Question 1

Simplify the following expression and write your answer using integers or fractions: $$\left( \frac{1}{9}y^2$ - \frac{1}{3}y + \frac{2}{9} \right) + \left( 5y^2$ + \frac{5}{6}y - \frac{1}{9} \right)$$

Accepted Answer

$$\frac{46}{9}y^2$ + \frac{1}{2}y + \frac{1}{9}$$

Question 2

Which of the following statements is true about the polynomial $$f(x) = x^3$ + x^6$ + x^8$?

Accepted Answer

The statement is false. For a polynomial to be a cubic polynomial, its term with the largest exponent on $$x$$ must have an exponent of 3. The term with the largest exponent is $$x^8$$, making it a polynomial of degree 8.

Question 3

Multiply and simplify the following rational expressions: $$\frac{15w^2$}{7} \cdot \frac{21}{55w}$$

Accepted Answer

$$\frac{9w}{11}$$

Question 4

Simplify the expression $$\left( \frac{10k^2$}{a^3$} \$$right)^2$$ and write your answer with only positive exponents.

Accepted Answer

$$\frac{100k^4$}{a^6$}$$

Question 5

A small company had sales of $$24,000 in its second year and 54$$,000 in its fifth year. Assuming the sales follow a straight line, what is the equation for sales $$y in $$year $$x$$?

Accepted Answer

$$y = 10,000x + 4,000$$

Question 6

Using the sales equation $$y = 10,000x + 4,000$$, after how many years will the sales surpass $$90,000$$?

Accepted Answer

9 years

Question 7

Joanne sells T-shirts with a marginal cost of $$2.50$$ per shirt and a fixed cost of $$50. $$What is the linear cost function $$C(x)$$ for producing $$x T-$$shirts?

Accepted Answer

$$C(x) = 2.50x + 50$$

Question 8

If Joanne sells T-shirts for $$6$$ each, how many must she sell to break even if her cost function is $$C(x) = 2.50x + 50$$?

Accepted Answer

15

Question 9

Given the function $$f(x)$$ graphed with domain $$[-3, 5]$$ and range $$[-5, 3]$$, which of the following is correct?

Accepted Answer

The domain is $$[-3, 5]$$ and the range is $$[-5, 3].$$

Question 10

A charter flight charges in the form $$R = 4000x - 20x^2$ per person, where x$ is the number of seats sold. What number of seats maximizes the revenue?

Accepted Answer

100

Question 11

Joanne wants to make a profit of $$700$$ selling T-shirts. If her cost function is $$C(x) = 2.50x + 50$$ and she sells each for $$6$$, how many T-shirts must she sell?

Accepted Answer

215

Question 12

Which of the following best describes how to determine the range of a function from its graph?

Accepted Answer

Find the highest and lowest points on the graph. The range will be all $$y-$$values between these points.

Question 13

Which of the following is the correct way to multiply $$\frac{15w^2$}{7} by$$ $$\frac{21}{55w}$$ and simplify?

Accepted Answer

$$\frac{15w^2$}{7} \cdot \frac{21}{55w} = \frac{9w}{11}$$

Question 14

If the cost to produce $$x$$ units is given by $$C(x) = 2.50x + 50$$ and the revenue is $$R(x) = 6x$$, what is the profit function $$P(x)$$?

Accepted Answer

$$P(x) = 3.5x - 50$$

Question 15

Which of the following is the correct interpretation of the slope in the sales equation $$y = 10,000x + 4,000$$?

Accepted Answer

The sales increase by $$10,000$$ each year.

Business Calculus Exam 1 Review: Step-by-Step Guidance

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