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SAT Problem Solving #1
Question #1: If a > 0,b > 0, a · b = 18 and a / b = 2 then:
a = 18 and b = 1
a = 6 and b = 6
a = 6 and b = 3
a = 18 and b = 9
a = 9 and b = 2
Question #2: The ratio of the radii of two circles is r
_{1}
/r
_{2}
= 6. What is the ratio of the perimeters P
_{1}
/P
_{2}
and the ratio of the areas of the two circles A
_{1}
/A
_{2}
?
perimeter ratio = 1/6, area ratio = 36
perimeter ratio = 36, area ratio = 6
perimeter ratio = 6, area ratio = 36
perimeter ratio = 1/8, area ratio = 8
perimeter ratio = 1/6, area ratio = 6
Question #3: For any x such that 0 < x < π/2, the expression (1 - sin
^{2}
x)/cos(x) + (1 - cos
^{2}
x)/sin(x) is equivalent to:
tan(x) + 1
sin(x)
sin(x) + cos(x)
1 - sin(x)
cos(x)
Question #4: A lottery sells 1000 tickets and there is only one winning number. 200 New Jersey residents buy 2 tickets each, 300 New York residents buy 1 ticket each and the rest are sold in Connecticut. What is the probability that the wining ticket was bought in New Jersey?
3/5
1/2
2/5
1/5
4/5
Question #5: Celsius degrees can be transformed in Fahrenheit degrees by using the formula : °C=(5/9)· (°F-32). What is
x
, if
x
degrees Celsius is equal to
x
degrees Fahrenheit?
40
-40
-20
20
-30
Question #6: In the (x,y) plane, what is the equation of the line that passes through the points (0,5) and (4,0)?
y = (5/4) · x + 4
y = (4/5) · x - 4
y = (4/5) · x + 4
y = -(5/4) · x + 5
y = (5/4) · x + 5
Question #7: A square with the side equal to √2 is inscribed in a circle. What is the area outside the square that is inside the circle?
¶ + 1
¶ - 1
¶ - 2
¶
¶ + 2
Question #8: What is the value of (x + 2y)
^{2}
if x
^{2}
+ 4 · y
^{2}
= 2 and x · y = 3
13
14
16
18
22
Question #9: What is the value of the median of an equilateral triangle with all sides equal to 5?
(5/2) · √3
5 · √3
(5/2) · 3
^{-3}
5
5/2
Question #10: The median and the average of the numbers -12, 4, -8, 10, 2, 2, 0, -4 and 2 are:
median = 0, average = -4/9
median = 0, average = 4/9
median = 2, average = -4/9
median = 2, average = 4/9
median = 2, average = 2/9