MATH #25

If f(x) = 4x³ - 4x² + 10, then what is f(-2) [f of negative 2]?

ANSWER: -38

If -4x - 9y - 3z = -10 and -5a - 9b = -6, then what is -9b - 15z - 45y - 20x - 5a?

ANSWER: -56

What is the surface area of a cube with volume 8?

ANSWER: 24

The perimeters of two similar figures have a ratio of 5:7. What is the ratio of their areas?

ANSWER: 25:49 (ACCEPT: 25/49)

If ln(x³)=6 [natural log of the quantity x cubed equals 6], what is ln(x²) [the natural log of the quantity x squared]?

ANSWER: 4

The variables x and y vary directly. Which of the following equations could represent the relationship between x and y? W) (1/5)x = 1/y [one fifth x equals 1 over y] X) x/y = 1/5 [x over y equals one fifth] Y) xy = 1/5 [x y equals one fifth] Z) xy = 5

ANSWER: X) x/y = 1/5

Which of the following inequalities has NO solutions? W) 7x + 4 > 3 X) |x - 1| > -10 [the absolute value of the quantity x minus 1 is greater than negative 10] Y) |x + 3| < -2 [the absolute value of the quantity x plus 3 is less than negative 2] Z) -100x + 5 ≥ 8

ANSWER: Y) |x + 3| < -2

The lines y = (a - 5)x + 5 [ y equals open parentheses a minus 5 close parentheses x plus 5] and y = -2x + 7 are perpendicular if a equals which of the following? W) -2/9 X) 9/2 Y) 5 Z) 11/2

ANSWER: Z) 11/2

Determine the largest possible real domain of y = √(𝑥−1)/√(𝑥²−1) [y equals the fraction with numerator the square root of the quantity x minus 1 and denominator the square root of the quantity x squared minus 1 ].

ANSWER: x > 1

An open box is to be made from a rectangular piece of material 8 inches by 6 inches by cutting equal squares of side x from the four corners and turning up the sides. In terms of x, give an expression for the volume of the box in cubic inches.

ANSWER: x(8- 2x)(6- 2x) (ACCEPT: 4x³ - 28x² + 48x)

The polynomial p(x) = x⁴ + 5x³ - 2x² - 24x has a zero at x = 2. Factor p completely.

ANSWER: x(x - 2)(x + 3)(x + 4) [NOTE: EXPRESSIONS IN ANSWER CAN BE IN ANY ORDER]

In terms of x and in standard polynomial form, what is the volume of a right rectangular prism with dimensions (x + 4), (x + 1), and (x + 6)?

ANSWER: x³ + 11x² + 34x + 24

If two 6-sided fair dice are rolled, providing your answer as a fraction in lowest terms, what is the probability that both numbers will be even?

ANSWER: ¹/₄

If a person walks 4 miles due north, 6 miles due east, then 4 miles due north, how far in miles is the person displaced from his or her original position?

ANSWER: 10

Providing your answer to one decimal place, find the value of the following fraction: 63! / 62!3! [the numerator is 63 factorial; the denominator is 62 factorial times 3 factorial].

ANSWER: 10.5

In a standard deck of cards with no jokers, providing your answer as a fraction in lowest terms, what is the probability of picking a card that is black or a number less than 10 (which includes aces)?

ANSWER: 11/13

After 40 times at bat, BJ has 9 hits. What is the least number of hits he would need in his next 30 times at bat so that he has hits in at least 31% of his total at-bats?

ANSWER: 13

For what values of x is the function f(x)=x²/(x²-4x+4) [f of x equals the fraction with numerator x squared and denominator x squared minus 4 x plus 4] NOT defined?

ANSWER: 2

How many distinct diagonals does a pentagon have?

ANSWER: 5

Mary travels for 110 miles averaging 55 miles per hour and for 150 miles averaging 50 miles per hour. What is Mary's average speed in miles per hour for the trip?

ANSWER: 52

Name all of the quadrants that contain solutions of the inequality 2x - y > 4 .

ANSWER: I, III, IV (ACCEPT: 1, 3, 4 or FIRST, THIRD, FOURTH)

Which of the following points is on the graph of the inverse of the function f(x) = 10^(x + 2) [f of x equals 10 to the power of the quantity x plus 2]? W) (100, 0) X) (0, 100) Y) (10, 0) Z) (0, 10)

ANSWER: W) (100, 0)

Which of the following is an equivalent form of 2/(3 + i) [2 over the quantity 3 plus i]? W) (3 - i)/4 [open parenthesis 3 minus i,close parenthesis, over 4] X) (3 - i)/5 [open parenthesis 3 minus i,close parenthesis, over 5] Y) (4 - i)/4 [open parenthesis 4 minus i,close parenthesis, over 4] Z) (4 - i)/5 [open parenthesis 4 minus i,close parenthesis, over 5]

ANSWER: X) (3 - i)/5

A certain radioactive element decays over time according to the equation y=R¹/₂^(x/300) [y equals R times one half to the power of the quantity x over 300], where R equals the number of grams that were present initially and x equals time in years. If 1000 grams were present initially, how many grams will remain after 900 years? W) 62.5 X) 125 Y) 250 Z) 500

ANSWER: X) 125

If the surface area of a cube is 96 square units, which of the following is the length of a diagonal of a face of the cube? W) 4 X) 4√2 Y) 4√3 Z) 16√2

ANSWER: X) 4√2