*Directions:** **Solve each problem. Do not use a calculator.*

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Question 1 |

- Marissa has built a new pool to replace her old one. The old pool is 5 feet long, 4 feet wide, and 2 feet high. It is currently half full. The new pool measures 5ft x 5ft x 4ft. If Marissa pours all of the water currently in the old pool into the new one, what fraction of the new pool will be filled?

1/8 | |

1/6 | |

1/5 | |

1/4 | |

1/3 |

Question 1 Explanation:

The correct answer is (C).

Volume of a rectangular solid = length x width x height.

Using this formula, the volume of the old pool is 5 x 4 x 2 = 40 ft

The pool is half full which mean it currently holds 40/2 = 20 ft3 of water.

The volume of the second pool is 5 x 5 x 4 = 100 ft

To find the fraction of the water to the total volume, divide the amount of water added to the pool by its total capacity. 20/100 = 1/5.

Volume of a rectangular solid = length x width x height.

Using this formula, the volume of the old pool is 5 x 4 x 2 = 40 ft

^{3}.The pool is half full which mean it currently holds 40/2 = 20 ft3 of water.

The volume of the second pool is 5 x 5 x 4 = 100 ft

^{3}.To find the fraction of the water to the total volume, divide the amount of water added to the pool by its total capacity. 20/100 = 1/5.

Question 2 |

- In the figure provided,
*a=b*. Which of the following must also be true?

a = y | |

z = a | |

x = y | |

x = y + z | |

y = z |

Question 2 Explanation:

The correct answer is (E). Angles a and y form a straight line and are therefore supplementary. Supplementary angles together equal 180 degrees.

Therefore y = 180 - a.

Angles b and z form a straight line and are, therefore, also supplementary. Supplementary angles = 180 degrees.

Therefore z = 180 - b.

Since a = b, 180 - a = 180 - b.

Therefore, y must equal z.

Therefore y = 180 - a.

Angles b and z form a straight line and are, therefore, also supplementary. Supplementary angles = 180 degrees.

Therefore z = 180 - b.

Since a = b, 180 - a = 180 - b.

Therefore, y must equal z.

Question 3 |

- If
*x*is the set of prime numbers and*y*is the set of all two-digit even integers, how many numbers are common to both sets?

0 | |

1 | |

2 | |

3 | |

4 |

Question 3 Explanation:

The correct answer is (A). All even integers are divisible by the number 2. The only even prime number is 2, which is not two-digits. Therefore, no number in set y would be prime, because there are no two-digit even prime numbers.

Question 4 |

- The table provided shows the number of ice cream possibilities at a certain ice cream store. All ice cream sold has exactly one flavor and one treat. If a chocolate ice cream is picked at random, what is the probability that it will have blue swirls?

1/3 | |

1/4 | |

5/12 | |

5/14 | |

4/9 |

Question 4 Explanation:

The correct answer is (A). According to the table, there are 3 chocolate ice creams without nuts, 5 with nuts, and 4 with blue swirls. So there are a total of 3+5+4 = 12 chocolate ice creams. Since 4 of these chocolate ice creams have the successful outcome (blue swirls) the probability of randomly choosing this will be 4/12 = 1/3.

Question 5 |

- What is the value of
*b*in the figure provided?

20 | |

35 | |

40 | |

55 | |

60 |

Question 5 Explanation:

The correct answer is (D). The angle measuring 40, the angle measuring 120, and the angle between them all form a straight line. They are therefore supplementary angles whose sum = 180.

Find the missing angle: 180-120-40=20. That angle with the 40-degree angle next to it make up an angle of the large triangle. This angle measures 40+20 = 60. The sum of the interior angles of a triangle is 180. Solve for b. 180-65-60 = 55.

Find the missing angle: 180-120-40=20. That angle with the 40-degree angle next to it make up an angle of the large triangle. This angle measures 40+20 = 60. The sum of the interior angles of a triangle is 180. Solve for b. 180-65-60 = 55.

Question 6 |

- Charlie lives halfway between Chicago and Hoopertown. Amanda lives halfway between Charlie and Chicago. Raymond lives between Charlie and Hoopertown. All three houses lie on a straight line from Chicago to Hoopertown. If Raymond lives 15 miles from Amanda and 23 miles from Chicago, how far does he live from Hoopertown?

5 Miles | |

7 Miles | |

9 Miles | |

12 Miles | |

35 Miles |

Question 6 Explanation:

The correct answer is (C). The given information tells us that Raymond lives 15 miles from Amanda and 23 miles from Chicago. Subtract these quantities to find the distance from Amanda’s house to Chicago: 23-15=8 miles. Amanda lives halfway between Charlie and Chicago, so the distance between her house and Charlie’s is 8 miles. The distance from Charlie’s house to Chicago is 8+8=16 miles. If Charlie lives 16 miles from Chicago and Raymond lives 23 miles from Chicago, then the distance between their houses must be 23-16=7. Since Charlie’s house is equidistant between Chicago and Hoopertown, the distance from Charlie’s to Hoopertown must also be 16 miles. Raymond lives 7 miles from Charlie so the distance from Raymond’s house to Hoopertown is 16-7=9 miles.

Question 7 |

- What is the slope of line
*c*?

-7/5 | |

-5/7 | |

5/7 | |

10/7 | |

7/5 |

Question 7 Explanation:

The correct answer is (B). Slope of a line is found by the following formula:

rise/run = (y2-y1)/(x2-x1).

The line in the figure passes through points (0,5) and (7,0).

Therefore x1= 0, x2=7, y1=5, and y2=0.

Plugging these values into the given formula yields (0-5)/(7-0) = -5/7.

rise/run = (y2-y1)/(x2-x1).

The line in the figure passes through points (0,5) and (7,0).

Therefore x1= 0, x2=7, y1=5, and y2=0.

Plugging these values into the given formula yields (0-5)/(7-0) = -5/7.

Question 8 |

- Which of the following equations represents
*y*in terms of*x*for all ordered pairs listed?

y = 4x/3 | |

y = 2x -2 | |

y = x + 5 | |

y = 3x ^{2} | |

y = 2x + 3 |

Question 8 Explanation:

The correct answer is (E). Plug values of x into each answer choice to see which equation yields the corresponding y values for all ordered pairs in the table. Only (E) y=2x+3 works for all ordered pairs:

y=2(2)+3 = 4+3 = 7

y=2(3)+3 = 6+3 = 9

y=2(4)+3 = 8+3 = 11.

y=2(2)+3 = 4+3 = 7

y=2(3)+3 = 6+3 = 9

y=2(4)+3 = 8+3 = 11.

Question 9 |

- If
*x*is a negative integer and*y*is a positive integer, which of the following expressions must be positive?

xy | |

y - x | |

y/x | |

x/y | |

x - y |

Question 9 Explanation:

The correct answer is (B). Properties of integers tell us that subtracting a negative integer is the same as adding its opposite. Since x is a negative number, its opposite is a positive number. y is also positive. Adding two positive numbers yields a positive result.

Alternate Solution: Plug values for x and y into each answer choice. See which expression yields a positive value.

Example: y = 4, x = -2

y-x = 4 - (-2)

= 4+2 = 6.

y-x produces a positive value.

Alternate Solution: Plug values for x and y into each answer choice. See which expression yields a positive value.

Example: y = 4, x = -2

y-x = 4 - (-2)

= 4+2 = 6.

y-x produces a positive value.

Question 10 |

- The wheel provided has 8 spokes. If
*e*= 50,*f*= 25 and*c*= 75, what is the valued of*h*?

25 | |

30 | |

35 | |

40 | |

45 |

Question 10 Explanation:

The correct answer is (B). Vertical angles have the same measure so:

a = e, b = f, c = g, and d = h.

The given information states that e = 50, f = 25 and c = 75. Therefore, we have the measures of angles a, b, and g. The only angles missing are d and h. We know they are equal, so we may use the same variable x to represent their angle measure.

There are 360 degrees in a circle. So the sum of all 8 angles will equal 360. Substituting known values gives us:

2(50) + 2(25) + 2(75) + 2x = 360.

Simplify to 100 + 50 + 150 + 2x = 360.

300 + 2x = 360.

Subtracting 300 from both sides yields 2x = 60.

Dividing both sides by 2 gives the value of x = 30. So both h and d = 30.

a = e, b = f, c = g, and d = h.

The given information states that e = 50, f = 25 and c = 75. Therefore, we have the measures of angles a, b, and g. The only angles missing are d and h. We know they are equal, so we may use the same variable x to represent their angle measure.

There are 360 degrees in a circle. So the sum of all 8 angles will equal 360. Substituting known values gives us:

2(50) + 2(25) + 2(75) + 2x = 360.

Simplify to 100 + 50 + 150 + 2x = 360.

300 + 2x = 360.

Subtracting 300 from both sides yields 2x = 60.

Dividing both sides by 2 gives the value of x = 30. So both h and d = 30.

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