*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.

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 $0.35 \ast 0.15$ of that number:

$0.35 \ast 0.15 = 0.0525x$

$0.35 \ast 0.15 = 0.0525x$

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:

$(125 *\ast 2) + (200 \ast 2) = 650$

$(125 *\ast 2) + (200 \ast 2) = 650$

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 $(13x − 5x) + 12 − 2y = 6$?

$y = 3x − 9$ | |

$y = 4x + 3$ | |

$y = −4x − 3$ | |

$y = 6x + 2$ | |

$y = −6x + 5$ |

Question 5 Explanation:

The correct answer is (B). Recall that slope-intercept form is $y = mx + b$ where $m$ is the slope and $b$ is the $y$-intercept. Solve for $y$:

$8x − 2y = −6$

$2y = 8x + 6$

Divide everything by 2:

$y = 4x + 3$

$8x − 2y = −6$

$2y = 8x + 6$

Divide everything by 2:

$y = 4x + 3$

Question 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:

9.99$m$ + 24.99

9.99$m$ + 24.99

Question 8 |

### $f(x) = −3x^3 + 4x^2 − x + 2$

### $g(x) = 2x^2 − x$

### What is $f(g(−1))$?

$−46$ | |

$−22$ | |

$0$ | |

$22$ | |

$46$ |

Question 8 Explanation:

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

Begin by evaluating $g(−1) = 2 + 1 = 3$

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

Begin by evaluating $g(−1) = 2 + 1 = 3$

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

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: $π \ast \text{diameter}$.

The diameter in this case can be found through the difference between the $x$ values:

$3 − (−3) = 6$, so $\pi \ast 6$ is the circumference.

The diameter in this case can be found through the difference between the $x$ values:

$3 − (−3) = 6$, so $\pi \ast 6$ 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:

$4 \ast 5 \ast 3 = 60$

$4 \ast 5 \ast 3 = 60$

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