SAT 数学教程全解析

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 1000567(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 them 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. 14B. 17C. 18D. 24E. 344. If x and y are two different integers and the product 35xy is the square of an integer, which of the following could be equal to xy?A. 5B.70C. 105D. 140E. 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 p x =t y and x-y=3, which of the following CANNOT equal t?A. 1B. 2C. 4D. 9E. 257. If 3t-3>6s+9 and t-5s<12, and s is a positive integer less than 4, then t could be any of the following EXCEPT A. 6 B. 8 C. 10 D.12 E. 238. 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. 3B. 7C. 10D. 13E. 309. If x is a positive integer greater than 1, and x3-4x is odd, then x must be(A) even (B) odd (C) prime (D) a factor of 8 (E) divisible by 810.If the graph above is that of f(x), which of the following could be f(x) A. f(x)= 3||x B. f(x)=|3|x C. f(x)=/x/+3 D. f(x)=|x+3| E. f(x)=|3x|11. xy=x+y. If y>2, what are all possible values of x that satisfy the equation above?A. x<0,B. 0<x<1C.0<x<2D.1<x<2E. x>2II. 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 marbles, then in terms of y, what was the average cost, in dollars, per bag of marbles? (A) 23y (B) 37y (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 Mr. 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 number 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 Students 03 16 22 3 1The table above shows how many students in a class of 12 preschoolers had 0,1,2, or 3 siblings. Later, a new student joined 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. 0B. 1C. 2D. 3E. 4（5）In a set of eleven different numbers, which of the following CANNOT affect the value of the 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, and 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 onlyB. I and II onlyC. I and III onlyD. II and III onlyE. I, II and III3. 集合部分(6) 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 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 F∪G, which of the following gives the correct value of f(j-g)?A. 4B. 8C. 10D. 11E. 18(7) 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 the number of members in set Z?A. x+y+kB. x+y-kC. x+y+2kD. x+y-2kE. 2x+2y-2k(8) Of the 240 campers at a summer camp, 5/6 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. 20B.40C. 80D.120E. 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 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 F∪G, which of the following gives the correct value of f(j-g)?A. 4B. 8C. 10D. 11E. 184. 排列组合题(10)Mr. Jones must choose 4 of the following 5 flavors of jellybean: apple, berry, coconut, 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. If 5 different colors areavailable for the design, how many differently painted designs are possible?A. 10B. 20C. 25D. 60E. 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 that increased from left to right?（14）.On the map above, X represents a theater, Y represents Chris’s house, and Z represents Peter’s house. Chris walks from his house to Peter’s house without passing the theater and then walks with Peter to the theater and then walks without walking by his own house again. 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?（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 numbers 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 positive 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 n th term, what is the value of n?(16) The 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. 11B. 7C. 4D. 3E. 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. Tom ’s weekly compensation consists of $300 plus 20 percent of his sale. Alison ’s 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 colleague ’s graduation, the m 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. m yB. p m y -C. p m py -D. mp m y )(- E. )(p m m py - (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 10percent off the regular price with an additional discount of 10 percent off the sale price?(A) $6 (B) $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 0<a <24 and 2<b <8, which of the following could have a remainder of 0 when divided by(A) b a (B) ab (C) a-b (D) a+b (E) ab(21) The alarm of Clock A rings every 4 minutes, the 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, and c are distinct positive integers, and 10% of abc is 5, then a+b could equalA. 1B. 3C. 5D. 6E. 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 finish the semester with an average score of 90 or higher?A. 90B. 92C. 94D. 96E. 97(24) Ifky 4 is the cube of an integer greater than 1, and k2=y, what is the least possible valueof y?A. 1B. 2C. 4D. 6E. 27III 代数问题(1) The height of the steam burst of a certain geyser varies with the length of 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)= 21(t-7) B. H(t)= 72 t C. H(t)=2-(t-7) D. H(t)= 7-2t E. H(t)= t72 （2） 4)The above graph could represent which of the following inequalities?A. y ≤x 1B. y< (21)xC. y ≥x 1 D . y ≥(21)x E . y ≥x -1/2 （3）The change in temperature is a function of the change in altitude in such a way that as the altitude increases, so dose the change in the temperature. For example, a gain of 1980 feet causes a 60F, which of the following could be the relationship of a and T?A. T(a)= a/300B. T(a)= a-330C. T(a)=330/aD. T(a)=330-aE. T(a)=330a（4） Let f(x) be defined as the least integer greater than x/5. Let g(x) be defined as the greatest integer less than x/5. What is the value of g(18)+f(102)? A. 21 B. 22 C. 23 D. 24 E. 25（5）Radioactive substance T-36 dose not stay radioactive forever. The time it takes for half of the element to decay is called a half-life. If, before any decay takes place, there is 1 gram of radioactive substance T-36, and the half-life is 7 days, how much remains after 28 days? A. 7-28 B. 2-4 C. 2-2 D. 1-28 E. 22(6) Luke purchased an automobile for $5000, and the value of the automobile decreases by 20 percent each year. The value, in dollars, of the automobile n years from the date of purchase is given by the function V , where V(n)=5000*(0.8)n . how many years from the date of purchase will the value of the automobile be $ 3200? A. 1 B. 1 C. 3 D. 4 E. 5(7) The cost of maintenance on an automobile increases each year by 10 percent, and Andrew paid$300 this year for maintenance on his automobile. If the cost c for maintenance on Andrew ’s automobile n years from now is given by the function c(n)=300x n , what is the value of x ?A. 0.1B. 0.3C. 1.1D. 1.3E. 30(8) h(t)= c- (d-4t)2At time t=0, a ball thrown upward from an initial height of 6 feet. Until the ball hit the ground, its height, in feet, after t seconds was given by the function h above, in which c and d are positive constants. If the ball reached its maximum height of 106 feet at time t=2.5, what was the height, in feet, of the ball at time t=1?(9) If k, n, x and y are positive numbers satisfying x -4/3 = k -2 and y 4/3 =n 2, what is (xy ) -2/3 in terms of n and k ?A. nk 1B. k nC. nk D. nk E. 1 (10)The figures above show the graphs of the function f and g . The function f is defined by f(x)=x 3-4x . the function g is defined by g(x)=f(x+h)+k , where h and k are constants. What is the value of hk ?A. -6B. -3C. -2D.3E. 6(11) Let [x] be defined as [x]=x 2-x for all values of x. if [a]= [a-2]. What is the value of a?A. 1B. 0.5C. 1.5D. 1.125E. 3(12) If k and h are constants and x 2+kx+7 is equivalent to (x+1)(x+h), what is the value of k ?A. 0B. 1C. 7D. 8E. cannot be determined(13) For all numbers a and b, let a^b be defined by a^b= ab+ a +b. For all numbers x, y, and z, which of the following must be true?I. x^y= y^xII. (x-1)^ (x+1)= (x^x) -1III. x^ (y+z) = (x^y) + (x ^ z)A. I onlyB. II onlyC. III onlyD. I and II onlyE. I, II and III(14)The graph above shows the function g, where g(x)= k(x+3)(x-3) for some constant k. If g(a- 1.2)= 0 and a>0, 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 of m?A. 8B. 16C. 24D. 32E. 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)]2III. f(a)+f(b)=f(2a)A. NoneB. I onlyC. I and III onlyD. II and III onlyE. I, II and 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. a≤4 II. b≤a III. b≤f(a)(A) I only(B) III only(C) I and II only(D) I and III only(E) I, and II and III（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, 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. 160B. 40C. 24D. 20E. 16（2）.In the figure above, a shaded polygon which has equal sides and angles is partially covered with asheet of blank paper. If x+y=80, how many sides does the polygon have?A. 10B. 9C. 8D. 7E. 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 isosceles, what is the perimeter of the unshaded hexagon?A. 16B.8+62C. 24D. 8+162E. 16+242（4）In the figure above, what is the value of c in terms of a and b?A. a+3b-180B. 2a+2b-180C. 180-a-bD. 360-a-bE. 360-2a-3b（5）The figure above shows an arrangement of 10 squares, each with side of length k inches. 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 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, and 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/yB. y+16000/yC. 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 is the greatest possible integer length of side PQ?A. 9B. 16C. 25D. 27E. 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+3πB. 10+3πC. 14+ 3πD. 1+6πE. 12+6π（11）In the figure above, QR is the arc of a circle with center P. If the length of the arc QR is 6π,what is the area of sector PQR?A. 108πB. 72πC. 54πD. 36πE. 9π（12）.The figure above consists of two circles that have the same center. If the shaded area is 64πsquare inches and the smaller circle has 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 each of the arcs of length b?A. 40B. 60C. 100D. 160E. 20o（14）In a certain machine, a gear makes 12 revolutions per minute. If the circumference of the gear is 3πinches, approximately how many feet will the gear turn in an hour?A. 6782B. 565C. 113D. 108E. 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 line l?（16）The coordinates for point A are (-2, 2) and the coordinates for point B are (4, 8). If line CD is parallel to the line AB, what is the slope of line CD?A. -1B. 0C. 1D. 2E. 4（17）Rectangle ABCD lies in the xy-coordinate plane so that its sides are not parallel to the axes. What is the product of the slopes of all four sides of rectangle ABCD?A. -2B. -1C. 0D. 1E. 2（18）Alice 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 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.)（19）.Line m (not shown) passes through O and intersects AB between A and B. what is one possible value of the slope of line m?立体几何部分：（1）In figure above, S is the midpoint of RT. What is the area of the shaded triangle?A. 14B. 16C. 265D. 18E. 46（2）A ball with a volume of 18 cubic inches is dropped into an aquarium that is partially filled with water. If the base of the aquarium measures 12 inches by 6 inches, how many inches will the level of water rise after the ball is submerged?A. 0.25 inchesB. 0.5 inchesC. 1 inchesD. 4 inchesE. 6 inches.（3）In the cube shown above, point B, C, and E are midpoints of three of the edges. Which of the following angles has the least measure?A.∠ XAYB. ∠ XBYC. ∠ XCYD. ∠ XDYE. ∠ XEY（4）.The pyramid shown above has altitude h and a square base of side m. The four edges that meet at V , the vertex of the pyramid, each have length e. If e=m, what is the value of h in terms of m?A. 2mB. 23mC. mD. 32m E. 2m（5）.The cube shown above has edges of length 2, and A and B are midpoints of two of the edges.What is the length of AB? A. 2 B. 3 C. 5 D. 6 E. 10（6）A sphere of radius r inside a cube touches each one of the six sides of the cube. What is the volume of the cube, in terms of r? A. r 3 B. 2 r 3 C. 4 r 3 D. 34πr 3 E. 8 r 3（7）A cube with volume 8 cubic centimeters is inscribed in a sphere so that each vertex of the cube touches the sphere. What is the length of the diameter, in centimeters of the sphere?A. 2B.6 C. 2.5 D. 23 E. 4。