Question #6: In the (x,y) plane, what is the equation of the line that passes through the points (0,5) and (4,0)?

(a) y = (5/4) • x + 4
(b) y = (4/5) • x - 4
(c) y = (4/5) • x + 4
(d) y = -(5/4) • x + 5
(e) y = (5/4) • x + 5

Answer: The equation of a line is y = m • x + n
First point, x = 0, y = 5, results in 5 = n

Second point: x = 4, y = 0, means 0 = m • 4 + n, or m = -n/4 or m= -5/4.
In conclusion, y = -(5/4) • x + 5 is the correct answer.
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Question #7: A square with the side equal to square root of 2 is inscribed in a circle. What is the area outside the square that is inside the circle?

(a) ¶ + 1
(b) ¶ - 1
(c) ¶ - 2
(d) ¶
(e) ¶ + 2


Answer: The diagonal of the square is √2 • √2 = (√ 2)2 = 2. This is also the diameter of the circle.
The area outside the square and inside the circle is:
Areacircle - Areasquare = ¶ • 22/4 - 2 = ¶ - 2
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Question #8: What is the value of (x + 2y) 2 if x 2 + 4 • y 2 = 2 and x • y = 3

(a) 13
(b) 14
(c) 16
(d) 18
(e) 22


Answer: (x + 2y) 2 = x 2 + 4 • y 2 + 4 • x • y = 2 + 12 = 14
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Question #9: What is the value of the median of an equilateral triangle with all sides equal to 5?

(a) (5/2) • √3
(b) 5 • √3
(c) (5/2) • 3-3
(d) 5/2
(e) 5

Answer: The median divides the equilateral triangle in two right triangles. Conform to the Pythagorean theorem, wherein the sum of the squares of the two legs is equal to the square of the hypotenuse,
m2 + (5/2)2= 52
m2 = 52 - (5/2)2 = 52 - 52/4 = (3/4) • 52
m = (5/2) • √3.
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Question #10: A parameter is measured during a scientific experiment and the results are -12, 4, -8, 10, 2, 2, 0, -4 and 2. The median and the average of these numbers are:
(a) median = 0, average = -4/9
(b) median = 0, average = 4/9
(c) median = 2, average = -4/9
(d) median = 2, average = 4/9
(e) median = 2, average = 2/9

Answer: You must arrange the numbers in order: -12, -8, -4, 0, 2, 2, 2, 4, and 10.
The median will be number in the middle of the row, that is 2.
The average will be (-12-8-4+0+2+2+2+4+10)/9 = -4/9.