sat数学真题精选

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1、SAT数学真题精选1. If 2 x + 3 = 9, what is the value of 4 x 3 ?(A) 5 (B) 9 (C) 15 (D) 18 (E) 212. If 4(t + u) + 3 = 19, then t + u = ?(A) 3 (B) 4 (C) 5 (D) 6 (E) 73. In the xy-coordinate (坐标) plane above, the line contains the points (0,0) and (1,2). If line M (not shown) contains the point (0,0) and is pe

2、rpendicular （垂直） to L, what is an equation of M?(A) y = -1/2 x (B) y = -1/2 x + 1 (C) y = - x (D) y = - x + 2 (E) y = -2x4. If K is divisible by 2,3, and 15, which of the following is also divisible by these numbers?(A) K + 5 (B) K + 15 (C) K + 20 (D) K + 30 (E) K + 455. There are 8 sections of seat

3、s in an auditorium. Each section contains at least 150 seats but not more than 200 seats. Which of the following could be the number of seats in this auditorium?(A) 800 (B) 1,000 (C) 1,100 (D) 1,300 (E) 1,7006. If rsuv = 1 and rsum = 0, which of the following must be true?(A) r 1 (B) s 1 (C) u= 2 (D

4、) r = 0 (E) m = 07. The least integer of a set of consecutive integers (连续整数) is 126. if the sum of these integers is 127, how many integers are in this set?(A) 126 (B) 127 (C) 252 (D) 253 (E) 2548. A special lottery is to be held to select the student who will live in the only deluxe room in a dorm

5、itory. There are 200 seniors, 300 juniors, and 400 sophomores who applied. Each seniors name is placed in the lottery 3 times; each juniors name, 2 time; and each sophomores name, 1 times. If a students name is chosen at random from the names in the lottery, what is the probability that a seniors na

6、me will be chosen?（A）1/8 (B) 2/9 (C) 2/7 (D) 3/8 (E) 1/2SAT考试数学练习题（一）1. If f(x) = x 3, where x is an integer, which of the following could be a value of f(x)?I 6II 0III -6A. I onlyB. I and II onlyC. II and III onlyD. I and III onlyE. I, II and IIICorrect Answer: A解析:Choice I is correct because f(x)

7、= 6 when x=3. Choice II is incorrect because to make f(x) = 0, x would have to be 3. But 3 is not the square of an integer. Choice III is incorrect because to make f(x) = 0, x would have to be 3 but squares cannot be negative. (The minimum value for x2 is zero; hence, the minimum value for f(x) = -3

8、)2. 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. 48B. 49C. 50D. 51E. 52Correct Answer: C解析:1 4n + 7 200. n can be 0, or -1. n cannot be -2 or any other negative integer or the expression 4n + 7 will be less than1. The larg

9、est value for n will be an integer (200 - 7) /4. 193/4 = 48.25, hence 48. The number of integers between -1 and 48 inclusive is 503. 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.

10、23B. 22C. 18D. 16E. 14Correct Answer: B解析:First you must realize that the sum of two 2-digit numbers cannot be more that 198 (99 + 99). Therefore in the given problem D must be 1. Now use trial and error to satisfy the sum 5A + BC = 143. A + C must give 3 in the units place, but neither can be 1 sin

11、ce all the digits have to be different. Therefore A + C = 13. With one to carry over into the tens column, 1 + 5 + B = 14, and B = 8. A + C + B + D = 13 + 8 + 1 = 224. 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 w

12、ater rise?(1 litre = 1000cm)A. 6B. 8C. 10D. 20E. 40Correct Answer: B解析:Total volume of water = 12 liters = 12 x 1000 cm3. The base of the aquarium is 50 x 30 = 1500cm3. Base of tank x height of water = volume of water. 1500 x height = 12000; height = 12000 / 1500 = 85. Six years ago Anita was P time

13、s as old as Ben was. If Anita is now 17 years old, how old is Ben now in terms of P ?A. 11/P + 6B. P/11 +6C. 17 - P/6D. 17/PE. 11.5PCorrect Answer: A解析:Let Bens age now be B. Anitas age now is A. (A - 6) = P(B - 6)But A is 17 and therefore 11 = P(B - 6). 11/P = B-6(11/P) + 6 = BSAT考试数学练习题（二）1. The d

14、istance 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 11II 1III 7A. I onlyB. II onlyC. I and II onlyD. II and III onlyE. I, II, or III.Correct Answer: E解析:Do not assume that AB and C are on a straight line. Make a diagram with

15、A and B marked 5 miles apart. Draw a circle centered on B, with radius 6. C could be anywhere on this circle. The minimum distance will be 1, and maximum 11, but anywhere in between is possible.2. 5 percent of 55 =A. 0.05B. 0.25C. 0.5D. 2.5E. 25Correct Answer: B解析:We can write the statement mathemat

16、ically, using x to mean of and /100 for per cent. So ( 5/100) x 55 = 5 x 5 /100 = 0.253. If pqr = 1 , rst = 0 , and spr = 0, which of the following must be zero?A. PB. QC. RD. SE. TCorrect Answer: D解析:If pqr = 1, none of these variable can be zero. Since spr = 0 , and since p and r are not zero, s m

17、ust be zero. (Note that although rst = 0, and so either s or t must be zero, this is not sufficient to state which must be zero)4.A. 1/5B. 6/5C. 6D. 64 / 5E. 64Correct Answer: E解析:65 = 64x 6(64 x 6) - 64 = 64(6 - 1) = 64 x 5 Now, dividing by 5 will give us 645. -20 , -16 , -12 , -8 .In the sequence

18、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. 0B. 200C. 440D. 668E. 762Correct Answer: E解析:All terms in the sequence will be multiples of 4. 762 is not a multiple of 4SAT考试数学练习题1. Which of the following could be a

19、 value of x, in the diagram above?A. 10B. 20C. 40D. 50E. any of the above2. 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 r

20、equired?A. 10B. 15C. 20D. 25E. 303. 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 : 1B. 10 : 5C. 15 : 2D. 20 : 2E. 25 : 24. A 3 by 4 rectangle is

21、 inscribed in circle. What is the circumference of the circle?A. 2.5B. 3C. 5D. 4E. 105. 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. 4B. 7C.

22、 8D. 12E. it cannot be determined from the information given.SAT考试数学练习题1. 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)2. ABCD is a square of side 3, and E and F are the mid points of sides AB and BC respecti

23、vely. What is the area of the quadrilateral EBFD ?A. 2.25B. 3C. 4D. 4.5E. 63. If n 0, which of the following must be greater than n?I 2nII nIII 2 - nA. I onlyB. II onlyC. I and II onlyD. II and III onlyE. None4. After being dropped a certain ball always bounces back to 2/5 of the height of its previ

24、ous bounce. After the first bounce it reaches a height of 125 inches. How high (in inches) will it reach after its fourth bounce?A. 20B. 15C. 8D. 5E. 3.25. n and p are integers greater than 15n is the square of a number75np is the cube of a number.The smallest value for n + p isA. 14B. 18C. 20D. 30E

25、. 50SAT考试数学练习题1. If a = 12, then a4 =A. 144B. 72C. 36D. 24E. 16Correct Answer: A解析:a4 = a2 x a2 = 12 x 12 = 1442. If n is even, which of the following cannot be odd?I n + 3II 3nIII n - 1A. I onlyB. II onlyC. III onlyD. I and II onlyE. I, II and IIICorrect Answer: B解析:In case I , even plus odd will g

26、ive odd. In case II, odd times even will give even. In case III even squared is even, and even minus odd is odd. (You can check this by using an easy even number like 2 in place of n). Only case II cannot be odd.3. One side of a triangle has length 8 and a second side has length 5. Which of the foll

27、owing could be the area of the triangle?I 24II 20III 5A. I onlyB. II onlyC. III onlyD. II and III onlyE. I, II and IIICorrect Answer: D解析:The maximum area of the triangle will come when the given sides are placed at right angles. If we take 8 as the base and 5 as the height the area = x 8 x 5 = 20.

28、We can alter the angle between the sides to make it less or more than 90, but this will only reduce the area. (Draw it out for yourself). Hence the area can be anything less than or equal to 20.4. A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the s

29、ame rate, in how many more days will its total consumption be 91 pounds?A. 12B. 11C. 10D. 9E. 8Correct Answer: E解析:Food consumed per day = 39/6. In the remaining days it will consume 91 - 39 pounds = 52 pounds. Now divide the food by the daily consumption to find the number of days. 52 / (39/6) = 52

30、 x (6 / 39) = 85. 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. 8pB. pqC. pq + 27D. -pE. (p - q)6Correct Answer: C解析:A perfect cube will have pr

31、ime factors that are in groups of 3; for example 125 has the prime factors 5 x 5 x 5 , and 64 x 125 will also be a cube because its factors will be 4 x 4 x 4 x 5 x 5 x 5. Consider the answer choices in turn. 8 is the cube of 2, and p is a cube, and so the product will also be a cube. pq will also be

32、 a cube as shown above.pq is a cube and so is 27, but their sum need not be a cube. Consider the case where p =1 and q = 8, the sum of pq and 27 will be 35 which has factors 5 x 7 and is not a cube. -p will be a cube. Since the difference between p and q is raised to the power of 6, this expression

33、will be a cube (with cube root = difference squared).SAT考试数学练习题1. What is the length of the line segment in the x-y plane with end points at (-2,-2) and (2,3)?A. 3B. 31C. 41D. 7E. 9Correct Answer: C解析:Sketch a diagram and calculate the distance (hypotenuse of a right triangle) using Pythagoras theor

34、em.Vertical height of triangle = 5 ; horizontal side = 4 ; hypotenuse = (25 + 16) = 412. n is an integer chosen at random from the set5, 7, 9, 11 p is chosen at random from the set2, 6, 10, 14, 18What is the probability that n + p = 23 ?A. 0.1B. 0.2C. 0.25D. 0.3E. 0.4Correct Answer: A解析:Each of the

35、integers in the first set could be combined with any from the second set, giving a total of 4 x 5 = 20 possible pairs. Of these the combinations that could give a sum of 23 are (5 + 18), and (9 + 14). This means that the probability of getting a sum of 23 is 2/20 = 1/103. A dress on sale in a shop i

36、s 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. 0.75DB. 0.76DC. 0.765DD. 0.775DE. 0.805DCorrect Answer: C解析:If the price is reduced by

37、 15 %, then the new price will be 0.85D. If this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85D = 0.765D4. All the dots in the array are 2 units apart vertically and horizontally. What is the length of the longest line segment that can be drawn joining any two points i

38、n the array without passing through any other point ?A. 2B. 22C. 3D. 10E. 20Correct Answer: E解析:The longest line segment that can be drawn without passing through any dots other than those at the beginning and end of the segment, such a line could go from the middle dot in the top row to either the

39、bottom left or right dot. In any case the segment will be the hypotenuse of a right triangle with sides 2 and 4. Using Pythagoras theorem the hypotenuse will be (2 + 4 ) = 205. If the radius of the circle with centre O is 7 and the measure of angle AOB is 100, what is the best approximation to the l

40、ength of arc AB ?A. 9B. 10C. 11D. 12E. 13Correct Answer: D解析:If the radius is 7, the circumference = 14. The length of the arc is 100/360 of the circumference. Taking as 22/7 we get. (100 x 14 x 22) / (360 x 7) which reduces to 440/ 36 = 12.22 (i.e. approx. 12)SAT数学重要公式14个SAT数学考试并不需要考生记忆数学公式，对于一些常用的

41、简单公式都会列在试卷的前面。但是对于一些可以帮助大家解题的小公式，大家还是了解记忆一些比较有好处。下面为大家搜集了这样的SAT数学公式，共14个，供大家参考。1.正整数n有奇数个因子,则n为完全平方数2.因子个数求解公式:将整数n分解为质因子乘积形式,然后将每个质因子的幂分别加一相乘.n=a*a*a*b*b*c则因子个数=(3+1)(2+1)(1+1)eg. 200=2*2*2 * 5*5 因子个数=(3+1)(2+1)=12个3.能被8整除的数后三位的和能被8整除;能被9整除的数各位数的和能被9整除.能被3整除的数,各位的和能被3整除.4.多边形内角和=(n-2)x1805.菱形面积=1/2

42、 x 对角线乘积6.欧拉公式： 边数=面数+顶点数-28.三角形余玄定理C2=A2+B2-2ABCOS,为AB两条线间的夹角9.正弦定理:A/SinA=B/SinB=C/SinC=2R(A,B,C是各边及所对应的角,R是三角形 外接圆的半径)10.Y=k1X+B1,Y=k2X+B2，两线垂直的条件为K1K2=-111.N的阶乘公式:N!=1*2*3*.(N-2)*(N-1)*N 且规定0!=1 1!=1Eg:8!=1*2*3*4*5*6*7*812. 熟悉一下根号2、3、5的值sqrt(2)=1.414 sqrt(3)=1.732 sqrt(5)=2.23613. .2/3 as many A as B: A=2/3*B.twice as many. A as B: A=2*B14. 华氏温度与摄氏温度的换算换算公式:(F-32)*5/9=CPS.常用计量单位的换算:(自己查查牛津大字典的附录吧)以上就是关于SAT数学重要公式的全部内容，包括了很多可以节省大家的解题时间，提高解题效率的小窍门。大家可以在备考自己的SAT数学考试的时候，进行适当的参考和练习，以便更好的应对SAT数学考试。