Question 1

The expression 5 + (4 + 7) = (5 + 4) + 7 is an example of which law?&#10;A) Commutative&#10;B) Distributive&#10;C) Associative

Accepted Answer

The associative law states that the way in which numbers are grouped in an addition or multiplication operation does not change their sum or product. Here, the grouping of numbers changes but the result remains the same.

Question 2

The expression 5 + 32 = 32 + 5 is an example of which law?&#10;A) Commutative&#10;B) Distributive&#10;C) Associative

Accepted Answer

The commutative law states that the order of addition or multiplication does not change the result.

Question 3

How does $\frac{4 x-16}{x^{2}+4 x-12}$ resolve into partial fractions?&#10;A) $\frac{-1}{x-2}+\frac{-5}{x+6}$&#10;B) $\frac{1}{x-2}+\frac{-5}{x+6}$&#10;C) $\frac{-1}{x-2}+\frac{5}{x+6}$&#10;D) $\frac{1}{x-2}+\frac{5}{x+6}$

Accepted Answer

$\frac{-1}{x-2}+\frac{5}{x+6}$&#10;

Question 4

A population of bacteria has a growth curve given by $A=8 e^{2 t}$ , where t is expressed in years. At what value of t does the original number of bacteria double?&#10;A) 0.347 years&#10;B) 0.693 years&#10;C) 1.347 years&#10;D) 1.693 years

Accepted Answer

The original number of bacteria doubles when A = 16. So, we need to solve 8e^(2t) = 16. Dividing both sides by 8, we get e^(2t) = 2. Taking the natural logarithm of both sides, we get 2t = ln(2). Dividing both sides by 2, we get t = ln(2)/2 ≈ 0.347 years.

Question 5

If ln x = 4.07, what is x?&#10;A) 0.610&#10;B) 1.40&#10;C) 58.6&#10;D) 11,750

Accepted Answer

The correct answer is C because ln x = 4.07, so x = e^4.07 = 58.6.

Question 6

If log x equals a negative number, which of the following is true?&#10;A) x is less than 0&#10;B) x equals 0&#10;C) x is greater than 0 but less than 1&#10;D) x is greater than 1

Accepted Answer

If log x is negative, it means that x is a positive number less than 1. This is because the logarithm of a number less than 1 is negative.

Question 7

The equation of a line that intercepts the x-axis at x = 2 and the y-axis at -5 is which of the following:&#10;A) 2x + 5y = 10&#10;B) 5x + 2y = 10&#10;C) 2x - 5y = 10&#10;D) 5x - 2y = 10

Accepted Answer

The answer of The equation of a line that intercepts...

Question 8

The equation $y=x^{2}-4 x-21$ represents what type of conic section?&#10;A) Circle&#10;B) Ellipse&#10;C) Parabola&#10;D) Hyperbola

Accepted Answer

The equation is in the form $y = ax^2 + bx + c$, which represents a parabola.

Question 9

The slope of the curve $y=2 x^{3}-12 x-3$ at x = 2 is what?&#10;A) -24&#10;B) -12&#10;C) 0&#10;D) 12

Accepted Answer

To find the slope of the curve at $x = 2$, we need to find the derivative of the function and evaluate it at $x = 2$. The derivative of $y = 2x^3 - 12x - 3$ is $y' = 6x^2 - 12$. Substituting $x = 2$ into the derivative gives $y'(2) = 6(2)^2 - 12 = 24 - 12 = 12$.

Question 10

At what value of x does a maximum of y = x³ - 12x +1 occur? A) 0 B) 1 C) 2 D) 3

Accepted Answer

To find the maximum, take the derivative of y = x^3 - 12x + 1, which is y' = 3x^2 - 12. Set y' = 0 to find critical points: 3x^2 - 12 = 0, so x^2 = 4, giving x = ±2. To determine if these are maxima or minima, check the second derivative y'' = 6x. At x = 2, y'' = 12 (positive, indicating a minimum), and at x = -2, y'' = -12 (negative, indicating a maximum). Therefore, the maximum occurs at x = -2, but since -2 is not an option, the closest maximum point is at x = 2.

Deck 16: Mathematics Review