WorksheetsFinal Examination in MATH 113 (Part 1A)
Total questions: 100
Worksheet time: 50mins
Name
Class
Date
1.
In general quadratic equation, if the discriminant is zero, the curve is a figure that represents a/an:
a)
Parabola
b)
Circle
c)
Ellipse
d)
Hyperbole
2.
A line segment from the focus of an ellipse to a point on the perimeter of the ellipse is called _____.
a)
Focal distance
b)
Focal radius
c)
Eccentricity
d)
Focal length
3.
In an ellipse, a chord which contains a focus and is line perpendicular to the major axis is called:
a)
Focal width
b)
Conjugate axis
c)
Focal chord
d)
Latus rectum
4.
What is the length of the latus rectum of the curve x² = 20y?
a)
5
b)
20
c)
√20
d)
√50
5.
A straight line where the curve approaches more and more closely but never touches it except at a limiting point of infinity.
a)
Asymptote
b)
Axis of symmetry
c)
Tangent
d)
Normal
6.
If a right circular cone is cut by a plane parallel to its base, it would reveal a/an:
a)
Circle
b)
Parabola
c)
Ellipse
d)
Hyperbola
7.
A locus of a point which move so that it is always equidistant from a fixed point (focus) and from a fixed straight line (directrix).
a)
Circle
b)
Ellipse
c)
Parabola
d)
Hyperbola
8.
If the discriminant of a quadratic equation is greater than zero, the graph is a/an:
a)
Circle
b)
Parabola
c)
Ellipse
d)
Hyperbola
9.
The eccentricity of a regular hyperbola is:
a)
√2
b)
√3
c)
2
d)
1.5
10.
What is the term given to a circle with radius equal to half the transverse axis of the hyperbola or major axis of an ellipse and its center is the center of the conics?
a)
Auxiliary circle
b)
Unit circle
c)
Inscribed circle
d)
Concentric circle
11.
The parabola y = -x² + x + 1 opens:
a)
To the right
b)
To the left
c)
Upward
d)
Downward
12.
What is a radical axis?
a)
The locus of points of different powers with respect to two circles.
b)
The locus of points of equal power with respect to two circles.
c)
The locus of points of equal power with respect to two ellipses.
d)
The locus of points of equal power with respect to two hyperbolas.
13.
A parabola with an orthogonal equation of y2 = 4x may be represented by which of the following parametric equations?
a)
x = 2t and y = t²
b)
x = t² and y = 2t
c)
x = 2t and y = 2t
d)
x = t² and y = t²
14.
What is a constant added to every indefinite integral that does not have limits of integration?
a)
Constant of integration
b)
Variable value
c)
Constrain value
d)
All of the above
15.
If limits of a definite integral are interchanged, what will happen to the integral?
a)
It will remain the same.
b)
its value will become the reciprocal of the original value.
c)
Its sign will change from + to - or from - to +.
d)
It will result to a logarithmic value.
16.
When can we say that an integral is divergent?
a)
When its limit exists as a finite number.
b)
When its limit exists as an infinite number.
c)
When its limit does not exist.
d)
When its limit is real number.
17.
What is a differential equation with two or more variables called?
a)
Unit differential equation
b)
Single differential equation
c)
Ordinary differential equation
d)
Partial differential equation
18.
A differential equation f(y) dy/dx= g(x). Where f is a function of y only and g is a function of x only can be solved by:
a)
direct integration
b)
separation of variable
c)
homogeneous solution
d)
Euler’s multiplier
19.
Some types of linear differential equations can be solved by using an integrating factor eʃ p(x)dx this integrating factor is also known as:
a)
Bernoulli’s multiplier
b)
Euler’s multiplier
c)
Libby’s multiplier
d)
Orthogonal multiplier
20.
The concept of orthogonal trajectories is used in the following branches of physics except one. Which one?
a)
Electrostatic
b)
Thermodynamics
c)
Hydrodynamics
d)
Work and energy
21.
Curve formed by uniform chain hanging freely from two points.
a)
Trisectrix
b)
Parabola
c)
Hyperbola
d)
Catenary
22.
Moment of inertia of any plane figure is expressed in units of length to the _____.
a)
first power
b)
second power
c)
third power
d)
fourth power
23.
If eccentricity is less than one, then the curve is:
a)
Parabola
b)
Ellipse
c)
Hyperbola
d)
Circle
24.
What type of conic has equation of Ax² + Cy² + Dx + Ey + F = 0?
a)
Circle
b)
Parabola
c)
Ellipse
d)
Hyperbola
25.
What is the graph of the equation Ax² + Bx + Cy² + Dy + Ex + F = 0?
a)
Circle
b)
Ellipse
c)
Parabola
d)
Hyperbola
26.
What is the semi-conjugate axis of the hyperbola x²/9 - y²/4 = 1?
a)
3
b)
-3
c)
-2
d)
2
27.
When the ellipse approaches a circle as a limiting shape, its eccentricity approaches:
a)
0
b)
1
c)
-1
d)
infinity
28.
A locus of a point which moves so that the sum of the distances from two fixed points (foci) is constant and is equal to the length of the major axis.
a)
Parabola
b)
Circle
c)
Ellipse
d)
Hyperbola
29.
The tangents to the parabola at the end points of its latus rectum intersect:
a)
at a distance equal to the length of the latus rectum from the focus
b)
at the vertex
c)
at the directrix
d)
none of the above
30.
The latus rectum of the parabola x² = 4ay is:
a)
a
b)
4a
c)
2√a
d)
16a²
31.
The axis of the hyperbola that passes though the foci, vertices and center is called:
a)
conjugate axis
b)
transverse axis
c)
major axis
d)
minor axis
32.
Confocal conics are conics:
a)
having the same foci
b)
whose foci coincide with the origin
c)
having no focus
d)
whose foci coincides with the vertices
33.
Given the polar equation r = 3/(1 + 3cosθ). This is a graph of a/an:
a)
ellipse
b)
parabola
c)
circle
d)
hyperbola
34.
Which of the following does not describe the orbit as observed from earth?
a)
Apogee
b)
Perigee
c)
Eccentricity
d)
Focus
35.
Evaluate the integral of tanh u du.
a)
In sinh u + C
b)
In cosh u + C
c)
cosh u + C
d)
coth u + C
36.
The integral of any quotient whose numerator is the difference of the denominator is the _____ of the denominator.
a)
Reciprocal
b)
Product
c)
Logarithm
d)
Derivative
37.
Many integrals may be evaluated by introducing a new variable of integration in place of the original variable, two variables being connected by some suitable formulas. This process is called _____.
a)
integration by parts
b)
integration by substitution
c)
partial derivatives
d)
the chain rule
38.
The value of x in trigonometric substitution with an integrand involving (a² - x²) is:
a)
a sec θ
b)
a tan θ
c)
a cos θ
d)
a sin θ
39.
What is referred to as the fundamental objects of Calculus?
a)
Integrals
b)
Differentials
c)
Integrals and Derivatives
d)
Derivatives
40.
In what century was calculus independently developed by Newton and Leibniz?
a)
15th
b)
16th
c)
17th
d)
18th
41.
An integral with no restrictions imposed on its independent variable is known as indefinite integral or antiderivative. What is another term for indefinite integral or antiderivative?
a)
Fixed integral
b)
Trivial integral
c)
Primitive integral
d)
Definite integral
42.
The existence of a certain elementary function does not necessarily imply that there must exist another elementary function of which the given function is the derivative. What do you call these functions?
a)
Complex integral functions
b)
Non-integrability functions
c)
Composite integral functions
d)
all of the above
43.
The _____ in integration expresses a given integral as the sum of a function and a known integral.
a)
chain rule
b)
induction formula
c)
reduction formula
d)
L'hopital rule
44.
Integrals that have integrands become infinite in the range of a finite interval of integration are called _____.
a)
Improper Integrals
b)
Complex Integrals
c)
Conjugate Integrals
d)
Composite Integrals
45.
What is an equation which contains an independent variable, a dependent variable and derivatives of the dependent variable with respect to the independent variable?
a)
Differential equation
b)
Variable equation
c)
Independent equation
d)
Dependent equation
46.
If a differential equation involves functions of two or more variables and some of their partial derivatives, the equation is a _____.
a)
ordinary differential equation
b)
partial differential equation
c)
compound differential equation
d)
complex differential equation
47.
What is the order of a differential equation?
a)
The order of the highest derivative that appears in the equation
b)
The order of the lowest derivative that appears in the equation
c)
The order of the middle derivative that appears in the equation
d)
The order of the average derivative that appears in the equation
48.
Which of the following is not a first-order differential equation?
a)
𝑑𝑦/𝑑𝑥 = 3𝑥² + 13𝑥 + 3
b)
𝜕𝑧/𝑑𝑥 = 3𝑥² + 5𝑥𝑦 + 4 - 4𝑦³
c)
𝜕²𝑦/𝜕𝑥 = 6x + 7
d)
𝜕𝑧/𝜕𝑦 = 7𝑥² - 10𝑥𝑦⁴
49.
The _____ of a differential equation whose terms are polynomials in the derivatives is defined as the highest power of the highest-order derivative; consequently the differential equation.
a)
order
b)
term
c)
degree
d)
solution
50.
When can we say that an expression is homogeneous?
a)
When the order is the same.
b)
When the degree of all the terms are the same.
c)
When the degree of all the terms are real numbers.
d)
When the degree of all the terms are 1.
51.
To triple the principal, one must use:
a)
integration
b)
derivatives
c)
logarithms
d)
implicit functions
52.
How do you call the axis of the hyperbola that passes through the center, the foci and vertices?
a)
Transverse axis
b)
Conjugate Axis
c)
Asymptotic axis
d)
Major Axis
53.
How do you call the distance of a point from the y-axis?
a)
Polar distance
b)
Coordinate
c)
Abscissa
d)
Ordinate
54.
Any number expressed in place-value notation with base 12 is known as:
a)
Duodecimal
b)
Deontic
c)
Decile
d)
Dedekind
55.
Which of the following events will cause the optimal lot size, given by the classic EOQ model with no shortages, to increase?
a)
A. A decrease in inventory carrying cost
b)
B. A decrease in demand
c)
C. An increase in demand
d)
A or C
56.
Another name for derivative is said to be:
a)
differential manifold
b)
partial derivative
c)
differential form
d)
differential coefficient
57.
A polygon with twelve sides is known as:
a)
dodecagon
b)
decagon
c)
decahedron
d)
dodecahedron
58.
It is a type of polygon in which each interior angle must be less than or equal to 180°, and all vertices 'point outwards' away from the interior. How do you call this polygon?
a)
Concave Polygon
b)
Convex polygon
c)
Regular polygon
d)
Irregular poly
59.
How do you call the integral of any quotient whose numerator is the differential of the denominator?
a)
Co-logarithm
b)
Logarithm
c)
Product
d)
Derivative
60.
When two planes intersect with each other, the amount of divergence between the two planes is expressed by measuring the:
a)
reflex angle
b)
dihedral angle
c)
polyhedral angle
d)
plane angle
61.
Which statement about a charge placed on a dielectric material is true?
a)
The charge increases the conductivity of the material.
b)
The charge is confined to the region in which the charge was placed.
c)
The charge is immediately lost to the atmosphere.
d)
The charge is instantly carried to the material’s surface.
62.
How do you call a polygon with 10,000 sides?
a)
Hectogon
b)
Chiliagon
c)
Myriagon
d)
Octacontagon
63.
In the problem of writing the equation of a certain curve with respect to another axes in which the new axes are parallel to the original axes and similarly directed is known as:
a)
Translation of axes
b)
Reversal of axes
c)
Notation of axes
d)
Relocation of axes
64.
What can you say to the following statement: “the volume of a circular cylinder is equal to the product of its base and altitude.”?
a)
Postulate
b)
Corollary
c)
Theorem
d)
Axiom
65.
“Whenever a net force acts on a body, it produces acceleration in the direction of the resultant force, an acceleration which is directly proportional to the resultant force and inversely proportional to the resultant force and inversely proportional to the mass of the body”. How do you call this theory?
a)
Newton’s First law of motion
b)
Newton’s Second Law of motion
c)
Faraday’s law of forces
d)
Hook’s law of equilibrium
66.
Which of the following is not a theorem on limits?
a)
The limit of the algebraic sum of several functions is equal to the sum of their limits.
b)
The limit of the product of several function is equal to the product of their limits.
c)
The limit of the difference of several functions is equal to the difference of their limits.
d)
The limit of the quotient of two functions is equal to the quotient of their limits, provided the denominator is not zero.
67.
What do you call the possible outcome of an experiment?
a)
A sample space
b)
A random point
c)
An event
d)
A finite set
68.
The angle that the line of sight to the object, makes with the horizontal, which is above the eye of the observer, is called as:
a)
angle of elevation
b)
angle of depression
c)
acute angle
d)
obtuse angle
69.
Hard water is water which contains soluble salts of which of the following elements?
a)
Sodium
b)
Sulfur
c)
Calcium
d)
Chlorine
70.
In Roman numerals, the doorframe written with the letter indicates that the number equivalent to the letter is to be multiplied by _____.
a)
100
b)
1,000
c)
100,000
d)
1,000,000
71.
A number system using a place value (or base) of 10.
a)
Decimal number system
b)
Denary Number system
c)
Denary Number system
d)
All of the Above
72.
A market situation where there is only one buyer and one seller.
a)
monopoly
b)
monopsony
c)
bilateral monopoly
d)
bilateral monopsony
73.
Mr. PME covered a distance of 55 km in 4 hours by driving his car 40 kph, part of the way, and by walking the remainder of the way at 5 kph. What part of the total distance did Mr PME go by car?
a)
7/11
b)
9/11
c)
8/11
d)
10/11
74.
Find the root mean square of 11, 23, and 35.
a)
25
b)
27
c)
26
d)
24
75.
Guards or Rails at least how many inches in height shall be provided on the exposed side of other building structures.
a)
42 inches
b)
34 inches
c)
12 inches
d)
64 inches
76.
What is the minimum diameter of hoisting and counterweight ropes in elevators?
a)
40 mm
b)
30 mm
c)
25 mm
d)
60 mm
77.
The angle of inclination of an escalator shall not exceed now > many degrees from the horizontal?
a)
45 degrees
b)
60 degrees
c)
30 degrees
d)
20 degrees
78.
No part of the boiler shall be closer than how many meter(s) from any wall?
a)
1 m
b)
2 m
c)
3 m
d)
4 m
79.
Boilers more than 46 sqm heating surface shall each be provided with how many means of feeding water?
a)
2 means of feeding water
b)
3 means of feeding water
c)
4 means of feeding water
d)
5 means of feeding water
80.
Each boiler shall have a steam gauge, with dial range of not less than one and one-half time and not more than how may times the maximum allowable working pressure?
a)
Twice
b)
Thrice
c)
4 times
d)
1.5 times
81.
When ammonia is used, the discharge may be into tank of water, which shall be used for no other purpose except ammonia absorption. At least 1 liter of water shall be provided for every:
a)
120 gallons of ammonia
b)
100 gallons of ammonia
c)
150 gallons of ammonia
d)
110 gallons of ammonia
82.
A flanged is applied to piping system of how many mini in diameter?
a)
100 mm and above.
b)
100 mm below
c)
50 mm and above
d)
more than 200 mm
83.
A boiler having a volume exceeding 120 gallons (454 L), a heat input exceeding 200,000 Btu/hr (58.6 kW), or an operating temperature exceeding 210 F(99C) that provides hot water to be used externally or itself.
a)
Hot water heating boiler
b)
Low pressure hot water heating boiler
c)
Miniature Boiler
d)
Package Boiler
84.
A boiler used for heating water or liquid to a pressure exceeding 160 psi (1,103 kPa) or to a temperature exceeding 250°F (121°C).
a)
Hot water heating boiler
b)
Low pressure hot water heating boiler
c)
Miniature Boiler
d)
Power Hot water Boiler (High Temperature Water Boiler)
85.
A burner smaller than the main burner that is ignited by a spark or other independent and stable ignition source, and provides ignition energy required to immediately light off the burner.
a)
Torch
b)
Small burner
c)
Pilot
d)
Miniature burner
86.
A pilot that burns during light off and that is shut off during normal operation.
a)
Continuous pilot
b)
Intermittent pilot
c)
Interrupted pilot
d)
Infinite pilot
87.
A refrigeration machinery rooms shall be of such dimensions that · all system parts are readily accessible with adequate space for maintenance and operations. An unobstructed walking space at least how many feet in width?
a)
3 feet
b)
8 feet
c)
5 feet
d)
2 feet
88.
The standard of Fire Alarm System.
a)
NFPA 12A
b)
NFPA 17
c)
NFPA 72
d)
NFPA 750
89.
Electrically non-conducting, volatile, or gaseous fire extinguisher. that does not leave residue upon evaporation.
a)
Clean agent
b)
Deluge System
c)
Dry chemical extinguishing agent
d)
Carbon dioxide extinguishing system
90.
An alarm caused by mechanical failure, malfunction, improper installation or lack of proper maintenance, or an alarm activated by caused that cannot be determined.
a)
Mechanical Alarm
b)
Unintended fire alarm
c)
Smoke Alarm
d)
Nuisance Alarm
91.
A solution of water and potassium-carbonete-based chemical, potassium-acetate-based chemical or a combination thereof, fanning and extinguishing agent.
a)
Halogenated extinguishing agent
b)
Foam extinguishing agent
c)
Wet-chemical extinguishing agent
d)
Manual wet agent
92.
A wet stand pipe connected to a water supply for the purpose of maintaining water within the system but to which does not have a water supply capable of delivering the system demand attached to the system. It requires water from a fire department pumper (or that like) to be pumped into the system through the fire department connection in order to supply the system demand.
a)
Manual Dry
b)
Manual Wet
c)
Bulk Storage
d)
Deluge
93.
Foam extinguishing system shall be provided in buildings used as _____.
a)
call center venue
b)
malls
c)
offices
d)
maintenance aircraft hangars
94.
High pressure cylinders shall be weighed and the date of hydrostatic test shall be verified at:
a)
3 months
b)
4 months
c)
6 months
d)
12 months
95.
Elevators are required for how many storey buildings?
a)
4 storey
b)
3 storey
c)
5 storey
d)
5 storey and above
96.
Any flexible plan building or open plan building in which the travel distance of how many meters to exits must have approved and supervised sprinkler systems?
a)
exceeds 46 m distance
b)
exceeds 40 m distance
c)
with 30 m distance
d)
more than 30 distance
97.
Sprinkler system shall have pressure zones so that sprinkler heads will not be subjected to pressure that is more than to _____.
a)
150 psi
b)
250 psi
c)
175 psi
d)
100 psi
98.
What is the minimum height from any highest point of any valve stem and the ceiling for new boiler installation if it is a single installation or self-contained boiler?
a)
915 mm
b)
2,130 mm
c)
1,025 mm
d)
550 mm
99.
Ducting used for conveying air at temperatures not exceeding what temperature to or from occupied areas of any occupancy through other than heating or air conditioning systems such as ventilation, for human usage, domestic kitchen range exhaust, bathroom exhaust ducts and domestic types clothes dryer exhaust ducts?
a)
121 deg. C
b)
100 deg. C
c)
150 deg. C
d)
95 deg. C
100.
LPG (liquefied Petroleum Gases) are mixture of hydrocarbons liquefied under pressure for efficient transportation, storage and use. LPG are generally composed of Ethylene, Propane, Propylene, Butane, Isobutene and Butylenes. However commercially they (LPG) are classified as mixtures of:
a)
Propane and Butane
b)
Propylene and Isobutene
c)
Ethylene and Propane
d)
Propane and Propylene
100 %
