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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)?
x = 1
x
_{1}
= 1, x
_{2}
= -1
x
_{1}
= 1, x
_{2}
= 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 2
^{x}
< 100, and at the same time the number 2
^{x}
+ 2 is an integer divisible by both 3 and 2?
1
2
3
4
5
Question #7: sin(x)cos(x)(1 + tan
^{2}
(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