*Difficulty Level – 2: Medium*

*Directions: **Solve each problem and then click on the correct answer. You are permitted to use a calculator on this test.*

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Question 1 |

If

*x*is an even integer and*y*is an odd integer, which of the following must be an odd integer?2 x + 2y | |

2 x − 2y | |

x + y + 1 | |

x + y + 2 | |

x − 2y |

Question 1 Explanation:

The correct answer is (D). To solve this problem, choose an even integer for

*x*and an odd integer for*y*and evaluate each of the answer choices. Set*x*= 0 and*y*= 1 → only*x*+*y*+ 2 will evaluate to an odd integer.Question 2 |

35% of 15% of

*x*is equivalent to which of the following?0.0525 x | |

0.125 x | |

0.25 x | |

0.525 x | |

5.25 x |

Question 2 Explanation:

The correct answer is (A). 35% of 15% of a number is 0.35 * 0.15 of that number:

0.35 * 0.15 = 0.0525

0.35 * 0.15 = 0.0525

*x*Question 3 |

A farmer has a rectangular field that measures 125 feet by 200 feet. He wants to enclose the field with a fence. What is the total length, in feet, he will need for the job?

350 | |

450 | |

550 | |

650 | |

750 |

Question 3 Explanation:

The correct answer is (D). This question is really asking for the perimeter of the field. Add up all of the sides to find the perimeter:

(125 * 2) + (200 * 2) = 650

(125 * 2) + (200 * 2) = 650

Question 4 |

The equation above is equivalent to which of the following?

^{1}⁄_{3} x y^{3} z^{3} | |

^{2}⁄_{3} x^{3} y^{5} z^{5} | |

^{4}⁄_{3} x^{2} y^{2} z^{2} | |

^{3}⁄_{4} x^{4} y^{2} z^{2} | |

^{8}⁄_{3} x^{4} y^{2} z^{3} |

Question 4 Explanation:

The correct answer is (B). Evaluate the expression to find the most simplified form. First evaluate the coefficients:

4 * 2 *

Combine each of these terms to get answer choice (B).

4 * 2 *

^{1}⁄_{3}*^{1}⁄_{4}=^{2}⁄_{3}*x***x*^{2}=*x*^{3}*y***y*^{2}**y*^{2}=*y*^{5}*z***z*^{3}**z*=*z*^{5}Combine each of these terms to get answer choice (B).

Question 5 |

What is the slope intercept form of (13

*x*− 5*x*) + 12 − 2*y*= 6?y = 3x − 9 | |

y = 4x + 3 | |

y = −4x − 3 | |

y = 6x + 2 | |

y = −6x + 5 |

Question 5 Explanation:

The correct answer is (B). Recall that slope-intercept form is

8

2

Divide everything by 2:

*y*=*mx*+*b*where*m*is the slope and*b*is the*y*-intercept. Solve for*y*:8

*x*− 2*y*= −62

*y*= 8*x*+ 6Divide everything by 2:

*y*= 4*x*+ 3Question 6 |

*A*and

*B*are reciprocals (when multiplied together their product is 1). If

*A*< −1, then

*B*must be which of the following?

B > 1 | |

B < 0 | |

0 < B < 1 | |

−1 < B < 0 | |

B < −1 |

Question 6 Explanation:

The correct answer is (D). If the product of two numbers is positive, the two numbers must have the same sign. That is, if

We are told that

So we know that

If we take reciprocals on both sides of the last inequality, we must flip the inequality sign. Hence:

So we know that

*ab*> 0, then either*a*> 0 and*b*> 0, or*a*< 0 and*b*< 0.We are told that

*A*< −1 (which implies that*A*< 0).So we know that

*B*< 0.If we take reciprocals on both sides of the last inequality, we must flip the inequality sign. Hence:

*B*> −1So we know that

*B*< 0, and*B*> −1. We can represent this as a compound inequality: −1 <*B*< 0Question 7 |

Magazine subscriptions cost $9.99 a month per magazine after an initial contract fee of $24.99. Which expression represents the cost of

*m*magazines?$9.99 + $24.99 m | |

$9.99 m + $24.99 | |

$24.99 - $9.99 m | |

$24.99 + m + $9.99 | |

$33.98 m |

Question 7 Explanation:

The correct answer is (B). Consider the given information: the initial contract fee is a one time price that will be added to the number,

*m*, of magazines times the cost per magazine so, 9.99*m*+ 24.99.Question 8 |

If ƒ(

*x*) = −3*x*^{3}+ 4*x*^{2}−*x*+ 2 and*g*(*x*) = 2*x*^{2}−*x*, what is ƒ(*g*(−1))?−46 | |

−22 | |

0 | |

22 | |

46 |

Question 8 Explanation:

The correct answer is (A). This question asks about function composition.

Begin by evaluating

Now evaluate ƒ(3) = −3 * 27 + 36 − 3 + 2 = −46

Begin by evaluating

*g*(−1) = 2 + 1 = 3Now evaluate ƒ(3) = −3 * 27 + 36 − 3 + 2 = −46

Question 9 |

The coordinates (−3, 5) and (3, 5) designate the diameter of a circle, what is its circumference?

π | |

2 π | |

4 π | |

6 π | |

12 π |

Question 9 Explanation:

The correct answer is (D). The circumference of a circle is the distance around defined by

3 − (−3) = 6, so

*π** diameter. The diameter in this case can be found through the difference between the x values:3 − (−3) = 6, so

*π** 6 is the circumference.Question 10 |

Richard wants to try every possible combination of meals available at his favorite restaurant. They offer 4 appetizers, 5 entrees, and 3 desserts. How many total meals will Richard have tried by the time he finishes?

12 | |

15 | |

20 | |

60 | |

120 |

Question 10 Explanation:

The correct answer is (D). To find the total number of combinations, we multiply the total number of options for each meal available:

4 * 5 * 3 = 60

4 * 5 * 3 = 60

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