Question #1: A rectangle is four times as long as it is wide. If the total area of the rectangle is 16 square inches, what is the length of the rectangle?
(a) 2 inches
(b) 4 inches
(c) 6 inches
(d) 8 inches
(e) 16 inches
Solution: If x is the width of the rectangle, the length is 4x.
The area of the rectangle is x4x = 4x2.
4x2 = 16 and x = 2 inches.
The length of the rectangle is 4x = 8 inches.
Question #2: What is f(f(2)) if f(x) = x2 + 2?
(a) 12
(b) 26
(c) 38
(d) 42
(e) 48
Answer:
f(2) = 22 + 2 = 6.
f(f(2)) = f(6) = 62 + 2 = 38.
Question #3:
Which of the following is a factored form of the expression 6x2 + x - 2?
(a) (3x + 2)(2x - 1)
(b) (2x + 2)(3x - 1)
(c) (3x + 2)(2x + 1)
(d) (3x - 2)(2x - 1)
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(e) (2x + 2)(3x - 2) Answer: 6x2 + x - 2 = 6x2 + 4x - 3x - 2 = 2x(3x + 2) - (3x + 2) = (3x + 2)(2x - 1).
Question #4: In the figure below, quadrilateral ABCD has AB parallel with CD. What is the area of triangle ABD?
(a) 3
(b) 4
(c) 6
(d) 8
(e) 9
凤山温泉度假村温泉票 The area of triangle ABD is equal to (1/2)ABDE, where DE is the altitude from D to AB.
AreaABD = (1/2)43 = 6.
Question #5: The radius of circle O is half the length of a side of square S.
Column AColumn B
Area of circle OArea of square S
(a) The quantity in Column A is greater then the quantity in Column B.
(b) The quantity in Column B is greater then the quantity in Column A.
(c) The two quantities are equal.
(d) The relationship cannot be determined from the information given.
Answer: The radius of circle is half the length of a side of the square, r = l/2.
The area of the circle will be r2
The area of the square will be l2 = (2r)2 = 4r2
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4 because = aprox. 3.14, so the quantity in Column B is greater then the quantity in Column A. Another simple way to solve this problem is to realize that a circle with the radius equal t
o half the length of a square could be inscribed in the square.
Question #6: If x2 - nx - 32 = 0 when x = 4, what is the value of n?
(a) -4
(b) 4
(c) 6
(d) -2
(e) 10
Answer: We substitute x = 4 in x2 - nx - 32 = 0.
42 - n4 - 32 = 0.
16 - 4n - 32 = 0.
n = -4.
Question #7: If f(x) = |x| and g(x) = x2, how many solutions has f(x) = g(x)?
(a) 1
(b) 2
(c) 3
(d) 4
(e) 5
Answer: The simplest way to solve this problem is to draw the 2 functions in the x, y plane.
We find that the 2 functions intersect each other in 3 locations, at
x = -1, 0 and 1.
Question #8: Given the list of integers: -2, 2, 0, 6, 8, 0, -5, 9, 10, 4, which of the followin
g statements is true?
(a) mode median average
(b) median mode average
(c) median average mode
(d) mode = median average
(e) average median mode
Answer: We need to rearrange the list of integers in ascending order: -5, -2, 0, 0, 2, 4, 6, 8, 9, 10. The average will be the sum of all integers divided by the number of integers, 32/10 = 3.2.
The median will be the mean of the two middle numbers, 2 and 4, so the median is 3.
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The mode is 0, as 0 occurs the most in the list.
The correct answer is mode median average.
Question #9: A vehicle runs from town A to town B at a speed of 20 miles/hour while another vehicle runs from town B to town A at a speed of 60 miles/hour. Both vehicles start their trips at the same time and the distance between towns is 100 miles. How long does it take from the time they start running to the moment they are at the same point on the road?
