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SAT模拟考试题:SAT数学练习题(13)

2016-08-11 16:52:25来源:网络

  Question #6: What are the solutions x of the equation ax·a1/x = 1, x ≠ 0 and a ≠ 1?

  (a) x = -1

  (b) x = 1

  (c) x1 = -1 and x2 = 1

  (d) The equation does not have real solutions

  (e) x = a

  Answer: ax·a1/x = ax + 1/x = 1 = a0

  x + 1/x = 0

  (x2 + 1)/x = 0

  x2 + 1 = 0. This equation does not have real solutions as x2 + 1 will always be positive.

  Question #7: If f(x) = |x| and g(x) = x2, how many solutions has f(x) = g(x)?

  (a) 1

  (b) 2

  (c) 3

  (d) 4

  (e) The equations does not have real solutions.

  Answer: The simplest way to solve this problem is to draw the 2 functions in the x, y plane.

SAT模拟考试题:SAT数学练习题(13)

  We find that the 2 functions intersect in 3 locations, for x = -1, 0 and 1.

  Question #8: If a, b and c are the sides of any triangle, which of the following inequalities is not true?

  (a) a·b > 0

  (b) a + b > c

  (c) a + c/2 >b

  (d) b + c > a

  (e) (a + b)·(b + c) > a·c

  Answer: The first answer is true, since the product of 2 positive reals will be positive.

  The second and the fourth answers are also true, since the sum of 2 sides of a triangle is always higher than the third side.

  The fifth answer is also true because it is just a multiplication of the second and fourth inequalities.

  Answer three should be the one that is not true, and we can verify this result with an example: an isosceles triangle with a = 3, b= 3, c= 10 will not satisfy the inequality.

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本文关键字: SAT模拟考试 SAT数学

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