Deck 5: Mathematics

Question 1

Which of the following methods can be used to determine the values of the trigonometric functions of a given angle?

A)Use your scientific calculator (or your own if you can find it).
B)Interpolate values from trigonometric tables in your recalculus book.
C)Derive the values using infinite series equations for sine and cosine functions.
D)All of the above

Answer 1

All of the above

Question 2

Fill in the blank: The right-hand column shown in the table below lists _______ for the indefinite integral F(x).F'(x) = f (x) F(x) = f(x)dx1/x Log | x |Sin x -cos xCos x Sin x

A)Derivatives
B)Elementary functions
C)Elementary integrals
D)None of the above

Answer 2

Elementary functions

Question 3

If y = 2x + 1, what is the arithmetic mean of 2x, 2x, y, and 3y, in terms of x?

A)2x
B)2x + 1
C)3 x + 1
D)None of the above

Answer 3

3 x + 1

Question 4

Alex runs a lemonade stand in the summertime. He averages $75 per week. How much will he make over the 12 weeks of his summer vacation?

A)$800
B)$844
C)$900
D)$924
E)$975

Question 5

Given a right triangle (ABC) with side a = 30.30 ft and side b = 20.20 ft, what is the length of the hypotenuse c?

A)3)64 ft
B)36.41 ft
C)364.16 ft
D)3641.62 ft

Question 6

A slope distance of 97.16 ft is measured directly between two points, A and B. The elevation of A is 80.88 ft and the elevation of B is 60.88 ft. Assuming that no temperature correction is required, what is the horizontal distance AB?

A)77.16 ft
B)95.08 ft
C)100.08 ft
D)117.16 ft

Question 7

A Type I error is defined as:

A)The error of rejecting a hypothesis when the hypothesis is false.
B)The error of not rejecting a hypothesis when the hypothesis is false.
C)The error of rejecting a hypothesis when the hypothesis is true.
D)All of the above

Question 8

A slope measurement of 814.20 ft is recorded and an angle measured with a hand level is 6°30'. What is the horizontal distance H for this slope distance?

A)807.70 ft
B)807.90 ft
C)808.96 ft
D)820.5 ft

Question 9

94% of Jim's income last year came from his salary. The rest came from awards his prize winning poodle won in dog shows. If he won $9,600 in dog shows, what was his total income?

A)$145,000
B)$160,000
C)$170,000
D)$120,000
E)$118,600

Question 10

Which of the following trigonometric functions of a right angle is incorrect?

A)Cosecant = 1/sine
B)Secant = 1/sine
C)Cotangent = 1/tangent
D)All of the above

Question 11

In theory, the weight of an observation is defined to be ______ to the variance (standard error squared) of the observation.

A)Proportional
B)Inversely proportional
C)Equal
D)None of the above.

Question 12

What is the cotangent of 31.5° to three significant figures?

A)0)315
B)0)613
C)1)632
D)None of the above

Question 13

How long will it take for Ron's $37,353 investment to double if he expects 9% returns?

A)5 years
B)8 years
C)9 years
D)9)5 years
E)10 years

Question 14

To find the percentage (p) of any number (n), which formula can be used?

A)(p x 100) ÷ n
B)(p x n) ÷ 100
C)100 - (p x n)
D)(n x 100) ÷ p

Question 15

Given a right triangle (ABC) with side a = 30.30 ft and hypotenuse c = 36.41 ft, what is the length of the side b?

A)20.19 ft
B)47.37 ft
C)67.56 ft
D)None of the above

Question 16

What is the outlier in the following set: 11, 22, 33, 44, 55, 112, 23, 34 and 45?

A)55
B)11
C)112
D)There is no outlier.

Question 17

At a certain time of the day, a fir tree casts a shadow 79 ft long. From the tip of the shadow, an angle from the horizontal to the top of the tree is approximately 35°. What is the height of the fir tree to the nearest foot?

A)44 ft
B)55 ft
C)55.32 ft
D)None of the above

Question 18

The table below gives the value of the linear function f for several values of x. What is the value of a + b?x 2 3 4f(x) a 8 b

A)6
B)10
C)12
D)None of the above

Question 19

Convert 75.2228° to degrees, minutes, and seconds.

A)75°13'22"
B)75°22'28"
C)75°37'13"
D)None of the above

Question 20

What is 5/12?

A).41666
B).42
C).4333
D).41333
E).415

Question 21

Use a calculator to find the sine of 46.3°

A)0)013
B)0)691
C)0)723
D)1)00

Question 22

When formulating answers to market-sizing questions, what's one of the best strategies to keep in mind?

A)Be sure to use exact numbers at all times.
B)Go slow and be as methodical as possible.
C)Estimate and round numbers whenever possible.
D)Pick odd numbers that aren't related to each other in any way.

Question 23

Given a triangle with sides a = 20 feet, b = 40 feet, and c = 56, what is the area in square feet?

A)71.67 ft²
B)116.00 ft²
C)281.68 ft²
D)None of the above

Question 24

Shane's Softball Production Company can produce 12 softballs in an hour. How many softballs can they produce in 14 hours?

A)154
B)160
C)168
D)172
E)188

Question 25

The given numbers are daily groundwater elevation readings from a monitoring well taken during a month experiencing snowmelt and extended rainfall events.7.6, 7.7, 4.3, 5.9, 5.0, 10.5, 7.7, 9.5, 12.0, 12.6, 6.5, 8.3, 8.2, 13.2, 12.6, 13.6, 14.1, 13.5, 11.5, 12.0, 10.4, 10.8, 13.1, 12.5, 10.4, 13.0, 14.1, 15.1What is the sample variance of these groundwater elevation readings?

A)8)764
B)9)089
C)10.56
D)None of the above

Question 26

A small firm allocates 28% of its gross profits into an account for insurance. Last year, the firm's gross profit was $400,000. What amount was deposited into the insurance account?

A)$100,000
B)$108,000
C)$109,500
D)$112,000
E)$128,000

Question 27

Convert 75°13'22" to decimal degrees.

A)75.1322°
B)75.223°
C)75.367°
D)None of the above

Question 28

Seven/Twelve has $4 million in sales over the past week. What were the approximate sales per day?

A)$589,000
B)$571,000
C)$518,200
D)$552,000
E)$578,750

Question 29

If the speed of a car is 200 km per hour, how may minutes does it take to travel 60 km?

A)3 1/3 hours
B)20 minutes
C)18 minutes
D)22 minutes
E)24 minutes

Question 30

What is 1/7?

A).142857
B).153
C).12
D).125
E).144

Question 31

Last year, Smith's Auto Shop made gross revenue of $460,000. This year, their gross revenue increased significantly - by an amazing 25%. What was the gross revenue this year?

A)$525,000
B)$550,000
C)$560,000
D)$575,000
E)$585,000

Question 32

Given a triangle with a base of 42.20 feet and a height of 63.10 feet, find the area of the triangle.

A)105.30 ft²
B)634.3 ft²
C)1,000 ft²
D)1,331.41 ft²

Question 33

The population of the town of Homeville increased by approximately 0.5% last year. If the population at the beginning of the year was 2,460, what was the approximate population by the end of the year?

A)2,472
B)2,960
C)2,465.
D)2,465
E)2,510

Question 34

What is 5/6?

A).8
B).8444
C).8333
D).825
E).875

Question 35

Which of the following is a Double Angle Identity formula?

A)Sin 2x = 2 sin xcosx
B)Sin (x + y) = sin xcosy - cosx sin y
C)Sin xcosy = ½ [sin(x + y) + sin (x - y)
D)All of the above

Question 36

In a game, one card is drawn from a complete deck of playing cards without jokers. If the card is a club or a queen, the gambler wins double his bet. Otherwise, the dealer keeps the money. How much better are the dealer's odds in this game?

A)50% better
B)38% better
C)32% better
D)44% better

Question 37

Every five minutes a baby is born in the Nigindia. How many babies are born in a year?

A)150,120
B)105,120
C)100,510
D)300,450
E)103,555

Question 38

A car that regularly sells for $29,600 has been marked down to $22,100. What is the approximate percentage of the discount?

A)20%
B)22%
C)25%
D)30%
E)33%

Question 39

What is the median for the numbers 89, 87, 94, 82, 89, 91, 95, 88, 90, 87, 92 and 93?

A)87 and 89
B)89.5
C)93
D)89.75

Question 40

Kenneth receives a 6% commission on all of his real estate sales. Half of his commission goes to his broker. What is Kenneth's part of the commission on $250,000 in sales?

A)$6,666
B)$7,000
C)$7,100
D)$7,250
E)$7,500

Question 41

A target consists of three concentric circles with radii of 1 ft, 2 ft, and 3 ft. If the probability of an arrow hitting the target at any point is equal, what is the probability that an arrow will hit the target in the outermost region of the circle?

A)1/3
B)5?
C)55.6%
D)None of the above.

Question 42

Brian is opening a small sporting goods store. After considering her market, she sets her initial sales goal at $32,000 a month. He knows that the rent for his store should be about 8% of sales. Approximately what should he plan to pay for rent, based on the sales figure given?

A)$2,400
B)$2,560
C)$3,200
D)$3,260
E)$3,305

Question 43

Sawyer's Pet Store has averaged a net profit of $2,500 for the past 11 weeks. What is the total net profit over this length of time?

A)$26,000
B)$27,500
C)$27,900
D)$28,000
E)$29,300

Question 44

A point is reflected first over the line y = x, then over the x-axis, then over the y-axis. The resulting point has the coordinates (73, 14). The coordinates of the original point were which of the following?

A)(-14, -73)
B)(-73, 14)
C)(73, -14)
D)(73, 14)

Question 45

A department store sells sweaters for $90. During a promotion, the sweaters are marked down 15%. What is the sale price of the sweaters?

A)$75.00
B)$76.50
C)$77.67
D)$78.14
E)$76.02

Question 46

Roger buys a 35 x 35 foot lot to source rocks for his pet rock project. How many square feet did he buy?

A)1,325
B)1,225
C)1,275
D)905
E)1,185

Question 47

Lance's bike team has 11 riders. They will each bike 83 miles in the race. How many miles will they bike?

A)913
B)917
C)922
D)931
E)934

Question 48

A variable that affects the data collected but is not accounted for or demonstrated in the statistical measure of the data is a:

A)Stealth variable
B)Lurking variable
C)Independent variable
D)Dependent variable

Question 49

What is the maximum number of 2 ½ foot pieces of wire that can be cut from a wire that is 48 feet long?

A)11
B)18
C)19
D)21
E)23

Question 50

What is the ratio of 8 feet to 28 inches?

A)2:7
B)7:24
C)24:7
D)7:2
E)5:3

Question 51

The test scores for eight students are 97, 94, 98, 97, 89, 92, 68 and 96. What would the seventh score be considered?

A)Outlier
B)Mean
C)Mode
D)Standard deviation

Question 52

A video store is offering a 7% discount on previously viewed videos. If the regular price of a video is $9.99, how much will the discount be?

A)63 cents
B)70 cents
C)74 cents
D)77 cents
E)80 cents

Question 53

If Martin invests $20,000 for 20 years and his investment earns 20% interest compounding quarterly, what will it be worth at the end of his investment period?

A)$991,228.82
B)$120,000.00
C)$244,529.20
D)$424,872.36

Question 54

It is sunny on 83% of the 120 days Silver Slides Waterpark is open on average. How many days will Silver Slides be open this summer?

A)100
B)102
C)98
D)99
E)92

Question 55

The given numbers are daily groundwater elevation readings from a monitoring well taken during a month experiencing snowmelt and extended rainfall events.7.6 7.7 4.3 5.9 5.0 10.5 7.7 9.5 12.0 12.6 6.5 8.3 8.2 13.2 12.6 13.6 14.1 13.5 11.5 12.0 10.4 10.8 13.1 12.5 10.4 13.0 14.1 15.1What is the standard deviation of these groundwater elevation readings?

A)3)01
B)8)76
C)9)08
D)None of the above.

Question 56

What is the mean for the following expenditures? $79.84, $278.99, $342.16, $466.25, $111.39, $502.47, $98.12

A)$278.99
B)$268.46
C)$354.22
D)$317.54

Question 57

Kathleen projects her expenditures for purchasing office supplies to be $85/week. How much will she spend on office supplies over a 4-week time span?

A)$290
B)$325
C)$340
D)$355
E)$342

Question 58

A company just distributed candy bars wrapped with golden tickets hidden within ordinary shipments of their product. The company spokesperson announces that there is a "one in one thousand chance" of someone finding a golden ticket when they open a candy bar, and that 500,000 candy bars have been distributed in the golden ticket promotion. If a person buys three of the candy bars, what is their chance of finding a golden ticket?

A)0)30%
B)3%
C)0)00%
D)0)03%

Question 59

What part of a poll or survey is considered the 'sample'?

A)The sum total of responses collected through the poll or survey
B)The group of people participating in the survey or poll who represent a larger population
C)The larger population the poll or survey is attempting to understand
D)The questions the participants are asked

Question 60

3/5 of workers at a company have enrolled in the 403(b) program. If 24 workers have enrolled in the program, how many workers are employed at this company?

A)36 workers
B)40 workers
C)42 workers
D)44 workers
E)45 workers

Question 61

In initial production of a new video game, it is discovered that the ratio of functional games to defective games is 20 to 1. If 360 games are produced, how many could be expected to be defective?

A)12 games
B)15 games
C)16 games
D)18 games
E)20 games

Question 62

What is the median for the following set of numbers? $3.27, $9.42, $6.15, $5.25, $7.62, $4.86, $2.94, $1.16

A)$6.15
B)$4.07
C)$5.45
D)$5.70

Question 63

1% is equal to 100 basis point. 44.5 percent is how many basis points greater than 34.5 percent?

A).1
B)10
C)100
D)1,000
E)10,000

Question 64

What is the mode for the following set of numbers? 1, 7, 8, 7, 9, 1, 2, 4, 5, 1, 3, 6, 6, 0, 9, 3, 0, 1, 4, 6

A)1
B)4)15
C)4
D)2)5

Question 65

Company A and Company B are awarded a $42,000 project that is to be divided between the companies in the ratio of 4:3. How much money should each company receive?

A)Company A gets $24,000 and Company B gets $18,000.
B)Company A gets $23,000 and Company B gets $19,000.
C)Company A gets $28,000 and Company B gets $14,000.
D)Company A gets $30,000 and Company B gets $12,000.

Question 66

Betty invested $10,000 at the beginning of the year. At the end of the year, her investment was worth $12,000. Ronnie also invested in the same fund. At the beginning of the year, he invested $15,000. How much will his investment be worth at the end of the year?

A)$18,000
B)$20,000
C)$21,000
D)$19,500
E)$16,200

Question 67

What is the mode for the following set of numbers? 27, 29, 26, 25, 24, 22, 26, 21, 23, 28

A)25.5
B)26
C)25.1
D)22

Question 68

What is 2/9?

A).17
B).19
C).1818
D).2222
E).235

Question 69

Dottie's Chocolates produces boxes of 25 chocolate drops for selling. How many chocolate drops would Dottie need to make to fill 60 boxes?

A)1,575
B)1,225
C)1,400
D)1,500
E)1,525

Question 70

Using data to predict what might occur in the future, beyond what the data set has explicitly demonstrated, is called:

A)Variable anticipation
B)The futures market
C)Predicate analysis
D)Extrapolation

Question 71

Data that is weighted toward one end of the numerical range in which it occurs is:

A)Diverse
B)Peaked
C)Overweight
D)Skewed

Question 72

What is the mode for the numbers 34, 62, 58, 49, 37, 85, 22, 44, 37 and 52?

A)48
B)46.5
C)61
D)37

Question 73

A business has decided to resurface a floor section in their warehouse. The section is a square that measures 15 feet on one side. How much is the area that needs to be resurfaced?

A)30 square feet
B)60 square feet
C)215 square feet
D)225 square feet
E)250 square feet

Question 74

The wholesale price of a fountain pen is $2.80. What will the new price be if a 5% increase is instituted?

A)$2.84
B)$2.90
C)$2.94
D)$2.96
E)$2.97

Question 75

People who score in the 95th percentile on an exam:

A)Earned a score of 95 on the test
B)Scored as well or better than 95% of the people who took the same exam
C)Scored in the top 95% of test takers
D)Answered 95% of the questions correctly

Question 76

The division of your company that you oversee contains 18 employees whose total salary last year was $855,000. The average salary of all company employees with the same level of responsibility and qualifications is $50,000. Is your department above or below the company average?

A)Below by 20%
B)Above by 10%
C)Below by 5%
D)Above by 15%