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Worksheets

Day 2 15-22

Total questions: 138

Worksheet time: 1hrs 9mins

Name
Class
Date
1.

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)

2.

The angular distance of a point on the terrestrial sphere from the north pole is called

a)

Coaltitude

b)

Latitude

c)

Altitude

d)

Codeclination

3.

Csc 520° is equal to

a)

Cos 20°

b)

Csc 20°

c)

Tan 45°

d)

Sin 20°

4.

What is the sine of 820°?

a)

0.984

b)

0.866

c)

-0.866

d)

-0.5

5.

The logarithm of the negative number is

a)

Imaginary

b)

Irrational

c)

Real

d)

Rational

6.

The sum of the squares of the sine and cosine of an angle.

a)

0

b)

1

c)

2

d)

3

7.

The logarithm of a number to the base e (2.7182....) is called

a)

Napierian logarithm

b)

Characteristic

c)

Mantissa

d)

Briggsian logarithm

8.

The characteristic is equal to the exponent of 10, when the number is written in

a)

Exponential form

b)

Scientific notation

c)

Logarithmic form

d)

Irrational number

9.

Napierian logarithms have a base closest to which number?

a)

2.72

b)

2.82

c)

2.92

d)

10

10.

The logarithm of 1 to any base is

a)

Indeterminate

b)

Zero

c)

Infinity

d)

One

11.

Sin (270° + B) is equal to

a)

-cos B

b)

sin B

c)

-sin B

d)

cos B

12.

The sum of the angles in an octant spheric triangle is

a)

180°

b)

270°

c)

360°

d)

540°

13.

The median of a triangle is the line connecting the vertex and the midpoint of the opposite side. For a given triangle, these medians intersects at a point which is called the

a)

Orthocenter

b)

Circumcenter

c)

Centroid

d)

Incenter

14.

The altitudes of the sides of the triangle intersects at the point known as

a)

Orthocenter

b)

Circumcenter

c)

Incenter

d)

Centroid

15.

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

16.

Log M – log N id equal to

a)

Log MN

b)

Log (M-N)

c)

Log M/N

d)

Log (N-M)

17.

The other form of log_a N = b is

a)

N = b^a

b)

N = a^b

c)

N = ab

d)

N = a/b

18.

The point of concurrency of the altitude of the triangle.

a)

Orthocenter

b)

Centroid

c)

Metacenter

d)

Incenter

19.

The point of concurrency of the perpendicular bisector of the sides of the triangle.

a)

Orthocenter

b)

Circumcenter

c)

Centroid

d)

Incenter

20.

The point of concurrency of the angle bisector of the triangle is called

a)

Orthocenter

b)

Circumcenter

c)

Centroid

d)

Incenter

21.

The inverse function of a logarithm is known as

a)

Antilogarithm

b)

Cologarithm

c)

Antiderative

d)

Antecedent

22.

The cologarithm of a number is the of the logarithm of a number.

a)

Positive

b)

Absolute value

c)

Negative

d)

Reciprocal

23.

The first table logarithms with 10 as base was developed in 1615 by

a)

James Naismith

b)

Henry Briggs

c)

John Napier

d)

John Wallis

24.

Who invented logarithms in 1614?

a)

John wallis

b)

Henry Briggs

c)

John Napier

d)

L’Hospital

25.

The number log_a b is called the of the system of a base a with respect to the system of base b.

a)

Coefficient

b)

Logarithm

c)

Modulus

d)

Exponent

26.

Napierian logarithm has a base of

a)

Pi

b)

10

c)

1

d)

e

27.

Log x = ln x.

a)

0.434

b)

10

c)

2.303

d)

e

28.

ln x = log x

a)

0.434

b)

10

c)

2.303

d)

e

29.

Which of the following cannot be a base for a logarithm?

a)

10

b)

Pi

c)

1

d)

e

30.

The integral part of a common logarithm is

a)

10

b)

E

c)

Mantissa

d)

Characteristic

31.

The mantissa of a logarithm is a

a)

Positive value only

b)

Negative value only

c)

Positive value, negative value or zero

d)

Positive value or zero

32.

For 0 < x < 1, ln x is

a)

Positive

b)

Zero

c)

Negative

d)

Between 0 and 1

33.

If 1 < N < 10, then

a)

1 < log N < 2

b)

0 < log N < 1

c)

2 < log N < 3

d)

-1 < log N < 0

34.

To change log_a to log_b N, multiple log_a N by

a)

Log_a b

b)

Log_b a

c)

Log_N a

d)

Log_N b

35.

The numbers log_a b and log_b a are

a)

Equal

b)

Equal but different in signs

c)

Reciprocal to each other

d)

Negative reciprocal to each

36.

Logarithm using 10 as base.

a)

Decimal logarithm

b)

Scientific logarithm

c)

Common logarithm

d)

Natural logarithm

37.

The logarithm of a product is the of the logarithms, and the logarithm of a quotient is the of the logarithms.

a)

Sum, difference

b)

Difference, sum

c)

Quotient, product

d)

Product, quotient

38.

When a logarithm is expressed as an integer plus a decimal (between 0 and 1), the integer is called

a)

Briggsian logarithm

b)

Napierian logarithm

c)

Mantissa

d)

Characteristic

39.

The characteristic of a logarithm is 3. The number between

a)

1 and 10

b)

10 and 100

c)

100 and 1000

d)

1000 and 10000

40.

The characteristics of the common logarithm of a number greater than 1 is

a)

Zero

b)

Positive

c)

Negative

d)

Zero or positive

41.

The characteristic is the exponent of 10, when the number is written in scientific notation.

a)

Equal to

b)

Greater than

c)

Less than

d)

None of the above

42.

If logarithm to base 10 (denoted as log_10) is called common logarithm is called natural logarithm, what do you call the logarithm of base 2 (denotes as lb)?

a)

Binary logarithm

b)

Bit logarithm

c)

Bilogarithm

d)

All of the above

43.

If the unknown is a conditional equation occurs as an exponent, the best way to solve the unknown is by

a)

Raising the power of both sides

b)

Taking the logarithm of both sides

c)

Extracting the root of both sides

d)

Applying the Newton’s method

44.

Angles of rotation with the same initial side and terminal side

a)

Terminal angles

b)

Conjugate angles

c)

Coterminal angle

d)

Supplementary angles

45.

An angle equal to one revolution of 360°

a)

Perigon

b)

Explement angle

c)

Reflex angle

d)

Supplement angle

46.

The angle which the line of sight to the object makes with the horizontal is above the eye of an observer

a)

Angle of depression

b)

Angle of elevation

c)

Acute angle

d)

Bearing

47.

The angle which the line of sight to the object makes with the horizontal is below the eye of an observer

a)

Angle of depression

b)

Angle of elevation

c)

Acute angle

d)

Bearing

48.

A triangle inscribed in a given triangle whose vertices are the feet of the three perpendiculars to the sides from the same point inside, the given triangle.

a)

Inscribed triangle

b)

Primitive triangle

c)

Pedal triangle

d)

Obtuse triangle

49.

The triangle with minimum perimeter but maximum area inscribed in another triangle is known as

a)

Pedal triangle

b)

Euclid’s triangle

c)

Primitive triangle

d)

None of the above

50.

A right triangle whose length of sides may be expressed as ratio of integral units

a)

Pedal triangle

b)

Isosceles triangle

c)

Scalene triangle

d)

Primitive triangle

51.

A triangle with no side equal is known as

a)

Acute triangle

b)

Oblique triangle

c)

Equilateral triangle

d)

Scalene triangle

52.

If two triangles have congruent bases, then the ratio of their areas equals the ratio of

a)

Their perimeters

b)

The length

53.

Which of the following is not a secondary part of a triangle?

a)

Altitudes

b)

Medians

c)

Exterior angles

d)

Sides

54.

Which of the following is not a property of a triangle?

a)

The sum of the three angles is always equal to two right angles

b)

The sum of two sides is less than the third side

c)

If the two sides are equal, the angles opposite are unequal.

d)

The altitudes of the triangle meet in a point.

55.

Given the sides of a triangle as 3 m and 5 m. The third side is

a)

Between 3 m and 8 m

b)

Greater than 8 m

c)

From 3 m to 7 m

d)

From 2 m to 8 m

56.

A straight from the vertex of a triangle to the midpoint of the opposite side is known as

a)

Altitude

b)

Median

c)

Height

d)

A or B

57.

Indicate the false statement

a)

An altitude of a triangle is a perpendicular drop from any vertex to the opposite side

b)

Three or more lines which have one point in common and said to be coplanar

c)

The altitudes of a triangle meet in a point

d)

A locus is a figure containing all the points and only those which fulfill a given requirement.

58.

The case of the solution of the triangle in the plane where the given data lead to two solutions

a)

Axioms of Euclid

b)

Absurb case

c)

Ambigous case

d)

All of the above

59.

The most proved theorem in Mathematics

a)

Gauss lemma

b)

Fermat’s theorem

c)

Ptolemy’s theorem

d)

Pythagorean theorem

60.

The least proved theorem in Mathematics.

a)

Goldbach conjecture

b)

Fermat’s last theorem

c)

Mersenne’s proportion

d)

Pappus proportions

61.

Equations used for checking the solution to a plane triangle using law of sine’s are as follows: (Equation) and (Equation). These equations are called

a)

Diophantine equations

b)

Mollweide’s equations

c)

Mohr equations

d)

Gauss equations

62.

Napier’s rule states that the sine of any middle part is equal to the product of the of the opposite parts.

a)

Sine

b)

Cosine

c)

Tangent

d)

Secant

63.

Napier’s rule states that the sine of any middle part is equal to the product of the of the adjacent parts.

a)

Sine

b)

Cosine

c)

Tangent

d)

Cotangent

64.

How many formulas may be derived from using the Napier’s Rules?

a)

5

b)

6

c)

8

d)

10

65.

The sum of all interior angles in a spherical triangle is always

a)

Greater than 180° but less than 270°

b)

Greater than 180° but less than 360°

c)

Greater than 180° but less than 540°

d)

Greater than 270° but less than 540°

66.

The maximum value for the longitude is

a)

90°

b)

180°

c)

45°

d)

360°

67.

The maximum value for a latitude is

a)

90°

b)

45°

c)

180°

d)

360°

68.

If R is the radius of a sphere and E is an spherical excess (in radians), then the area of a spherical triangle is

a)

Pi R^2 E

b)

R^2 E

c)

½ R^2 E

d)

R^2 / E

69.

One minute of the great circle arc on the surface of the earth is equivalent to

a)

1 statute mile

b)

1 nautical mile

c)

60 statute mile

d)

60 nautical mile

70.

A spherical triangle with all angles equals to a right triangle is called spherical triangle.

a)

Birectangular

b)

Quandrantal

c)

Trirectangular

d)

Right

71.

A spherical triangle with at least one side is a quarter of a great circle is called spherical triangle.

a)

Octant

b)

Quadrantal

c)

Trirectangular

d)

Birectangular

72.

One of the two great circles intersecting at right angle at the piles and dividing equinoctial points and ecliptic into 4 parts

a)

Nadir

b)

Zenith

c)

Declination

d)

Colure

73.

The radius of the earth used in spherical trigonometry is

a)

3989 statute miles

b)

3979 statute miles

c)

3969 statute miles

d)

3959 statute miles

74.

The difference between a nautical mile and a statute mile

a)

800 feet

b)

900 feet

c)

1000 feet

d)

500 feet

75.

Manila has a longitude of 121°05’E. What is the time difference between Manila and Greenwich, England which is at prime meridian?

a)

8 hours and 40 minutes

b)

8 hours and 34 minutes

c)

8 hours and 14 minutes

d)

8 hours and 4 minutes

76.

The earth is divided into how may time zone?

a)

24

b)

18

c)

16

d)

12

77.

In a spherical triangle, two angles (or sides) are on the same species if they are both

a)

Between 0° and 180°

b)

Between 0° and 90°

c)

Between 90° and 180°

d)

Between 0° and 90° or both between 90° and 180°

78.

Spherical degree is a unit of a spherical area taken as 1/720 of the surface of the sphere. How many spherical degrees a hemisphere have?

a)

360°

b)

720°

c)

180°

d)

270°

79.

Which of the following statements is false about spherical trigonometry?

a)

If two angles of a spherical triangle are equal, the sides opposite are equal and conversely

b)

If two angles of a spherical triangle are unequal, and the greater side lies opposite the greater angle, and conversely.

c)

The sum of two sides of a spherical triangle is greater than the third sides.

d)

The sum of all interior angles of a spherical triangles is 360°

80.

The sum of the sides of a spherical triangles is always less than

a)

270°

b)

360°

c)

540°

d)

180°

81.

The sum of any two angles of a spherical triangle is

a)

Greater than 180°

b)

Less than 180°

c)

Less than 180° + the third angle

d)

Greater than 180° + the third angle

82.

Refers to the angular distance from the equator measured along a meridian.

a)

Longitude

b)

Latitude

c)

Meridian

d)

Declination

83.

Refers to the angle at either pole between the meridian passing through a point and some fixed meridian known as the prime meridian.

a)

Longitude

b)

Latitute

c)

Declination

d)

Equinox

84.

Is half of a great circle terminated by the North Pole and South Pole

a)

Longitude

b)

Latitude

c)

Declination

d)

Meridian

85.

When the hypotenuse of a right spherical triangle is less than 90°

a)

The two legs are on the same quadrant

b)

The two legs are on the different quadrant

c)

One leg is one the first quadrant and the other on the second quadrant

d)

None of the above

86.

When the hypotenuse of a right spherical triangle is greater than 90°.

a)

The two legs are on the same quadrant

b)

The two legs are on the different quadrant

c)

One leg is one of the first quadrant and the other on the second quadrant

d)

None of the above

87.

The point where a ray from the center of the earth through an observer’s position on it intersects the celestial sphere is call the observer’s

a)

Zenith

b)

Nadir

c)

Pole

d)

Equinox

88.

The point that is diametrically opposite the zenith is called

a)

Pole

b)

Equinox

c)

Nadir

d)

Celestial meridian

89.

al sphere is call the observer’s

a)

Zenith

b)

Nadir

c)

Pole

d)

Equinox

90.

The point that is diametrically opposite the zenith is called

a)

Pole

b)

Equinox

c)

Nadir

d)

Celestial meridian

91.

The great circles through the north and south celestial poles are called

a)

Hour circles

b)

Celestial meridians

c)

Elevated poles

d)

A and B

92.

An oblique equilateral parallelogram:

a)

Square

b)

Rectangle

c)

Rhombus

d)

Trapezoid

93.

Mil is a unit of

a)

Angle

b)

Length

c)

Angle and length

d)

Weight

94.

The perpendicular segment from a vertex of the triangle to the line containing the opposite side

a)

Altitude

b)

Median

c)

Angle bisector

d)

D. Apothem

95.

The angle which the line of sight to the object makes with the horizontal is below the eye of the observer

a)

Angle of depression

b)

Angle of elevation

c)

Acute angle

d)

Bearing

96.

A pair of equal angles form by parallel lines and a third line intersecting the parallel lines.

a)

Alternate angles

b)

Vertical angles

c)

Oblique angles

d)

Adjacent angles

97.

The point at the top of a pyramid or triangle

a)

Apex

b)

Helix

c)

Vertex

d)

Convex

98.

The theorem that shows the relation between the three sides of the triangle and the length the medium of the triangle from one vertex to the opposite sides of the triangle.

a)

Apponias theorem

b)

Bramagupthas theorem

c)

Descartes theorem

d)

Pythagoras theorem

99.

The inverse of cosine function or arc cosine is known as

a)

Acosec

b)

Acosech

c)

Acosh

d)

Acos

100.

The inverse of hyperbolic cosine or arcosh is known as

a)

Acosec

b)

Acosech

c)

Acosh

d)

Acos

101.

The logarithm having a base 2 is known as

a)

Binary logarithm

b)

Briggsian logarithm

c)

Naperian logarithm

d)

Natural logarithm

102.

The perpendicular bisector of the sides of a triangle pass through a common point which is equivalent from the three vertices of the triangle is called

a)

Excenter

b)

Circumcenter

c)

Incenter

d)

Orthocenter

103.

The circle circumscribing a triangle has its center at the intersection of the perpendicular bisector of the triangle.

a)

Excircle

b)

Incircle

c)

Escribed circle

d)

Circum circle

104.

Any line segment joining a vertex of a triangle to a point on the opposites side

a)

Median

b)

Secant line

c)

Cevian

d)

Euclidian line

105.

The logarithm of the reciprocal of a number equal to the additive inverse of its logarithm

a)

Antilogarithm

b)

Cologarithm?

c)

Natural logarithm

d)

Reciprocal logarithm

106.

Another term for radius of an escribed circle of a triangle

a)

Inradius

b)

Circumradius

c)

Orthoradius

d)

Eradius

107.

The center of an escribed circle of a triangle

a)

Ecenter

b)

Incenter

c)

Orthocenter

d)

Circumcenter

108.

An angle whose vertex is a point on the circle and whose sides are chords

a)

Circumscribed angle

b)

Escribed angle

c)

Inscribed angle

d)

Reflex angle

109.

The decimal part of the logarithm of a number

a)

Characteristic

b)

Mantissa

c)

Base

d)

Exponent

110.

The square of the hypotenuse of a right triangle is equal to the squares of the squares of the other two sides or legs

a)

Pythagorean theorem

b)

Ptolemy’s theorem

c)

Aristotle’s theorem

d)

Euclid’s theorem

111.

The triangle formed inside a triangle by connecting the points where the altitudes of the triangle touches the opposite sides as drawn from each vertices

a)

Inscribed triangle

b)

Median triangle

c)

Pedal triangle

d)

Ortho triangle

112.

The trigonometric function equal to one minus the cosine function

a)

Versed sine

b)

Co-versed sine

c)

Arcsine

d)

Arcsine

113.

Numbers between 0 and 1 have

a)

Positive logarithms

b)

Negative logarithms

c)

Complex logarithms

d)

Zero logarithm

114.

The logarithm of 1 to the base 8 is

a)

1

b)

1/8

c)

0

d)

8

115.

The logarithm of one is

a)

Indeterminate

b)

Zero

c)

Infinity

d)

undefined

116.

The space between two lines meeting at a point called vertex

a)

angle

b)

plane

c)

distance

d)

altitude

117.

A path consisting of two or more straight lines

a)

curve line

b)

locus

c)

trial

d)

broken line

118.

The longest side of a right triangle or the side opposite to the right angle.

a)

Slant height

b)

Leg

c)

Hypotenuse

d)

Base

119.

The distance between a center and a vertex of a regular polygon.

a)

Apothem

b)

Median

c)

Long radius

d)

Hypotenuse

120.

The perpendicular bisector of a line segment

a)

Mediator

b)

Divider

c)

Altitude

d)

Orthobisector

121.

The angular distance of an astronomical body above or below an observer’s horizon.

a)

Altitude

b)

Slant height

c)

Azimuth

d)

Normal

122.

The angle between any two radii is

a)

Inscribed angle

b)

Central angle

c)

Polar angle

d)

Dihedral angle

123.

Refers to a line of symmetry of a given figure

a)

Reference

b)

Symmetry

c)

Boundary

d)

Axis

124.

A single line which forms a tangent to two or more separate curves.

a)

Common secant

b)

Common tangent

c)

Chord

d)

Normal

125.

An angle that is half the straight angle

a)

Acute angle

b)

Right angle

c)

Reflex angle

d)

Oblique angle

126.

A line drawn between any two non-adjacent vertices of a polygon

a)

Altitude

b)

Median

c)

Bisector

d)

Diagram

127.

The procedure for estimating intermediate value that are not listed in a table of numerical values.

a)

Interpolation

b)

Manipulation method

c)

Telescoping process

d)

Trial and error method

128.

The operation of root extraction

a)

Involution

b)

Evolution

c)

Rationalization

d)

Manipulation

129.

The operation of raising to an integral power x^n

a)

Involution

b)

Evolution

c)

Rationalization

d)

Expansion

130.

A plane surface of a geometric figure

a)

Base

b)

Plane

c)

Face

d)

Surface

131.

Each interior angle of an equilateral triangle is equal to

a)

30°

b)

60°

c)

90°

d)

45°

132.

The difference between an approximate value and the true value which it approximates

a)

Error

b)

Balance

c)

Residue

d)

Correction factor

133.

A unit of angle measurement with one revolution equivalent to 400 gradians

a)

Gradian

b)

Degree

c)

Mil

d)

Revolution

134.

A right triangle whose length of sides may be expressed as ratio of integral units.

a)

Pedal triangle

b)

Isosceles triangle

c)

Scalene triangle

d)

Primitive triangle

135.

A triangle with no side equal is known as

a)

Acute triangle

b)

Oblique triangle

c)

Equilateral triangle

d)

Scalene triangle

136.

If two triangles have congruent bases, then the ratio of their areas equals the ratio of

a)

Their perimeter s

b)

Their sides

c)

The lengths of their altitudes

d)

None of the above

137.

In an isosceles right triangle, the hypotenuse is times as long as each of the legs.

a)

Sqrt(2)

b)

Sqrt(3)

c)

2

d)

3

138.

Which of the following is not a secondary part of a triangle?

a)

Altitudes

b)

Medians

c)

Exterior angles

d)

Sides