term. If t is the first term of the sequence and t=!0. what is the ratio of the second term to the firs

8、t termA)Lt?17. 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 1plumber and 2 trainees, how many different such teams are possiblep. r. and s are three different prime numbers greater than

9、2, and n = p * r * s, howmany positive factors, including 1 and n. does n have18. If the sum of the consecutive integersfrom -22 to x, inclusive, is 72,what is the value of x (A) 23(B) 25(C) 50(D) 75(E) 9417. For all positive integers j and k. let j R k be defined as the whole numberremainder when j

10、 is divided by k. If 13 Rk = 2, what is the value of k19, In a set of eleven different numbers, which of the following CANNOT affect the value of the median(A) Doublingeachnumber(B) Increasing each number by10(C) Increasing the smallest numberonly (D) Decreasing the largestnumber only (E) Increasing

11、 thelargest number only15. A store charges $28 for a certain type of sweater. This price is 40 percent morethan the amount it costs the store to buy one of these sweaters. At an end-of-seasonsale, store employees can purchase any remaining sweaters at 30 percent off the store'scost How much woul

12、d it cost an employee topurchase a sweater of this type at this sale (A) $(B)$ (C)$ (D)$ (E) $and Corinne stand back-to-back. They each take 10 steps in opposite directions away from each other and stop. Alice then turns around, walks toward Corinne. and reaches her in 17 steps. The length of one of

13、 Alice's steps is how many times the length of one of Corinne's steps (All of Alice's steps are the same length and all of Corinne's steps are the same length.)14. If n and p are integers greater than 1 and if p is a factor of both n +3 and n+ 10. what is the value of p(A) 3(B) 7(C)1

14、0(D) 13(E) 3016. In a mixture of peanuts and cashews, the ratio by weight of peanuts to cashews is5 to 2. How many pounds of cashews will there be in 4 pounds of this mixture14. How many integers greater than 20 and less than 30 are each the product of exactly two different numbers, both of which ar

15、e prime(A) Zero(B) One(C) Two(D) Three(E) Four20. If k is a positive integer, which of the following must represent an even integer that is twice the value of an odd integer(A) 2k(B) 2k + 3(C) 2k+ 4(D) 4k+1(E) 4k+ 2类型2 :18. The shaded region in the figure above is bounded by the x-axis, the line x=4

16、, and the graph of y = f(x).If the point (a, b) lies in the shaded region, whichof the following must be trueI. a < 4II. b < aIII. b < f(a) (A) Ionly(B) III only(C) I and IIonly (D) I andIIIonly(E)I. II, and III19. At a bottling company, machine A f川s,a bottle with spring water and machine

17、B acceptsthe bottleonly if the number of fluidis betweenounces 11 and 12 If machine B accepts a88bottlecontaining n fluid ounces, which of the followingdescribes all possiblevalues of n(A),- |n + 12| 二 |© I吁以4 o |n + 12|0(E) ohe saves the rest7. Dwayne has a newspaper route for which he collect

18、s k dollars each day. From this amount he pays out k/3 dollars per day for the cost of the papers, and of the money. In terms of k, how many days will it take Dwayne to save $1,000(D) 15lt5001,000LOOP(A)(B)(O(D)(E) 1,500/17. In the xy-coordinate plane, the graph of x = y*y -4 intersects line l at (0

19、, p) and (5, t). What is the greatest possible value of the slope of18. Esther drove to work in the morning at an average speed of 45 miles per hour. She returned home in the evening along the same route and averaged 30 miles per hour. If Esther spent a total of one hour commuting to and from work,

20、how many miles did Esther drive to work in the morning14. If (a + bF = (a - b) A, which of the following must betrue (A) b = 0(B) a + b = 1(C) a - b = 1(D) aA2 + bA2 = 1(E) aA2 - bA2 = 115. The figure above shows the graphs of y = x*x and y = a - x*x for some constanta. If the length ofPQis equal to

21、 6, what is the valueof a (A) 6(B) 9(C) 1218. During a sale, a customer can buy one shirt for x dollars. Each additional shirt the customer buys costs z dollars less than the first shirt. For example, the cost of the second shirt is x - z dollars. Which of the following represents the customer's

22、 cost, in dollars, for n shirts bought during this sale(A) x + (n - )(x - z)(B) x + n(Jt - z)(C) n(x - z)(D) ,.8 一2 n(E)(1-力+心电 n16. Let the function h be defined by h(x) = 14 + xA2/4. If h(2m) = 9m, what is one possible value of m16. If x is an integer greater than 1 and if y = x + 1/x, which of th

23、e following must be true I. y =! x II. y is an integer.III. xy > 处2(A) I only(B) III only(C) I and IIonly (D) I andIII only (E) I,II, and III6. If m and k are positive and 10(mA2)*kA-1= 100m, what is mA-1! interms of k (A) k/10(B) k/90(C) kA10 (D)1/10k(E) 1/90k8. The figure above shows the graph

24、of a quadratic function f that has a minimum at the point (1,1). If f(b) = f(3), which of the following could be the value of b(A) -3(B) -2(C) -1(D) 1(E) 516. If a + 2b is equal to 125 percent of 4b, what is the value of a/bMAZE COMPLETION TIMESs biology experiment involved timing 12 hamsters in a m

25、aze. Each hamster received at least one practice before being timed. The scatter plot above shows the time each hamster took to complete the maze and the corresponding number of practices that each hamsterreceived. Based on the data, which of the following functions best models the relationship betw

26、een t, the number of seconds to complete the maze, and p, the number of practices (A) t(p) =44 (B) t(p) = p (C) t(p)= 44p (D) t(p) = p/44(E)t(p)= p+ 4420. For all numbers .t and v. let the operation be defined by x v = xy - yIf a and b re positive integers, which of the following can be equal to zer

27、o I. a bII. (a + b) b IIl. a (a + b) (A) I only (B) II only(C)IIlonly (D) Iand ll (E)I and IllX哽 Figure noidrawn 如 scsdc.(A)118. In the figure above, ABCD is a rectangle. Points A and C lie on the graph of y = p*xA3, where p is a constant. If the area of ABCD is 4, what is the value of p14. f 0 

28、3; x £ 8 and *1 £ v 5 3, which of the -rfoDowing jives the sei of al! possible values of xy ?(A)邛二 AiB) 0 < jt £ 24(C) -I S xv < H(D) -1 S 耳，£ 24(E) -8 £ 个 £ 24hit) = c - (J - 4r)*18. At bmt r = 0t a ball was thrown upward from an inidal height of 6 fett. Until th

29、e ball 血 die ground, its height tn feet after / seconds was ci ven by the function h above, in which c and d are posilive constants. If the ball reached iis maximum height of 106 f«i ai time t = 2.5.5"hat was the height, in feeL of the ball at lime f - I 019. If k, n, x, and y are positive

30、 numbers satisfying x a(-4/3)= kA-2 and yA(4/3)=门人2, what is(xy)A(-2/3 in terms of n and k(B)与 kk(C) £ n(D) nJt(E) I16. Let be defined w C .r ：) = J for ail values of 工 If C g ) * ( q-D what is the value of s ?(B)1/2 (C)3/2(D) 6/5(E) 38. The price of ground coffee beans is d dollars for 8 ounce

31、s and each ounce makes ccups of brewed coffee. In terms of c and d. what is the dollar cost of the ground coffeebeans required to make 1 cup of brewed coffee© 7(D)c(E)15. IfxA2-yA2 = 10 and x +y = 5. what is the valueof x - y18. The average (arithmetic mean) of the test scores of a class of p s

32、tudents is 70.and the average of the test scores of a class of n students is 92. When the scores ofboth classes are combined, the average score is 86.What is the value of p/n17. Luke purchase。un automobile tor、工uuu. ana se . value of (he automobile decreases by 20 percent each year. Tbc value, in do

33、llars, of the automobilen years from the date of purchase is given by thefunction V. where V(/i)=ow manv (A) (B) (Q (D) (E)years from the date of purchase will the value of (heautomobile be $3100 ?One Two Three Four Five(C) 2414. Which of the following is equivalent to h(m + 1) (A) g(m)(B) g(m) +l (

34、C)g(m)-1(D)h(m)+1 (E)h(m)-1has containers of two different sizes. The total capacity of 16 containers of-one sizeis x gallons, and the total capacity of 8 containers of the other size is also x gallons, and x > 0. In terms of x, what is the capacity, in gallons, of each of the larger containers (

35、A) 4x(B) 2x(C)x/2(D)x/8(E)x/1618. Let the function f be defined by f(x) = xA2+ 18. If m is a positive number such that f(2m) = 2f(m), what is the value ofm19. The cost of maintenance on an automobile increases each year by 10 percent, andAndrew paid S300 this year for maintenance on his automobile.

36、If the costc for maintenance on Andrew's automobile n years from now is given by the functionc(n) = 300xAn, what is the value of x(A)(B)(C)(D)(E) 30xy = 7 and x- y = 5. then xA2*y-xyA2=(A) 2(D) 35(E) 7017. Line m (not shown) passes through O and intersects AB between A and B. What is one possibl

37、e value of the slope of line m17. If k and h are constants and xA2+kx+7is equivalent to(x + 1)(x + h). what is the value of k (A) 0(B) 1(C) 7(D) 8(E) It cannot be determined from the information given.15. If - - for positive inteeers<i - I >t ft * I k*“ and k. whai is the value of i ?(A) 1(B)

38、5(C) 24(D) 25(E) 2616. To celebrate a colleague's graduation,the m coworkers in an office agreed tocontribute equally to a catered lunch thatcosts a total of y dollars.If p of the coworkersfail to contribute, which of the followingrepresents the additionalamount, in dollars,thatchof the remainin

39、g coworkers must contribute to pay for the lunch(E)- p)类型318. In the xy-coordinate plane, the distance between point B(10, 18) and point A(x,3) is 17. What is one possible value of x16. The pattern shown above is composed of rectangles. This pattern is used repeatedly to completely cover a rectangul

40、ar region 12L units long and 10L units wide. How many rectangles of dimension L by W are needed(A) 30(B) 36(C) 100(D) 150(E)18030° and18. In the figure above, AB = BC and DE = EF = DF If the measure of /.ABC is the measure of /.BDE is 50 ° , what is the measure of /DFA (A) 30 (B) 35°

41、(C) 40° (D) 45° (E) 50_r>17. The three-dimensional figure above has two parallel bases and 18 edges. Line segmentsare to be drawn connecting vertex V with each of the other 11 vertices in the figure.How many of these segments will not lie on an edge of the figure15. In the figure(-L3)ab

42、ove, what is the sum. in terms of n, of the degree measuresof the four angles marked with arrows (A) n (B) 2n (O 180 - n(D) 360 - n(E) 360 -2nMe逐 Figure a'drawn 立16. The figure above consists of two circles that have the same center. If the shaded area is 64pi square inches and the smaller circl

43、e has a radius of 6 inches, what is the radius, in inches, of the larger circle(A) -6(B) -3f and g. The function f is20. The figures above show the graphs of the functions defined by f(x) = xA3 - 4x. The function g is defined by g(x) = f(x + h) + k, where h and k it are constants. What is the value

44、of hk9（3）s （a）乙-（。）15. The cube shown above has edges of length 2, and A and 8 are midpoints of two of the edges. What is the length of AB (not shown)the figure above, arc SBT is one quarter of a circle with center R and radius 6. Ifthe length plus the width of rectangle ABCRis 8. then the perimeter

45、 of the shaded region is(A) 8 - 3pi(B) 10+3pi(C) 14+3pi(D) 1 + 6pi(E) 12+6pi16. In rectangle ABCD, point E is the midpoint of BC. If the area of quadrilateral ABEDis 2/3, what is the area of rectangle ABCD(A)1/2(B)3/4 (C)8/9 (D)1(E)8/3ABCD lies in the xy -coordinate plane so that its sides are not p

46、arallel to the axes.What is the product of the slopes of all four sides of rectangle ABCD(A) -2乙(3)l (a)0(9)l- (a)I15°ztIT116. In the figure above, y+z= (A)180 (B)195 (C)215 (D)230(E)245arcs of length18. The figure above shows part of a circle whose circumference is 45. If 2 and length b contin

47、ue to alternate around the ensure circle so that there are 18 arcs of each length, what is the degree measure of each of the arcs of length b(A) 4。(B) 6 ° (C)10° (D) 16° (E) 20°bjpte: Figuie not drtwn o leak.20. If the five line segments in the figure above are all congruent, what is the ratioof