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13: Given the list of integers: -2, 2, 0, 6, 8, 0, -5, 9, 10, 4, which of the following statements is true?

　　(a) mode < median < average

　　(b) median < mode < average

　　(c) median < average < mode

　　(d) mode = median < average

　　(e) average < median < mode

Answer:

We need to rearrange the list of integers in order: -5, -2, 0, 0, 2, 4, 6, 8, 9, 10. The average will be the sum of all integers divided by the number of integers, 32/10 = 3.2

The median will be the mean of the 2 middle numbers, 2 and 4, so the median is 3.

The mode is 0, as 0 occurs the most in the list.

The correct answer is mode < median < average.

14: 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.

15: 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.

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

延伸阅读：

SAT数学专项练习题（三）

SAT数学专项练习题（四）

SAT数学专项练习题（五）

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