maths eassessment Flashcards
what r the 4 types of sampling
simple random, systematic, stratified, quota
what is a simple random sampling
sampel where eahc member of the population is equally likely to be included in the sample
what is a systematic sample
takes members of the population at regular intervals
whats is stratified sampling
identifies different sections of the population and ensures that those groups r represented in appropriate proportions
what is a quota sample
when the sampling frame is unknown so enough data is collected until enough pieces of data is found.
when does a quadratic have a repeated real number solution
when b^2-4ac=0
when is a quadratic factorizable
when b^2-4ac>0
when is a quadratic not factorizable
when b^2-4ac<0
how much of a population is within 1 standard deviation in a normal distribution
68%
how much of a population is within 2 standard deviation in a normal distribution
95
how much of a population is within 3 standard deviation in a normal distribution
99.7%
what is a sector
a triangle with a curved side inside the circle
what is a segment
part of a triangle separated by a chord
list all 7 circle theorems
thales theorem: an angle inscribed in a semicricle is a right angle
opposite angles in a cyclic quadrilateral r supplementary
angles in the same segment subtended by equal chords r equal in size
alternate segment theorem (the triangle thing): angle between a chord and tangent at a point is equal to the angle subtended by the chord in the alternate segment
angle subtended by a chord at the center is twice the angle at the circumference.
intersecting chords theorem (AX * BX = CX * DX)
Tangent chord theorem (PX * QX = TX^2)
list the 5 rules for triangle congruency
sss, sas, asa, aas, rhs
list 3 rules for similarity
SAS (scale factor)
SSS (Scale factor)
AA
how to complete the square
add (b/2)^2
how to find x coordinate of vertex
-b/2a
density formula
mass/volume
what is degree of a vertex
no. of edges leaving a vertex
does a loop count as 1 or two vertex
2
when is a graph complete
when every vertex is directly connected directly to everyother vertex by an edge
when is a graph connected
if every point on the graph can be reached from any other point on the graph
what is a walk
any route through a graph (edges and vertex can be repeated)
what is a trail
a walk but edges cant be repeated
what is a circuit
a trail which starts and end at the same vertex
what is a path
a route through a graph from one vertex to another which does not repeat any vertices or edges
what is a cycle
a path which starts and ends at the same vertex
what is a traversable graph
if u can draw it without taking ur pen off the paper or retracing ur steps
when can a graph be traversable
if it only has even vertices or exactly 2 odd vertices
what is an eulerian circuit
a connected graph with only even vertices, it can be traversed starting from any point and it well end where it started, it therefore has an eulierian trail
what is an eulerian trail
a connected graph with 2 odd vertices makes it so that any trail which traverses the graph starts at one odd vertex and ends at the other therefore it has an eulerian trail.
list another name for a eulerian trail
eulerian path or semi eulerian graph
what is an hamiltonian path
path which travels thru every vertex exactly once
what is an hamiltonian cycle
a path which travels thru every vertex exactly once and returns to its original point
formula for hamiltonian cycles of a complete graph with n vertices
((n-1)!)/2
gradient of perpendicular lines
-1/m or negative reciprocal
gradients of parallel lines
same
4 parallel line rules
alternate interior angles r equal
alternate exterior angles r equal
corresponding angles r equal
consecutive interior angles r supplemetary
equation of a line
y=mx+c
gradient formula
(y2-y1)/x2-x1
properties of rhombus (sides, angles, diagonal
- all 4 sides r equal
- opposite angles r equal
- diagonals meet at 90
- diagonals bisect each other
properties of kite (angles, sides, diagonals
bottom two sides r equal and top 2 r equal
diagonals
vertical (long) diagonal is perpendicular bisector of horizontal (short) one.
long diagonal bisects the angles
properties of parallelogram
opposite sides r parallel and equal
opposite angles r equal
properties of isosceles trapezoid
non base angles r congruent
non base sides r congruent
base sides r parallel
angle in regular hexagon
120
angle in regular pentagon
108
arithmetic series primary formula
(n(u1+un))/2
arithmetic series secondary formula
(n/2) * (2a+(n-1)d)
geometric series formulas
a * (r^n -1)/(r-1) when r>1 or r<-1
a * (1-r^n )/(1-r) when absolute value of r is lesser than one
sum to infinity for geometric series when absolute value of r is lesser than one
a/(1-r)
state 2 uses of static electricity
insecticides
photocopier
what is the direction of conventional current
positive to negative
current formula
I = change in charge/time
voltage formula with energy
energy transferred/charge moved
what is resistance
tendency of a material to resist the flow of electric charge, unit is ohm
what is voltage
differ
