SAT 数学经典训练题二  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 ? 