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

Accepted Answer

The following ways can be used to determine the values of the trigonometric functions of a given angle: use a scientific calculator; interpolate values in published trigonometric tables; and derive values using infinite series equations. However, the most time efficient way to determine trigonometric function values is to use a scientific calculator or downloaded app on your smart phone. Published trigonometric tables are heavy to carry, and deriving the answers on your own requires a long and involved effort that may result in frustration and/or consultations with nerdy math professors.

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

Accepted Answer

The right-hand column shown in the give table lists the elementary functions for the indefinite integral F(x). The corresponding derivatives are shown in the left-hand column of the table. Tables of standard integrals can be developed for easy reference when evaluating other integrals.

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

Accepted Answer

the arithmetic mean of 2x, 2x, y, and 3y, where y = 2x +1 is 3x + 1.
Solution
The arithmetic mean (average) is equal to the sum of the items divided by the number of items.
Average = (2x + 2x + y + 3y)/4 = (4x + 4y)/4 = x + y
Substituting 2x +1 for y: x + (2x + 1) = 3x + 1
Check (assume x = 3): (6 + 6 + 7 + 3(7))/4= 10 = 3(3)+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

Accepted Answer

12 x $75 = $900. We could certainly figure this out by breaking up the 12 and multiplying 10 x $75 and adding that to 2 x $75 to reach the answer. However, it is much easier to calculate mentally by halving and doubling. This works fabulously when one of the numbers is even. In this case, our number 12 is even, so we will do the halving with that one, and we will do the doubling with 75.
12 x 75 is the same as 6 (which is 12 halved) x 150 (which is 75 doubled). This is the same as 3 (which is 6 halved) x 300 (which is 150 doubled). We can easily determine that 3x300 is 900. Those are much "friendlier" numbers to deal with than 12x75.
Key Takeaway: When multiplying two numbers together, and one of the numbers is even, use the halving and doubling technique to find friendlier numbers to multiply mentally. This takes a decent amount of practice. It also helps to know what numbers are friendly and unfriendly to you, and what number easily turn into friendly ones.

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

Accepted Answer

The length of the hypotenuse c is 36.41 ft. Solution Use right triangle formula c² = a² + b² Where a = 30.30 ft b = 20.20 ft c2 = (30.30 ft)² + (20.20 ft)² = 918.10 ft² + 408.04 ft² = 1,326.14 ft² c = (1,326.14 ft2) ^½ = 36.41 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

Accepted Answer

The horizontal distance AB is equal to 95.08 ft. Solution Use the horizontal distance equation H = (D² - V²)^1/2 Where D = slope distance = 97.16 ft V = elevation distance = 80.88 ft - 60.88 ft = 20 ft H = [(97.16 ft)² - (20 ft) ² ] ^1/2 = 95.08 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

Accepted Answer

A Type I error is defined as the error of rejecting a hypothesis when the hypothesis is true. A Type II error is one in which a hypothesis is not rejected when it is false. The error of rejecting a hypothesis when the hypothesis is false is not an error. The probability of a Type I error occurring during a test is referred to as the "level of significance" of the test.

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

Accepted Answer

The horizontal distance H for a slope measurement of 814.20 ft and angle of 6°30' is 808.96 ft.
Solution
Use the horizontal distance formula H = L cos a
Where L = 814.20 ft
A = 6°30'
Step 1
Convert angle 6°30' to DMS: 6°30' = 6.5°
Step 2
H = L cos 6.5 = (814.20 ft)(0.994) = 808.96 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

Accepted Answer

$160,000.
In this case, 94% is a pretty lousy number to work with. 6% is much better.
If 6% equals $9,600, then 1% = $1,600. Thus, 100% is equal to $160,000.
Key Takeaway: This question is all about speed. By finding easy numbers to work with, you can do this question in a flash.

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

Accepted Answer

The statement secant = 1/sine is incorrect. Secant = 1/cosine where the cosine equals the adjacent side/hypotenuse of a right triangle.

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.

Accepted Answer

In theory, the weight of an observation is defined to be inversely proportional to the variance of the observation. That means that the smaller an observation error is, the more accurate the observation will be and therefore, the bigger weight the observation should be assigned.

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

Accepted Answer

The cotangent of 31.5° is 1.632.
Solution (steps taken are dependent on type of scientific calculator used)
Step 1:
Using a calculator in the degree mode, enter 31.5 and press the TAN key.
The tangent of 31.5° is 0.613.
Step 2:
Press the 1/X key to calculate the cotangent.
The cotangent of 31.5 is 1.632.

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

Accepted Answer

To calculate this answer mentally, use the Rule of 72.
Divide 72 by the rate of growth. In this example, Ron's money would double in 8 years (72/9). The rule of 72 is a quick mental calculation tool that provides an estimate of how long it would take an investment to grow double.
Key Takeaway: For a few days, practice this every time you see a growth rate in the news paper or at work.

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

Accepted Answer

To find the percentage of any number, such as 42% of 677, for example, multiply the percentage in its whole value by the number, then divide the product by 100. (42 x 677) ÷ 100 = 284.34.

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

Accepted Answer

The length of side b is 20.19 ft. Solution Use right triangle formula c² = a² + b² Where a = 30.30 ft c = 36.41 ft b² = c² - a² = (36.41 ft)2- (30.30 ft)² = 1325.69 ft² - 918.09 ft2 = 407.60 ft² b = (407.60 ft²)^½½ = 20.19 ft

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.

Accepted Answer

The outlier is 112. An outlier is any number that is widely divergent from the rest of a data set, and it can be deduced logically, in many cases. It can be found arithmetically as well. An outlier is usually any number that is more than two standard deviations from the mean. The mean of the number set is about 42 (42.11). The standard deviation for the set is about 29.5. 42 + 29.5 + 29.5 = 101; therefore, any number greater than 101 is an outlier in this set. 101 < 112, therefore 112 is an 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

Accepted Answer

The height of the fir tree to the nearest foot is 55 ft.
Solution
Use the equation tan ? = opposite/adjacent
Where ? = 35°
Adjacent = 79 ft
Opposite = tangent 35° x 79 ft
= (0.700) x 79 ft
= 55.32 ft -> rounded to 55 ft

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

Accepted Answer

The value of a + b is none of the listed answers. The value of a + b is 16.
Solution
Use the linear function equation.
f(x) = mx + b
1. When x = 3, 3m+b = 8. "Guess and check" values for m and b
When m = 2, b = 2
2. Find the missing outputs in the table
f(2) = 2(2) + 2 = 6
f(4) = 4(2) + 2 = 10
3. Add a + b
6 + 10 = 16

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

Accepted Answer

75.2228° is equal to75°13'22" in degrees, minutes and seconds.
Solution
One minute is defined as 1/60 of a degree (1° = 60 minutes)
One second is defined as 1/60 of a minute (one minute = 60 seconds)
Therefore, 1° = (60 minutes per degree) (60 seconds per minute) = 3600 seconds
1. Convert the decimal part of the angle reading (0.2228°) to minutes:
(0.2228°)(60 minutes per degree) = 13.368 minutes
2. Convert the decimal part of 13.368 minutes to seconds:
(0.368 minutes) (60 seconds per minute) = 22 seconds
3. Add together to obtain DMS 75°13'22"

Question 20

What is 5/12?
A).41666
B).42
C).4333
D).41333
E).415

Accepted Answer

5/12 is .41666. The 6s repeat forever.
Key Takeaway: Things frequently come in dozens, so dividing by 12 in case interviews can be quite common.
1/12 = .083333
5/12 = .41666
7/12 = .58333
11/12 = .916666
There is a bit of a pattern in there, but we don't think it's helpful to try to use a pattern. Rather, just take the time to memorize these 4 decimals. The rest can be reduced.

Quiz 5: Mathematics

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

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

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

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?

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 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 Type I error is defined as:

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?

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?

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

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

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

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

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

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?

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

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?

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

Convert 75.2228° to degrees, minutes, and seconds.

What is 5/12?