1. In general, engineering problems are mathematical models of physical situations.
a. True
b. False
2. Mathematics is a language that has its own symbols and terminology. As an engineering
student, you need to learn mathematical symbols and their meanings.
a. True
b. False
3. Greek alphabetic characters quite commonly are used to express angles, dimensions, and
physical variables in drawings and in mathematical equations and expressions. It is therefore
very important to be familiar with these characters in order to communicate with other engineers.
a. True
b. False
4. What is the name of the following Greek alphabetic character?
a. Epsilon
b. Zeta
c. Gamma
d. Lambda
5. What is the name of the following Greek alphabetic character?
a. Omega
b. Mu
c. Gamma
d. Lambda
6. What is the name of the following Greek alphabetic character?
a. Omega
b. Mu
c. Gamma
d. Lambda
7. The simplest form of models commonly used to describe a wide range of engineering
situations is
a. linear equations.
b. nonlinear equations.
c. exponential equations.
d. logarithmic equations.
8. In the spring equation F = k x, the spring force, F is called
a. a dependent variable
b. an independent variable
c. none of the above
9. In the spring equation F = k x, the deformation of the spring, x is called
a. a dependent variable
b. an independent variable
c. none of the above
10. The quantity or numerical value within a linear model that shows by how much the
dependent variable changes each time a change in the independent variable is introduced is
known as
a. the x-intercept.
b. the y-intercept.
Test Bank Engineering Fundamentals, 5th ed. Chapter 18
c. the dependent intercept.
d. the slope.
11. Find the slope of the line that passes thru the points (2,1) and (8,5).
12. The pitch of a roof refers to its “steepness” and is expressed in terms of the number of inches
the roof rises for each 12 inches of run. For example, an 8-12 pitch means that the roof rises 8
inches vertically for each 12 inches of horizontal run. What is the slope of a roof with an 8-12
pitch?
13. Find an equation of the line through (1,-3) with a slope of
2
1
−
.
14. Find an equation of the line that passes through the points (-1,2) and (3,-4).
15. Find an equation of the line through (5,2) that is parallel to the line
0564 =++ yx
.
Test Bank Engineering Fundamentals, 5th ed. Chapter 18
16. Find an equation of the line through (5,2) that is perpendicular to the line
0564 =++ yx
.
17. For many engineering situations, nonlinear models are used to describe the relationships
between dependent and independent variables because they predict the actual relationships more
accurately than linear models do.
a. True
b. False
18. For many engineering situations, exponential and logarithmic models are used to describe the
relationships between dependent and independent variables because they predict the actual
relationships more accurately than linear models do.
a. True
Test Bank Engineering Fundamentals, 5th ed. Chapter 18
b. False
19. For nonlinear models (equations) the slope is constant.
a. True
b. False
20. Hooke’s Law describes the relationship between force F and deflection x in a spring
according to the following equation:
kxF=
. Which type of mathematical model is used in
Hooke’s Law?
a. Linear model
b. Nonlinear model
c. Exponential model
d. Logarithmic model
21. The velocity of an object under constant acceleration can be modeled using the following
function: v(t) = v0 + at
where v = velocity
v0 = initial velocity
a = acceleration
t = time
Which type of mathematical model is used to describe velocity in this application?
a. Linear model
b. Nonlinear model
c. Exponential model
d. Logarithmic model
22. The path of flight (trajectory) of a football thrown by a quarterback is described by the
following function:
( ) ( )
0
2
22
0
tan
cos2 yxx
v
g
xy ++
−=
where y = vertical position of football relative to the ground
y0 = vertical launch position of football relative to the ground
x = horizontal position of football relative to launch position
g = magnitude of gravitational acceleration
v0 = launch speed
θ = launch angle relative to horizontal
Which type of mathematical model is used here to describe the football’s trajectory?
a. Linear model
b. Nonlinear model
c. Exponential model
d. Trigonometric model
23. The path of flight (trajectory) of a football thrown by a quarterback is described by the
following function:
( )
77.0002.0 2++−= xxxy
where y = vertical position of football relative to the ground (ft)
x = horizontal position of football relative to launch position (ft)
How high above the ground is the football as it leaves the quarterback’s hand?
a. 0.002 ft
b. 0.7 ft
c. 7 ft
d. 7.7 ft
24. The path of flight (trajectory) of a football thrown by a quarterback is described by the
following function:
( )
77.0002.0 2++−= xxxy
where y = vertical position of football relative to the ground (ft)
x = horizontal position of football relative to launch position (ft)
How high above the ground is the football when it is 30 yards downfield from the quarterback?
a. 26.2 ft
b. 29.8 ft
c. 13.8 ft
d. 53.8 ft
25. The position of an object subjected to constant acceleration can be described by the following
function:
( )
2
2
1
00 attvxtx ++=
where
=x
position (m)
=
0
x
initial position (m)
=
0
v
initial velocity (m/s)
=a
acceleration (m/s^2)
=t
time (sec)
Which type of mathematical model is used here to describe the object’s position?
a. Linear model
b. Nonlinear model
c. Exponential model
d. Trigonometric model
26. The gravitational force between two masses is modeled using the following function:
( )
221
r
mm
GrF =
where
=F
gravitational force (Newtons)
2
2
11
10673.6 kg
mN
G
−
=
=
1
m
mass number 1 (kilograms)
=
2
m
mass number 2 (kilograms)
=r
distance between centers of masses (meters)
Which type of mathematical model is used here to describe the gravitational force?
a. Linear model
b. Nonlinear model
c. Exponential model
d. Trigonometric model
27. Perform the following operations on the given matrices:
−
−=
351
707
124
A
−
−
=
754
335
121
B
?=+ BA
27. Perform the following operations on the given matrices:
−
−=
351
707
124
A
−
−
=
754
335
121
B
?=− BA
Test Bank Engineering Fundamentals, 5th ed. Chapter 18
28. Perform the following operations on the given matrices:
−=
1021
502
583
A
−
=
025
596
4107
B
?= BA
29. Given the following matrix:
−
−=
1051
707
129
A
find
T
A
.
30. Given the following matrix:
=34
15
A
calculate the determinant of
A
.
31. Given the following matrix:
−
−=
351
707
A
calculate the determinant of
A
.
32. Solve the following set of equations using matrices:
1453
1552
6
=++−
=++
=++
cba
cba
cba
33. Solve the following set of equations using the Gaussian method:
EQ2 15
EQ1 642
=−
=+
yx
yx
34. A company advertises a gadget at the regular price of $8, with a coupon for a second gadget
at half price. The company sold 50 gadgets for a total of $364. How many coupons were
redeemed?
35. Calculus is commonly divided into two broad areas:
a. single variable and multivariable calculus.
b. differential and integral calculus.
c. vector and matrix calculus.
d. linear and nonlinear calculus.
36. The rate of change refers to how a dependent variable changes with respect to an independent
variable.
a. True
b. False, that’s the definition of slope.
37. Calculate the average rate of change for the following function:
( )
3
xxf =
between
1=x
and
3=x
Test Bank Engineering Fundamentals, 5th ed. Chapter 18
38. Calculate the average rate of change for the following function:
( )
2
xxf =
between
0=x
and
2−=x
39. Calculate the average rate of change for the following functions:
( )
2
xxf =
between
0=x
and
2=x
40. The term rate of change always refers to how a physical quantity varies with time.
a. True
b. False
41. Find the derivative of
( )
5+= xxf
.
42. Find the derivative of
( )
75
2−+= xxxf
.
43. Find the derivative of
( )
xxxf 32 3+=
.
44. Find the derivative of
( )
5
123
2
23
++
+−+
=xx
xxx
xf
.
Test Bank Engineering Fundamentals, 5th ed. Chapter 18
45. Evaluate:
( )
+−+ dxxxx 7464 23
46. Evaluate:
( )
+dxxx
5
2
9
47. Many engineering problems are modeled using differential equations with a set of
corresponding boundary and/or initial conditions.
a. True
b. False
48. What kind of mathematical model contains derivatives of functions?
a. nonlinear equation
b. differential equation
c. exponential equation
d. logarithmic equation
49. Boundary conditions provide information about what is happening physically at the
boundaries of a problem.
a. True
b. False
50. Initial conditions tell us about the initial conditions of a system (at time t = 0), before a
disturbance or a change is introduced.
a. True
b. False