sat數(shù)學考試試題

1、SAT 數(shù)學真題精選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, the n t + u = ?(A) 3(B) 4(C) 5(D) 6(E) 73. In the xy-coord in ate (坐標)pla ne above, the line contains the poi nts (0,0) and (1,2).If line M (not show n) contains the point (0,0) and is perpe

2、 ndicular(垂直)to L, what is an equatio n 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 followi ng is also divisible by these numbers?(A) K + 5(B) K + 15(C) K + 20(D) K +30(E) K + 455. There are 8 secti ons of seats in an au

3、ditorium. Each secti on contains at least 150seats but not more tha n 200 seats. Which of the follow ing could be the nu mber of seatsin 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 followi ng must be true?(A) r 1(B) s 1(C) u= 2(D) r = 0(E)m = 0

4、7. The least integer of a set of consecutive integer 連續(xù)整數(shù))is 126. ifthe sum of these in tegers is 127, how many in tegers are in this set?(A) 126(B) 127(C) 252(D) 253(E)2548. A special lottery is to be held to select the stude nt who will live in theonly deluxe room in a dormitory. There are 200 sen

5、iors, 300 juniors, and 400sophomores who applied. Each seniorpcsnamteeslottery 3times; each junior s name, 2 time; and each sophomore s namea student s name is chosen at random from the names in the lottery, what isthe probability that a senior s name will be chosen?(A) 1/8(B) 2/9(C) 2/7(D)3/8(E) 1/

6、2Questi on #1: 50% of US college stude nts live on campus. Out of all stude nts liv ing oncampus, 40% are graduate stude nts. What perce ntage of US stude nts are graduatestude nts liv ing on campus?(A) 90%(B) 5%(C) 40%(D) 20%(E) 25%Question #2: In the figure below, MN is parallel with BC and AM/AB

7、= 2/3.What is the ratio between the area of triangle AMN and the area of triangleABC?(C) 4/9(D) 1/2(B) 2/3(A)2.275(B)3.250(C)2.250(D)3.375(E)2.500Questio n #8: Find the value of x if x + y = 13 and x - y = 5.(A)2(B)3(C)6(D)9(E)4Question #9:USUKMedals32gold14silver41bronze(E) 2/9Questio n #3: If a2+

8、3 is divisible by 7, which of the follow ing values can bea?(A)7(B)8(C)9(D)11(E)4Questio n #4: What is the value of b, if x = 2 is a soluti on of equatio n X - b x + 1 = 0?(A)1/2(B)-1/2(C)5/2(D)-5/2(E)2Questi on #5: Which value of x satisfies the in equality | 2x | 2 and n 2, how many (m, n) pairs s

9、atisfy the inequality m 0, what are the solution(A) x = 1(C) x1= 1, x2= 0(B)X1= 1, X2= -1(D) x = 0(E)x = -1Questi on #2: What is the len gth of the arc AB in the figure below, if O is thecenter of the circle and triangle OAB is equilateral? The radius of the circle isQuesti on #3: What is the probab

10、ility that some one that throws 2 dice gets a 5and a 6? Each dice has sides nu mbered from 1 to 6.(a)1/2(b)1/6(c)1/12(d)1/18(e) 1/36Questi on #4: A cyclist bikes from tow n A to tow n B and back to tow n A in 3hours. He bikes from A to B at a speed of 15 miles/hour while his return speedis 10 miles/

11、hour. What is the dista nce betwee n the 2 tow ns?(a)11 miles (b)18 miles(c)15 miles(d)12 miles(e)10 milesQuestio n #5: The volume of a cube-shaped glass C1 of edgeis equal to halfthe volume of a cyli nder-shaped glass C2. The radius of C2 is equal to theedge of C1. What is the height of C2?(c) 3 n(

12、d) 4 n(a)(e)(a)2a /n(b)a /n(c)a / (2)n(d)a /n(e)a +nQuestio n #6: How many in tegers x are there such that 2 5 must be true in which one of thefollowi ng cases?I. x 7III. x 01 Three unit circles are arranged so that each touches the other two. Findthe radii of the two circles which touch all three.2

13、. Find all real numbers x such that x + 1 = |x + 3| - |x - 1|.3.Given x = (1 + 1/n)n, y = (1 + 1/n)n+1, show that xy= yx.(2) Show that 12- 22+ 32- 42+ . + (- 1)n+1n2= (- 1)n+1(1 + 2 + . + n).44 All coefficients of the polynomial p(x) are non-negative and none exceedp(0). If p(x) has degree n, show t

14、hat the coefficient of x in p(x)2is at mostp(1)2/2.5. What is the maximum possible value for the sum of the absolute values ofthe differe nces betwee n each pair of n non-n egative real nu mbers whichdo not exceed 1?6. AB is a diameter of a circle. X is a point on the circle other than the midpo int

15、of the arc AB. BX meets the tangent at A at P, and AX meets the tangent atB at Q. Show that the line PQ, the tangent at X and the line AB are con current.7. Four points on a circle divide it into four arcs. The four midpoints form aquadrilateral. Show that its diago nals are perpe ndicular.8. Find the smallest positive integer b for which 7 + 7b + 7b2is a fourthpower.9. Show that there are no positive integers m, n such that 4m(m+1)= n(n+1).10.ABCD is a con vex quadrilateral with area 1. The lines AD, BC meet atX. The midpoi nts of the diag on als AC and