WorksheetsDay 2 15-22
Total questions: 138
Worksheet time: 1hrs 9mins
Sin A cos B – cos A sin B is equivalent to:
Cos (A-B)
Sin (A-B)
Tan (A-B)
Cos2 (A-B)
The angular distance of a point on the terrestrial sphere from the north pole is called
Coaltitude
Latitude
Altitude
Codeclination
Csc 520° is equal to
Cos 20°
Csc 20°
Tan 45°
Sin 20°
What is the sine of 820°?
0.984
0.866
-0.866
-0.5
The logarithm of the negative number is
Imaginary
Irrational
Real
Rational
The sum of the squares of the sine and cosine of an angle.
0
1
2
3
The logarithm of a number to the base e (2.7182....) is called
Napierian logarithm
Characteristic
Mantissa
Briggsian logarithm
The characteristic is equal to the exponent of 10, when the number is written in
Exponential form
Scientific notation
Logarithmic form
Irrational number
Napierian logarithms have a base closest to which number?
2.72
2.82
2.92
10
The logarithm of 1 to any base is
Indeterminate
Zero
Infinity
One
Sin (270° + B) is equal to
-cos B
sin B
-sin B
cos B
The sum of the angles in an octant spheric triangle is
180°
270°
360°
540°
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
Orthocenter
Circumcenter
Centroid
Incenter
The altitudes of the sides of the triangle intersects at the point known as
Orthocenter
Circumcenter
Incenter
Centroid
The angle which the line of sight to the object makes with the horizontal which is above the eye of the observer is called
Angle of depression
Angle of elevation
Acute angle
Bearing
Log M – log N id equal to
Log MN
Log (M-N)
Log M/N
Log (N-M)
The other form of log_a N = b is
N = b^a
N = a^b
N = ab
N = a/b
The point of concurrency of the altitude of the triangle.
Orthocenter
Centroid
Metacenter
Incenter
The point of concurrency of the perpendicular bisector of the sides of the triangle.
Orthocenter
Circumcenter
Centroid
Incenter
The point of concurrency of the angle bisector of the triangle is called
Orthocenter
Circumcenter
Centroid
Incenter
The inverse function of a logarithm is known as
Antilogarithm
Cologarithm
Antiderative
Antecedent
The cologarithm of a number is the of the logarithm of a number.
Positive
Absolute value
Negative
Reciprocal
The first table logarithms with 10 as base was developed in 1615 by
James Naismith
Henry Briggs
John Napier
John Wallis
Who invented logarithms in 1614?
John wallis
Henry Briggs
John Napier
L’Hospital
The number log_a b is called the of the system of a base a with respect to the system of base b.
Coefficient
Logarithm
Modulus
Exponent
Napierian logarithm has a base of
Pi
10
1
e
Log x = ln x.
0.434
10
2.303
e
ln x = log x
0.434
10
2.303
e
Which of the following cannot be a base for a logarithm?
10
Pi
1
e
The integral part of a common logarithm is
10
E
Mantissa
Characteristic
The mantissa of a logarithm is a
Positive value only
Negative value only
Positive value, negative value or zero
Positive value or zero
For 0 < x < 1, ln x is
Positive
Zero
Negative
Between 0 and 1
If 1 < N < 10, then
1 < log N < 2
0 < log N < 1
2 < log N < 3
-1 < log N < 0
To change log_a to log_b N, multiple log_a N by
Log_a b
Log_b a
Log_N a
Log_N b
The numbers log_a b and log_b a are
Equal
Equal but different in signs
Reciprocal to each other
Negative reciprocal to each
Logarithm using 10 as base.
Decimal logarithm
Scientific logarithm
Common logarithm
Natural logarithm
The logarithm of a product is the of the logarithms, and the logarithm of a quotient is the of the logarithms.
Sum, difference
Difference, sum
Quotient, product
Product, quotient
When a logarithm is expressed as an integer plus a decimal (between 0 and 1), the integer is called
Briggsian logarithm
Napierian logarithm
Mantissa
Characteristic
The characteristic of a logarithm is 3. The number between
1 and 10
10 and 100
100 and 1000
1000 and 10000
The characteristics of the common logarithm of a number greater than 1 is
Zero
Positive
Negative
Zero or positive
The characteristic is the exponent of 10, when the number is written in scientific notation.
Equal to
Greater than
Less than
None of the above
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)?
Binary logarithm
Bit logarithm
Bilogarithm
All of the above
If the unknown is a conditional equation occurs as an exponent, the best way to solve the unknown is by
Raising the power of both sides
Taking the logarithm of both sides
Extracting the root of both sides
Applying the Newton’s method
Angles of rotation with the same initial side and terminal side
Terminal angles
Conjugate angles
Coterminal angle
Supplementary angles
An angle equal to one revolution of 360°
Perigon
Explement angle
Reflex angle
Supplement angle
The angle which the line of sight to the object makes with the horizontal is above the eye of an observer
Angle of depression
Angle of elevation
Acute angle
Bearing
The angle which the line of sight to the object makes with the horizontal is below the eye of an observer
Angle of depression
Angle of elevation
Acute angle
Bearing
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.
Inscribed triangle
Primitive triangle
Pedal triangle
Obtuse triangle
The triangle with minimum perimeter but maximum area inscribed in another triangle is known as
Pedal triangle
Euclid’s triangle
Primitive triangle
None of the above
A right triangle whose length of sides may be expressed as ratio of integral units
Pedal triangle
Isosceles triangle
Scalene triangle
Primitive triangle
A triangle with no side equal is known as
Acute triangle
Oblique triangle
Equilateral triangle
Scalene triangle
If two triangles have congruent bases, then the ratio of their areas equals the ratio of
Their perimeters
The length
Which of the following is not a secondary part of a triangle?
Altitudes
Medians
Exterior angles
Sides
Which of the following is not a property of a triangle?
The sum of the three angles is always equal to two right angles
The sum of two sides is less than the third side
If the two sides are equal, the angles opposite are unequal.
The altitudes of the triangle meet in a point.
Given the sides of a triangle as 3 m and 5 m. The third side is
Between 3 m and 8 m
Greater than 8 m
From 3 m to 7 m
From 2 m to 8 m
A straight from the vertex of a triangle to the midpoint of the opposite side is known as
Altitude
Median
Height
A or B
Indicate the false statement
An altitude of a triangle is a perpendicular drop from any vertex to the opposite side
Three or more lines which have one point in common and said to be coplanar
The altitudes of a triangle meet in a point
A locus is a figure containing all the points and only those which fulfill a given requirement.
The case of the solution of the triangle in the plane where the given data lead to two solutions
Axioms of Euclid
Absurb case
Ambigous case
All of the above
The most proved theorem in Mathematics
Gauss lemma
Fermat’s theorem
Ptolemy’s theorem
Pythagorean theorem
The least proved theorem in Mathematics.
Goldbach conjecture
Fermat’s last theorem
Mersenne’s proportion
Pappus proportions
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
Diophantine equations
Mollweide’s equations
Mohr equations
Gauss equations
Napier’s rule states that the sine of any middle part is equal to the product of the of the opposite parts.
Sine
Cosine
Tangent
Secant
Napier’s rule states that the sine of any middle part is equal to the product of the of the adjacent parts.
Sine
Cosine
Tangent
Cotangent
How many formulas may be derived from using the Napier’s Rules?
5
6
8
10
The sum of all interior angles in a spherical triangle is always
Greater than 180° but less than 270°
Greater than 180° but less than 360°
Greater than 180° but less than 540°
Greater than 270° but less than 540°
The maximum value for the longitude is
90°
180°
45°
360°
The maximum value for a latitude is
90°
45°
180°
360°
If R is the radius of a sphere and E is an spherical excess (in radians), then the area of a spherical triangle is
Pi R^2 E
R^2 E
½ R^2 E
R^2 / E
One minute of the great circle arc on the surface of the earth is equivalent to
1 statute mile
1 nautical mile
60 statute mile
60 nautical mile
A spherical triangle with all angles equals to a right triangle is called spherical triangle.
Birectangular
Quandrantal
Trirectangular
Right
A spherical triangle with at least one side is a quarter of a great circle is called spherical triangle.
Octant
Quadrantal
Trirectangular
Birectangular
One of the two great circles intersecting at right angle at the piles and dividing equinoctial points and ecliptic into 4 parts
Nadir
Zenith
Declination
Colure
The radius of the earth used in spherical trigonometry is
3989 statute miles
3979 statute miles
3969 statute miles
3959 statute miles
The difference between a nautical mile and a statute mile
800 feet
900 feet
1000 feet
500 feet
Manila has a longitude of 121°05’E. What is the time difference between Manila and Greenwich, England which is at prime meridian?
8 hours and 40 minutes
8 hours and 34 minutes
8 hours and 14 minutes
8 hours and 4 minutes
The earth is divided into how may time zone?
24
18
16
12
In a spherical triangle, two angles (or sides) are on the same species if they are both
Between 0° and 180°
Between 0° and 90°
Between 90° and 180°
Between 0° and 90° or both between 90° and 180°
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?
360°
720°
180°
270°
Which of the following statements is false about spherical trigonometry?
If two angles of a spherical triangle are equal, the sides opposite are equal and conversely
If two angles of a spherical triangle are unequal, and the greater side lies opposite the greater angle, and conversely.
The sum of two sides of a spherical triangle is greater than the third sides.
The sum of all interior angles of a spherical triangles is 360°
The sum of the sides of a spherical triangles is always less than
270°
360°
540°
180°
The sum of any two angles of a spherical triangle is
Greater than 180°
Less than 180°
Less than 180° + the third angle
Greater than 180° + the third angle
Refers to the angular distance from the equator measured along a meridian.
Longitude
Latitude
Meridian
Declination
Refers to the angle at either pole between the meridian passing through a point and some fixed meridian known as the prime meridian.
Longitude
Latitute
Declination
Equinox
Is half of a great circle terminated by the North Pole and South Pole
Longitude
Latitude
Declination
Meridian
When the hypotenuse of a right spherical triangle is less than 90°
The two legs are on the same quadrant
The two legs are on the different quadrant
One leg is one the first quadrant and the other on the second quadrant
None of the above
When the hypotenuse of a right spherical triangle is greater than 90°.
The two legs are on the same quadrant
The two legs are on the different quadrant
One leg is one of the first quadrant and the other on the second quadrant
None of the above
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
Zenith
Nadir
Pole
Equinox
The point that is diametrically opposite the zenith is called
Pole
Equinox
Nadir
Celestial meridian
al sphere is call the observer’s
Zenith
Nadir
Pole
Equinox
The point that is diametrically opposite the zenith is called
Pole
Equinox
Nadir
Celestial meridian
The great circles through the north and south celestial poles are called
Hour circles
Celestial meridians
Elevated poles
A and B
An oblique equilateral parallelogram:
Square
Rectangle
Rhombus
Trapezoid
Mil is a unit of
Angle
Length
Angle and length
Weight
The perpendicular segment from a vertex of the triangle to the line containing the opposite side
Altitude
Median
Angle bisector
D. Apothem
The angle which the line of sight to the object makes with the horizontal is below the eye of the observer
Angle of depression
Angle of elevation
Acute angle
Bearing
A pair of equal angles form by parallel lines and a third line intersecting the parallel lines.
Alternate angles
Vertical angles
Oblique angles
Adjacent angles
The point at the top of a pyramid or triangle
Apex
Helix
Vertex
Convex
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.
Apponias theorem
Bramagupthas theorem
Descartes theorem
Pythagoras theorem
The inverse of cosine function or arc cosine is known as
Acosec
Acosech
Acosh
Acos
The inverse of hyperbolic cosine or arcosh is known as
Acosec
Acosech
Acosh
Acos
The logarithm having a base 2 is known as
Binary logarithm
Briggsian logarithm
Naperian logarithm
Natural logarithm
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
Excenter
Circumcenter
Incenter
Orthocenter
The circle circumscribing a triangle has its center at the intersection of the perpendicular bisector of the triangle.
Excircle
Incircle
Escribed circle
Circum circle
Any line segment joining a vertex of a triangle to a point on the opposites side
Median
Secant line
Cevian
Euclidian line
The logarithm of the reciprocal of a number equal to the additive inverse of its logarithm
Antilogarithm
Cologarithm?
Natural logarithm
Reciprocal logarithm
Another term for radius of an escribed circle of a triangle
Inradius
Circumradius
Orthoradius
Eradius
The center of an escribed circle of a triangle
Ecenter
Incenter
Orthocenter
Circumcenter
An angle whose vertex is a point on the circle and whose sides are chords
Circumscribed angle
Escribed angle
Inscribed angle
Reflex angle
The decimal part of the logarithm of a number
Characteristic
Mantissa
Base
Exponent
The square of the hypotenuse of a right triangle is equal to the squares of the squares of the other two sides or legs
Pythagorean theorem
Ptolemy’s theorem
Aristotle’s theorem
Euclid’s theorem
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
Inscribed triangle
Median triangle
Pedal triangle
Ortho triangle
The trigonometric function equal to one minus the cosine function
Versed sine
Co-versed sine
Arcsine
Arcsine
Numbers between 0 and 1 have
Positive logarithms
Negative logarithms
Complex logarithms
Zero logarithm
The logarithm of 1 to the base 8 is
1
1/8
0
8
The logarithm of one is
Indeterminate
Zero
Infinity
undefined
The space between two lines meeting at a point called vertex
angle
plane
distance
altitude
A path consisting of two or more straight lines
curve line
locus
trial
broken line
The longest side of a right triangle or the side opposite to the right angle.
Slant height
Leg
Hypotenuse
Base
The distance between a center and a vertex of a regular polygon.
Apothem
Median
Long radius
Hypotenuse
The perpendicular bisector of a line segment
Mediator
Divider
Altitude
Orthobisector
The angular distance of an astronomical body above or below an observer’s horizon.
Altitude
Slant height
Azimuth
Normal
The angle between any two radii is
Inscribed angle
Central angle
Polar angle
Dihedral angle
Refers to a line of symmetry of a given figure
Reference
Symmetry
Boundary
Axis
A single line which forms a tangent to two or more separate curves.
Common secant
Common tangent
Chord
Normal
An angle that is half the straight angle
Acute angle
Right angle
Reflex angle
Oblique angle
A line drawn between any two non-adjacent vertices of a polygon
Altitude
Median
Bisector
Diagram
The procedure for estimating intermediate value that are not listed in a table of numerical values.
Interpolation
Manipulation method
Telescoping process
Trial and error method
The operation of root extraction
Involution
Evolution
Rationalization
Manipulation
The operation of raising to an integral power x^n
Involution
Evolution
Rationalization
Expansion
A plane surface of a geometric figure
Base
Plane
Face
Surface
Each interior angle of an equilateral triangle is equal to
30°
60°
90°
45°
The difference between an approximate value and the true value which it approximates
Error
Balance
Residue
Correction factor
A unit of angle measurement with one revolution equivalent to 400 gradians
Gradian
Degree
Mil
Revolution
A right triangle whose length of sides may be expressed as ratio of integral units.
Pedal triangle
Isosceles triangle
Scalene triangle
Primitive triangle
A triangle with no side equal is known as
Acute triangle
Oblique triangle
Equilateral triangle
Scalene triangle
If two triangles have congruent bases, then the ratio of their areas equals the ratio of
Their perimeter s
Their sides
The lengths of their altitudes
None of the above
In an isosceles right triangle, the hypotenuse is times as long as each of the legs.
Sqrt(2)
Sqrt(3)
2
3
Which of the following is not a secondary part of a triangle?
Altitudes
Medians
Exterior angles
Sides
