ALG GEOM TRIGO

permutation

Arrangement of objects in a specific order.

combination

does not involve the arrangement of objects nor the order of selection

Mutually Exclusive Events

impossible for more than one of them to happen in a single trial

Independent Events

happening of one does not affect the probability of happening of the other

Dependent events

happening of one affects the probability of happening of the other

Conditional Probability

probability that event B occurs given that event A occured

bell shaped curve

when Normal probability distribution is plotted, it gives a

Normal probability distribution

widely used of all probability distributions

Poisson experiments

experiments yielding number of outcomes during a given time interval

Plane Geometry

deals with the properties of plane figures or geometrical shapes of two dimensions such as angles, triangles, square, polygons, conic section

concave

polygon having at least one interior angle greater than 180

convex

polygon where all interior angles are less than 180

regular

polygon having all sides equal and all angles equal

similar

polygons whose corresponding angles are equal, and corresponding sides are proportional

apothem

a line from the center of a regular polygon perpendicular to one of its sides

radius

an apothem is equal to the ___ of the circle

quadrilaterals

polygon bounded by four straight lines

quadrilaterals

also known as quadrangle or tetragon

circle

a closed plane curve every point of which is equidistant to a fixed point called its center

chord

line segment formed by joining two points on the circle

diameter

longest chord of a circle

arc

set of points on the circle that are bounded by two endpoints that are also on the circle

sector

region bounded by two radii of a circle and the included arc of 2 radii

segment

a region bounded by an arc and the chord joining the endpoints of the arc

product of the segments of the other

if 2 chords intersect in a circle, the product of the lengths of 1 chord equal the

radius through the point of tangency

every tangent line of a circle is perpendicular to the ___

cyclic quadrilateral

quadrilateral whose vertices lie on the circumference of a circle

Ptolemy's Theorem

for any cyclic quadrilateral, the product of the diagonals equals the sum of the product of the opposite side

right triangle w/ diameter as hypothenuse

an inscribed triangle whose side is a diameter is also a ____

Incenter

point of intersection of the angle bisectors of the triangle

Incenter

center of the inscribed circle

In-circle

largest circle that can fit inside the triangle and touch all three sides

in-circle

circle inscribed in a triangle

circum-circle

Circle circumscribing a triangle has its center at the intersection of the perpendicular bisector of the triangle

circum-circle

circle that passes through all the vertices of the triangle

circumcenter

The point of intersection of the perpendicular bisectors of a triangle

ex-circle

escribed circle

prism

polyhedron with 2 faces parallel and congruent and whose remaining faces are parallelograms

right prism

a prism which has its lateral faces, thus its axis, perpendicular to the base

oblique prism

a prism in which the lateral edges are not perpendicular to the bases

truncated prism

a portion of a prism formed by passing a plane not parallel to the base and intersecting all the lateral edges.

truncated prism

This solid has two non-parallel bases which are both polygons of the same number of edges.

pyramid

polyhedron that contains triangular lateral faces with a common vertex and a polygonal base

polyhedron

term for solid geometry

base

pyramids are named according to their

polyhedrons

solids whose faces are plane polygons

regular polyhedrons

solids with all its face identical regular polygons

cylinder

prism with two circular bases

cone

formed by a set of line segments connecting the apex, to all the points on the circumference of the circular base that is in a plane that does not contain the apex

sphere

a round solid figure with every point on its surface equidistant from its center

spherical segment

solid defines by cutting a sphere or a ball with a pair of parallel planes

spherical zone

portion of the surface of a sphere included between 2 parallel planes

spherical zone

lateral area of a spherical segment

spherical cone

solid generated by rotating a sector of a circle about an axis which passes through the center of the circle, but which contains no points inside the sector

spherical lune

portion of the surface of a sphere bounded by 2 half great circles and an included arc

spherical wedge

solid bounded by 2 half great circles and an included arc

frustum

the remaining portion obtained after removing the top portion when a pyramid or a cone is cut parallel to base

great circle

a circle on the surface of a sphere that lies in a plane passing through the sphere's center

small circle

circle constructed by a plane crossing the sphere not in its center

spherical angle

Angle formed by intersection of two great circles

spherical triangle

a triangle on the surface of the sphere formed by the intersection of three great circles

polar distance

least distance on a sphere from a point on the circle to its pole

latitude

angular distance of the point from the equator ranges from 0 to 90 deg at the pole

longitude

angular distance between the prime meridian and meridian through the point ranges from 0 at the prime meridian to 180 deg eastward and -180 deg westward

Period

T, interval over which the graph of a function repeats

Amplitude

A, greatest distance of any point on the graph from a horizontal line which passes halfway between the max and min values of the function

Frequency

number of repetitions/ cycles per unit of times

phase shift

is how far the function is shifted horizontally from the usual position

median

line drawn from one vertex to the midpoint of its opposite side

median

intersect at a common point called the centroid of the triangle

greater

in an oblique spherical triangle, the greater side has a ___ angle

conic sections

locus (or path) of a point that moves such that the ratio of its distance from a fixed point (focus) and a fixed line (directrix) is constant

eccentricity

constant ratio of the conic

locus

focus

directrix

in a conic section, the path (or ____) of a point that moves such that the ratio of its distance from a fixed point (____) and a fixed line (_____) is constant

parabola

locus of a point that moves such that its distance from a fixed point called focus is always equal to its distance from a fixed line called directrix

ellipse

locus of a point that moves such that the sum of its distance from two fixed points called foci is constant

hyperbola

locus of a point that moves such that the difference pf its distance between two fixed points called the foci is constant

asymptote

A line that a curve approaches, as it heads towards infinity.

latus rectum

horizontal line through focus

Parabola

given Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, and B = 0

what is the conic section if only one term is squared

Hyperbola

given Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, and B = 0

what is the conic section if A and C have opposite signs

Circle

given Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, and B = 0

what is the conic section if A = C (same sign)

Ellipse

given Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, and B = 0

what is the conic section if A ≠ C (same sign)

Parabola

given Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, and B ≠ 0

what is the conic section if B^2 - 4AC = 0

Ellipse

given Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, and B ≠ 0

what is the conic section if B^2 - 4AC < 0

Hyperbola

given Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, and B ≠ 0

what is the conic section if B^2 - 4AC > 0

MSTT

After 1582, the first day of the century can only be the days