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7: What is the value of the median of an equilateral triangle with all sides equal to 5?

　　(a) (5/2) · √3

　　(b) 5 · √3

　　(c) (5/2) · 3-3

　　(d) 5/2

　　(e) 5

Answer: The median divides the equilateral triangle in two right triangles. Conform to the Pythagorean theorem, wherein the sum of the squares of the two legs is equal to the square of the hypotenuse,

m2 + (5/2)2= 52

m2 = 52 - (5/2)2 = 52 - 52/4 = (3/4) · 52

m = (5/2) · √3.

8: A parameter is measured during a scientific experiment and the results are -12, 4, -8, 10, 2, 2, 0, -4 and 2. The median and the average of these numbers are:

　　(a) median = 0, average = -4/9

　　(b) median = 0, average = 4/9

　　(c) median = 2, average = -4/9

　　(d) median = 2, average = 4/9

　　(e) median = 2, average = 2/9

Answer:

You must arrange the numbers in order: -12, -8, -4, 0, 2, 2, 2, 4, and 10.

The median will be number in the middle of the row, that is 2.

The average will be (-12-8-4+0+2+2+2+4+10)/9 = -4/9.

9: If a, b and c are consecutive integers, a < b < c, and a + b + c = 96, what is the value of b?

　　(a) 30

　　(b) 31

　　(c) 32

　　(d) 33

　　(e) 34

Answer:

If a, b and c are consecutive numbers, b = a + 1 and c = a + 2.

Then, a + (a + 1) + (a + 2) = 96, so 3·a + 3 = 96.

a = (96 - 3)/3 = 31.

b = a + 1 = 32.

延伸阅读：

SAT数学练习题（一）

SAT数学练习题（二）

SAT数学练习题（三）

更多阅读资料：
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