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SAT 数学经典训练题二
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导读:Question #1: f(x) = 1/(x + 1) and g(x) = x + 1. What are the values of x for which f(x) = g(x)?(a) x1 = 0 and x2 = 2(b) x1 = 0 and x2 = 1(c) x1 = 2 and x2 = -2(d) x1 = 0 and x2 = - ...

Question #1: f(x) = 1/(x + 1) and g(x) = x + 1. What are the values of x for which f(x) = g(x)?  (a) x1 = 0 and x2 = 2  (b) x1 = 0 and x2 = 1  (c) x1 = 2 and x2 = -2  (d) x1 = 0 and x2 = -2  (e) x1 = 1 and x2 = -2  Answer: f(x) = g(x) means x + 1 = 1/(x + 1);  (x + 1) · (x + 1) = 1;  x2 + 2 · x = 0  x · (x + 2) = 0 so x1 = 0 and x2 = -2.  (d) is the correct answer.  Question #2: A website had 2,000 unique visitors in 5 days. At the same rate, how many days are needed to achieve 12,000 unique visitors?  (a) 15 days  (b) 30 days  (c) 40 days  (d) 120 days  (e) 20 days  Answer: 2000 visitors in 5 days means that the website has 2000/5 = 400 visitors/day.  12,000 visitors / (400visitors / day) = 30 days.  Question #3: If a is an integer chosen randomly from the set {3, 4, 5, 9} and b is an integer chosen randomly from the set {3, 8, 12, 15}, what is the probability that a/b is an integer?  (a) .25  (b) .2  (c) .125  (d) .375  (e) .4  Answer: We have 4 possible integers for a and 4 for b, so the number of possible combinations for (a / b) is 16  a/b is an integer only for 2 combinations:  1. a = 3 and b = 3  2. a = 9 and b = 3  The probability that a/b is an integer is 2/16 = 1/8 = .125 and (c) is the correct answer.  Question #4: Two of the sides of a triangle are 7 and 6. What of the following could be the perimeter of the triangle?  (a) 14  (b) 26  (c) 18  (d) 9  (e) 12  Answer: The angle between the two sides should be higher than 0 degrees and the third side should be higher than 7 - 6 = 1. The perimeter should be higher than 7 +6 +1 = 14  The angle between the two sides should be lower than 180 degrees and the third side should be lower than 7 + 6 = 13. The perimeter should be lower than 7 + 6 + 13 = 26  (c) is the only value between 14 and 26.  Question #5: What is the line in the coordinate plane that is perpendicular to y = m · x + n and passes through the origin?  (a) y = (-1/m) · x  (b) y = (-1/m) · x - 1/n  (c) y = (-m) · x  (d) y = (-m) · x - n  (e) y = (-2m) · x  Answer: The line y = a · x + b, passes through the origin (0,0), so 0 = a · 0 + b, b = 0  (b) and (d) answers excluded, a simple test can be done to find the right answer, e.g. y = 2 · x will be perpendicular to y = -(1/2) · x. The right answer is (a).  Question #6: Given the table below, which of the following answers describes the relation between x and y?  x y  0 1  2 5  4 17  5 26  (a) y = x + 5  (b) y = x2 + 1  (c) y = 2 · x + 1  (d) y = 3 · x - 1  (e) y = 4 · x + 1  Answer: From the pair x = 0 and y = 1, we realize that only answers (b), (c) and (e) could be correct answers.  Examining the 3 choices, we find that the correct answer is (b)  Question #7: The median m divides the ABC triangle in 2 triangles, ABM and ACM. What is the ratio between the areas of the 2 triangles, AreaABM/AreaACM ?

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