*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?

$2x + 2y$ | |

$2x − 2y$ | |

$x + y + 1$ | |

$x + y + 2$ | |

$x − 2y$ |

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?

$0.0525x$ | |

$0.125x$ | |

$0.25x$ | |

$0.525x$ | |

$5.25x$ |

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 |

$4xyz*2x^2y^2*\dfrac{1}{3}z^3*\dfrac{1}{4}y^2*z$

### The equation above is equivalent to which of the following?

$\dfrac{1}{3} x y^3 z^3$ | |

$\dfrac{2}{3} x^3 y^5 z^5$ | |

$\dfrac{4}{3} x^2 y^2 z^2$ | |

$\dfrac{3}{4} x^4 y^2 z^2$ | |

$\dfrac{8}{3} x^4 y^2 z^3$ |

Question 4 Explanation:

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

$4 * 2 * \frac{1}{3} * \frac{1}{4}= \frac{2}{3}$

$x*x^2=X^3$

$y * y^2 * y^2 = y^5$

$z * z^3 * z = z^5$

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

$4 * 2 * \frac{1}{3} * \frac{1}{4}= \frac{2}{3}$

$x*x^2=X^3$

$y * y^2 * y^2 = y^5$

$z * z^3 * z = z^5$

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?

$B \gt 1$ | |

$B \lt 0$ | |

$0 \lt B \lt 1$ | |

$−1\lt B \lt0$ | |

$B \lt −1$ |

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 $ab \gt 0$, then either $a \gt 0$ and $b \gt 0$, or $a \lt 0$ and $b \lt 0$.

We are told that $A \lt −1$ (which implies that $A \lt 0$).

So we know that $B \lt 0$.

We also know that $AB=1$, so $A=\dfrac{1}{B}$

Since $A=\dfrac{1}{B}$, and $A \lt -1$, we can infer that $\dfrac{1}{B} \lt -1$

If we take reciprocals on both sides of the last inequality, we must flip the inequality sign. Hence: $B \gt −1$

So we know that $B \lt 0$, and $B \gt −1$. We can represent this as a compound inequality: $−1 \lt B \lt 0$

We are told that $A \lt −1$ (which implies that $A \lt 0$).

So we know that $B \lt 0$.

We also know that $AB=1$, so $A=\dfrac{1}{B}$

Since $A=\dfrac{1}{B}$, and $A \lt -1$, we can infer that $\dfrac{1}{B} \lt -1$

If we take reciprocals on both sides of the last inequality, we must flip the inequality sign. Hence: $B \gt −1$

So we know that $B \lt 0$, and $B \gt −1$. We can represent this as a compound inequality: $−1 \lt B \lt 0$

Question 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?

$\$9.99 + \$24.99m$ | |

$\$9.99m + \$24.99$ | |

$\$24.99 - \$9.99m$ | |

$\$24.99 + m + \$9.99$ | |

$\$33.98m$ |

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?

$π$ | |

$2π$ | |

$4π$ | |

$6π$ | |

$12π$ |

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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