A circle has a radius of 5 inches. What's its approximate area?
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Correct answerA
ExplanationExplanation: The area of a circle is A = πr2. A = π52. π is approximately 3.14, so 3.14 x 25 means A is approximately 78.5 inches.
What's the volume of a box measuring 12- inches long by 8-inches deep by 10-inches high?
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Correct answerA
ExplanationExplanation: Volume equals length times width times height (V = lwh). 12 x 8 x 10 = 960 cubic inches.
A woman has Z dollars to spend. After she spends $500, how much money does she have left?
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Correct answerD
ExplanationExplanation: You need to subtract the money that she spent ($500) from the original money that she had (Z).
In a bag of candy, there are 4 Tootsie Rolls, 3 Lollipops, 5 Hershey Kisses and 6 Starbursts. If you select one piece of candy at random, what is the probability that it will be a lollipop?
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Correct answerC
ExplanationExplanation: There are 18 total pieces of candy and 3 lollipops. Therefore, the probability of picking one lollipop is 3/18 which simplifies to 1/6.
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Correct answerD
ExplanationExplanation: If two powers have the same base, they can be multiplied by keeping the base and adding the exponents together. In this case, x is the same as x1.
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Correct answerC
ExplanationExplanation: x2 - 6x + 9 = (x- 3)(x-3) = (x- 3)2
(x + 3)(x + 5) = __________. 
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Correct answerC
ExplanationExplanation: Use the FOIL method (First, Outside, Inside, Last) to solve. x2 + 3x + 5x + 3 x 5
What is another way to write 2.25 x 1002?
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Correct answerC
ExplanationExplanation: 1002 = (100)(100), or 10,000 (10,000)(2.25) = 22,500
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Correct answerD
ExplanationExplanation: Step 1: Subtract 2 from each side of the equation in order to eliminate -2 from the left side. (You are undoing the addition.) 3x + 2 - 2 = -13 - 2 3x = -15 Step 2: Now divide each side by 3 to find x. (You are undoing the multiplication.) 3x/3 = -15/3 x = -5
Question 10
Single choice
A cube has a volume of 64 cubic feet. The surface area of the cube is __________.
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Correct answerC
ExplanationExplanation: A cube is made up of equal length sides (s). The volume of a cube is s x s x s. Therefore, s = 4 in this case (4 x 4 x 4=64). A cube is made up of 6 squares, each with an area of s x s. Therefore, the surface area of a cube is 6 x s x s = 6 x 4 x 4 = 96
Question 11
Single choice
(3 x 3)(5 - 3)(6 + 2) = x2. What's the value of x?
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Correct answerB
ExplanationExplanation: First solve the left side of the equation: (9)(2)(8) = 144. So x2 = 144. Find the square root of each side: x = 12.
Question 12
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Correct answerD
ExplanationExplanation: 4! (4 factorial) = 4 x 3 x 2 x 1 = 24.
Question 13
Single choice
What is another way to write 43?
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Correct answerD
ExplanationExplanation: 4 x 4 x 4 = 64.
Question 14
Single choice
Which of these is a cylinder?
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Correct answerD
ExplanationExplanation: A cylinder is a solid figure whose upper and lower bases are circles; a can of vegetables is one example of a cylinder. An orange is a sphere; a stick of butter is a rectangular solid; and a hula hoop is (for all practical purposes) a two-dimensional figure, a circle.
Question 15
Single choice
If x = 4, then x4 ÷ x = __________.
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Correct answerC
ExplanationExplanation: Substitute 4 for all x's in the problem. 44 ÷ 4 = (4 x 4 x 4 x 4) ÷ 4 = 256 ÷ 4 = 64.
Question 16
Single choice
A floor is made up of hexagonal tiles, some of which are black and some of which are white. Every black tile is completely surrounded by white tiles. How many white tiles are there around each black tile?
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Correct answerC
ExplanationExplanation: A hexagon has six sides. Each of the six sides of the black tile must touch a side of a white tile, so there are six white tiles surrounding black tiles. 
Question 17
Single choice
The base of a cylindrical can is a circle whose diameter is 2 inches. Its height is 7 inches. How many cubic inches are there in the volume of the can? Use 22/7 for the value of π.
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Correct answerB
ExplanationExplanation: The volume of a cylinder is equal to the product of its height and the area of its base. The base is a circle. The area of a circle is πr2, where π = 22/7 and r is the radius. Since the diameter is 2 inches, the radius (which is one-half the diameter) is 1 inch. Area of circular base = 22/7 x 1/1 x 1/1 = 22/7 The height is 7 inches. 22/7 x 7/1 = 22 cubic inches
Question 18
Single choice
A circle measures 12 feet in diameter. What's its area to the nearest foot?
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Correct answerC
ExplanationExplanation: The area of a circle equals π times the radius squared. The radius is 1⁄2 the diameter. A = πr2. A = π62= π36. If π is approximately 3.14, the area of the circle is approximately 3.14 x 36 or 113 feet.
Question 19
Single choice
√-9 is an example of a(an) __________.
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Correct answerB
ExplanationExplanation: The square root of a negative number doesn't exist as far as real numbers are concerned. In mathematics, this is called an imaginary number.
Question 20
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Question 21
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If x = 12, what is the value of p in this equation? p = x2/6 - 4
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Question 22
Single choice
A cube has a volume of 512 cubic inches. What is the length of one side of the cube?
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Question 23
Single choice
If a circle has a radius of 12 feet, what's its circumference most nearly?
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Correct answerC
ExplanationExplanation: Circumference equals π x diameter, and diameter is equal to two times the radius. Or C = π x d, and d = 2r. C = π x 24. If you round π to 3.14, the answer is about 75.36 or about 75 feet.
Question 24
Single choice
Solve for x: 2x - 6 = x + 5
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Correct answerB
ExplanationExplanation: Isolate x on one side of the equation: 2x - 6 = x + 5 2x - 6 -x = x + 5 - x x - 6 = 5 x - 6 + 6 = 5 + 6 x = 11 Check by substituting 11 for x in the original equation.
Question 25
Single choice
 What is the circumference of a circle with center at point A if the distance from point X to Y is 42?
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Question 26
Single choice
 Angle AB (shown above) is a(n) __________.
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Correct answerD
ExplanationExplanation: Angles measuring more than 90 degrees are obtuse angles.
Question 27
Single choice
If 5y2 = 80, y is __________.
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either a positive or negative number
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Correct answerC
ExplanationExplanation: The square root of a squared positive number can either be positive or negative.
Question 28
Single choice
How much water must be added to 1 liter of a 5% saline solution to get a 2% saline solution?
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Correct answerB
ExplanationExplanation: Use the equation (0.05) (1) = (0.02) x: the left side represents 5% of 1 liter; the right side represents 2% of some amount of water. From the equation, x = 2.5. Subtracting the 1 liter of water already present in the 5% solution, you will find that 1.5 liters need to be added.
Question 29
Single choice
What is the prime factorization of 100?
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Correct answerB
ExplanationExplanation: 100 = 4 x 25 = (2 x 2) x (5 x 5) = 22 x 52.
Question 30
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Question 31
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(675 x 3)/5 = __________.
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Question 32
Single choice
Solve for x: x2 - 2x - 15 = 0
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Correct answerC
ExplanationExplanation: This is a quadratic equation that can be solved by factoring and setting each factor equal to zero. x2 - 2x - 15 = 0 (x - 5)(x + 3) = 0 x - 5 = 0x + 3 = 0 x = 5x = -3
Question 33
Single choice
If (5 + 1)(6 ÷ 3)(8 - 5) = (3 + 3)x, then x = __________.
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Correct answerD
ExplanationExplanation: Solve the first half of the equation. (6) (2) (3) = 36. Therefore, 36 = (3 + 3)x, which turns into 36 = 6x. Isolate x. 36 ÷ 6 = 6x ÷ 6 6 = x To check your answer, substitute 6 for x.
Question 34
Single choice
If 2 + x ≥ 4, what is the value of x?
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Correct answerB
ExplanationExplanation: 2. Or, x ≥ 2. To check your answer, substitute 2 for x. 2 + 2 ≥ 4. True, so the answer is correct.
Question 35
Single choice
The average of 80, 46, 32, and 22 is __________.
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Question 36
Single choice
If 0.05 ÷ x = 1, then x = __________.
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Correct answerA
ExplanationExplanation: Multiply both sides of the equation by 0.05 to isolate x: 0.05 ÷ x x 0.05 = 1 x 0.05 or x = 0.05. Check by substituting 0.05 for x in the original equation.
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