# MATHEMATICS

MULTIPLE CHOICE

1. The Polk family purchases a home for $225,000, make a down payment of 25%, and finances

the rest with a 30-year fixed-rate mortgage at an annual interest rate of 3.9% compounded

monthly. What is the amount of their monthly mortgage payment?

1. _______

A. $1085.00 C. $848.97

B. $1061.25 D. $849.00

2. Customers shopping at a particular supermarket spend a mean time shopping of 33 minutes,

with a standard deviation of 9 minutes. Assuming a normal distribution, what is the probability

that a randomly chosen customer will spend between 15 and 51 minutes shopping in the

supermarket?

2. ______

A. 0.3413 C. 0.6826

B. 0.9544 D. 0.7580

3. The Tralfaz appliance company manufactures small electric grills. The company has

production costs defined as 𝐶(𝑥) = 9.15𝑥 + 27200 where x is the number of grills made each month. Revenue is defined as 𝑅(𝑥) = 21.95𝑥 where x is the number of grills sold each month. How many grills must be sold each month for this manufacturing process to break even?

3. ________

A. 875 B. 1240 C. 2125 D. 2973

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4. Find the values of x and y that maximize the objective function P = 9x + 5y for the feasible

region shown below.

A. ( 3 , 0 ) 4. _______

B. ( 1 , 2 )

C. ( 2 , 0 )

D. ( 0 , 3 )

5. In the dice game “Yahtzee”, five-of-a-kind gives the maximum score for a single turn. What

is the probability of getting 5 “5”s in a single roll of 5 six-sided dice?

5. ________

A. 5 36 (0.138889) ⁄ C. 1 1296 (0.000772)⁄

B. 1 30⁄ (0.033333) D. 1 7776⁄ (0.000129)

6. Which of the following statements is NOT true? 6. ______

A. If all of the data values in a data set are identical, then the standard deviation is 0.

B. The standard deviation is the square root of the variance.

C. The variance can be a negative number

D. The variance is a measure of the dispersion or spread of a distribution about its mean.

7. If K = {3, 7, 11, 15} and M = {7, 12, 15, 18}, list {𝒙|𝒙 ∈ 𝑲 𝒐𝒓 𝒙 ∈ 𝑴} 7. ______

A. { 3, 7, 11, 12, 15, 18 } C. { ∅ }

B. { 3, 7, 7, 11, 12, 15, 15, 18 } D. { 7, 15 }

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8. Determine which shaded region corresponds to the solution region of the system of linear

inequalities

𝑥 + 2𝑦 ≤ 4 𝑥 ≥ 0 4𝑥 + 𝑦 ≤ 4 𝑦 ≥ 0

5. _______

GRAPH A.

GRAPH B.

GRAPH C.

GRAPH D.

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9 – 10. At Burger Heaven a “double” contains 2 meat patties and 6 pickles, whereas a “triple”

contains (wait for it!) 3 meat patties and 3 pickles. Near closing time one day, only 24 meat

patties and 48 pickles are available. If a “double” sells for $1.50 and a “triple” sells for $2.00,

then how many of each should be made in order to maximize profit? Let x represent number of

“double” burgers and y represent number of “triple” burgers.

9. Identify the production constraint for meat patties:

9. _______

A. 2𝑥 + 3𝑦 ≤ 48 C. 6𝑥 + 3𝑦 ≥ 48

B. 2𝑥 + 3𝑦 ≤ 24 D. 6𝑥 + 3𝑦 ≥ 24

10. State the objective function.

10. _______

A. 𝑃 = 1.5𝑥 + 2𝑦 C. 𝑃 = 24𝑥 + 48𝑦

B. 𝑃 = 48𝑥 + 24𝑦 D. 𝑃 = 2𝑥 + 1.5𝑦

11. You can win Transylkota’s “Deep-6” lottery jackpot if you correctly choose 6 non-repeating

integer numbers between 1 and 36 (in any order) and those numbers are drawn. You buy one

ticket. What is the probability that it’s the jackpot winner?

11. ______

A. 𝑃(𝐸) = 6 366 ⁄ C. 𝑃(𝐸) = 1 𝐶36,6⁄

B. 𝑃(𝐸) = 1/𝑃36,6 D. 𝑃(𝐸) = 1 36 6⁄

12. Find the equation of the line passing through (9, 3) and ( – 3 , 1): 12. ______

A. 2x – 3y = 9 B. 2x – 3y = – 9 C. x + 6y = 3 D. x – 6y = – 9

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______________________________________________________________________________

SHORT ANSWER (Work not required to be shown)

13. Consider the following graph of a line.

(a) Determine the slope.

______________

Answer: ______________

(b) State the y-intercept.

______________ Answer: ______________

(c) Find the slope-intercept form of

the equation of the line:

______________________

14. “Guilt and focusing on decision making” (Gangemi & Mancini, Journal of Behavioral

Decision Making, Vol 20, Jan 2007) reported on 171 volunteer students participating in an

experiment where each was randomly assigned to one of three groups. One group was made to

feel guilty, one group was made to feel angry, and the third group was not influenced.

Immediately after reaching these emotional states, the students were asked to decide whether or

not to spend lots of money to repair a very old car (not a “historic”/antique). The “stated” option

was “spend the money to repair the car”. The following raw data was recorded:

Emotional State Choose stated option C Don’t choose stated option C’ Totals

Guilt 45 12 57

Anger 8 50 58

Neutral 7 49 56

Totals 60 111 171

(Report your answers as fractions or as decimal values rounded to the nearest hundredth.)

Find the probability that a randomly-selected student:

(a) is in the “guilt” emotional state, or chooses the stated

option:

Answer: ______________

(b) chooses the stated option, given that the student is in the

“guilt” state:

Answer: ______________

(c) chooses the stated option and is in the “guilt” state? Answer: ______________

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15. Let 𝑛(𝐴) = 55, 𝑛(𝐵) = 65, 𝑛(𝐴 ∪ 𝐵) = 85, and 𝑛(𝑈) = 100.

a. Determine 𝑛(𝐴′) : ___________________________________

b. Determine 𝑛[(𝐴 ∪ 𝐵) − (𝐴 ∩ 𝐵)] : ___________________________________

c. Determine 𝑛(𝐴′ ∩ 𝐵′): ___________________________________

SHORT ANSWER, with work required to be shown, as directed.

16. There is a collection of 13 books. 8 of the books are fiction and 5 of the books are non-

fiction. As an assignment, a student must read 6 of the books over the summer.

(a) In how many ways can 6 of the 13 books be chosen? Show work.

(b) In how many ways can the 6 books be chosen, if 3 of the books must be fiction and 3 of the

books must be non-fiction? Show work.

(c) If 6 books are selected at random from the collection of 13 books, what is the probability that

3 are fiction and 3 are non-fiction? Give answer as a fraction or as a decimal rounded to nearest

ten-thousandth (4 places after decimal) Show work.

______________________________________________________________________________

17. Solve the system of equations using elimination by addition, substitution, or augmented

matrix methods (your choice). Show work.

4𝑥 + 3𝑦 = −7

3𝑥 − 2𝑦 = −18

______________________________________________________________________________

18. Cara needs $9,000 in 11 years. What amount can she deposit at the end of each quarter at

8% annual interest compounded quarterly so she will have her $9,000? Show work.

A. $129.49 C. $134.01

B. $204.55 D. $125.19

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19. According to Symantec Corporation, “2016 Internet Security Threat Report”

(https://www.symantec.com/security-center/threat-report), “spear-phishing” cyberattacks against

American small businesses are steadily increasing. 18% of all “spear-phishing” cyberattacks

against American businesses in 2011 targeted businesses with less than 250 employees. In 2015,

43% of all “spear-phishing” cyberattacks against American businesses targeted businesses with

less than 250 employees.

(a) Which of the following linear equations could be used to predict annual percentage of

all “spear-phishing” cyberattacks against US businesses that target “small” businesses

(“y”) in a given year “x” since 2011, where x = 0 represents the year 2011?

Explain/show work.

𝐴. 𝑦 = 0.16𝑥 + 18 𝐶. 𝑦 = 0.16𝑥 + 2011

𝐵. 𝑦 = 6.25𝑥 + 18 𝐷. 𝑦 = 6.25𝑥 + 2011

(b) Use the equation from part (a) to predict the percentage of all “spear-phishing”

cyberattacks against US businesses that will target “small” businesses in the year 2018.

Round answer to nearest tenth of a percent. Show work.

(c) Fill in the blanks to interpret the slope of the equation: The rate of change of percent

of all “spear-phishing” cyberattacks against US businesses that target “small” businesses

with respect to time is __________ per ___________. (Include units of measurement.)

______________________________________________________________________________

20. The feasible region shown below is bounded by lines x + 2y = 2, x + y = 2, and y = 0.

Find the coordinates of corner point A. Show work.

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21. A local car rental agency charted daily demand as shown in the following table:

Number of customers 8 10 12 14 16

Probability 0.3 0.2 0.3 0.1 0.1

Find the expected number of customers. Show work