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Worksheets

MESL

Total questions: 500

Worksheet time: 4hrs 10mins

Name
Class
Date
1.

1. The equation y = a + bx is an algebraic expression for which of the following choices?

a)

A. Cosine expansion series

b)

B. A circle in polar form

c)

C. Projectile motion

d)

D. Straight line 

2.

2. What is the acid test ratio?

a)

a.  The ratio of owner’s equity to total current liabilities

b)

b.  The ratio of all assets to actual current liabilities

c)

c.  The ratio of current assets (exclusive of inventory) to the total current liabilities

d)

d.  The ratio of gross margin to operating, sates, and administrative expenses

3.

3. How do call an energy required to move 1 Coulomb of charge through an element.

a)

a)Current

b)

Voltage

c)

Power

d)

Resonance

4.

4. This is a number sequence where the succeeding term is obtained by adding the last pair of preceding terms such as the sequence (1, 1, 2, 3, 5, 8 …). How do you call this number sequence?

a)

A.Euler’s number

b)

A.Fermat number

c)

A.Fibonacci number

d)

A.Fourier series

5.

5. If the roots of an equation are zero, then, how do you classify the solutions?

a)

Extraneous solutions

b)

a.Trivial solutions

c)

a.Conditional solutions

d)

a.Ambiguous solutions

6.

6. In electricity, how do you call the rate of charge flow?

a)

Potential difference

b)

Current

c)

Voltage

d)

Power

7.

7. This law in electrical circuits states, “The algebraic sum of currents entering a node (or a closed boundary) is zero”. How do you call this law? 

a)

a)Kirchhoff's current law

b)

a)Ohm’s current law

c)

a)Kirchhoff’s voltage law 

d)

a)Ohm’s voltage law

8.

8. This law in electrical circuits state, “The algebraic sum of all voltages around a closed path (or loop) is zero”. How do you call this law?

a)

a)Kirchhoff's current law

b)

a)Kirchhoff’s voltage law

c)

a)Ohm’s current law

d)

Ohm’s voltage law

9.

9. In electrical, what is the SI unit of conductance? 

a)

a)Ohm

b)

Mho

c)

Siemens

d)

Ampere

10.

10. Which of the following is the equivalent of 1 Ampere? 

a)

a)1 Coulomb per second

b)

a)1 Joule per Coulomb

c)

a)1 Volt per Ampere

d)

a)1 Ampere per Coulomb

11.

11. What do you think is the lessening of the value of an asset due to a decrease in the quantity available as a coal, oil and timber in forests?

a)

a)Depletion

b)

Amortization

c)

Depreciation

d)

Investment

12.

12. 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)

a)Maximum point

b)

a)Minimum point

c)

a)Point of tangency

d)

a)Point of inflection

13.

13. How do you call the axis of the hyperbola that passes through the center, the foci and vertices?

a)

a)Transverse axis

b)

a)Conjugate Axis

c)

a)Asymptotic axis

d)

a)Major Axis

14.

14. What is a number, which could not be expressed as a quotient of two integers?

a)

Natural

b)

Rational

c)

Irrational

d)

Surd

15.

15. How do you call the opposite of the prefix nano?

a)

Peta

b)

Tera

c)

Giga

d)

a)Hexa

16.

16. What do you call a triangle having three unequal sides?

a)

Obtuse

b)

Scalene

c)

Oblique

d)

Isosceles

17.

How do you call the distance of a point from the y-axis?

a)

a)Polar distance

b)

Coordinate

c)

Abscissa

d)

Ordinate

18.

18. This is the measure of central tendency defined as the most frequent score. How do you call this measure of central tendency?

a)

Median

b)

Mode

c)

Mean

d)

Deviation

19.

19.Which of the following is the equivalent of 1 mil?

a)

a)One-tenth of an inch

b)

a)One-thousandth of an inch

c)

a)One millionth of an inch

d)

a)One-half of an inch

20.

20. A polygon with ten sides is said to be:

a)

Dodecagon

b)

Decagon

c)

Decahedron

d)

Dodecahedron

21.

21. Any number expressed in place-value notation with base 12 is known as:

a)

Duodecimal

b)

Deontic

c)

Decile

d)

Dozedecimal

22.

22. Another name for derivative is said to be:

a)

a.Differential manifold

b)

a.Partial derivative

c)

a.Differential form

d)

a.Differential coefficient

23.

23. Another term for rhombus is said to be:

a)

Dichotomy

b)

Diamond

c)

a.Cyclic quadrilateral

d)

Bi-rectangular

24.

24. A prefix denoting a multiple of ten times any of the physical units of the system international.

a)

Deka

b)

Nano

c)

Hecto

d)

Exa

25.

25. The father of plane geometry.

a)

Euclid

b)

Pythagoras

c)

Aristotle

d)

Galileo

26.

26. This is the case of a solution of a plane triangle where the given data leads to two solutions. How do you call this case?

a)

a)Ambiguous case

b)

a)Quadratic case

c)

a)Extraneous case

d)

a)Conditional case

27.

27. 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)

a)Concave Polygon

b)

a)Convex polygon

c)

a)Regular polygon

d)

a)Irregular polygon

28.

28. It is a series of equal payments occurring at equal intervals of time where the first payment is made after several periods, after the beginning of the payment. How do you call this payment?

a)

a)Deferred annuity

b)

a)Delayed annuity

c)

a)Progressive annuity

d)

a)Simple annuity

29.

29. What do you think is the negotiation of wage rates, conditions of employment, etc. by representatives of the labor force and management?

a)

a)Union trade

b)

a)Union rally

c)

a)Collective bargaining

d)

a)Cooperative

30.

30. How do you call a type of bond where the corporation’s owner name is recorded and the interest is paid periodically to the owners with their asking for it?

a)

a)Registered bond

b)

a)Preferred bond

c)

a)Incorporator’s bond

d)

a)Bail bond

31.

31. How do you call the integral of any quotient whose numerator is the differential of the denominator?

a)

a)Co-logarithm

b)

a)Logarithm

c)

a)Product

d)

a)Derivative

32.

32. What is a regular polygon that has 27 diagonals?

a)

a)Nonagon

b)

a)Hexagon

c)

a)Pentagon

d)

a)Heptagon

33.

33. 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)

a)Matheson formula

b)

a)Diophantine formula

c)

a)Richardson-Duchman formula

d)

a)Stirling’s Approximation

34.

34. What is the reason why an ivory soap floats in water?

a)

a) All matter has mass

b)

b) The specific gravity of ivory soap is greater than that of water

c)

c) The density of ivory soap is unity

d)

d) The specific gravity of ivory soap is less than that of water

35.

35. When two planes intersect with each other, the amount of divergence between the two planes is expressed by measuring the:

a)

a)Reflex angle

b)

a)Dihedral angle

c)

a)Polyhedral angle

d)

a)Plane angle

36.

36. What do you think is the output or sales at which income is insufficient to equal operating cost?

a)

a)Break even point 

b)

a)Depreciation

c)

a)Investment

d)

a)Cash flow

37.

37. What is an estimate of assets’ net market value at the end of its estimated life?

a)

a)Book value

b)

a)Depreciation

c)

a)Salvage value

d)

a)Cash flow

38.

38. What do you think is the lessening of the value of an asset due to a decrease in the quantity available as a coal, oil and timber in forests?

a)

a)Depletion

b)

a)Amortization

c)

a)Depreciation

d)

a)Investment

39.

39. What can you say about the present worth of all depreciation over the economic life of the item?

a)

a)Maintenance

b)

a)Capital recovery

c)

a)Depreciation recovery 

d)

a)Annuity

40.

40. What do you think is the provision in the contract that indicates the possible adjustment of material cost and labor cost?

a)

a)Secondary clause

b)

a)Specification

c)

a)Escalatory clause

d)

a)General provision

41.

41. This is the process of determining the value of certain property for specific reasons. Guess, what is this?

a)

a)Amortization

b)

a)Investment

c)

a)Appraisal

d)

a)Depreciation

42.

42. How do you call those products or services that are directly used by people to satisfy their wants?

a)

a)Consumer goods and services

b)

a)Producer goods and services

c)

Necessity products and services 

d)

Luxury products and services

43.

43. These are used to produce consumer goods and services. Guess, what are these?

a)

a)Consumer goods and services

b)

a)Producer goods and services

c)

Necessity products and services 

d)

Luxury products and services

44.

44. What do you think are those products or services that are required to support human life and activities that will be purchased in somewhat the same quantity even though the price varies considerably?

a)

a)Consumer goods and services

b)

a)Producer goods and services

c)

Necessity products and services 

d)

Luxury products and services

45.

45. How do you call a cylinder with elliptical cross section?

a)

a.Ellipsoid

b)

a.Cylindroid

c)

a.Hyperboloid 

d)

a.Paraboloid

46.

46. How do you call a market whereby there is only one buyer of an item for which there are no goods substitutes?

a)

a)Monopoly

b)

a)Monopsony 

c)

a)Oligopoly

d)

a)Oligopsony

47.

47. Which statement about a charge placed on a dielectric material is true?

a)

a.  The charge increases the conductivity of the material

b)

b.  The charge is confined to the region in which the charge was placed.

c)

c.  The charge is immediately lost to the atmosphere

d)

d.  The charge is instantly carried to the material’s surface

48.

48. Which of the following is not a property of magnetic field lines?

a)

a) Magnetic field lines have no beginnings and no ends

b)

b) The lines cross themselves only at right angles

c)

c) The line intersect surfaces of equal intensity at right angles

d)

d) The field is stronger where the lines are closer together

49.

49. Tesla is a unit of which of the following?

a)

a)Magnetic induction

b)

a)Inductance

c)

a)Capacitance

d)

a)magnetic flux

50.

50. What is a pole pitch?

a)

a)The angle at which the pole windings are wound

b)

a)The space on the stator allocated to two poles

c)

 The space on the stator allocated to one pole

d)

d) The mica used to insulate the poles from each other

51.

51. How do you call a polygon with 10 000 sides?

a)

Hectagon

b)

Chilliagon

c)

Myriagon

d)

Octacontagon

52.

52. Any line segment joining a vertex of a triangle to a point on the opposite side is called as:

a)

a)Newton line

b)

Secant

c)

Cevian

d)

a)Euclidian line

53.

53. It is any influence capable of producing a change in the motion of an object.

a)

Force

b)

Acceleration

c)

Friction

d)

Velocity

54.

54. How do you call the amount needed at the beginning of operations and permits the enterprise to begin functioning before it receives any income from the sales of its product or service.

a)

a)Initial working capital

b)

a)Regular working capital

c)

a)Annuity

d)

a)Equity 

55.

55. 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)

a)Translation of axes

b)

a)Reversal of axes

c)

a)Notation of axes

d)

a)Relocation of axes

56.

56. 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

57.

57. If the eccentricity is less than one, then curve is known as:

a)

Ellipse

b)

Hyperbola

c)

Parabola

d)

Circle

58.

58. 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

59.

59. What is the study of the properties of figures of three dimensions?

a)

Physics

b)

a)Solid geometry

c)

a)Plane geometry

d)

a)Trigonometry

60.

60. A type of bond, without any security behind them except a promise to pay by the issuing corporation is known as:

a)

a.Collateral trust bond

b)

a.Mortgage bond

c)

a.Debenture bond

d)

a.Joint bond

61.

61. A situation whereby payment is made for work not done. The term also applies to the case where more workers are used than a reasonable requirement for efficient operation.

a)

a.Downtime pay

b)

a.Check-in-pay

c)

a.Feather bedding

d)

a.Moon lighting

62.

62. The difference between what a negotiable paper is worth in the future and its present worth is known as:

a)

a.Book value

b)

a.Salvage value

c)

a.Sunk value

d)

Discount

63.

63. The temperature to which the air must be cooled at constant temperature to produce saturation.

a)

a.Absolute temperature

b)

a.273 K

c)

a.Dew point

d)

a.Critical temperature

64.

64. A net force that will give to a mass of one gram an acceleration of 1 cm/s2 is said to be:

a)

Newton

b)

Ergs

c)

a.Kilogram force

d)

Dyne

65.

65. A change in position, specified by a length and a direction is said to be:

a)

Displacement

b)

Acceleration

c)

Velocity

d)

a.Dynamic equilibrium

66.

66. The process of one substance mixing with another because of molecular motion is known as:

a)

Adhesion

b)

Diffusion

c)

Cohesion

d)

Confusion

67.

67. Those cost that arise at the result of a change in operations or policy or it is the ratio of a small increment cost and a small increment of output.

a)

a.Increment cost

b)

a.Differential cost

c)

a.Marginal cost

d)

a.Promotion cost

68.

68. The index that gives the rate earned per share based on current price per share is called as

a)

a.Price-earning ratio

b)

a.Operating expense ratio

c)

a.Dividend yield

d)

a.Equity ratio

69.

69. A regular polyhedron having 12 regular pentagons is called as:

a)

Icosahedron

b)

Octahedron

c)

Dodecahedron

d)

a.Tetrahedron

70.

70.Two angles whose sum is 360o is called:

a)

a.Explementary angles

b)

a.Complimentary angles

c)

a.Supplementary angles

d)

a.Elementary angles

71.

71. What is an annuity?

a)

The future worth of a present amount.

b)

a)A series of uniform amounts over a period of time

c)

c) The present worth of a future amount

d)

d) An annual repayment of a loan

72.

72. When using net present worth calculations to compare two projects, which of the following could invalidate the calculation?

a)

Use of the same discount rate for each period

b)

a)Differences in the magnitudes of the projects

c)

c) Evaluating over different time periods 

d)

d) Mutually exclusive projects

73.

73. What must two investments with the same present worth and unequal lives have?

a)

a)Different equivalent uniform annual cash flows

b)

a)Identical salvage values

c)

c) Different salvage values

d)

d) Identical equivalent uniform annual cash flows

74.

74. Which of the following is true regarding the minimum attractive rate of return used in judging proposed investments?

a)

a.  It is much smaller than the interest rate used to discount expected cash flows from investments

b)

b.  It is frequently a policy decision made by an organization’s management

c)

c.  It is larger than the intere

d)

d.  It is not relevant in engineering economy studies

75.

75. Which of the following situations has a conventional cash flow so that an internal rate of return can be safely calculated and used?

a)

a.  Your company undertakes a mining project in which the land must be reclaimed at the end of the project.

b)

b.  You invest in a safe dividend stock and receive dividends each year.

c)

c.  You lease a car and pay by the month

d)

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.

76.

76. The economic order quantity (EOQ) is defined as the order quantity which minimizes the inventory cost per unit time. Which of the flowing is not an assumption of the basic EOQ model with no shortages?

a)

a) Reordering is done when the inventory is zero

b)

b) There is an upper bound on the quantity ordered

c)

c) The entire reorder quantity I delivered instantaneously

d)

d) The demand rate is uniform and constant

77.

77. 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)

d) a or c

78.

78. What is a borrower of a particular loan almost always required to do during repayment?

a)

a) Pay exactly the same amount of principal each payment

b)

b) Repay the loan over an agreed-upon amount of time

c)

c) Pay exactly the same amount of interest each payment

d)

d) Pay the interest only whenever failure to pay the principal

79.

79. How to you classify work-in-process?

a)

a)A liability

b)

a)An expense

c)

a)A revenue

d)

a)An asset

80.

80. What is the indirect product cost (IPC) spending variance?

a)

a.  The IPC volume adjusted budget minus the total IPC absorbed

b)

b.  The IPC volume adjusted budget [fixed + volume (variable IPC rate)]

c)

c.  The difference between actual IPC and IPC volume adjusted budget

d)

d.  The difference between actual IPC and IPC absorbed

81.

81. A leak from a faucet comes out in separate drops. Which of the following is the main cause of this phenomenon?

a)

a)Air resistance

b)

a)Gravity 

c)

a)Surface tension

d)

a)Viscosity of the fluid

82.

82. Which of the following elements and compounds is unstable in its pure form?

a)

a)Hydrochloric acid 

b)

a)Carbon dioxide

c)

a)Sodium

d)

a)Helium

83.

83. What is the actual geometric shape of the methane molecule?

a)

Tetrahedral

b)

Pyramidal

c)

a)Square planar

d)

Linear

84.

84. A substance is oxidized when which of the following occurs?

a)

a)It losses electrons

b)

a)It becomes more negative

c)

c) It gives off heat

d)

d) It absorbs energy

85.

85. Reactions generally proceed faster at higher temperatures because of which of the following?

a)

a)The molecules are less energetic

b)

b)The activation energy is less

c)

c) The molecules collide more frequently

d)

d) Both b) & c) above

86.

86. Which one of the following statements regarding organic substances is false?

a)

a.  Organic matter is generally stable at very high temperatures

b)

b.  Organic substances generally dissolve in high-concentration acids

c)

c.  All organic matter contains carbon

d)

d.  Organic substances generally do not dissolve in water.

87.

87. Which of the following affects most of the electrical and thermal properties of materials?

a)

a)The weight of the atoms

b)

a)The weight of the protons

c)

c) The electrons, particularly the outermost one

d)

d) The magnitude of electrical charge of the protons

88.

88. What are the valence electrons?

a)

a)The electrons of complete quantum shells

b)

a)Electrons with positive charge

c)

c) The outer-shell electrons

d)

d) The K-quantum shell electrons

89.

89. How do you call the strong bond between hydrogen atoms?

a)

a)Ionic and metallic bonds

b)

a)The covalent bond

c)

a)The ionic bond

d)

a)The metallic bond

90.

90. What are Van der Waals forces?

a)

a)Forces present only in gases

b)

a)Forces not present in liquids

c)

c) Primary bonds between atoms

d)

d) Weak secondary bonds between atoms

91.

91. Which of the following materials is not a viscoelastic material?

a)

Metal

b)

Plastic

c)

Rubber

d)

Glass

92.

92. In molecules of the same composition, what are variations of atomic arrangements known as?

a)

Isomers

b)

Polymers

c)

Monomers

d)

a)Crystal systems

93.

93. Which of the following is false?

a)

a.  The acceleration of a body rotating with a constant angular velocity is zero.

b)

b.  Angular momentum for rigid bodies may be regarded as the product of angular velocity and inertia.

c)

c.  The radius of gyration for a mass of uniform thickness is identical to that for a planar area of the same shape.

d)

d.  Kinematics is the study of the effects of motion, while kinetics is the study of the causes of motion.

94.

104. Points that lie in the same plane:

a)

Coplanar

b)

Collinear

c)

Oblique

d)

Parallel

95.

105. What do you call the one-fourth of a great circle?

a)

Cone

b)

Pyramid

c)

Chord

d)

Quadrant

96.

106.  A plane closed curve, all points of which are the same distance from a point within, called the center.

a)

a)Arc

b)

Radius

c)

Circle

d)

Chord

97.

107. What do you call the replacement of the original cost of an investment?

a)

a)Pay off 

b)

a)Return on investment

c)

a)Breakeven

d)

a)Capital recovery

98.

109. If y’’(x) = 0, then the point is:

a)

a)Minimum point

b)

a)Maximum point

c)

a)Inflection point

d)

a)Critical point

99.

For a given function, it is found that f(t) = f(-t). What type of symmetry does f(t) have?

a)

A. odd symmetry

b)

B. even symmetry

c)

C. Rotational symmetry

d)

D. Quarter-wave symmetry

100.

Which number has four significant figures?

a)

A. 0.0014

b)

B. 0.01414

c)

C. 0.141

d)

D. 1.4140

101.

Naperian logarithm have a base closest to which number?

a)

A. 2.17

b)

B. 2.72

c)

C. 3.14

d)

D. 10

102.

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. an exponential

b)

B. a sinusoid

c)

C. a tangent

d)

D. a parabola

103.

To find the angle of the triangle given only the lengths of the

a)

A.  The law of cosines

b)

B. the law of sines

c)

C. the law of tangents

d)

D. the inverse-square law

104.

Which is true regarding the signs of the natural functions for angles between 90° and 180°?

a)

A. the tangent is positive

b)

B. the cotangent is positive

c)

C. the cosine is negative

d)

D. the sine is negative

105.

What is the inverse natural function of the cosecant?

a)

A. secant

b)

B. sine

c)

C. cosine

d)

D. cotangent

106.

The graphical presentation of a cumulative frequency distribution in a set of statistical data is called ____

a)

A. histogram

b)

B. kurtosis

c)

C. lepticurtic

d)

D. ogive

107.

A statement of truth of which follows with little or no proof from a theorem

a)

A. axiom

b)

B. hypothesis

c)

C. corollary

d)

D. conclusion

108.

It is a sequence of numbers such that the succesive terms differ by a constant.

a)

A. arithmetic progression

b)

B. infinite progression

c)

C. geometric progression

d)

D. harmonic progression

109.

A frequency curve which is composed of series of rectangles constructed with the steps as the base and the frequency as the height.

a)

A. histogram

b)

B. ogive

c)

C. frequency of distribution

d)

D. bar graph

110.

If the roots of an equation are zero, then they are classified as

a)

A. hyperbolic solution

b)

B. zeros of function

c)

C. extraneous roots

d)

D. trivial roots

111.

Convergent series is a sequence of decreasing number or when the succeeding term is ____ the preceding term.

a)

A. greater than

b)

B. equal to

c)

C. lesser than

d)

D. none of the above

112.

If a = b then b = a. This illustrates what axiom in algebra?

a)

A. symmetric axiom

b)

B. reflexive axiom

c)

C. transitive axiom

d)

D. replacement axiom

113.

A and B are independent events. The probabilty 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)

A. Pa - Pb

b)

B. Pb - Pab

c)

C. Pa x Pb

d)

D. Pab/Pa

114.

Two or more equation are equal if and only if they have the same

a)

A. solution set

b)

B. degree

c)

C. order

d)

D. variable set

115.

In any square matrix, when the elements of any two rows are exactly the same, the determinant is

a)

A. zero

b)

B. positive integer

c)

C. negative integer

d)

D. unity

116.

The ratio or product of two expressions in direct or inverse relation with each other is called

a)

A. ratio and proportion

b)

B. means

c)

C. extremes

d)

D. constant of variation

117.

Is a sequence of terms whose reciprocals form an arithmetic progression?

a)

A. geometric progression

b)

B. harmonic progression

c)

C. algebraic progression

d)

D. ratio and proportion

118.

An array m x n quantities which represent a single number system composed of elements in rows and columns is known as

a)

A. transposed matrix

b)

B. cofactor of a matrix

c)

C. matrix

d)

D. determinant

119.

Binary number system is a system of notation for real number that uses the place method with 2 as the base, what is another name of binary number system

a)

A. binary digits

b)

B. binumber system

c)

C. dyadic number system

d)

D. bits

120.

The number 0.123123123…. is a/an

a)

A. irrational number

b)

B. surd

c)

C. rational number

d)

D. transcendental

121.

MCMXCIV is the roman numeral equivalent to

a)

A. 1974

b)

B. 1984

c)

C. 1994

d)

D. 2994

122.

A sequence of numbers where the succeeding term is greater than the preceding term is called

a)

A. dissonant series

b)

B. convergent series

c)

C. divergent series

d)

D. isometric series

123.

Terms that differs only in numeric coefficients are known as

a)

A. unlike terms

b)

B. unequal terms

c)

C. like terms

d)

D. similar equations

124.

In complex algebra, we use diagram to represent complex plane commonly called

a)

A. Argand diagram

b)

B. Venn diagram

c)

C. Maxwell diagram

d)

D. Cartesian diagram

125.

7 + 0i is?

a)

A. an irrational number

b)

B. real number

c)

C. imaginary number

d)

D. a variable

126.

The number of successful outcomes divided by the number of possible outcomes is

a)

A. odd

b)

B. combination

c)

C. permutation

d)

D. probability

127.

If a two digit number has x for its unit digit and y for its tens digit, the number is represented as

a)

A. x + y

b)

B. y – x

c)

C. 10y + x

d)

D. 10x – y

128.

A statement of truth which is admitted without proof

a)

A. axiom

b)

B. theorem

c)

C. postulate

d)

D. corollary

129.

The part of theorem which is assumed to be true

a)

A. corollary

b)

B. hypothesis

c)

C. postulate

d)

D. conclusion

130.

Refers to the construction of drawing of lines and figures the possibility of which is admitted without proof

a)

A. corollary

b)

B. theorem

c)

C. postulate

d)

D. hypothesis

131.

A mathematical statement which has neither been proved nor denied by counterexamples

a)

A. fallacy

b)

B. conjecture

c)

C. theorem

d)

D. paradox

132.

A proved proposition which is useful mainly as preliminary to the proof of a theorem

a)

A. lemma

b)

B. hypothesis

c)

C. postulate

d)

D. corollary

133.

Axioms are propositions of a general logical nature (about equal or unequal ) while ______ are propositions concerning objects and constructions.

a)

A. theorems

b)

B. corollaries

c)

C. conclusions

d)

D. postulates

134.

A ______ is an ancillary theorem whose results is not for the proof

a)

A. postulate

b)

B. lemma

c)

C. hypothesis

d)

D. conclusion

135.

Statements that are accepted without discussion or proof are called axioms. The word “axiom” comes from the Greek “axioma” which means

a)

A. worth

b)

B. correct

c)

C. true

d)

D. perfect

136.

In mathematical and other fields of logical reasoning, axioms are used as basis for the formulation of statements called

a)

A. lemma

b)

B. hypothesis

c)

C. postulate

d)

D. theorem

137.

“The product of two or more number is the same in whatever order they are multiplied “. This refers to

a)

A. Associative law of addition

b)

B. associative law of multiplication

c)

C. commutative law of multiplication

d)

D. distributive law of multiplication

138.

If a = b, then b can replace a in any equation. This illustrates what law of identity?

a)

A. reflexive law

b)

B. law of symmetry

c)

C. transitive law

d)

D. substitution law

139.

If a = a , then it illustrates what law of identity?

a)

A. reflexive law

b)

B. law of symmetry

c)

C. transitive law

d)

D. substitution law

140.

If a = b and b = c , then a = c this illustrates

a)

A. reflexive law

b)

B. law of symmetry

c)

C. transitive law

d)

D. substitution law

141.

The axiom which related addition and multiplication is the ______ law

a)

A. commutative

b)

B. associative

c)

C. distributive

d)

D. none of the above

142.

Any combination of symbols and numbers related by the fundamental operation of algebra is called a/an

a)

A. equation

b)

B. algebraic expression

c)

C. term

d)

D. algebraic sum

143.

The algebraic expression consisting of a sum of any number of terms is called a

a)

A. multinomial

b)

B. summation

c)

C. binomial

d)

D. monomial

144.

An equation which is satisfied by all values of the variables for which the members of equation defined is known as

a)

A. linear equation

b)

B. rational equation

c)

C. conditional equation

d)

D. irrational equation

145.

An equation in which some or all of the known quantities are represented by letters is called

a)

A. redundant equation

b)

B. literal equation

c)

C. linear equation

d)

D. irrational equation

146.

An equation in which the variable appear under the radical symbol

a)

A. irradical equation

b)

B. irrational equation

c)

C. quadratic equation

d)

D. linear equation

147.

An equation which, because of some mathematical process, has required an extra root is sometimes called as

a)

A. redundant equation

b)

B. literal equation

c)

C. linear equation

d)

D. defective equation

148.

Any equation which, because of some mathematical process, has fewer roots than its original is sometimes called as

a)

A. redundant equation

b)

B. literal equation

c)

C. linear equation

d)

D. defective equation

149.

An algebraic expression which can be represented as a quotient of two polynomials

a)

A. irrational algebraic equation

b)

B. reduced algebraic expression

c)

C. rational algebraic equation

d)

D. complex algebraic equation

150.

A statement containing one or more variables and having the property that it becomes either true or false when the variables are given specific values from their domains.

a)

A. solution

b)

B. problem

c)

C. open sentence

d)

D. worded problem

151.

Any algebraic term is a/an __________ term in certain representing numbers if it consists of the products of possible integral powers of these numbers and a factor not containing them.

a)

A. integral

b)

B. rational

c)

C. irrational

d)

D. integral rational

152.

An equation in x and y which is not easily solved for y in terms of x is called

a)

A. explicit

b)

B. implicit function

c)

C. discontinuity

d)

D. quadratic

153.

The number which are represented with letters.

a)

A. variables

b)

B. unknowns

c)

C. literal numbers

d)

D. terms

154.

Equations whose members are equal only for certain or possibly no value of the unknown.

a)

A. conditional equations

b)

B. inequalities

c)

C. unconditional equations

d)

D. temporary equations

155.

An algebraic expression consisting one term.

a)

A. monomial

b)

B. binomial

c)

C. linear

d)

D. monomode

156.

In algebra, this consists of products and quotients of ordinary numbers and letters which represent  numbers.

a)

A. expression

b)

B. term

c)

C. equation

d)

D. coefficient

157.

An expression of two terms is called

a)

A. polynomial

b)

B. duomial

c)

C. binomial

d)

D. all of the above

158.

The degree of a polynomial or equation is the

a)

A. maximum exponent

b)

B. maximum sum of exponents

c)

C. exponent of the first variable

d)

D. maximum exponent of x

159.

What is the degree of the polynomial 3x4y + 2x3z3 – 4yz2  ?

a)

A. 6th

b)

B. 5th

c)

C. 4th

d)

D. 3rd

160.

Any fraction which contains one or more fractions in either numerator or denominator, or both is called

a)

A. compound fraction

b)

B. composite fraction

c)

C. complex fraction

d)

D. all of the above

161.

A common fraction with unity for numerator and a positive integer as denominator (i.e. 1/n)

a)

A. ordinary fraction

b)

B. unit fraction

c)

C. common fraction

d)

D. improper fraction

162.

If the absolute value of the numerator of a fraction is smaller than the denominator, it is called

a)

A. proper fraction

b)

B. improper fraction

c)

C.  Decimal fraction

d)

D. mixed number

163.

A number that consists of an integer part (which may be zero) and a decimal part less than unity that follows the decimal marker, which may be a point or a comma

a)

A. proper fraction

b)

B. improper fraction

c)

C.  Decimal fraction

d)

D. mixed number

164.

Considered as the “counting numbers”

a)

A. integers

b)

B. rational numbers

c)

C. irrational numbers

d)

D. natural numbers

165.

A number represented by a non-terminating, non-repeating decimal.

a)

A. irrational number

b)

B. rational number

c)

C. natural number

d)

D. integer

166.

The completeness axiom proved that the real number system has numbers other than

a)

A. integers

b)

B. rational numbers

c)

C. natural numbers

d)

D. irrational numbers

167.

The concept of spread of a random variable or a set of observations.

a)

A. variance

b)

B. standard deviation

c)

C. dispersion

d)

D. range

168.

A number containg a non-terminating but repeating decimal is a/an

a)

A. integer

b)

B. rational number

c)

C. natural number

d)

D. irrational number

169.

A positive integer which has no perfect-square factor greater than 1.

a)

A. radical expression

b)

B. square integer

c)

C. square integer

d)

D. square-free integer

170.

Numbers are used to describe a

a)

A. magnitude

b)

B. position

c)

C. magnitude and position

d)

D. none of the above

171.

Are symbols or combinations of symbols which describe a number.

a)

A. numerals

b)

B. digits

c)

C. terms

d)

D. notations

172.

Which of the following is not classified as an integer?

a)

A. negative numbers

b)

B. positive numbers

c)

C. zero

d)

D. imaginary numbers

173.

When an imaginary number is raised to an even exponent, it

a)

A. becomes infinite

b)

B. becomes negative imaginary number

c)

C. becomes relatively small number

d)

D. becomes real number

174.

The complex number is in the form of a + bi. If a = 0, what do you call the resulting number?

a)

A. absolute value of the complex number

b)

B. pure imaginary number

c)

C. argument

d)

D. irrational number

175.

For a complex number a + bi, the real number √("a2 + b2"  ) is __________ of the complex number.

a)

A. absolute value

b)

B. magnitude

c)

C. modulus

d)

D. all of the above

176.

The ________ of two complex number is found by multiplying each term of the one by every term of the other.

a)

A. sum

b)

B. difference

c)

C. product

d)

D. quotient

177.

A number which can be expressed as a quotient of two integers (division of zero is excluded) is called

a)

A. irrational number

b)

B. rational number

c)

C. imaginary number

d)

D. real number

178.

A prime number has exactly how many divisors?

a)

A. 1

b)

B. 2

c)

C. 3

d)

D. 4

179.

A prime number is an integer greater than 1 which has

a)

A. 1 as its only positive divisor

b)

B. itself as only  positive divisor

c)

C. 1 and itself as its only positive divisors

d)

D. 1 and its additive inverse as its only positive divisor

180.

An integer which is the product of two integers, both different from 1 and -1 is called

a)

A. prime number

b)

B. composite number

c)

C. rational number

d)

D. compound number

181.

A composite number has at least ____ divisors.

a)

A. 1

b)

B. 2

c)

C. 3

d)

D. 4

182.

Two natural numbers a and b are ________. If their greatest common divisor is one.

a)

A. relatively prime

b)

B. relatively composite

c)

C. equal

d)

D. reciprocal

183.

Number used to count the objects or ideas in a given collection.

a)

A. cardinal numbers

b)

B. irrational numbers

c)

C. ordinal numbers

d)

D. numerals

184.

Numbers which is used to state the position of individual objects in a sequence.

a)

A. cardinal numbers

b)

B. irrational numbers

c)

C. ordinal numbers

d)

D. numerals

185.

An integer number that is equal to the sum of all its possible divisors except the number itself is called

a)

A. amicable number

b)

B. perfect number

c)

C. defective number

d)

D. redundant number

186.

An integer the sum of all its possible divisors except the number itself is greater than the integer is called

a)

A. abundant number

b)

B. perfect number

c)

C. defective number

d)

D. amicable number

187.

An integer the sum of all its possible divisors except the number itself is less than the integer is called

a)

A. abundant number

b)

B. amicable number

c)

C. friendly number

d)

D. defective number

188.

What is the smallest perfect number possible?

a)

A. 1

b)

B. 6

c)

C. 12

d)

D. 8

189.

All perfect numbers are

a)

A. even numbers

b)

B. odd numbers

c)

C. prime numbers

d)

D. composite numbers

190.

Two integer numbers are said to be ____ if each is the sum of all possible divisors of the other.

a)

A. perfect numbers

b)

B. defective numbers

c)

C. amicable numbers

d)

D. Fermat’s numbers

191.

What is another name for amicable numbers?

a)

A. compatible numbers

b)

B. friendly numbers

c)

C. Fermats numbers

d)

D. Inconsistent numbers

192.

What is the smallest pair of friendly number?

a)

A. 180 and 190

b)

B. 200 and 120

c)

C. 220 and 284

d)

D. 220 and 264

193.

Prime numbers that appear in pair and differ by 2 (e.g. 3 and 5, 11 and 13 etc.) are called

a)

A. Mersenne primes

b)

B. prime number theorem

c)

C. twin primes

d)

D. pseudo primes

194.

“Every even integer greater than 2 can be written as the sum of two primes”. This is known as

a)

A. Fermat’s last theorem

b)

B. Goldbach conjecture

c)

C. Prime number theory

d)

D. Mersenne primes

195.

“Every positive integer greater than 1 is a prime or can be expresses as a unique product  of primes and powers”. This is known as

a)

A. Fundamental theorem of arithmetic

b)

B. Pseudo prime theorem

c)

C. Prime number theorem

d)

D. Mersenne’s Theorem

196.

“Every sufficiently large off number can be expresses as a sum of three prime numbers” this is known as

a)

A. Goldbach conjecture

b)

B. Vinogradov’s theorem

c)

C. Pascal’s Law

d)

D. Mersenne’e theorem

197.

The term “ratio” comes from Latin verb “ratus” meaning

a)

A. to divide

b)

B. to estimate

c)

C. to get the mean

d)

D. to make a proportion

198.

In the proportion of four quantities, the first and fourth terms are referred to as the

a)

A. means

b)

B. extremes

c)

C. denominators

d)

D. numerators

199.

The first term of a ratio is called

a)

A. antecedent

b)

B. consequent

c)

C. mean

d)

D. extreme

200.

The second term of a ratio is called

a)

A. antecedent

b)

B. mean

c)

C. consequent

d)

D. extreme

201.

The _____ is the square root of the product of the extremes.

a)

A. antecedent

b)

B. consequent

c)

C. mean proportional

d)

D. mean

202.

If the means of a proportion are equal, their commo value is called

a)

A. mean

b)

B. extreme

c)

C. mean proportional

d)

D. extreme proportional

203.

The theorem that in every arithmetic progression a, a + d, a = 2d,…, where a and d are relatively prime.

a)

A. Fibonacci theorem

b)

B. Gauss theorem

c)

C. Lejeune theorem

d)

D. Dirichlet Theorem

204.

A statement that one mathematical expression is greater than or less than another is called

a)

A. absolute condition

b)

B. non-absolute condition

c)

C. inequality

d)

D. conditional expression

205.

If an equality is true for all values of the variable, it is a/an

a)

A. conditional inequality

b)

B. equivalent inequality

c)

C. absolute inequality

d)

D. non-conditional inequality

206.

If the same number is added to both sides of an inequality, the inequality

a)

A. becomes negative

b)

B. becomes positive

c)

C. is reversed

d)

D. is preserved

207.

An inequality is preserved if both sides are multiplied by

a)

A. zero

b)

B. – 1

c)

C. a positive number

d)

C. a negative number

208.

An inequality is reversed if both sides are multiplied by

a)

A. zero

b)

B. – 1

c)

C. a positive number

d)

D. a negative number

209.

Division of a population or same into two groups based either on measurable variables (e.g. age under 18, age over 180) or on attributes (e.g. male, female).

a)

A. decomposition

b)

B. denomination

c)

C. deviance

d)

D. dichotomy

210.

A 3 x 2 matrix can be multiplied to a

a)

A. 3 x 2 matrix

b)

B. 3 x 3 matrix

c)

C. 2 x 5 matrix

d)

D. row matrix

211.

If there are as many equations as unknowns, the matrix of the coefficient is a

a)

A. row matrix

b)

B. column matrix

c)

C. square matrix

d)

D. rectangular matrix

212.

A method of solving linear equation with several unknowns simultaneously using determinants.

a)

A. Simpson’s rule

b)

B. Cramer’s rule

c)

C. Trapezoidal rule

d)

D. Chain rule

213.

Using Cramer’s rule, the determinant of the coefficient is always the

a)

A. numerator of a quotient

b)

B. denominator of the quotient

c)

C. the quotient itself

d)

D. none of the above

214.

In any square matrix, when the elements of any two rows are exactly the same (i.e. row 1 = row 2 = row 3, or row 2 = row 3…), the determinant is

a)

A. zero

b)

B. positive integer

c)

C. negative integer

d)

D. unity

215.

When the corresponding elements of two rows of a determinant are proportional, then the value of the determinant is

a)

A. one

b)

B. indeterminate

c)

C. infinite

d)

D. zero

216.

An array of m x n quantities which represent a single number and is composed of elements in rows and columns is known as

a)

A. transpose of a matrix

b)

B. determinant

c)

C. co-factor of a matrix

d)

D. matrix

217.

When two rows are interchanged in position, the value of the determinant will

a)

A. remain unchanged

b)

B. be multiplied by – 1

c)

C. become zero

d)

D. become infinite value

218.

If every elements of a row (or column) are multiplied by a constant, k, then the value of the determinant is

a)

A. multiplied by – k 

b)

B. zero

c)

C. one

d)

D. multiplied by k

219.

If two rows of a determinant are interchange, the determinant

a)

A. changes sign

b)

B. changes sign and value

c)

C. remains unchanged

d)

D. becomes the inverse of the former

220.

Which of the following cannot be an operation of matrices?

a)

A. addition

b)

B. subtraction

c)

C. multiplication

d)

D. division

221.

An irrational number which is a root of a positive integer of fraction is called

a)

A. radical

b)

B. radix

c)

C. surd

d)

D. radicant

222.

The symbol bn\sqrt[n]{b}   means the principal nth root “n” is called the

a)

A. radicand

b)

B. radical

c)

C. radix

d)

D. index

223.

In the bn\sqrt[n]{b}  , “b” is called the

a)

A. radicand

b)

B. radical

c)

C. radix

d)

D. index

224.

The symbol  \sqrt[]{}    is called

a)

A. radical

b)

B. radical symbol

c)

C. index

d)

D. A or B

225.

The rules of combining radicals follow the rules for

a)

A. signed numbers

b)

B. logarithms

c)

C. fractional exponents

d)

D. factoring

226.

When a number has both a positive and negative nth root, the principal nth root is

a)

A. the positive root

b)

B. the negative root

c)

C. both the positive and negative root

d)

D. none of the above

227.

Every positive number has _____ nth root

a)

A. zero

b)

B. two

c)

C. two

d)

D. three

228.

The principal nth root of a negative number is the negative root if n is

a)

A. even

b)

B. odd

c)

C. positive

d)

D. negative

229.

To eliminate a surd, multiply it by its

a)

A. square

b)

B. cube

c)

C. reciprocal

d)

D. conjugate

230.

A radical which is equivalent to a non-terminating and non-repeating decimal

a)

A. irrational number

b)

B. natural number

c)

C. surd

d)

D. transcendental number

231.

A radical expressing an irrational number is called a

a)

A. surd

b)

B. radix

c)

C. index

d)

D. complex number

232.

A surd which contains at least one rational term.

a)

A. pure surd

b)

B. mixed surd

c)

C. binomial surd

d)

D. conjugate surd

233.

A surd that contains no rational number, that is, all its factors or terms are surds, example √3 or √3+√2

a)

A. mixed surd

b)

B. pure surd

c)

C. binomial surd

d)

D. conjugate surd

234.

The process of removing surd from a denominator is to

a)

A. rationalize the denominator

b)

B. invert the divisor and proceed to multiplication

c)

C. get its multiplicative inverse

d)

D. multiply it why its additive inverse

235.

A quadratic equation of the form ax2 + c = 0, without the coefficient of the first degree term is a/an

a)

A. general quadratic equation

b)

B. pure quadratic equation

c)

C. quadratic polynomial

d)

D. incomplete quadratic equation

236.

In the quadratic equation Ax2 + Bx + C = 0, when the roots are multiplied, the result is

a)

A. C/A

b)

B. – B/A

c)

C. – C/A

d)

D. A/C

237.

In the quadratic equation Ax2 + Bx + C = 0, when the roots are added, the result is

a)

A. C/A

b)

B. – B/A

c)

C. – C/A

d)

D. A/C

238.

If the discriminant of a quadratic equation is less than zero, the equation has

a)

A. no real roots

b)

B. one root only

c)

C. two real roots

d)

D. none of the above

239.

When can we say that the two roots of a quadratic equation are equal?

a)

A. when discriminant is greater than 1

b)

B. when discriminant is zero

c)

C. when the coefficient of the second degree term is equal to the coefficient of the first degree term

d)

D. none of the above

240.

What is the discriminant of the quadratic equation Ax2 + Bx + C = 0  

a)

A. 𝐵2−4𝐴𝐶\sqrt[]{𝐵^2−4𝐴𝐶}

b)

B. 𝐵2−4𝐴𝐶𝐵^2−4𝐴𝐶

c)

C. 𝐵2+4𝐴𝐶𝐵^2+4𝐴𝐶

d)

D. 𝐵2+4𝐴𝐶\sqrt[]{𝐵^2+4𝐴𝐶}

241.

What determines the nature of the roots of the quadratic equation?

a)

A. coefficient

b)

B. discriminant

c)

C. factors

d)

D. all of the above

242.

The real roots of a cubic equation are the

a)

A. points of inflection of the graph of the equation

b)

B. points of intersection of the graph of the equation with the x-axis

c)

C. points of intersection of the graph of the equation with the y-axis

d)

D. obtained by using the quadratic formula

243.

For a cubic equation, we produce three distinct real roots only if the discriminant is

a)

A. equal to zero

b)

B. less than zero

c)

C. greater than zero

d)

D. either less than or greater than zero

244.

For a cubic equation, the discriminant is found to be greater than zero. The roots are

a)

A. one real and two conjugate complex roots

b)

B. three distinct roots

c)

C. three real roots , which two are equal

d)

D. none of these

245.

A succession of numbers in which one number is designated as first , another as second, another as third and so on is called

a)

A. series

b)

B. arrangement

c)

C. arrangement

d)

D. sequence

246.

The repeating decimal 0.333… is a geometric series of a1 = 0.3 and r =

a)

A. 3/10

b)

B. 1/10

c)

C. 10

d)

D. 5

247.

The number between two geometric terms.

a)

A. means

b)

B. arithmetic means

c)

C. geometric means

d)

D. median

248.

The sum of the first terms of a series is called the nth ______.

a)

A. sum

b)

B. sequence

c)

C. arrangement

d)

D. partial sum

249.

The sum of the terms of an arithmetic progression

a)

A. arithmetic means

b)

B. arithmetic sequence

c)

C. arithmetic series

d)

D. all of the above

250.

The harmonic mean between a and b.

a)

A. (a + b)/2

b)

B. 2ab/(a + b)

c)

C. (a + b)/ab

d)

D. ab/(a + b)

251.

The arithmetic mean of a and b is

a)

A. (a + b)/2

b)

B. 2ab/(a + b)

c)

C. (a + b)/ab

d)

D. ab/(a + b)

252.

The geometric mean of a and b is

a)

A. (a + b)/2

b)

B. 2(a + b)

c)

C. ab/(a + b)

d)

D. √ab

253.

Are numbers which can be drawn as dots and arranged in triangular shape ( i.e. 1, 3, 6, 10, 15, 21…)

a)

A. triangular number

b)

B. square numbers

c)

C. pentagonal numbers

d)

D. tetrahedral numbers

254.

A figure numbers which can be drawn as dots and arranged in square shape ( i.e. 1, 4, 9, 16, 25…)

a)

A. cubic numbers

b)

B. square numbers

c)

C. pyramid numbers

d)

D. pentagon numbers

255.

A sequence 1, 5, 12, 22, 35… is known as

a)

A. oblong numbers

b)

B. pentagonal numbers

c)

C. cubic numbers

d)

D. pyramid numbers

256.

A sequence 1, 8, 27, 64, 125, 216… is known as

a)

A. Pyramid numbers

b)

B. Cubic numbers

c)

C. tetrahedral numbers

d)

D. square numbers

257.

A sequence 1, 4, 10, 20, 35, 56… is known

a)

A. Pyramid numbers

b)

B. Cubic numbers

c)

C. tetrahedral numbers

d)

D. square numbers

258.

A sequence of numbers where every term is obtained by adding all the preceding terms a square number series such as 1, 5, 14, 30, 55, 91…

a)

A. Pyramid numbers

b)

B. Tetrahedral numbers

c)

C. Euler’s numbers

d)

D. Triangular numbers

259.

A sequence of numbers where the number is equal to the sum of the two preceding numbers such as 1, 1, 2, 3, 5, 8, 13, 21… is called

a)

A. Fermat’s numbers

b)

B. Fibonacci numbers

c)

C. Gaussian numbers

d)

D. Archimedean numbers

260.

What is the multiplicative inverse of the integer 5?

a)

A. 1

b)

B. 5

c)

C. – 5

d)

D. 1/5

261.

What is the additive identity element?

a)

A. 0

b)

B. 1

c)

C. – 1

d)

D. infinity

262.

What is the multiplicative identity element?

a)

A. 0

b)

B. 1

c)

C. – 1

d)

D. infinity

263.

The number 0 such that 0 + a = a for all a is called

a)

A. additive inverse

b)

B. additive identity

c)

C. commutative law of addition

d)

D. associative law of addition

264.

The additive inverse of a complex number a + bi is

a)

A. a – bi

b)

B. a + bi

c)

C. –a – bi

d)

D. –a + bi

265.

All real numbers have additive inverse, commonly called

a)

A. reciprocals

b)

B. opposites

c)

C. addends

d)

D. equivalent

266.

All real numbers except zero have multiplicative inverses, commonly called

a)

A. equivalent

b)

B. factors

c)

C. opposites

d)

D. reciprocals

267.

The number zero has no

a)

A. multiplicative inverse

b)

B. additive inverse

c)

C. multiplicative identity

d)

D. additive identity

268.

What is the additive inverse of a + bi?

a)

A. bi

b)

B. –a – bi

c)

C. 1/(a + bi)

d)

D. a –bi

269.

What is the multiplicative inverse of a + bi?

a)

A. 0

b)

B. 1

c)

C. – a –bi

d)

D. (a/ a2a^2    – b2b^2  ) – bi/( a2a^2 + b2b^2 )

270.

Which of the following is NOT a property of a binomial expansion of (x+y)n(x+y)^n  ?

a)

A. power is decreasing

b)

B. power of y is increasing

c)

C. sum of exponents in each term = n

d)

D. number of terms = n – 1

271.

A triangular array numbers forming  the coefficient of the expansion of a binomial is called

a)

A. Egyptian triangle

b)

B. Golden triangle

c)

C. Pascal’s triangle

d)

D. Bermuda triangle

272.

The coefficient of the second term of the expansion of (x + y)n is always equal to

a)

A. n

b)

B. n – 1

c)

C. n + 1

d)

D. n/2

273.

How is a number in the Pascal’s triangle obtained?

a)

A. by getting the product of the two numbers directly above it

b)

B. by getting the sum of the two numbers directly above it

c)

C. by getting the difference of the two numbers directly above it

d)

D. by getting the mean of the two numbers directly above it

274.

If the sign between the terms of the binomial is negative, its expansion will have signs which are

a)

A. all positive

b)

B. all negative

c)

C. alternate starting with positive

d)

D. alternate starting with negative

275.

In the absence of the Pascal’s triangle, the coefficient of any term of the binomial expansion can be obtained by dividing the product of coefficient  of the preceding term by ____ of the preceding term.

a)

A. the exponent of y

b)

B. the exponent of y +1

c)

C. the exponent of y – 1

d)

D. the square root of y

276.

The fundamental principle of counting states that is one thing can be done in “m” different ways and another thing  can be done in “n” different ways, then the two things can be done in _____ different ways.

a)

A. m + n

b)

B. m x n

c)

C. m! + n!

d)

D. mnm^n  

277.

Is the arrangement of the object s in specific order.

a)

A. permutation

b)

B. combination

c)

C. probability

d)

D. any two of the above

278.

Is the arrangement of the objects regardless of the order they are arranged.

a)

A. permutation

b)

B. combination

c)

C. probability

d)

D. any two of the above

279.

The shifting of the entire order sequence of elements one or more steps forwards to backward – the first element taking the position of the last , or vice versa without changing the order of the elements in the sequence is called

a)

A. inversion

b)

B. cyclic permutation

c)

C. transportation

d)

D. identical elements

280.

The number of elements in the collection being permuted is the _____ of the permutation

a)

A. degree

b)

B. sum

c)

C. index

d)

D. all of the above

281.

The ratio of the successful outcomes over the total possible outcomes is called

a)

A. combination

b)

B. permutation

c)

C. probability

d)

D. speculation

282.

The value of the probability of any outcome will never be equal to nor exceed

a)

A. 0.1

b)

B. 0.5

c)

C. 0.75

d)

D. 1

283.

If two events A and B are mutually exclusive events and the probability that A will happen is Pa and the probability that b will occur is Pb, then the probability that A or B happen is

a)

A. Pa + Pb

b)

B. Pa x Pb

c)

C. Pa/Pb

d)

D. Pb/Pa

284.

A and B are two independent events. The probability that A can occur is p and that for both A and B to occur is q. the probability that event B can occur is

a)

A. p + q

b)

B. p – q

c)

C. p/q

d)

D. q/p

285.

If the probability of occurrence of a is Pa, what is the probability that will nor  occur?

a)

A. 1/Pa

b)

B. 1 - Pa

c)

C. 1 + Pa

d)

D. √Pa

286.

In statistics, a pictorial description  of the probability concepts of independent and dependent events is called

a)

A. Venn diagram

b)

B. histogram

c)

C. frequency polygon

d)

D. ogive

287.

The difference between the highest score and the lowest score in the distribution

a)

A. deviation

b)

B. range

c)

C. median

d)

D. mode

288.

The second power of the standard deviation is called

a)

A. mode

b)

B. central tendency

c)

C. variance

d)

D. dispersion

289.

A graph of cumulative frequency distribution plotted at class makes and  connected by straight lines.

a)

A. histogram

b)

B. Venn diagram

c)

C. Ogive

d)

D. Scattergram

290.

A point in the distribution of scores at which 50 percent of the scores fall below and 50 percent of the scores fall above

a)

A. mode

b)

B. mean

c)

C. median

d)

D. range

291.

A number that occurs most frequent in a group of numbers.

a)

A. median

b)

B. mode

c)

C. means

d)

D. standard deviation

292.

The difference between an approximate value of a quantity and its exact value or true value

a)

A. relative error

b)

B. absolute error

c)

C. mistake

d)

D. relative error

293.

It is the quotient of the absolute error divided by the true value

a)

A. relative error

b)

B. relative change

c)

C. absolute error

d)

D. mistake

294.

Refers to a value which is  not exact but might be accurate enough for some specific considerations

a)

A. approximate value

b)

B. absolute value

c)

C. relative value

d)

D. accurate value

295.

If the absolute error does not exceed a half unit in the last digit, this digit is usually referred to as the

a)

A. significant digit

b)

B. leading digit

c)

C. reliable digit

d)

D. relative digit

296.

The most significant digit of the number 0.2015 is

a)

A. 0

b)

B. 1

c)

C. 2

d)

D. 5

297.

The ____ is stated in the magnitude of the absolute or relative error of the approximated value

a)

A. precision

b)

B. accuracy

c)

C. mistake

d)

D. error

298.

The first non-zero digit from the left of the number.

a)

A. whole number

b)

B. leading digit

c)

C. tens digit

d)

D. units digit

299.

It is any of the digit from 1 to 9 inclusive, and 0 except when it is used to place a decimal.

a)

A. leading digit

b)

B. significant figure

c)

C. decimal number

d)

D. numerals

300.

In algebra, the operation of the root extraction is called

a)

A. evolution

b)

B. involution

c)

C. revolution

d)

D. indexing

301.

The operation of raising to the integral power known as

a)

A. evolution

b)

B. involution

c)

C. revolution

d)

D. indexing

302.

Each of two or more numbers which is multiplied together to form a product are called

a)

A. terms

b)

B. expression

c)

C. dividends

d)

D. factors

303.

When the factors of a product are equal, the product is called _____ of the repeated factor.

a)

A. coefficient

b)

B. identity

c)

C. power

d)

D. algebraic sum

304.

A relation in which every ordered pair (x, y) has one and only one value of y that corresponds to the value of x is called

a)

A. term

b)

B. coordinates

c)

C. function

d)

D. domain

305.

Indicate the false statement

a)

A. the objects in a set are called its elements

b)

B. even numbers is either rational or irrational

c)

C. the additive inverse of number “a” is 1/a

d)

D. the negative of zero is zero

306.

A symbol holding a place for an unspecified constant is called

a)

A. arbitrary constant

b)

B. parameter

c)

C. variable

d)

D. all of the above

307.

Which of the following is NOT true about significant figures?

a)

A. all non-zero digits are significant

b)

B. any zero between non-zero digits are significant

c)

C. any zero not needed for placing a decimal point is not significant

d)

D. zeros used for the purpose of placing a decimal point are not significant

308.

The sum of any point number and its reciprocal is

a)

A. always less than 2

b)

A. always less than 2

c)

C. always greater than 2

d)

D. always equal to the number’s additive inverse

309.

What is the absolute value of a number less than one but greater than negative one raised to exponent infinity?

a)

A. infinity

b)

B. zero

c)

C. one

d)

D. indeterminate

310.

If a is an odd number and b is an even number, which of the following must be even?

a)

A. a + b

b)

B. a – b

c)

C. ab

d)

D. a/b

311.

In the equation n x m = q, n is called the

a)

A. multiplier

b)

B. minuend

c)

C. multiplicand

d)

D. product

312.

Any one of the individual constants of an expressed sum of constant is called

a)

A. addend

b)

B. multiple

c)

C. factor

d)

D. summation

313.

In the equation 5 + 2 = 7, 5 is known as

a)

A. augend

b)

B. minuend

c)

C. dividend

d)

D. addend

314.

A number of the form a + bi with a and b real constant and i is the square root of – 1.

a)

A. imaginary number

b)

B. complex number

c)

C. radical

d)

D. compound number

315.

The absolute value of a non-zero number is

a)

A. always zero

b)

B. always negative

c)

C. always positive

d)

D. sometimes zero and sometimes positive

316.

A polynomial which is exactly divisible by two or more polynomials is called

a)

A. least common denominator

b)

B. common multiple

c)

C. factors

d)

D. binomial

317.

A polynomial with real coefficient can be factored into real linear factors and irreducible _____ factors

a)

A. linear

b)

B. quadratic

c)

C. cubic

d)

D. repeated

318.

If the degree of the numerator is one more than the degree of the denominator, the quotient is a ____ polynomial

a)

A. linear

b)

B. quadratic

c)

C. cubic

d)

D. quartic

319.

Which of the following statements is NOT true?

a)

A. the sum of even numbers is even

b)

B. the difference of even numbers is even

c)

C. the product of even numbers is even

d)

D. the quotient of even numbers is even

320.

For every law of addition and subtraction, there is a parallel law for multiplication and division, except division by

a)

A. negative values

b)

B. zero

c)

C. one

d)

D. positive values

321.

Indicate the false statement:

a)

A. the multiplicative identity is 1

b)

B. the product of a positive number and a negative number is negative

c)

C. ab = ba is the associative law for multiplication

d)

D. x2 – y2 = (x + y)(x – y)

322.

For any two rational number a/b and c/d, which of the following relations is true?

a)

A. a/b + c/d = ab/cd

b)

B. a/b + cd = (ab + cd)/ad

c)

C. a/b + c/d = (ad +cb)/bd

d)

D. ab + cd = ac/bd

323.

Two rational numbers a/b and c/d are said to be equal if

a)

A. ad = bc

b)

B. ac = bd

c)

C. ab = cd

d)

D. a + b = c + d

324.

Any number divided by infinity equals

a)

A. 0

b)

B. 1

c)

C. infinity

d)

D. indeterminate

325.

The study of the properties of positive integers is known as

a)

A. number of theory

b)

B. theory of equation

c)

C. set theory

d)

D. arithmetic

326.

Indicate the false statement

a)

A. a quotient of two polynomials is called as rational algebraic expression

b)

B. a3a^3  – b3b^3  = (a + b) (a2 – ab + b2)

c)

C. the equation ax + b = 0 has exactly one root

d)

D. the equation 3x23x^2   + 2y22y^2  – 3x + 2y = 10

327.

A number is said to be in _____ when it is written as the product of a number having the decimal point just after the leading digit, and a power of 10

a)

A. scientific notation

b)

B. exponential

c)

C. irrational

d)

D. logarithm

328.

A number which cannot be a root of an integral rational equation is called

a)

A. transcendental number

b)

B. Euler’s number

c)

C. irrational number

d)

D. natural number

329.

Refers to the numbers which are not the roots of any algebraic equation

a)

A. irrational numbers

b)

B. transcendental numbers

c)

C. imaginary numbers

d)

D. composite

330.

All numbers multiplied by ____ equals unity

a)

A. negative of the number

b)

B. one

c)

C. conjugate

d)

D. its reciprocal

331.

The numbers denoted as “e” and equal to 2.718… is called the

a)

A. Einstein constant

b)

B. Euler’s number

c)

C. Fibonacci number

d)

D. Fermat’s number

332.

A notation that represent the product of all positive integers from 1 to a number, n, inclusive

a)

A. factorial

b)

B. exponent

c)

C. summation

d)

D. all of the above

333.

Simplify  n!(n−1)!\frac{n!}{\left(n-1\right)!}  

a)

A. n + 1

b)

B. n – 1 

c)

C. (n + 1)!

d)

D. n

334.

The factorial symbol (!) was introduced in 1808 by

a)

A. Christian Goldbach

b)

B. Christian Kramp

c)

C. Christian Leatner

d)

D. Robert Hooke

335.

The conjecture that every even number (except 2) equals the sum of two prime numbers.

a)

A. Goldbach conjecture

b)

B. Fibonacci series

c)

C. Number conjecture

d)

D. Fermat’s last theorem

336.

The unending sequence of integers formed according to the rule that each integer is the sum of the preceding two

a)

A. Fermat’s last theorem

b)

B. Fibonacci numbers

c)

C. Goldbach conjecture

d)

D. triangular numbers

337.

It was conjecture that the number in the Fp = 2p + 1 will always result to a prime number, however proved wrong. What do you call the numbers obtained using the said formula?

a)

A. Mersene numbers

b)

B. Fermat numbers

c)

C. Euler numbers

d)

D. Pseudo number

338.

A theorem which states that if n > 2, the equation xn + yn = zn can not be solved in positive integers x, y and z

a)

A. Pythagorean theorem

b)

B. Mersenne theorem

c)

C. Goldbach theorem

d)

D. Fermat’s theorem

339.

The number π = 3.141592563… if only four decimals are required, it becomes 3.1415 This process is called

a)

A. rounding off

b)

B. truncation

c)

C. rounding up

d)

D. rounding down

340.

A set of all subsets of a given set, containing empty set and the original set

a)

A. empty

b)

B. null

c)

C. power set

d)

D. union

341.

A set containing the elements that is common  to the original sets

a)

A. union

b)

B. intersection

c)

C. normal set

d)

D. subset

342.

If an infinite series has a finite sum, it is referred to as a

a)

A. convergent series

b)

B. divergent series

c)

C. geometric series

d)

D. none of the above

343.

If an infinite series has no sum, it is referred to as a

a)

A. convergent series

b)

B. divergent series

c)

C. geometric series

d)

D. none of the above

344.

The sum of the factorial infinite 1/1! + 1/2! + 1/3! + 1/4!... is

a)

A. π

b)

B. e

c)

C. √2

d)

D. √3

345.

Refers exclusively to equations with integer solution

a)

A. determinate equations

b)

B. indeterminate equations

c)

C. Diophantine equations

d)

D. L’Hospital’s equations

346.

“My Dear Aunt Sally” is the basic rule used I operation of algebra. Which is used in determining the signs of trigonometric functions in all quadrants?

a)

A. all chemists thick solution

b)

B. all students can think

c)

C. all students take chemistry

d)

D. all teachers can sing

347.

The investigation of numbers, space, and many generalizations of these concepts created by the intellectual genius of man

a)

A. science

b)

B. arts

c)

C. mathematics

d)

D. astronomy

348.

QED is often written at the end of a proof to indicate that its conclusion has been reached. This means

a)

A. quod erat daciendum

b)

B. duod erat demonstrandum

c)

C. quod erat decientrandum

d)

D. none of the above

349.

A sequence of numbers where the succeeding term is greater than the preceding term

a)

A. isometric series

b)

B. divergent series

c)

C. dissonant series

d)

D. convergent series

350.

The process of reasoning wherein a final conclusion is obtained by experimental method.

a)

A. mathematical deduction

b)

B. mathematical opposition

c)

C. mathematical conversion

d)

D. mathematical induction

351.

The set of all subsets of a given set, containing the empty set and the original set

a)

A. intersection

b)

B. power set

c)

C. proper subset

d)

D. improper subset

352.

A sequence having a defined first and last term is called

a)

A. infinite sequence

b)

B. convergent sequence

c)

C. divergent sequence

d)

D. finite sequence

353.

A series is said to be  ____ if it converges when the terms are replaced by their absolute value

a)

A. absolute convergent

b)

B. conditional convergent

c)

C. infinite convergent

d)

D. finite convergent

354.

A convergent series is said to be  ____ if it diverges when the terms are replaces by their absolute values

a)

A. absolute convergent

b)

B. conditional convergent

c)

C. infinite convergent

d)

D. finite convergent

355.

Refers to the product of the several prime numbers occurring in the denominations, each taken with its greater multiplicity.

a)

A. least common denominator

b)

B. least common multiple

c)

C. least square

d)

D. A or B

356.

The sum of all the exponents of the several variables of the term is referred to as the _____ of the term

a)

A. power

b)

B. degree

c)

C. partial product

d)

D. absolute power

357.

Venn diagram is a pictorial representation which helps us visualize the relations and operations with sets. This was introduced by

a)

A. John Venn

b)

B. Jan Michael Venn

c)

C. James Venn

d)

D. Stephen Venn

358.

The symbol of equality (=) was introduced in 1557 by

a)

A. Bhaskara

b)

B. Brahmagupta

c)

C. Leonhard Euler

d)

D. Robert Recorde

359.

•In general quadratic equation, if the discriminant is zero, the curve is a figure that represent a/an

a)

a) Parabola

b)

b) Circle

c)

c) Ellipse

d)

d) Hyperbola

360.

•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 x or vice versa, such function is called

a)

a) Logarithmic function

b)

b) Implicit function

c)

c) Explicit function

d)

d) Continuous function

361.

•In polar coordinate system, the length of the ray segment from a fixed origin is known as _______.

a)

a) Amplitude

b)

b) Radius vector

c)

c) Hypotenuse

d)

d) Minimum point

362.

•Given the equations 3x² + 2x – 5y + 7 = 0. Determine the curve.

a)

  a) Ellipse

b)

b) Parabola

c)

  c) Hyperbola

d)

d) Circle

363.

•If eccentricity is less than one, then the curve is

a)

  a) Parabola

b)

  b) Ellipse

c)

c) Hyperbola

d)

d) Circle

364.

•Of what quadrant is A, if sec A is positive and csc A is negative?

a)

a) IV

b)

b) I

c)

c) III

d)

d) II

365.

•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)

  a) Circle

b)

b) Parabola

c)

c) Hyperbola

d)

d) Ellipse

366.

•What type of conic has equation of Ax² + Cy² + Dx + Ey + F = 0?

a)

  a) Circle

b)

b) Parabola

c)

c) Ellipse

d)

d) Hyperbola

367.

•4x² - 256 = 0 is the equation of a/an

a)

  a) Parabola

b)

b) Parallel lines

c)

c) Circle

d)

d) Ellipse

368.

•The graph of r = a + b cos Ø is a

a)

a) Lemniscate

b)

b) Lituus

c)

c) limacon

d)

d) Cardiod

369.

•In an ellipse, a chord which contains a focus and is in line perpendicular to the major axis is called

a)

a) focal width

b)

b) conjugate axis

c)

  c) focal chord

d)

d) latus rectum

370.

•If all the y-terms have even exponents, the curve is symmetric with respect to the ___

a)

  a) x-axis

b)

  b) origin

c)

c) y-axis

d)

d) line 45° with the-axis

371.

•If 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)

  a) Circle

b)

  b) Hyperbola

c)

  c) Parabola

d)

  d) Ellipse

372.

•If the equation is unchanged by the substitution of –x for x, its curve is symmetric with respect to the

a)

a) x-axis

b)

b) y-axis

c)

c) origin

d)

d) line 45° with the axes

373.

•What type of curve is generated by a point which moves in uniform circular motion about an axis, while travelling with a constant speed parallel to the axis?

a)

a) Spiral of Archimedes

b)

  b) Epicycloid

c)

  c) Cycloid

d)

  d) Helix

374.

•What is the graph of the equation Ax² + Bx + Cy² + Dy + Ex + F = 0

a)

a) circle

b)

b) ellipse

c)

  c) parabola

d)

  d) hyperbola

375.

•It represents the distance of a point from y-axis

a)

a) Ordinate

b)

b) Abscissa

c)

c) Coordinates

d)

  d) Polar distance

376.

•A line passing through the focus and perpendicular to the directrix of a parabola

a)

a) axis of parabola

b)

b) tangent line

c)

  c) secant line

d)

  d) latus rectum

377.

•Locus of points on a side which rolls along a fixed line

a)

a) cardiod

b)

b) epicycloid

c)

c) cycloid

d)

  d) hypocycloid

378.

•What is the length of the latus rectum of the curve x² = 20y ?

a)

a) 5

b)

b) 20

c)

  c) √‾20

d)

  d) √‾5

379.

•If the product of the slopes of any two straight lines is negative 1, one of these is said to be ___ to the other

a)

a) parallel

b)

  b) skew

c)

  c) non-intersecting

d)

  d) perpendicular

380.

•What is the curve represented by the equation r = aѲ ?

a)

  a) Spiral of Archimedes

b)

b) Rosette

c)

  c) Cardiod

d)

  d) Lemniscate

381.

•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)

a) Ellipse

b)

  b) Circle

c)

  c) Parabola

d)

  d) Hyperbola

382.

•The semi-conjugate axis of the hyperbola ( x²/9 ) – ( y²/4 ) = 1

a)

  a) 3

b)

b) -3

c)

  c) 2

d)

  d) -2

383.

•The length of the latus rectum of the parabola y=4px² is

a)

  a) 4p

b)

  b) 2p

c)

c) 1/4p

d)

  d) -4p

384.

•The tangent function is negative in what quadrants?

a)

  a) I and III

b)

  b) IV

c)

  c) II and IV

d)

  d) III

385.

•The Cartesian or rectangular coordinates system was first introduces

a)

  a) Newton

b)

  b) Galileo

c)

c) Descartes

d)

  d) Euclid

386.

•Also known as the x-coordinate

a)

a) Abscissa

b)

  b) Ordinate

c)

  c) Polar ordinate

d)

  d) Radius vector

387.

•The x-coordinate of a point is positive in what quadrants?

a)

  a) I and II

b)

b) II and IV

c)

  c) I and IV

d)

  d) II and III

388.

•The y-coordinate of a point is positive in what quadrants?

a)

a) II and III

b)

  b) I and II

c)

  c) III and IV

d)

d) II and IV

389.

•State the quadrants in which the coordinates (15, -2) lies

a)

  a) I

b)

  b) II

c)

  c) III

d)

  d) IV

390.

•The rectangular coordinates system used to represent a complex number

a)

  a) Argand diagram

b)

  b) Venn diagram

c)

  c) Complex diagram

d)

d) Maxwell’s diagram

391.

•A Cartesian coordinates system in which the axes are not perpendicular

a)

a) Parallelogram coordinates system

b)

  b) Oblique coordinates system

c)

  c) Polar coordinates system

d)

  d) Argand diagram

392.

•The angle of rotation about the origin of the positive x-axis into the point with rectangular coordinates (a, b), representing the complex number  a + bi is called ____ of the complex number.

a)

  a) amplitude

b)

  b) argument

c)

  c) phase angle

d)

  d) all of the above

393.

•The rectangular coordinates system in space is divided into eight compartments called

a)

  a) quadrant

b)

  b) octants

c)

  c) cubicles

d)

  d) octodrants

394.

•The angle of inclination of a straight line is the angle it makes with the

a)

  a) positive x-axis

b)

b) negative x-axis

c)

c) positive y-axis

d)

  d) negative y-axis

395.

•The points where the curve crossed the coordinates axes are called as the ___ with the axes

a)

  a) asymptotes

b)

  b) intercepts

c)

  c) intersections

d)

d) tangent and normal

396.

•A line which is perpendicular to the x-axis has slope equal to

a)

  a) zero

b)

  b) one

c)

c) infinity

d)

  d) either zero or infinity

397.

•A horizontal line has a slope of

a)

  a) zero

b)

  b) negative

c)

  c) infinity

d)

  d) positive

398.

•A line parallel to the y-axis at a directed distance x₁ has the equation

a)

a) y = y₁

b)

  b) x = x₁

c)

  c) y = x₁

d)

  d) x = y₁

399.

•Let m₁ and m₂ be the respective slopes of two perpendicular lines. Then

a)

  a) m₁ + m₂ = 1

b)

  b) m₁ + m₂ = 0

c)

  c) m₁ x m₂ = 1

d)

  d) m₁ x m₂ = -1

400.

•If all the y-terms have even exponents, the curve is symmetric with respect to the

a)

  a) line 45° with the axis

b)

  b) x-axis

c)

  c) y-axis

d)

  d) origin

401.

•If the equation is unchanged by the substitution of –x for x an –y for y simultaneously, its curve is symmetric with respect to the

a)

  a) x-axis

b)

  b) y-axis

c)

  c) line 45° with the axes

d)

  d) origin

402.

•If all of the terms of an equation have even exponents if all of the terms have odd exponents, the curve is symmetric with respect to the

a)

  a) x-axis

b)

  b) y-axis

c)

c) line 45° with the axes

d)

  d) origin

403.

•If two linear equation, the x-coefficient of the first is equal to the y-coefficient of the send and the y-coefficient of the first is numerically equal but of opposite sign to the x-coefficient of the second, or vice-versa, the lines represented are

a)

  a) parallel to each other

b)

  b) perpendicular to each other

c)

  c) at 45° with each other

d)

  d) none of the above

404.

•A cubic equation has either three real roots or one real root and two conjugate imaginary roots. The real roots are the points of intersection with

a)

  a) the x-axis

b)

  b) the y-axis

c)

  c) line 45° with the axes

d)

  d) the z-axis

405.

•If two equations have the same line as their graph, the equations are said to be

a)

  a) dependent

b)

  b) consistent

c)

c) independent

d)

  d) linear

406.

•The points (a, 1), (b, 2), (c, 3) are collinear. Which of the ff. is TRUE

a)

  a) c – b = c – a

b)

  b) c – b = b – a

c)

  c) c – a = a – b

d)

  d) c – a = b – a

407.

•In a linear equation Ax + By + C = 0, if B = 0, then the equation has the form of x= -C/A. This line is

a)

  a) parallel to the x-axis

b)

  b) parallel to the y-axis

c)

  c) 45° with the axis

d)

  d) intersecting the origin

408.

•The straight lines 4x – y + 3 = 0 and 8x – 2y + 6 = 0 are

a)

  a) perpendicular to each other

b)

  b) intersecting but not perpendicular

c)

  c) parallel to each other

d)

  d) coincident

409.

•Which of the ff. is the intercept form of an equation for straight lines?

a)

a) y = mx + b

b)

  b) ( x / a ) + ( y / b ) = 1

c)

  c) y – y₁ = m (x – x₁)

d)

  d) origin

410.

A straight line where the curve approaches more and more closely but never touches it except at a limiting point of infinity

a)

  a) Asymptotes

b)

  b) Axis of symmetry

c)

  c) Tangent

d)

  d) Normal

411.

•Who coined the word “asymptote” ?

a)

a) John Venn

b)

  b) John Navier

c)

  c) Thomas Hobbes

d)

  d) John Wallis

412.

•The path of a point which moves according to a given law or equation

a)

  a) Cycloid

b)

  b) Asymptote

c)

  c) formula

d)

  d) Directrix

413.

•The curve traced by a point moving in a plane is shown as the ___ of the point

a)

  a) parameter

b)

  b) pattern

c)

  c) formula

d)

  d) locus

414.

•A conic section is curve which is the intersection of

a)

  a) two cones

b)

  b) a cone and a line

c)

  c) a cone and a plane

d)

  d) a cone and an axis

415.

•When the ellipse approaches a circle as a limiting shape, its eccentricity approaches

a)

  a) 0

b)

  b) 1

c)

  c) -1

d)

  d) infinity

416.

•The set of points in a plane, the sum of whose distances form a fixed points is a constant, is

a)

  a) circle

b)

  b) parabola

c)

  c) hyperbola

d)

  d) ellipse

417.

•If a right circular cone is cut by a plane parallel to its base, it would reveal a/an

a)

  a) circle

b)

  b) parabola

c)

  c) ellipse

d)

  d) hyperbola

418.

•A ___ to a circle is aline that has exactly one point in common with the circle

a)

  a) diameter

b)

  b) secant

c)

  c) normal

d)

  d) tangent

419.

•A conic section whose eccentricity is always less than 1

a)

a) Parabola

b)

  b) Circle

c)

  c) Ellipse

d)

  d) Hyperbola

420.

•A locus of appoint 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)

  a) Parabola

b)

  b) Circle

c)

  c) Ellipse

d)

  d) Hyperbola

421.

•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 to the directrix is D, its eccentrcity, is

a)

  a) D/c

b)

  b) D/a

c)

  c) c/D

d)

  d) c/a

422.

•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)

  a) Circle

b)

  b) Ellipse

c)

  c) Parabola

d)

  d) Hyperbola

423.

•The angle between the tangents at the end points of the latus rectum of a parabola is

a)

  a) 45°

b)

  b) 75°

c)

  c) 75°

d)

  d) 90°

424.

•The tangents to the parabola at the end points of its latus rectum intersect

a)

  a) at a distance equal to the length of the latus rectum from the focus

b)

  b) at the vertex

c)

  c) at the directrix

d)

  d) none of the above

425.

•In 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)

  a) circle

b)

  b) parabola

c)

  c) ellipse

d)

  d) hyperbola

426.

•If the discriminant of a quadratic equation is greater than zero, the graph is a/an

a)

  a) circle

b)

  b) parabola

c)

  c) ellipse

d)

  d) hyperbola

427.

•A hyperbola passing through the focus of a parabola and perpendicular to the axis of symmetry

a)

  a) Directrix

b)

  b) Translated axis

c)

  c) Latus rectum

d)

  d) Axis

428.

•The latus rectum of the parabola x² = 4ay is

a)

  a) a

b)

  b) 4a

c)

  c) 2√‾a

d)

  d) 16a²

429.

•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)

  a) 2ab

b)

  b) 4ab

c)

  c) 2b²/a

d)

  d) 2a²/b

430.

•The eccentricity of a regular hyperbola is

a)

  a) √‾2

b)

  b) √‾3

c)

  c) 2

d)

  d) 1.5

431.

•A parabola has an eccentricity

a)

  a) equal to 1

b)

b) less than 1

c)

  c) greater than 1

d)

  d) of infinity

432.

•The axis of the parabola that passes through the foci, vertices and center is called

a)

a) conjugate axis

b)

b) transverse axis

c)

  c) major axis

d)

  d) minor axis

433.

•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)

  a) Auxiliary circle

b)

  b) Unit circle

c)

  c) Inscribed circle

d)

  d) Concentric circle

434.

•Which of the following is NOT a central conic?

a)

  a) circle

b)

b) parabola

c)

  c) ellipse

d)

  d) hyperbola

435.

•Confocal conics are conics

a)

a) having the same foci

b)

  b) having no focus

c)

  c) whose foci coincide with the origin

d)

d) whose foci coincides with the vertices

436.

•Which of the ff. is NOT true?

a)

a) A confocal ellipse and hyperbola always  intersect at right angle

b)

  b) A prime number is not a composite number

c)

  c) A cosecant curve is a periodic function of period 360

d)

  d) A conjecture is an axiom

437.

•If an ellipse and a hyperbola have the same foci, they are said to be

a)

a) central conics

b)

b) quartic conics

c)

  c) confocal conics

d)

  d) congruent conics

438.

•The parabola y = -x² + x + 1 opens

a)

  a) to the right

b)

  b) to the left

c)

  c) upward

d)

d) downward

439.

•A line segment joining two of its points and passing through a focus of a conic.

a)

  a) Latus rectum

b)

  b) Focal radius

c)

  c) Focal chord

d)

  d) Chord contrast

440.

•Given the polar equation

  r=3 / (1 + 3cosѲ). This is a graph of a/an

a)

a) ellipse

b)

b) parabola

c)

  c) circle

d)

  d) hyperbola

441.

•The equation r = 4cosѲ is a/an

a)

  a) ellipse

b)

  b) circle

c)

  c) hyperbola

d)

  d) parabola

442.

•In polar coordinates system, the distance of any point P from the origin is called

a)

  a) distance

b)

  b) polar angle

c)

  c) polar distance

d)

  d) radius vector

443.

•The plane curve traced out by a fixed point on the circle as the circle rolls along a line

a)

  a) Envelope

b)

  b) Epicycloid

c)

  c) Lemniscate

d)

  d) Cycloid

444.

•A plane curve traced by a fixed point on a circle as it rolls along outside of a fixed circle

a)

a) Epicycloid

b)

  b) Hypocycloid

c)

  c) Cycloid

d)

  d) Envelope

445.

•A plane curved traced by a fixed point on a circle as it rolls along the inside of a fixed circle

a)

  a) Epicycloid

b)

  b) Hypocycloid

c)

  c) Cycloid

d)

  d) Envelope

446.

•The equation x3 + y3 – 3axy = 0 represents a

a)

a) cardiod

b)

  b) Lemniscate

c)

  c) Folium of Descartes

d)

  d) Strophoid

447.

•Continuous curve traced by a point moving around fixed point in same plane are steadily increasing or decreasing distance.

a)

  a) Spiral

b)

  b) Helix

c)

  c) Lemniscate

d)

  d) Limacon

448.

•Curve which is locus of centers of curvature of another curve envelope of all its normal

a)

  a) Helix

b)

  b) Evolute

c)

  c) Spiral

d)

  d) Cardiod

449.

•Locus of the ultimate intersections or curves in a system of curves

a)

  a) Evolute

b)

  b) Pencil

c)

c) Envelope

d)

  d) Helix

450.

•Curve formed by uniform chain hanging freely from two points

a)

  a) Trisectrix

b)

  b) Parabola

c)

  c) Hyperbola

d)

  d) Catenary

451.

•The locus of a point such that its radius vector is proportional to its vectorial angle

a)

  a) Folium of Descartes

b)

  b) Spiral of Archimedes

c)

  c) Spiral of Pythagoras

d)

  d) Helix

452.

•The graph of the equation r = aco2Ѳ is a

a)

  a) limacon

b)

  b) lemniscate

c)

  c) rosette

d)

  d) spiral

453.

•The locus of a point which rolls on a straight line ( x-axis) 

a)

a) Cycloid

b)

  b) Epicycloid

c)

  c) Astroid

d)

d) Trochoid

454.

•The equation r = a(1 = cosѲ) is a polar equation of

a)

  a) hypocycloid

b)

  b) cycloid

c)

  c) cardiods

d)

  d) spiral

455.

•The equation r² = a² cosѲ is a

a)

a) rosette

b)

b) limacon

c)

  c) lemniscates

d)

  d) spiral

456.

•The equation r = a cosѲ is a

a)

  a) rosette

b)

  b) limacon

c)

  c) lemniscates

d)

  d) spiral

457.

•The equation r - aѲ = 0 is a

a)

a) rosette

b)

  b) limacon

c)

  c) lemniscate

d)

  d) spiral

458.

•The equation r = acosѲ + b is a

a)

  a) rosetter

b)

  b) limacon

c)

  c) lemniscates

d)

  d) spiral

459.

•The equation r = a(secѲ – tanѲ) is a

a)

  a) rosetter

b)

  b) strophoid

c)

  c) trisectrix

d)

  d) lemniscate

460.

•The equation r = a(4cosѲ – secѲ) is a

a)

  a) cardiod

b)

b) trisectrix

c)

  c) strophoid

d)

  d) fishmouth

461.

•The equation

  (x² + 2ay – a²)² = y²(a² + x²) is a

a)

a) rosette

b)

  b) cocked hat

c)

c) fishmouth

d)

  d) spiral

462.

•The equation x² + y² = a² is a

a)

  a) cocked hat

b)

  b) fishmouth

c)

  c) trisectrix

d)

  d) lames quartic

463.

•The equation ax² = y²(2a – y) is a

a)

  a) the top

b)

b) cocked hat

c)

  c) fishmouth

d)

  d) lames quartic

464.

•The equation (x² + y²)² = ax²y is a

a)

  a) bifolium

b)

  b) cocked hat

c)

  c) spiral

d)

  d) limacon

465.

•The equation   y² = (x² + 1)² (2 - x²)² is a

a)

  a) cocked hat

b)

  b) fishmouth

c)

c) lemniscates

d)

  d) spiral

466.

•The curve or surface that is tangential to each of the family of curves or surfaces

a)

  a) envelope

b)

  b) pencil

c)

  c) family

d)

  d) cusp

467.

•A curve that describes the locus of the centers of curvatures of another curve to which its tangents are normal

a)

  a) involute

b)

  b) evolute

c)

  c) lemniscate

d)

  d) cusp

468.

•___ is formed by intersection of rays from the point reflected or refracted from a curve surface

a)

  a) envelope

b)

  b) evolute

c)

  c) caustic

d)

  d) parabola

469.

This is the process of expressing a polynomial as the product of another polynomial or monomial of lower degree. What is this mathematical process?

a)

Decomposition

b)

Rationalization

c)

Factoring

d)

a)Polynomial damping

470.

•Determine the outside diameter of a hollow steel tube that will carry a tensile load of 500 kN at a stress of 140 MPa. Assume the wall thickness to be 0ne-tenth of the outside diameter.

a)

a) 123 mm

b)

b) 103 mm

c)

c) 113 mm

d)

•d) 93 mm

471.

Adding more solute to an already saturated solution will cause the excess solute to settle to the bottom of the container. What is this process called?

a)

a) Precipitation

b)

b) Hydration 

c)

c) Dehydration

d)

•d) Saturation

472.

• The length of time at which the original cost of capital used to purchase a unit has already been recovered.

a)

a) Economic life

b)

•b) Write off period 

c)

c) Physical life

d)

•d) Salvage life

473.

•The actual interest earned by a given principal is known as:

a)

a) Compound interest

b)

b) Simple interest

c)

c) Effective interest

d)

•d) Nominal interest

474.

•When using the net present value method for capital budgeting analysis, the required rate of return is called all of the following except the

a)

•A. Risk-free rate.

b)

•B. Cost of capital.

c)

•C. Discount rate.

d)

•D. Cutoff rate.

475.

1.An economic study is made of the total annual cost (C) for a series of alternative investments (P) for a given project. If C is plotted as the ordinate versus P, most desirable investment occurs when.

a)

A.dC/dP = 1

b)

A.dC/dP = 0

c)

A.dC/dP = Co

d)

A.dC/dP = +1

476.

The following cost item which is common to both fixed and operating cost of an enterprise, is

a)

interest

b)

depreciation

c)

taxes

d)

supplies

477.

The center gravity of an isosceles triangle whose height h is on the median line

a)

A.2/3 h from the vertex

b)

A.2/3 h from the base

c)

A.1/3 h from the vertex

d)

A.1/3 h from the vertex

478.

To comply the requirement of the Mechanical Engineering Law on the minimum compliment of mechanical engineers, a mechanical plant with a combined prime movers rating of 373 kw must have in its employ the following:

a)

A.1 PME , 1 Rme and 1 CPM

b)

A.1 PME and 2 RME

c)

A.1 RME and 2 CPM

d)

A.1 RME in-charge every shift

479.

Before an RME may be allowed to take the licensure examinations for PME, he must have an active practice of

a)

A.5 years

b)

A.4 years

c)

A.3 years

d)

D.  6 years

480.

6. Mechanical Plant engineer (MPE) may be allowed to take the licensure examinations for PME if ________.

a)

A.he has 4 years of active as a MPE

b)

A.he graduated with a BSME degree and 4 years as an RME

c)

A.he has a BSME degree, passed the examinations for RME and 4 years as RME

d)

A.none of these

481.

7. The only country that recognizes the mechanical engineering license of Filipinos issued by the Professional Regulation Commission and allowed to use the license in their country is______

a)

A.America

b)

England

c)

Japan

d)

none of these

482.

A statement of equality between two ratios

a)

valuation

b)

theorem

c)

A.power factor  

d)

proportion

483.

The side opposite the right angle of a right triangle

a)

quadrilateral

b)

apothem

c)

hypotenuse

d)

median

484.

11. Two triangles are congruent if two angles and the included side of one arc equal respectively to two angles and the included side of the other

a)

axiom

b)

postulate

c)

corollary

d)

theorem

485.

The National Association for Mechanical Engineers accredited by the PRC.

a)

PAMEE

b)

AGMEEP

c)

PSME

d)

IIEE

486.

Minimum grade of Mechanical Engineer required in the design and preparation of plans of a 280 kw diesel power plant

a)

RME

b)

CPM

c)

PME

d)

MPE

487.

The decrease in value of property due to passage of time

a)

devaluation

b)

depletion

c)

A.salvage value

d)

depreciation

488.

The differences between the book value and the actual lower resale value is

a)

A.salvage value

b)

A.resale value

c)

A.fixed cost

d)

A.sunk cost

489.

17. It occurs when a unique product or service is available only from a single supplier and entry of all other possible suppliers prevented

a)

monopoly

b)

competition

c)

profitability

d)

inventory

490.

18. The radius of a circle inscribe in a triangle with sides of 5, 7 and 10 is

a)

1774

b)

1477

c)

1744

d)

1747

491.

The ratio of the annual revenues to the annual expenses

a)

benefit-to-cost-ratio

b)

A.income ratio

c)

A.rate of return

d)

A.cost sales

492.

The reciprocal of 20 is

a)

0.50

b)

20

c)

0.20

d)

0.05

493.

A rectangle with equal sides

a)

A.rhombus

 

b)

B.trapezoid

c)

C.rectangle

d)

D.square

494.

22. The sum of the sides of a polygon

a)

A.circumference

b)

B.perimeter

c)

C.square

d)

D.hexagon

495.

23. A tax on imports

a)

A.import tariffs

b)

B.import quote

c)

C.value added tax

d)

D.capital account

496.

24. A line that meets a plane but is not perpendicular to it, in relation to the plane

a)

A.parallel

b)

B.collinear

c)

C.coplanar

d)

D.oblique

497.

25. Which is not a qualification of an applicant for ME board examination

a)

A.he must be holder of BSME degree

b)

B.he must be a citizen of the Philippines

c)

C.he must be at least 18 years old

d)

D.he must be a Certified Plant Mechanic

498.

26. Those funds that are required to make the enterprise or project a going concern

a)

A.banking

b)

B.accumulate account

c)

C.working capital

d)

D.principal or present worth

499.

27. The length of time during which the property may be operated at a profit

a)

A.length of time

b)

B.economic life

c)

C.physical life

d)

D.life

500.

28. Worth of the property as shown in the accounting records of an enterprise

a)

A.fair value

b)

B.market value

c)

C.use value

d)

D.book value

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