完整版sat数学考试试题doc.docx

1、完整版sat数学考试试题docSAT 数学真题精选1. If 2 x + 3 = 9, what is the value of 4 x3 ?(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)

2、and is perpendicular （垂直） to L, whatis 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 seats

3、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) r

4、 = 0 (E) m = 0第 1 页 共 11 页7. The least integer of a set of consecutive integers ( 连续整数 ) is 126. if the sum ofthese 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

5、in a dormitory. There are 200 seniors, 300 juniors, and 400 sophomores whoapplied. Each senior s name is placed in the lottery 3 times; each junior s natime; and each sophomore s name, 1 times. If a student s name is chosen at randomfrom the names in the lottery, what is the probability that a senio

6、r s name will bechosen?（ A ）1/8 (B) 2/9 (C) 2/7 (D) 3/8 (E) 1/2Question #1: 50% of US college students live on campus. Out of all students living oncampus, 40% are graduate students. What percentage of US students are graduatestudents living on campus?(A) 90% (B) 5% (C) 40% (D) 20% (E) 25%Question #

7、2: In the figure below, MN is parallel with BC and AM/AB = 2/3. What is theratio between the area of triangle AMN and the area of triangle ABC?(A) 5/9 (B) 2/3 (C) 4/9 (D) 1/2 (E) 2/9Question #3: If a 2 + 3 is divisible by 7, which of the following values can be a?第 2 页 共 11 页(A)7 (B)8 (C)9 (D)11 (E)

8、4Question #4: What is the value of b, if x = 2 is a solution of equation x(A)1/2(B)-1/2(C)5/2(D)-5/2(E)2Question #5: Which value of x satisfies the inequality | 2x | 2 and n 2, how many (m, n) pairs satisfy the inequalitym n 100?(A)2(B)3(C)4(D)5(E)7Question #7: The US deer population increase is 50%

9、 every 20 years. How may timeslarger will the deer population be in 60 years ?(A)2.275(B)3.250(C)2.250(D)3.375Question #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:USUK321441The number of medals won at a track and field championship is shown in the tableabove.

10、What is the percentage of bronze medals won by UK out of all medals won bythe 2 teams?2- b x + 1 = 0?(E)2.500Medalsgoldsilverbronze(A)20% (B)6.66% (C)26.6% (D)33.3% (E)10%第 3 页 共 11 页Question #10: The edges of a cube are each 4 inches long. What is the surface area, insquare inches, of this cube?(A)

11、66 (B)60 (C)76 (D)96 (E)65Question #1: The sum of the two solutions of the quadratic equation f(x) = 0 is equalto 1 and the product of the solutions is equal to -20. What are the solutions of theequation f(x) = 16 - x ?(a) x1= 3 and x2= -3(b) x1 = 6 and x2 = -6(c) x1 = 5 and x2 = -4(d) x1 = -5 and x

12、2 = 4(e) x1= 6 and x2= 0Question #2: In the (x, y) coordinate plane, three lines have the equations:l 1: y = ax + 1l 2: y = bx + 2l 3: y = cx + 3Which of the following may be values of a, b and c, if line l 3 is perpendicular to bothlines l 1 and l 2 ?(a) a = -2, b = -2, c = .5 (b) a = -2, b = -2, c

13、 = 2(c) a = -2, b = -2, c = -2 (d) a = -2, b = 2, c = .5(e) a = 2, b = -2, c = 2第 4 页 共 11 页Question #3: The management team of a company has 250 men and 125 women. If200 of the managers have a master degree, and 100 of the managers with the masterdegree are women, how many of the managers are men w

14、ithout a master degree?(a) 125 (b) 150 (c) 175 (d) 200 (e) 225Question #4: In the figure below, the area of square ABCD is equal to the sum of theareas of triangles ABE and DCE. If AB = 6, then CE =(a) 5(b) 6(c) 2(d) 3(e) 4Question #5:If and are the angles of the right triangle shown in the figure a

15、bove, then sin2 +sin 2 is equal to:(a) cos( ) (b) sin( ) (c) 1 (d) cos 2 ( ) (e) -1Question #6: The average of numbers (a + 9) and (a - 1) is equal to b, where a and b areintegers. The product of the same two integers is equal to (b - 1) 2 . What is the value ofa?(a) a = 9 (b) a = 1 (c) a = 0 (d) a

16、= 5 (e) a = 11第 5 页 共 11 页Question #1: If f(x) = x and g(x) = x, x 0,solutionswhatareofthef(x) = g(x)?(A) x = 1 (B)x 1 = 1, x 2 = -1(C)x 1 = 1, x 2 = 0 (D)x = 0(E)x = -1Question #2: What is the length of the arc AB in the figure below, if O is the center ofthe circle and triangle OAB is equilateral?

17、 The radius of the circle is 9(a) (b) 2 (c) 3 (d) 4 (e) /2Question #3: What is the probability that someone that throws 2 dice gets a 5 and a 6?Each dice has sides numbered from 1 to 6.(a)1/2 (b)1/6 (c)1/12 (d)1/18 (e)1/36Question #4: A cyclist bikes from town A to town B and back to town A in 3 hou

18、rs. Hebikes from A to B at a speed of 15 miles/hour while his return speed is 10 miles/hour.What is the distance between the 2 towns?(a)11 miles (b)18 miles (c)15 miles (d)12 miles (e)10 milesQuestion #5: The volume of a cube-shaped glass C1 of edge a is equal to half thevolume of a cylinder-shaped

19、glass C2. The radius of C2 is equal to the edge of C1.What is the height of C2?(a) 2 a / (b)a / (c) a / (2 ) (d)a / (e)a + 第 6 页 共 11 页Question #6: How many integers x are there such that 2 x 5 must be true in which one of the followingcases?I. x 7 III. x 01.Three unit circles are arranged so that e

20、ach touches the other two. Find the radii of the two circles which touch all three.第 7 页 共 11 页2.Find all real numbers x such that x + 1 = |x + 3| - |x - 1|.3. (1)Given x = (1 + 1/n)n , y = (1 + 1/n)n+1 , show that xy = y x .(2)Show that 12 - 2 2+ 3 2 - 4 2 + . + (-1)n+1 n 2 = (-1)n+1 (1 + 2 + . + n

21、).4.All coefficients of the polynomial p(x) are non-negative and none exceed p(0). Ifp(x) has degree n, show that the coefficient of x n+1 in p(x) 2 is at most p(1) 2/2.第 8 页 共 11 页5. What is the maximum possible value for the sum of the absolute values of thedifferences between each pair of n non-n

22、egative real numbers which do notexceed 1?6.AB is a diameter of a circle. X is a point on the circle other than the midpoint of the arc AB. BX meets the tangent at A at P, and AX meets the tangent at B at Q. Show that the line PQ, the tangent at X and the line AB are concurrent.7. Four points on a c

23、ircle divide it into four arcs. The four midpoints form aquadrilateral. Show that its diagonals are perpendicular.第 9 页 共 11 页8. Find the smallest positive integer b for which 7 + 7b + 7b 2 is a fourth power.9.Show that there are no positive integers m, n such that 4m(m+1) = n(n+1).10.ABCD is a conv

24、ex quadrilateral with area 1. The lines AD, BC meet at X. The midpoints of the diagonals AC and BD are Y and Z. Find the area of the triangle XYZ.第 10 页 共 11 页11. A square has tens digit 7. What is the units digit?12.Find all ordered triples (x, y, z) of real numbers which satisfy the following system of equations:xy = z - x - y xz = y - x - z yz = x - y - z第 11 页 共 11 页