SAT数学Problem Solving练习题(2)-智课教育出国考试.pdf

智 课 网 S A T 备 考 资 料 SAT数学Problem Solving练习题 2 智课教育出国考试 SAT数学Problem Solving练习题 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 xy 01 25 417 526 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 a 1 b 1 2 c 2 d It cannot be determined from the information given e 3 Answer The areas of the 2 triangles will be equal because they are both 1 2 h BC 2 where h is the altitude The correct answer is a Question 8 Out of 25 mining companies 14 extract copper 16 extract silver and 1 extracts neither copper nor silver How many companies extract both silver and copper a 1 b 6 c 2 d 15 e 3 Answer If x is the number of companies that extract both metals 1 the number of companies that extract copper only is 14 x 2 the number of companies that extract silver only is 16 x There are 4 types of companies that extract copper only silver only both copper and silver neither copper nor silver Their total should be 25 25 14 x 16 x x 1 x 31 25 6 Question 9 The isosceles triangle ABC from the figure below has the BAC angle 400 What is the angle ADE if DE is half of BC a 70o b 35o c 40o d It cannot be determined from the information given e 75o Answer There is an infinite number of segments DE that will have half the length of BC Fig 1 and Fig 2 show 2 possibilities The correct answer is d Question 10 For any a 1 a4 1 a 1 a a3 a2 a b a