**Difficulty Level – 3: Medium / Difficult**

*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 |

A number,

*x*, is decreased by 40% then increased by 25%. What is the final result in terms of*x*?0.55 x | |

0.575 x | |

0.65 x | |

0.7 x | |

0.75 x |

Question 1 Explanation:

The correct answer is (E). To solve this, set

100 − 0.4 * 100 = 60

60 + 0.25 * 60 = 75

Because

*x*= 100 and perform the operations. One hundred is a great number to choose here because 1% of 100 is 1.100 − 0.4 * 100 = 60

60 + 0.25 * 60 = 75

Because

*x*= 100 was our initial value, we want to choose the answer choice that gives us 75 when we substitute 100 for*x*, 0.75 * 100 = 75, so answer choice (E) is correct.Question 2 |

Question 2 Explanation:

The correct answer is (A). Evaluate the expression.

The second expression evaluates to 4 *

^{1}⁄_{3}to the 4th power is^{1}⁄_{81}and*y*^{1⁄3}raised to the 4th power is^{4}⁄_{3}so the first expression is*y*^{4⁄3}divided by 81.The second expression evaluates to 4 *

*x*^{4}**y*^{2}. Our coefficient becomes^{4}⁄_{81}and our*x*is to the 4th power and when multiplying*y*^{4⁄3}and*y*^{2}, we add the exponents to get*y*^{10⁄3}.Question 3 |

The expression (

*x*+*y*) [*z*− (*x*−*y*)] is equivalent to which of the following?xz − x^{2} + 2xy + y^{2} | |

2 xz + x^{2} − yz + y^{2} | |

xz − x^{2} + yz + y^{2} | |

xz + x^{2} − yz − y^{2} | |

xyz + y^{2} − xy + yz + y^{2} |

Question 3 Explanation:

The correct answer is (C). Recall order of operations and the distributive property to answer this question. The second bracket simplifies to

*z*−*x*+*y*and to this we multiply (*x*+*y*). Begin by distributing the*x*through (*z*−*x*+*y*) and to this add the distribution of*y*through (*z*−*x*+*y*) to get answer choice (C).Question 4 |

There are 32 marbles in a jar: 14 blue, 10 red, 5 green, and 3 yellow. Sally pulls one marble, randomly, from the jar. Without replacing the marble, she pulls another marble. What is the probability that both marbles will be red?

^{40}⁄_{426} | |

^{41}⁄_{456} | |

^{43}⁄_{476} | |

^{44}⁄_{476} | |

^{45}⁄_{496} |

Question 4 Explanation:

The correct answer is (E). The probability of selecting a red marble on the first draw is

^{10}⁄_{32}because there are 10 red marbles and 32 total marbles. After removing the first red marble there are now 9 red marbles and 31 total marbles left so^{9}⁄_{31}chance of selecting the second red marble. To find the probability of both events occurring, we multiply the probabilities to get^{9 * 10}⁄_{32 * 31}which reduces to^{45}⁄_{496}.Question 5 |

If

*x*+*y*= 7 and*x*−*y*= 3, what is*x*^{2}−*y*^{2}= ?4 | |

21 | |

25 | |

36 | |

40 |

Question 5 Explanation:

The correct answer is (B). We can either use the system of equations to solve for

*x*and*y*individually to find that*x*= 5 and*y*= 2 which gives 25 − 4 = 21, or we can see that if we multiply (*x*+*y*) and (*x*−*y*) we will be left with*x*^{2}−*y*^{2}, 7 * 3 = 21.Question 6 |

The circumference of a large wedding cake is 60 inches. If the cake is divided evenly into 12 slices, what is the length of the arc, in inches, made by 5 combined slices?

12 | |

13 | |

15 | |

20 | |

25 |

Question 6 Explanation:

The correct answer (E). Recall that the circumference is the distance around a circle. If the cake is divided into 12 equal slices, each arc length will be 5. Summing 5 of these slices will give 25.

Question 7 |

A rectangle measures 65 inches by 77 inches. What is the length of the diagonal of the rectangle (rounded to the nearest hundredth)?

100.77 | |

110.77 | |

125.07 | |

134.67 | |

137.77 |

Question 7 Explanation:

The correct answer is (A). Use the Pythagorean Theorem to solve this problem. Recall that the sum of the side lengths squared equals the hypotenuse squared, so 65

^{2}+ 77^{2}= diagonal^{2}. Take the square root of both sides to find the length and round to the nearest hundredth.Question 8 |

If ƒ(

*x*) =*x*^{2}+ 2*x*+ 2, what is ƒ(*x*+*h*)?2 x^{2} + 4hx + h^{2} − 2x − 2h | |

x + h^{2} + 2xh + 2 + h | |

x^{2} + 2x + 2xh + 2h + h^{2} + 2 | |

x^{2} + 4xh + 4h^{2} + 2x | |

2 x^{2} + 2xh + 2h^{2} + 2x + 2 |

Question 8 Explanation:

The correct answer is (C). To solve this problem we will substitute (

ƒ(

Evaluate the expression using the distributive property to arrive at:

*x*+*h*) for every*x*in our function ƒ(*x*):ƒ(

*x*+*h*) = (*x*+*h*)^{2}+ 2(*x*+*h*) + 2.Evaluate the expression using the distributive property to arrive at:

*x*^{2}+ 2*x*+ 2*xh*+ 2*h*+*h*^{2}+ 2.Question 9 |

In the figure above, lines

*d*and*f*are parallel and the angle measures are as given. What is the value of*x*?35 | |

60 | |

85 | |

100 | |

120 |

Question 9 Explanation:

The correct answer is (C). Since vertical angles are congruent, the angle vertical to the 35-degree angle also has a measure of 35 degrees. The supplement of the 120-degree angle has a measure of 60 degrees, so we then have a triangle with angles measuring 35, 60, and

35 + 60 +

*x*degrees, as shown in the figure provided. Since the angles of a triangle add to 180 degrees:35 + 60 +

*x*= 180*x*= 180 − 35 − 60*x*= 85 degreesQuestion 10 |

Which of the following represents the equation of the line that passes through the point (2, 3) with a slope of −⅓?

y = 2x + 4 | |

y = 4x + 2 | |

y = −⅓x + ^{11}⁄_{3} | |

y = −3x + ^{11}⁄_{3} | |

y = −^{2}⁄_{3}x + ^{11}⁄_{3} |

Question 10 Explanation:

The correct answer is (C). Recall that when provided with a point and the slope of a line, we can use point-slope formula to write an equation for the line. The point slope formula is

*y*−*y*1 =*m*(*x*−*x*1) where (*x*1,*y*1) is the point provided and m is the slope. Plug in the point and slope provided and solve for*y*:*y*− 3 = −⅓ (*x*− 2)*y*= −⅓*x*+^{11}⁄_{3}
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