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WorksheetsMESL 1.1
Total questions: 105
Worksheet time: 53mins
1. For a given function, it is found f(t)=f(-t). What type of symmetry does f(t) have ?
a. Odd Symmetry
b. Even Symmetry
c. Rotational Symmetry
d. Quarter-wave Symmetry
2. Which number has four significant figures?
a. 0.0014
b. 0.01414
c. 0.141
d. 1.4140
2. Naperian logarithm have a base closest to which number?
a. 2.17
b. 2.72
c. 3.14
d. 10
4. If the second derivative of the equation of a curve is equal to the negative of the equation of the same curve, the curve is.
a. An exceptional
b. A sinusoid
c. A tangent
d. A parabola
1. To find the angle of a triangle, given only lengths of the sides, one would use
a. The law of cosines
b. The law of sines
c. The law of tangents
d. The inverse-square law
6. Which is true regarding the signs of the natural functions for angles between 90° and 180°?
a. The tangent is positive
b. The cotangent is positive
c. The cosine is negative
d. The sine is negative
7. What is the inverse natural function of the cosecant?
a. Secant
b. Sine
c. Cosine
d. Cotangent
8. The graphical presentation of a cumulative frequency distribution in a set of statistical data is called _____________.
a. Histogram
b. Kurtosis
c. Lepticurtic
d. Ogive
9. A statement of truth of which follows with little or no proof from a theorem.
a. Axiom
b. Hypothesis
c. Corollary
d. Conclusion
10. It is sequence of numbers such that the successive terms differ by a constant.
a. Arithmetic Progression
b. Infinite Progression
c. Geometric Progression
d. Harmonic Progression
11. A frequency curve which is composed of series of rectangles constructed with the steps as the base and the frequency as the height.
a. Histogram
b. Ogive
c. Frequency Distribution
d. Bar Graph
12. If the roots of an equation are zero, then they are classified as;
a. Hyperbolic solution
b. Zeros of function
c. Extraneous roots
d. Trivial solution
13. Convergent series is a sequence of decreasing number or when the succeeding term is _________ the preceding term.
a. Greater than
b. Equal to
c. Lesser than
d. None of the above
14. If a = b then b=a. This illustrates what axiom in algebra?
a. Symmetric axiom
b. Reflexive axiom
c. Transitive axiom
d. Replacement axiom
15. A and B are independent events. The probability that event A will occur is Pa and the probability that A and B will occur is Pab. From these two statements, what is the probability that event B will occur?
a. Pa – Pab
a. Pb – Pab
a. Pa x Pb
a. Pab/Pa
16. When f(x) is negative the curve of y= f(x) is concave _______
a. Downward
b. To the right
c. Upward
d. To the left
17. If the second derivative of the equation of a curve is equal to the negative of the equation of that same curve, the curve is
a. A paraboloid
b. A sinusoid
c. A cissoid
d. An exponential
18. A function F(x) is called _____ of F(x) = f(x)
a. Explicit Function
b. Derivative
c. Implicit function
d. Antiderivative
19. Points of derivatives which do not exists ( and so equals zero) are called ________
a. Stationary points
b. Minimum points
c. Maximum points
d. Minimum and maximum
20. At the point of inflection where x= a,
a. f^n(a) not equal to 0
b. f^n(a) = 0
c. f^n(a) > 0
d. f^n(a) = 0
21. At the maximum point, the slope of the tangent line is
Negative
Infinity
Positive
a. Zero
22. What is the point where the second derivative is zero?
Maxima
Minima
Inflection point
Inflection point
23. The point of the curve where the second derivative of a function is equal to zero is called
Maxima
Minima
Point of inflection
Critical point
24. The point of the curve where the first derivative of a function is zero and the second derivative is positive is called
Maxima
Minima
Point of inflection
Critical point
25. Evaluate the integral of tanh u du.
ln sin h u + c
ln cos h u + c
cos h u + c
cot h u + c
26. The derivative of with respect to x is
a. a^u ln a du/dx
b. a^u ln u du/dx
c. u^a ln u du/dx
d. u^a ln a du/dx
27. If y= tanhx, find dy/dx.
a. sech²x
b. -sech²x
c. Sech x tanh x
d. –sech x tanh x
28. The field of mathematics which rest on upon the fundaments concept of limits and was created by Newton and Leibniz.
a. Physics
b. Calculus
c. Boolean Algebra
d. Quantum Mechanics
29. The _______ of a relation is the set of second elements of the pair in the relation.
Domain
Range
Graph
Function
30. A relation in which there is exactly one range element associated with each domain element.
Graph
set
formula
function
31. To comply with the requirement of the Mechanical Engineering Law on the minimum complement of mechanical engineers, a mechanical plant with a combine prime movers rating 373 kW must have in its employ the following
a. 1 PME, 1 RME and 1 CPM
b. 1 RME, 2 CPM
c. 1 PME, 2 RME
d. 1 RME is charge of every shift
32. Mechanical Plant Engineer (MPE) may be allowed to take the licensure examination for PME if.
a. He has 4 years practice as a PME
b. If he graduated with a BSME degree and has a 4 years of practice as a RME
c. If he has a BSME degree, passed the examinations for RME and has 4 years practice as RME.
d. NONE OF THESE
33. The only country that recognizes the mechanical engineering licensure of Filipinos issued by the Professional Regulation Commission and allowed to used the practice as RME.
a. America
b. Canada
c. Japan
d. None of these
34. The ratio between the average load and total available capacity
a. Load factor
b. Power factor
c. Demand factor
d. Capacity factor
35. 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. 1000
c. 100000
d. 1000000
36. In Roman numerals, the bar written above the letter indicates that the number equivalent to the letter is to be multiplied by
a. 100
b. 1000
c. 10000
d. 100000
37. Indicate the false statement about rules of divisibility.
a. The number is divisible by 9 if the sum of its digit is divisible by 8
b. The number is divisible by 12 if it is divisible by 4 and 3
c. The number is divisible by 4 if the number formed by the last 2 digits by the last 2 digits is divisible by 3
d. The number is divisible is divisible by 5 if it ends with 5 or 0
38. The base number of the number system.
a. Index
b. Radix
c. Cologarithm
d. Logarithm
39. What is another name of octal number system?
a. Octonary number system
b. Octenary number system
c. Octonumber system
d. Octonumerals
40. A number system using a plane value or base of 20
a. Sexagesimal number system
b. Duodecimal number system
c. Bidecimal number system
d. Vigesimal number system
41. A number system using a place value or base of 60
a. Sexagesimal number system
b. Septenary number system
c. Senary number system
d. Sexadecimal number system
42. 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 above
43. What is the radix of the binary number system?
10
16
6
2
44. A number system which needs sixteen symbols, the 10 numerals and the letters A, B, C D, E and F is called.
a. Octal number system
b. Duodecimal number system
c. Vigesimal number system
d. Hexadecimal number
45. The terms “ dozen” and “gross” used what number system?
a. Decimal number system
b. Duodecimal number decimal
c. Bidecimal number system
d. Vigesimal number system
46. In general quadratic equation, if the discriminant is zero, the curve is a figure that represent a/an
a. parabola
b. circle
c. ellipse
d. hyperbola
47. Equations relating x and y that cannot readily be solved explicitly for y as a function of x or for x as a function of y. Such equations may nonetheless determine y as a function of x or vice versa, such function is called.
a. logarithm function
b. implicit function
c. explicit function
d. continuous function
48. In polar coordinates system the length of the ray segment from a fixed origin is known as _________.
a. Amplitude
b. Radius vector
c. Hypotenuse
d. Minimum point
49. Given the equations 3x²+2x-5y + 7 =0. Determine the curve.
Ellipse
Parabola
Hyperbola
a. Circle
50. If eccentricity is than one, then the curve is;
a. Parabola
b. Ellipse
c. Hyperbola
d. Circle
51. Of what quadrant is A, if sec A is positive and csc A is negative?
a. IV
b. I
c. III
d. II
52. If the general equation of the conic is Ax² + 2Bxy + Cy²+ Ey + F =0, and B²-4AC˃0, then the conic is a/an
a. Circle
b. Parabola
c. Hyperbola
d. Ellipse
53. What type of conic has equation of Ax² + Cy² + Dx + Ey + F = 0?
a. Circle
b. Parabola
c. Ellipse
d. Hyperbola
54. 4x²-256=0 is the equation of a/an
Parabola
Parallel lines
Circle
Ellipse
55. The graph of r = a + b cos θ is a
a. Lemniscate
b. Lituus
c. Limacon
d. Cardiod
56. In an ellipse, a chord which contains a focus and is in line perpendicular to the major axis is called;
a. Focal width
b. Conjugate axis
c. Focal chord
d. Latus rectum
57. If all the y-terms have even exponents, the curve is symmetric with respect to the __________.
a. X-axis
b. Origin
c. Y-axis
d. Line 45° with the x-axis
58. It 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
59. If the equation is unchanged by the substitution of –x to x, its curve is symmetric with respect to the
a. X-axis
b. Y-axis
c. Origin
d. Line 45° with the x-axis
60. 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. Spiral of Archimedes
b. Epicycloid
c. Cycloid
d. Helix
61. Which one of the following contains only items which are considered fixed charges?
a. Interest, taxes, amortization, insurance, rent
b. Amortization, insurance, steam cost, painting, cleaning
c. Interest, taxes, replacements, labor for repairs
d. Interest, taxes, rent, power cost, oil cost
62. An economic study is made of the total amount cost (c) for the series of alternative investment (p) for a given project. If C is plotted as the ordinate versus P, the most desirable occurs when
a. dC/dP = 1
b. dC/dP = CO
c. dC/dP = 0
d. dC/dP = +1
63. Reduction in the level of national income and output usually accompanied by the fall in the general price level.
a. Devaluation
b. Deflation
c. Inflation
d. Depreciation
64. It is a series of equal payments occurring at equal interval of time.
a. Annuity
b. Debt
c. Amortization
d. Deposit
65. The place where buyers and sellers come together
a. Market
b. Business
c. Recreation center
d. Buy and sell section
66. A market whereby there is only one buyer of an item for which there are no good substitute.
a. Monopsony
b. Oligopoly
c. Monopoly
d. Oligopsony
67. It is a series of equal payments occurring at equal interval of time where the first payment is made after several periods, after the beginning of the payment.
a. Perpetuity
b. Ordinary annuity
c. Annuity due
d. Deferred annuity
68. The total income equals the total operating cost.
a. Balanced sheet
b. In-place value
c. Check and balance
d. Break even-no gain no loss
69. Kind of obligation which has no condition attached.
a. Analytic
b. Pure
c. Gratuitous
d. Private
70. Direct labor cost incurred in the factory and direct materials cost are the costs of all materials that go into production. The sum of these two direct costs is known as
a. GS and A expenses
b. Operating and maintenance costs
c. Prime cost
d. O and M costs
71. An index of short term paying ability is called
a. Receivable turn-over
b. Profit margin ratio
c. Current ratio
d. Acid-test ratio
72. An artificial expenses that spreads the purchase price of an asset or another property over a number of years.
a. Depreciation
b. Sinking fund
c. Amnesty
d. Bond
73. Estimated value at the end of the useful life.
a. Market value
b. Fair value
c. Salvage value
d. Book value
74. Consists of the actual counting or determination of the actual quantity of the materials on hand as of a given date.
a. Physical inventory
b. Material update
c. Technological assessment
d. Material count
75. Additional information of prospective bidders on contract documents issued prior to bidding date.
a. Delict
b. Escalatory
c. Technological assessment
d. Bid bulletin
76. An annulus is a plane figure which is composed of two concentric circles. The area of the annulus can be calculated by getting the difference between the area of the larger circle and the area of the smaller circle. Also, its area can be calculated by removing the hole. This method is called.
a. Law of extremities
b. Law of reduction
c. Law of deduction
d. Sharp theorem
77. Each of the faces of a regular hexahedron is a
a. Square
Triangle
Rectangle
Circle
78. It is a polyhedron of which two faces are equal polygons in parallel planes and the other faces are parallelograms.
Tetrahedron
a. Prism
Frustum
Prismatoid
79. The apothem of a polygon is ________ of its inscribed circle
a. Radius
b. Circumference
c. Diameter
d. Length
80. Each angle of regular dodecagon is equal to
a. 135
b. 150
c. 125
d. 105
81. The area bounded by two concentric circles is called
a. Ring
b. Disk
c. Annulus
d. Sector
82. One-fourth of a great circle is called
a. Cone
b. Sector
c. Quadrant
d. Arc
83. Points that lie on the same plane is called
a. Coplanar
b. Parallel
c. Collinear
d. Oblique
84. The volume of a circular cylinder id equal to the product of its base and altitude.
a. Axiom
b. Postulate
c. Theorem
d. Corollary
85. The study of properties of figures in three dimensions
a. Physics
b. Plane trigonometry
c. Solid geometry
d. Trigonometry
86. A plane closed curve, all points of which are the same distance from a point within, called the center
a. Polyhedron
b. Polygon
c. Circle
d. Ellipse
87. What is the angle of and less than 2.
a. Straight line
b. Obtuse angle
c. Oblique angle
d. Acute angle
88. What is the value in degrees of 1 radian?
a. 90°
b. 57.3°
c. 60°
d. 33°
89. Prisms are named according to their ___________.
Diagonals
Sides
Vertices
Bases
90. In plane geometry, two circular arcs that together make up a full circle are called
a. Coterminals arcs
b. Conjugate arcs
c. Congruent arcs
d. Half arcs
91. Sin A cos B – cos A sin B is equivalent to :
a. Cos (A- B)
b. Sin (A- B)
c. Tan (A- B)
d. Cos2 (A- B)
92. The angular distance of a point on the terrestrial sphere from the north pole is called
Colatitude
Latitude
Altitude
Codeclination
93. Csc 520° is equal to
a. Cos 20°
b. Csc 20 °
c. Tan 45°
d. Sin 20 °
94. What is the sine of 820°?
a. 0.984
b. 0.866
c. -0.866
d. -0.5
95. The logarithm of the negative number is
a. Imaginary
b. Irrational
c. Real
d. Rational
96. The sum of the squares of the sine and cosine of an angle.
0
1
2
3
97. The logarithm of a number to the base e(2.7182……) is called
a. Napierian logarithm
b. Characteristic
c. Mantissa
d. Briggsian logarithm
98. The characteristic is equal to the exponent of 10, when the number is written in
a. Exponential form
b Scientific notation
c. Logarithm form
d. Irrational number
99. Napierian logarithms have a base closest to which number?
a. 2.72
b. 2.82
c. 2.92
d. 10
100. The logarithm of 1 to any base is
a. Indeterminate
b. Zero
c. Infinity
d. One
101. Sin(270°+) is equal to
a. –cos beta
a. Sin beta
a. –sin beta
a. cos beta
102. The sum of the angles in an octant spheric triangle is
a. 180°
b. 270°
c. 360°
d. 540°
103. The median of a triangle is the line connecting the vertex and the midpoint of the opposite side. For given triangle, these medians intersects at a point which is called the
a. Orthocenter
b. Circumcenter
c. Centroid
d. Incenter
104. The altitudes of the sides of the triangle intersects at the point known as
a. Orthocenter
Circumcenter
a. Incenter
d. Centroid
105. The angle which the line of sight to the object makes with the horizontal which is above the eye of the observer is called
a. Angle of depression
b. Angle of elevation
c. Acute angle
d. Bearing
