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SAT数学Problem Solving练习题(三)

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  今天为大家准备了“SAT数学Problem Solving练习题(三)”, 供各位备考SAT的考生们参考使用,来提高自己的托福成绩!

  Question #1: In the x,y plane, which of the following statements are true?

  I. Line y + x = 5 is perpendicular to line y - x = 5.

  II. Lines y + x = 5 and y - x = 5 intersect each other on the y axis.

  III. Lines y + x = 5 and y - x = 5 intersect each other on the x axis.

  (a) I and III are both true.

  (b) I is the only true statement.

  (c) II is the only true statement.

  (d) I and II are both true.

  Answer: y + x = 5 can be written as y = -x + 5. The slope of this equation is m1 = -1.

  y - x = 5 can be written as y = x + 5. The slope of this equation is m2 = 1.

  m2 = -1/m1 so the 2 lines are perpendicular.

  We also need to find where the 2 lines intersect. If we add the 2 equations, 2·y = 10, y = 5.

  From the first equation, x = 5 - y = 5 - 5 = 0. In conclusion the lines intersect at (0, 5) and this point is on the y axis.

  In conclusion I and II statements are correct.

  Question #2: If a is an integer chosen randomly from the set {3, 5, 6, 9} and b is an integer chosen randomly from the set {2, 3, 4}, what is the probability that a/b is an integer?

  (a) .125

  (b) .250

  (c) .333

  (d) .5

  (e) .55

  Answer: We have 4 possible integers for a and 3 for b, so the number of possible combinations for a/b is 4 · 3 = 12.

  a/b is an integer only for 4 combinations:

  1. a = 3 and b = 3

  2. a = 6 and b = 2

  3. a = 6 and b = 3

  4. a = 9 and b = 3

  The probability that a/b is an integer is 4/12 = 1/3 = .333.

  Question #3: What is the value of integer a, if x = 2 is a solution of the equation √(a + x) = 2·x?

  (a) a = 10

  (b) a = 12

  (c) a = 14

  (d) a = 16

  (e) a = 18

  Answer: If we square the equation we get a + x = 4·x2

  By replacing x with 2, a + 2 = 4·22, so a + 2 = 16.

  In conclusion, a = 14.

  Question #4: What is the value of (3x + 1 - 3x) / (3x - 3x - 1)?

  (a) 6

  (b) 3x

  (c) 3x + 1

  (d) 3x - 1

  (e) 3

  Answer: The numerator of the fraction is: 3x + 1 - 3x = 3x·(3 - 1) = 2 · 3x

  The denominator of the fraction is: 3x - 3x - 1 = 3x - 1·(3 - 1) = 2 · 3x - 1

  We can write the fraction as (2 · 3x) / (2 · 3x - 1) = 3x / 3x - 1 = 3

  Question #5: Two diameters of a circle create an angle AOB of 45o between them. What is the length of arc AB if the radius of the circle is 10/??

  (a) 5/2

  (b) 3/2

  (c) 2

  (d) 4

  (e) 6

  Answer: The circumference of the circle is 2·?·r = 2·?·10/? = 20.

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