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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) 21

2. If 4(t + u) + 3 = 19, then t + u = ? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7

3. 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 perpendicular （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 = -2x 4. 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 + 45

5. There are 8 sections of seats 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) 1,700

6. If rsuv = 1 and rsum = 0, which of the following must be true? (A) r < 1 (B) s < 1 (C) u= 2 (D) r = 0 (E) m = 0

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7. 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) 254

8. A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are 200 seniors, 300 juniors, and 400 sophomores who applied. Each senior’s name is placed in the lottery 3 times; each junior’s name, 2 time; and each sophomore’s name, 1 times. If a student’s name is chosen at random from the names in the lottery, what is the probability that a senior’s name will be chosen? （A）1/8 (B) 2/9 (C) 2/7 (D) 3/8 (E) 1/2

Question #1: 50% of US college students live on campus. Out of all students living on campus, 40% are graduate students. What percentage of US students are graduate students living 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 = 2/3. What is the ratio 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) 2/9

Question #3: If a2 + 3 is divisible by 7, which of the following values can be a?

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(A)7

(B)8

(C)9

(D)11

(E)4

Question #4: What is the value of b, if x = 2 is a solution of equation x2 - b · x + 1 = 0? (A)1/2 (B)-1/2 (C)5/2 (D)-5/2 (E)2

Question #5: Which value of x satisfies the inequality | 2x | < x + 1 ? (A)-1/2 (B)1/2 (C)1 (D)-1 (E)2

Question #6: If integers m > 2 and n > 2, how many (m, n) pairs satisfy the inequality mn < 100? (A)2 (B)3 (C)4 (D)5 (E)7

Question #7: The US deer population increase is 50% every 20 years. How may times larger will the deer population be in 60 years ? (A)2.275 (B)3.250 (C)2.250 (D)3.375 (E)2.500

Question #8: Find the value of x if x + y = 13 and x - y = 5. (A)2 Question #9: US 3 1 4 UK 2 4 1 Medals gold silver bronze (B)3 (C)6 (D)9 (E)4

The number of medals won at a track and field championship is shown in the table above. What is the percentage of bronze medals won by UK out of all medals won by the 2 teams? (A)20% (B)6.66% (C)26.6% (D)33.3% (E)10%

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Question #10: The edges of a cube are each 4 inches long. What is the surface area, in square inches, of this cube? (A)66 (B)60 (C)76 (D)96 (E)65

Question #1: The sum of the two solutions of the quadratic equation f(x) = 0 is equal to 1 and the product of the solutions is equal to -20. What are the solutions of the equation f(x) = 16 - x ? (a) x1 = 3 and x2 = -3 (c) x1 = 5 and x2 = -4 (e) x1 = 6 and x2 = 0 Question #2: In the (x, y) coordinate plane, three lines have the equations: l1: y = ax + 1 l2: y = bx + 2 l3: y = cx + 3 Which of the following may be values of a, b and c, if line l3 is perpendicular to both lines l1 and l2? (a) a = -2, b = -2, c = .5 (c) a = -2, b = -2, c = -2 (e) a = 2, b = -2, c = 2 (b) a = -2, b = -2, c = 2 (d) a = -2, b = 2, c = .5 (b) x1 = 6 and x2 = -6 (d) x1 = -5 and x2 = 4

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Question #3: The management team of a company has 250 men and 125 women. If 200 of the managers have a master degree, and 100 of the managers with the master degree are women, how many of the managers are men without a master degree? (a) 125 (b) 150 (c) 175 (d) 200 (e) 225

Question #4: In the figure below, the area of square ABCD is equal to the sum of the areas of triangles ABE and DCE. If AB = 6, then CE =

(a) 5 Question #5:

(b) 6

(c) 2

(d) 3

(e) 4

If α and β are the angles of the right triangle shown in the figure above, then sin2α + sin2β is equal to: (a) cos(β ) (b) sin(β ) (c) 1 (d) cos2(β ) (e) -1

Question #6: The average of numbers (a + 9) and (a - 1) is equal to b, where a and b are integers. The product of the same two integers is equal to (b - 1)2. What is the value of a? (a) a = 9 (b) a = 1 (c) a = 0 (d) a = 5 (e) a = 11

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Question #1: If f(x) = x and g(x) = √x, x≥ 0, what are the solutions of f(x) = g(x)? (A) x = 1 (C)x1 = 1, x2 = 0 (E)x = -1 Question #2: What is the length of the arc AB in the figure below, if O is the center of the circle and triangle OAB is equilateral? The radius of the circle is 9 (B)x1 = 1, x2 = -1 (D)x = 0

(a) π

(b) 2 ·π

(c) 3 ·π

(d) 4 ·π

(e) π/2

Question #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)1/36

Question #4: A cyclist bikes from town A to town B and back to town A in 3 hours. He bikes 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 miles

Question #5: The volume of a cube-shaped glass C1 of edge a is equal to half the volume of a cylinder-shaped glass C2. The radius of C2 is equal to the edge of C1. What is the height of C2? (a)2·a /π (b)a / π (c)a / (2·π) (d)a / π (e)a + π

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Question #6: How many integers x are there such that 2x < 100, and at the same time the number 2x + 2 is an integer divisible by both 3 and 2? (a)1 (b)2 (c) 3 (d) 4 (e)5

Question #7: sin(x)cos(x)(1 + tan2(x)) = (a)tan(x) + 1 (c)sin(x) (e)sin(x) + cos(x) Question #8: If 5xy = 210, and x and y are positive integers, each of the following could be the value of x + y except: (a)13 (b) 17 (c) 23 (d)15 (e)43 (b)cos(x) (d)tan(x)

Question #9: The average of the integers 24, 6, 12, x and y is 11. What is the value of the sum x + y? (a)11 (b)17 (c)13 (d)15 (e) 9

Question #10: The inequality |2x - 1| > 5 must be true in which one of the following cases? I. x < -5 II. x > 7 III. x > 0

1. Three unit circles are arranged so that each touches the other two. Find the radii of the two circles which touch all three.

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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 = yx. (2) Show that 12 - 22 + 32 - 42 + ... + (-1)n+1n2 = (-1)n+1(1 + 2 + ... + n).

4. All coefficients of the polynomial p(x) are non-negative and none exceed p(0). If p(x) has degree n, show that the coefficient of xn+1 in p(x)2 is at most p(1)2/2.

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5. What is the maximum possible value for the sum of the absolute values of the differences between each pair of n non-negative real numbers which do not exceed 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 circle divide it into four arcs. The four midpoints form a quadrilateral. Show that its diagonals are perpendicular.

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8. Find the smallest positive integer b for which 7 + 7b + 7b2 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 convex 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.

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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

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