SATII数学Level1Level2练习题.docVIP

SATII数学Level1Level2练习题 SAT2 数学 Level 1 习题 1 Question #1: If f(x) = x and g(x) = √x, x≥ 0, what are the solutions of f(x) = g(x)? x=1 x1 = 1, x2 = -1 x1 = 1, x2 = 0 x=0 x = -1 Question #2: What is the length of the arc AB in the figure below, if O is the center of the circle and triangle OAB is equilateral? The radius of the circle is 9. ? 2 ·? 3 ·? 4 ·? ?/ 2 Question #3: What is the probability that someone that throws 2 dice gets a 5 and a 6? Each dice has sides numbered from 1 to 6. 1/2 1/6 1/12 1/18 1/36 Question #4: A cyclist bikes from town A to town B and back to town A in 3 hours. He bikes from A to B at a speed of 15 miles/hour while his return speed is 10 miles/hour. What is the distance between the 2 towns? 11 miles 18 miles 15 miles 12 miles 10 miles Question #5: The volume of a cube-shaped glass C1 of edge a is equal to half the volume of a cylinder-shaped glass C2. The radius of C2 is equal to the edge of C1. What is the height of C2? 2·a / ? a/? a / (2·?) a/? a+? Question #6: How many integers x are there such that 2x 100, and at the same time the number 2x + 2 is an integer divisible by both 3 and 2? 1 2 3 4 5 Question #7: sin(x)cos(x)(1 + tan2(x)) = tan(x) + 1 cos(x) sin(x) tan(x) sin(x) + cos(x) Question #8: If 5xy = 210, and x and y are positive integers, each of the following could be the value of x + y except: 13 17 23 15 43 Question #9: The average of the integers 24, 6, 12, x and y is 11. What is the value of the sum x + y? 11 17 13 15 9 Question #10: The inequality |2x - 1| 5 must be true in which one of the following cases? I. x -5 II. x 7 III. x 0 II only I, II and II I and II only I and III only I only ?  Question #1: If f(x) = x and g(x) = √x, x≥ 0, what are the solutions of f(x) = g(x)? (a) x1 = 1, x2 = -1 (b) x1 = 1, x2 = 0 (c) x = 1 (d) x = 0 (e) x = -1 o  Answer: x = √x, if we square the left and right terms of the equ