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Standardized Tests Math and Science Practice

SAT II Problem Solving #1

Question #1: If f(x) = x and g(x) = √x, x≥ 0, what are the solutions of f(x) = g(x)?

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.

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.

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?

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?

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?

Question #7: sin(x)cos(x)(1 + tan2(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:

Question #9: The average of the integers 24, 6, 12, x and y is 11. What is the value of the sum x + y?

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