WorksheetsDay 3 page 23-29
Total questions: 111
Worksheet time: 56mins
The area of the annulus can be calculated by getting the difference between the area of the larger circle and the area of the smaller circle. Also, its area can be calculated by removing the hole.
Law of extremities
Law of reduction
Law of deduction
Sharp theorem
Each of the faces of a regular hexahedron is a
Square
Triangle
Rectangle
Hexagon
It is a polyhedron of which two faces are equal polygons in parallel planes and other faces are parallelograms
Tetrahedron
Prism
Frustum
Prismatoid
The apothem of a polygon is or its inscribed circle.
Radius
Circumference
Diameter
Length
Each angle of regular dodecagon is equal to
135
150
125
105
The area bounded by two concentric circles is called
Ring
Disk
Annulus
Sector
One-fourth of a great circle is called
Cone
Sector
Quadrant
Arc
Points that lie on the same plane are called
Coplanar
Parallel
Collinear
Oblique
The volume of a circular cylinder is equal to the product of its base and altitude
Axiom
Postulate
Theorem
Corollary
The study of properties of figures in three dimensions.
Physics
Plane trigonometry
Solid geometry
Trigonometry
A plane closed curve, all points of which are the same distance from a point within, called the center.
Polyhedron
Polygon
Circle
Ellipse
What is the angle of pi and less than 2pi?
Straight line
Obtuse angle
Oblique angle
Acute angle
What is the value in degrees of 1 radian?
90°
57.3°
60°
33°
Prisms are named according to their
Diagonals
Sides
Vertices
Bases
In plane geometry, two circular arcs that together make up a full circle are called
Coterminal arcs
Conjugate arcs
Congruent arcs
Half arcs
Polygons are classified according to the number of
Vertices
Sides
Diagonals
Angles
When two planes intersect with each other, the amount of divergence between the two plans is expressed by measuring the
Dihedral angle
Plane angle
Polyhedral angle
Reflex angle
An angular unit equivalent to 1/4000 of the circumference of a circle is called
Mil
Degree
Radian
Grad
Express 45° in mils
80
800
1600
2700
The arc length equal to the radius of the circle is called
Radian
Quarter sector
Sector
Semicircle
A five-pointed star is also known as
Pentagon
Pentatron
Pentagram
Quintagram
If two or more lines have a single point which lies on all of them, then they are
Collinear
Coplanar
Concurrent
Conjugate
The action of bringing one geometric figure into coincidence with another is called
Transposition
Translation
Superposition
Projection
A line that intersect two or more lines at distinct points
Tangent line
Transversal
Bisector
Median
An arc length equal to the radius of a circle
Grad
Radian
Degree
Mil
An angle which is 1/400th of the full revolution.
Gon
Mil
Degree
Radian
Another term for gon
Grad
Mil
Centesimal degree
A and C
An angle whose vertex is a point on the circle and whose sides are chords is known as
Interior angle
Vertical angle
Acute angle
Inscribed angle
An angle greater than the right angle but less than a straight angle
Acute angle
Obtuse angle
Reflex angle
Oblique angle
Any angle greater than a straight angle but less than two straight angles is known as angle
Compliment
Supplement
Complex
Reflex
The angle formed by the prolongation of one side and the adjacent side of the polygon
Interior angle
Acute angle
Exterior angle
Explementary angle
Two angles which have the same vertex and the sides of one are form by extending the sides one are form by extending the sides of the other.
Adjacent angles
Vertical angles
Vertical angles
Deflection angles
Another term for exterior angle
Vertical angle
Inscribed angle
Reflex angle
Deflection angle
What is the sum of all deflection angles in given polygon?
Always less than 360°
Always equal to 360°
Always greater than 360°
Always equal to 180°
The coterminal angle is 120° is
240°
-240°
480°
-480°
Two planes intersect each other. What is the term for the angle formed perpendicular to the intersection of two planes?
Solid angle
Plane angle
Base angle
Dihedral angle
When a terminal side of an angle coincides with an axis, the angle is a
Co-terminal angle
Right angle
Quandrantal angle
Reflex angle
If the exterior angle of a polygon is obtuse, its corresponding interior angle is
An acute angle
Also an obtuse angle
A reflex angle
Always greater than 180°
The measure of 2.25 revolutions counterclockwise is
835°
805°
810°
815°
Solid angles are measured in
Mil
Radians
Steradians
Circular mils
What is the largest measure (in steradians) of a solid angle
2pi
4pi
8pi
pi
Steradians measure in space in analog of measured in the plane
radians
degrees
mils
grads
A part of a circle is called
sector
segment
chord
arc
It is a union of the chord of a circle and the intercepted arc
Sector
Segment
Lune
Zone
A of a circle in the figure bounded by two radii and the intercepted arc.
Major arc
Minor arc
Segment
Sector
The apothem of a polygon is the of its inscribed circle
Radius
Circumference
Diameter
Length
As the area of the circle increases, the ratio of its circumference to its diameter
Increases
Remains constant
Decreases
Will be equal to 1
A circle is said to be to a polygon having the same perimeter with that of the circle
Congruent
Isoperimetric
Proportional
Convex
Which of the following is NOT a property of a circle?
Through 3 points not in a straight line, only one circle can be drawn.
A tangent to a circle is perpendicular to the radius at the point of tangency and conversely.
An inscribed angle is measured by one half of the intercepted arc.
The arcs of two circles subtended by equal central angles are always equal.
All circles having the same center but of unequal radii are called
Concentric circles
Eccentric circles
Inner circles
Pythagorean circles
Two chords of a circle which joints a point on the circle to the end points of a diameter and forms a right angle.
Complementary chords
Supplementary chords
Focal chords
Chords of contrast
The center of the inscribed circle of a triangle is known as known as of the triangle.
Circumcenter
Incenter
Excenter
Orthocenter
Supplementary chords are two chords which join a point on the circle to the endpoints of a diameter. The supplemental chords subtend a/an angle.
Acute
Right
Obtuse
Reflex
A circle of radius R has a curvature of
R^2
1/R
2R
Sqrt(R)
star described by the diagonal of a regular pentagon.
Perigon
Pentagram
Penacle
Pentagram or penacle
The geometric figure remaining after a parallelogram has been removed from the corner of a large similar polygon.
Gnomon
Gaussian plane
Lozenge
An oblique-angled parallelogram with four sides equal is called
Rhombus
Diamond
Lozenge
All of the above
A non-convex quadrilateral with two pairs of adjacent equal sides is called
Trapezium
Kite
Deltroid
Diamond
What is another term for parallelogram?
Rectangle
Quadrangle
Diamond
Rhomboid
Prisms are classified according to their
Bases
Prism
Truncated prism
Prismatoid
A Solid cut of a given solid by two non parallel planes is called
Frustum
Prism
Truncated prism
Prismatoid
A polyhedron having bases two polygons in parallel planes and for lateral faces triangles or trapezoids with one side lying on the other base of the polyhedron.
Pyramid
Cone
Prismatoid
Truncated prism
Portion of the regular solid left after cutting off the upper part by a plane parallel to the base.
Frustum
Ungula
Truncated solid
Prismatoid
Body or space bounded by surface every point of which is equidistant from a point within
Circle
Sphere
Spheroid
Ellipsoid
A solid bounded by a zone and the planes of the zone’s base.
Spherical sector
Spherical segment
Lune
Spherical excess
The intersection of the sphere and the plane through the center is called
Great circle
Small circle
Poles
Polar distance
The portion of a sphere enclosed between two great semi-circles having common end points, including the semi-circle
Spherical excess
Spherical segment
Zone
Lune
A portion of the surface of a sphere included between two parallel planes.
Spherical excess
Spherical segment
Zone
Lune
If R is the radius of the sphere and h is the distance between two parallel planes, the area of the zone is
2 pi R h
4 pi R h
pi h^2 (3R-h)/3
4 pi (R-h)
The solid bounded by two great circles and the surface of a sphere is known as
Spherical zone
Spherical segment
Spherical cone
Spherical wedge
A cone or cylinder with its top cut off by a plane oblique to the base.
Frustum
Prismoid
Prismatoid
Ungula
A term given to cylinder with elliptical cross-section
Cylindroid
Cylindoid
Ovaloid
Deltroid
A doughnut-like surface of revolution generated by rotating the circle through 360° in space about a line in its place but now passing through the circle.
Torus
Annulus
Anchor
All of the above
A regular solid star in a shape that is radiating from center like rays of star.
Envelop
Caustic
Evolute
Pencil
The regular polyhedron is a solid with all its face identical regular polygons. The regular polyhedrons are also known as
Euclidian solids
Pythagorean solids
Platonic solids
Newtonian solids
There are how many regular polyhedral known to man?
5
3
7
10
An icosahedron is a regular polyhedron of faces.
12
14
16
20
A regular polyhedron with 6 sides is called
Dodecahedron
Hexahedron
Tetrahedron
Octahedron
The face of a regular tetrahedron is a
Square
Pentagon
Hexagon
Triangle
The face of a regular octahedron is a
Square
Pentagon
Hexagon
Triangle
The face of a regular dodecahedron is a
Square
Pentagon
Hexagon
Triangle
The face of a regular Icosahedron is a
Square
Pentagon
Hexagon
Triangle
Which regular polyhedron does not have a face a triangle?
Pentagram
Pentagon
Stellated solid
Archimedean solid
How many edges are there in a dodecagon?
6
12
30
8
A tetrahedron has vertices.
4
3
6
5
Given two solids and a plane. Supposed that every plane parallel to the given plane intersecting one of the two solids, also interacts the other and gives cross-sections with the same area, then the two solids have the same volume. This is known as the
Unit postulate
Plane postulate
Parallel postulate
Cavalieri’s postulate
Who formulated the Cavalieri’s Principle?
Harold Cavalieri
Buenventura Cavalieri
Joefry Cavalieri
Carl Cabalieri
A line segment that is divided into two segments, a greater a and a smaller b such that the length of a + b is to a and a is to b. Such division is known as
Golden segment
Golden ratio
Golden proportion
All of the above
The volume of a paraboloid is equal to the volume of circumscribing cylinder.
1/3
1/2
1/4
2/3
The portion of a sphere included between two parallel planes.
Spherical wedge
Spherical pyramid
Spherical segment?
Spherical sector
The portion of a sphere generated by the revolution of a circular sector about any diameter of the circle of which the sector is a part.
Spherical wedge
Spherical pyramid
Spherical segment
Spherical sector?
A solid bounded by a surface all points of which are equidistant from a point call the center.
Ellipsoid
Sphere?
Paraboloid
Hyperboloid
The portion of a sphere bounded by a spherical polygon and the planes of its sides.
Spherical wedge
Spherical segment
Spherical pyramid?
Spherical sector
The intersection of a sphere and a plane not passing through the center.
Great circle
Small circle?
Poles of circle
Hair circle
The ends of a diameter of a sphere which is perpendicular to the plane of a circle of the sphere.
Great circle
Small circle
Poles of a circle?
Hair circle
The opening between two great circle arcs
Spherical polygon
Spherical distance
Spherical angle?
Spherical arc
The portion of a spherical surface bounded by three or more great circle arcs.
Spherical polygon?
Spherical distance
Spherical angle
Spherical arc
A spherical polygon of the three sides.
Spherical polygon
Spherical wedge
Spherical triangle?
Spherical angle
The portion of a cone included between the base and a section parallel to the base.
Circle
Parallelepiped
Right prism
Truncated cone?
In general quadratic equation, if the discriminant is zero, the curve is a figure that represent a/an
Parabola
Circle
Ellipse
Hyperbola
Equations relating x and y that cannot readily be solved explicitly for y as a function of x or for x as a function of y. Such equations may nonetheless determine y as a function of x or vice versa, such function is called
Logarithmic function
Implicit function
Explicit function
Continuous function
In polar coordinates system, the length of the ray segment from a fixed origin is known as.
Amplitude
Radius vector
Hypotenuse
Minimum point
Given the equations 3x^2 + 2x – 5y + 7 = 0. Determine the curve
Ellipse
Parabola
Hyperbola
Circle
If eccentricity is less than one, then the curve is
Parabola
Ellipse
Hyperbola
Circle
Of what quadrant is A, if sec A and csc A is negative?
IV
I
III
II
If the general equation of the conic is Ax^2 + 2Bxy + Cy^2 + Ey + F = 0, and B^2 – 4AC > 0, then the conic is a/an
Circle
Parabola
Hyperbola
Ellipse
What type of conic has equation of Ax^2 + Cy^2 + Dx + Ey + F = 0?
Circle
Parabola
Ellipse
Hyperbola
4x^2 – 256 = 0 is the equation of a/an
Parabola
Parallel lines
Circle
ellipse
The graph of r = a + b cosθ is a
Lemniscate
Lituus
Limacon
Cardioid
In an ellipse, a chord which contains a focus and is in line perpendicular to the major axis is called
Focal width
Conjugate axis
Focal chord
Latus rectum
If all the y-terms have even exponents, the curve is symmetric with respect to the.
X-axis
Origin
Y-axis
Line 45° with the x-axis
