WorksheetsFinal Examination in MATH 113 (Part 1B)
Total questions: 100
Worksheet time: 50mins
Name
Class
Date
1.
They are frequently described as “Paraffinic", "naphthenic mixed base," according to the physical characteristics.
a)
Crude oils
b)
Gaseous fuels
c)
Premium oil
d)
LPG
2.
Foundation mass should be how many times the weight of the machinery it is supposed to support?
a)
3 to 5 times
b)
2 to 3 times
c)
5 to 7 times
d)
10 to 20 times
3.
Foundation bolts of specified size should be used surrounded by a pipe sleeve with an inside diameter of at how many times the diameter of anchor bolt.
a)
3 times
b)
twice
c)
4 times
d)
1.5 times
4.
The variable inside the integral is called variable of integration or integration variable. It is sometimes referred to as:
a)
calculus variable
b)
dummy variable
c)
limits variable
d)
limits range
5.
An integral that defined by limit values of the independent variable is called _____.
a)
fixed integral
b)
trivial integral
c)
primitive integral
d)
definite integral
6.
The reduction formula in integration is also known as _____.
a)
Chain Rule
b)
L'hopital Rule
c)
Trapezoidal Rule
d)
Recursion Formula
7.
When can we say that an integral is convergent?
a)
When its limit exists as finite number.
b)
When its limit exists as an infinite number.
c)
When its limit does not exist.
d)
When its limit is imaginary number.
8.
What is a differential equation with only one variable called?
a)
Unit differential equation
b)
Single differential equation
c)
Ordinary differential equation
d)
Partial differential equation
9.
What are the solutions of differential equations?
a)
Numbers
b)
Variables
c)
Functions
d)
Equations
10.
Equations of the form: 𝑑²𝑡/𝑑𝑥² + 𝑛²y = 0. Where n is any number are called:
a)
simple harmonic differential equation
b)
lagrange differential equation
c)
auxiliary differential equation
d)
non-homogeneous differential equation
11.
A curve which intersects all angles of a given family at the right angles is called:
a)
orthogonal trajectory
b)
right curves
c)
right-angled projectors
d)
all of the above
12.
What curves were first studied by the French mathematicians Rene de Sluze and named by Blaise Pascal and generated by the following Cartesians equation yⁿ = k(a - x)ᵖ xᵐ where n, m and p as integers?
a)
Circles of Sluze
b)
Curves of Sluze
c)
Balls of Sluze
d)
Pearls of Sluze
13.
What type of curve is generated by a point which moves in uniform circular motion about an axis, while traveling with a constant speed parallel to the axis?
a)
Cycloid
b)
Epicycloid
c)
Spiral of Archimedes
d)
Helix
14.
The maximize the horizontal range of the projectile, which of the following applies?
a)
Maximize velocity
b)
Maximize the angle of elevation and velocity
c)
Maximize the angle of elevation
d)
The tangent function of the angle of trajectory must be equal to 1.
15.
Which of the following situations has a conventional cash flow so that an internal rate of return can be safely calculated and used?
a)
Your company undertakes a mining project in which the land must be reclaimed at the end of the project.
b)
You invest in a safe dividend stock and receive dividends each year.
c)
You lease a car and pay by the month.
d)
Your company invests heavily in a new product that will generate profits for two years. To keep profits high for 10 years, the company plans to reinvest heavily after two years.
16.
A branch of mathematics which uses the properties of numbers by using symbols or letters to represent numbers in arithmetic operations which usually variables and unknown quantities which usually involves the use and rearranging or equations.
a)
Trigonometry
b)
Algebra
c)
Geometry
d)
Calculus
17.
Given the equation 3x² + 2x -5y + 7 = 0. Determine the curve.
a)
Ellipse
b)
Parabola
c)
Hyperbola
d)
Circle
18.
If the general equation of the conic is Ax² + 2Bxy + C𝑦 2 + Dx + Ey + F = 0, and B² - 4AC > 0, then the conic is a/an _____.
a)
Circle
b)
Parabola
c)
Hyperbola
d)
Ellipse
19.
What can be defined as the set of all points in the plane the sum of whose distances from two fixed points is a constant?
a)
Circle
b)
Hyperbola
c)
Parabola
d)
Ellipse
20.
What is the locus of a point that moves in a plane so that the difference of the distances from two fixed points of the locus is constant?
a)
Ellipse
b)
Circle
c)
Parabola
d)
Hyperbola
21.
A conic section is a curve which is the intersection of:
a)
two cones
b)
a cone and a line
c)
a cone and a plane
d)
a cone and an axis
22.
A conic section whose eccentricity is always less than 1.
a)
Parabola
b)
Circle
c)
Ellipse
d)
Hyperbola
23.
The angle between the tangents at the end points of the latus rectum of a parabola is:
a)
45°
b)
60°
c)
75°
d)
90°
24.
A chord passing through the focus of a parabola and perpendicular to the axis of symmetry.
a)
Directrix
b)
Translated axis
c)
Latus rectum
d)
Axis
25.
A parabola has an eccentricity:
a)
equal to 1
b)
less than 1
c)
greater than 1
d)
of infinity
26.
Which of the following is NOT a central conic?
a)
Circle
b)
Parabola
c)
Ellipse
d)
Hyperbola
27.
A line segment joining two of its points and passing through a focus of a conic.
a)
Latus rectum
b)
Focal radius
c)
Focal chord
d)
Chord of contrast
28.
Which of the following is false about a rectangular hyperbola?
a)
It has an eccentricity of the square root of 2.
b)
Its asymptotes are mutually perpendicular.
c)
When stretched along one or both of its asymptotes, it will remain unchanged.
d)
It was first studied by Pythagoras.
29.
An ellipse centered at the origin with axes 2a and 2b where a>b has parametric equations of:
a)
x = a cos t and y = b sin t
b)
x = sin t and y = b cos t
c)
x = cot t and y =sec t
d)
x = tan t and y = cot t
30.
Archimedes developed the first theory of integration using his method of _____.
a)
approximation
b)
quadratures
c)
domains
d)
estimates
31.
What is a definite integral?
a)
An integral evaluated between two limits.
b)
An integral that has a constant of integration
c)
An integral that has no bound limits.
d)
An integral which can be integrated by direct integration
32.
The following are non-integrability functions (functions that cannot be integrated) except one. Which one?
a)
∫ sin x cos 2x dx
b)
∫ sin x/x dx
c)
∫ eˣ/x dx
d)
∫ 1/ln x dx
33.
If f continuous function in the integral [a, b], then there exists a number c between a and b such that ᵇ∫ f(x) dx = b(a) • f(c). This statement is known as:
a)
Average Variable Theorem for Integrals
b)
Average Integral Theorem
c)
Mean-value Theorem for Integrals
d)
Continuous Value Theorem
34.
Pappus first proposition states, “The surface area of a surface of revolution is equal to the product of the arc length of the generating curve and the length of the generating curve and the length of the path described by its centroid.” This proposition is also known as:
a)
Kepler’s first rule
b)
Guldrin’s first rule
c)
Joule’s first rule
d)
Pythagoras first rule
35.
What do you call the equation that describes how something changes in discrete time steps?
a)
Integral equation
b)
Difference equation
c)
Differential equation
d)
Diophantine equation
36.
What does the term “homogeneous” in a differential equation means?
a)
It means that the right-hand member of a linear differential equation is 0.
b)
It means that the right-hand member of a linear differential equation is not zero.
c)
It means that the right-hand member of a linear equation is the same as the left hand member.
d)
It means that both the left-hand member and the right-hand member are 0.
37.
The equation dy/dx + P(x) y = Q(x) yⁿ is known as:
a)
Euler equation
b)
Libby equation
c)
Bernoulli equation
d)
Auxiliary equation
38.
In general linear differential equation the value d/dx is normally replaced with D. What do you call the term D?
a)
Differential factor
b)
Differential operator
c)
Differential solution
d)
Differential trajectory
39.
_____ is formed by intersection of rays from the point reflected or refracted from a curve surface.
a)
Envelope
b)
Evolute
c)
Caustic
d)
Parabola
40.
This is a point where the concavity of a curve changes or when the slope of the curve is neither increasing nor decreasing. What is this point commonly called?
a)
Maximum point
b)
Minimum point
c)
Point of tangency
d)
Point of inflection
41.
What do you call a triangle having three unequal sides?
a)
Obtuse
b)
Oblique
c)
Scalene
d)
Isosceles
42.
A polygon with ten sides is said to be:
a)
dodecagon
b)
decagon
c)
decahedron
d)
dodecahedron
43.
When a line y = mx + b slopes downwards from left to right, the slope m is:
a)
less than zero
b)
greater than zero
c)
equal to zero
d)
equal to 1
44.
The area bounded by two concentric circles is called as:
a)
annulus
b)
ring
c)
disk
d)
sector
45.
A chord of a conic section that passes through a focus is called:
a)
Directrix
b)
Focal length
c)
Focal distance
d)
Focal chord
46.
4x² - 256 = 0 is the equation of a/an:
a)
Parabola
b)
Parallel lines
c)
Circle
d)
Ellipse
47.
A line passing through the focus and perpendicular to the directrix of a parabola is called _____.
a)
Axis of parabola
b)
Tangent line
c)
Secant line
d)
Latus rectum
48.
The length of the latus rectum of the parabola y = 4px² is:
a)
4p
b)
2p
c)
1/4p
d)
-4p
49.
The set points in a plane, the sum of whose distances from a fixed points is a constant, is:
a)
Circle
b)
Parabola
c)
Hyperbola
d)
Ellipse
50.
If the distance from the center to the focus of an ellipse is c, from the center to the vertex is a and from the center of directrix is D, its eccentricity is:
a)
D/c
b)
D/a
c)
c/D
d)
c/a
51.
In a general equation of a conic section, Ax² + Bxy + Cy² + Dx + Ey + F = 0, if A and C have different signs, then the curve is a/an:
a)
Circle
b)
Parabola
c)
Ellipse
d)
Hyperbola
52.
If a and b are lengths of semi-major and semi-minor axis of an ellipse respectively, then what is the length of its latus rectum?
a)
2ab
b)
4ab
c)
2b²/a
d)
2a/b²
53.
The locus of a moving point in a plane so that the difference of its distances from two fixed points (foci) is constant.
a)
Circle
b)
Parabola
c)
Ellipse
d)
Hyperbola
54.
If an ellipse and hyperbola have the same foci, they said to be:
a)
central conics
b)
quartic conics
c)
confocal conics
d)
congruent conics
55.
The equation r = 4cosθ is a/an:
a)
ellipse
b)
circle
c)
hyperbola
d)
parabola
56.
A hyperbola centered at the origin with the transverse axis 2a and conjugate axis 2b has the parametric equation of:
a)
x = a tan t and y = b sect t
b)
x = a sect and y = b tan t
c)
x = a cos t and y= b sin t
d)
x = a sin t and y = cos t
57.
The integral of sinm θ cosn dθ can easily be determined by using Wallis formula provided the limits are from:
a)
0 to 𝜋
b)
0 to 𝜋/2
c)
0 to 𝜋/4
d)
0 to 2 𝜋
58.
If the eccentricity is less than one, then curve is known as:
a)
Ellipse
b)
Hyperbola
c)
Parabola
d)
Circle
59.
Points that lie in the same plane.
a)
Coplanar
b)
Collinear
c)
Oblique
d)
Parallel
60.
Any line segment joining a vertex of a triangle to a point on the opposite side is called as:
a)
Newton line
b)
Secant
c)
Cevian
d)
Euclidian line
61.
How do you call a ring-shaped surface or solid obtained by rotating a circle about a coplanar line that does not intersect?
a)
Torus
b)
Annulus
c)
Circoloid
d)
Annular
62.
What is the study of the properties of figures of three dimensions?
a)
Physics
b)
Solid geometry
c)
Plane geometry
d)
Trigonometry
63.
It is defined that the momentum of a moving object is the product of its mass, m, and velocity, V. In Newton’s Law of Motion, what is the rate of change of momentum with respect to time?
a)
Power
b)
Momentum
c)
Energy
d)
Force
64.
When a homogeneous, flexible cord is held at the two ends and allowed to sag freely on its own weight, it will produce a curve very similar to a parabola opening upwards. How do you call this curve?
a)
Parabola
b)
Catenary
c)
Cycloid
d)
Epicycloids
65.
How do you call the line passing through the focus and perpendicular to the directrix of a parabola?
a)
Latus rectum
b)
Axis of the parabola
c)
Transverse axis
d)
Major axis
66.
What is an artificial expense that spreads the purchase price of an asset or other property over a number of years?
a)
Depreciation
b)
Amnesty
c)
Sinking fund
d)
Bond
67.
How do you call a sequence of numbers where the succeeding term is greater than the preceding term?
a)
Dissonant series
b)
Isometric series
c)
Convergent series
d)
Divergent series
68.
It refers to a straight line, which a curve approaches closely, but never meets or touches the curve.
a)
Asymptote
b)
Directrix
c)
Latus rectum
d)
Line segment
69.
The whole is greater than any one of its parts. This statement is known as:
a)
postulate
b)
axiom
c)
hypothesis
d)
theorem
70.
In complex algebra, we use a diagram to represent a complex plane commonly called as:
a)
Venn diagram
b)
Histogram
c)
Argand diagram
d)
Funicular diagram
71.
10 to the negative power of 18 is the value of the prefix.
a)
Atto
b)
Femto
c)
Micro
d)
Pico
72.
What is the ratio of the distance between the foci to the distance between the vertices in either hyperbola or ellipse?
a)
Eccentricity
b)
Latus rectum
c)
Variance
d)
Deviation
73.
How do you classify this interest rate, which specifies the actual rate of interest on the principal for one year?
a)
Nominal rate
b)
Rate of return
c)
Exact interest rate
d)
Effective rate
74.
It is a collection of numbers or letters used to represent a number arranged properly in rows and columns.
a)
Determinant
b)
Matrix
c)
Array
d)
equation
75.
A perpendicular segment from a vertex of the triangle to the line containing the opposite side is known as:
a)
median
b)
altitude
c)
angular bisector
d)
perpendicular bisector
76.
The equation y = a₁ + a₂x is an algebraic expression for which the following choices?
a)
a cosine expansion series
b)
projectile motion
c)
projectile energy
d)
a straight line
77.
Two triangles are congruent if two angles and the included side of one are equal respectively to two angles and the included side of the other.
a)
Theorem
b)
Corollary
c)
Axiom
d)
Postulate
78.
Which of the following properties are intensive properties? I. Temperature; II. Pressure; III. Composition; IV. Mass
a)
I only
b)
IV only
c)
I and II
d)
I, II, and III
79.
The base number of the number system.
a)
Index
b)
Radix
c)
Cologarithm
d)
Logarithm
80.
A number system using a place value (or base) of 20.
a)
Sexagesimal number system
b)
Duodecimal number system
c)
Bidecimal number system
d)
Vigesimal number system
81.
How to you classify work-in-process?
a)
A liability
b)
An expense
c)
A revenue
d)
An asset
82.
The father of plane geometry.
a)
Euclid
b)
Pythagoras
c)
Aristotle
d)
Galileo
83.
What do you think is the negotiation of wage rates, conditions of employment, etc. by representatives of the labor force and management?
a)
Union trade
b)
Union rally
c)
Collective bargaining
d)
Cooperative
84.
How do you call the formula used to compute the value of n factorial, which is in symbolic form (n!), where n is large number?
a)
Matheson formula
b)
Diophantine formula
c)
Richardson-Duchman formula
d)
Stirling’s Approximation
85.
What is an estimate of assets’ net market value at the end of its estimated life?
a)
Book value
b)
Depreciation
c)
Salvage value
d)
Cash flow
86.
This is the process of determining the value of certain property for specific reasons. Guess, what is this?
a)
Amortization
b)
Investment
c)
Appraisal
d)
Depreciation
87.
How do you call a cylinder with elliptical cross section?
a)
Ellipsoid
b)
Cylindroid
c)
Hyperboloid
d)
Paraboloid
88.
The 72 rule of thumb is used to determine:
a)
how many years money will triple
b)
how many years money will double
c)
how many years to amass 1 million
d)
how many years to quadruple the money
89.
To triple the principal, one must use:
a)
integration
b)
derivatives
c)
logarithms
d)
implicit functions
90.
A currency traded in a foreign exchange market for which the demand is consistently high in relation to its supply.
a)
Money market
b)
Hard currency
c)
Treasury bill
d)
Certificate of deposit
91.
Everything a company owns and which has a money value is classified as an asset. Which of the following is classified as an asset?
a)
Intangible assets
b)
Fixed assets
c)
Trade investments
d)
All of these
92.
Which an example of an intangible asset?
a)
Cash
b)
Investment in subsidiary companies
c)
Furnitures
d)
Patents
93.
Lands, buildings, plant and machinery are examples of:
a)
current assets
b)
trade investments
c)
fixed assets
d)
intangible assets
94.
An increase in the value of a capital asset is called:
a)
Profit
b)
capital gain
c)
capital expenditure
d)
capital stock
95.
The reduction in the money value of a capital asset is called:
a)
capital expenditure
b)
capital loss
c)
loss
d)
deficit
96.
It is a negotiable claim issued by a bank in lieu of a term deposit.
a)
Time deposit
b)
Bond
c)
Capital gain
d)
Certificate of deposit
97.
Any particular raw material or primary product (e.g. cloth, wool, flour, coffee...) is called:
a)
Utility
b)
Necessity
c)
Commodity
d)
Stock
98.
It denotes the fall in the exchange rate of one currency in terms of others. The term usually applies to floating exchange rates.
a)
Currency appreciation
b)
Currency devaluation
c)
Currency float
d)
Currency depreciation
99.
The deliberate lowering of the price of a nation's currency in terms of the accepted standard (Gold, American dollar or the British pound).
a)
Currency appreciation
b)
Currency float
c)
Currency devaluation
d)
Currency depreciation
100.
The residual value of a company's assets after all outside liabilities (shareholders excluded) have been allowed for.
a)
Dividend
b)
Equity
c)
Return
d)
Par value
100 %
