Equations Flashcards
Total sum of angles on a Polygon?
180 (n-2)
Each angle in an equilateral (equiangular) Polygon
180 (n-2)/2
Vertical angles
equal
Linear pairs
supplementary
Alternate interior angles
Congruent
Corresponding angles
Congruent
Central Angles
(an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B.)
Twice the angle at the circumference
Inscribed angle
angle formed in the interior of a circle when two chords intersect on the circle
Half the angle at the centre
With tangent lines
inscribed angle formed by a secant and tangent line is half of the angle measure of the arc it intercepts.
90°
Cyclic quadrilaterals
quadrilateral. drawn inside a circle.
Opposite angles are supplementary
Perimeter of a parallelogram
2(a+b)
Circumference of a circle
C=2πr
Arc length (angles given in °)
n/360 X 2πr
Arc length (angles given in radians )
r@
Triangle (3 sides) (A)
s=0.5(a+b+c)A=√s(s-a)(s-b)(s-c)
Triangle (trigonometry) (A)
1/2 ab sinC
Parallellogram (A)
A=axh
Trapezoid (trapezium) (A)
A=(b1+b2)/2
Kite (A)
A=d1xd2/2
Regular polygon (A)
A=apothem X perimeter/2
Annulus (A)
the region between two concentric circles
A=π(R⌃2-r⌃2)
Sector (angle given in °) (A)
A sector of a circle is a pie-shaped part of a circle made of the arc along with its two radii.
A=n/360 πr⌃2
Sector (angle given in radians) (A)
@/2r⌃2
Segment (A)
(a set of points consisting of two points of the line called the endpoints, and all of the points of the line between the endpoints)
A=R⌃2/2 (π/180C - SinC)
Prism (SA)
SA= surface area
SA+2(ab+bc+ac)
Cylinder (SA)
SA= surface area
2πr⌃2+2rh
Pyramid (SA)
SA= surface area
LW+L√(w/2)⌃2+h⌃2+w√(1/2)⌃2+h⌃2
Cone (SA)
SA= surface area
πr(r+√h⌃2+r⌃2)
Sphere (SA)
SA= surface area
4πr⌃2
Prism (volume)
V=Ah
A=area of the cross section, h=height/length
Pyramid (volume)
V=Ah/3
1/3 X area of base X perpendicular height
Sphere
V=4/3πr3
Law of cosines
a⌃2=b⌃2+c⌃2-2ab cosA
Midpoint
M=(X1+X2/2, Y1+Y2/2)
Distance
d=√(x2-x1)⌃2+(y2-y1)⌃2
Standard Form (linear equations)
Ax+By=C
Slope intercept form
u=mx+b
Direct Variation
y=AX
Slope of parallel lines
the same
(This means that as x increases, so does y
as x decreases, so does y
the ratio between them always stays the same.)
Slope of perpendicular lines
opposite reciprocal
Standard form (quadratic equations)
y=ax⌃2+bx+c
Intercept form
y=a(x-p)(x-q)
vertex form
y=a(x-h)⌃2=k
Quadratic formula
(-b+or-√b⌃2-4ac)/2a
Discriminant
b⌃2-4ac
Inverse matrix (2x2)
A = a b
c d
(To find the inverse of a 2x2 matrix: swap the positions of a and d, put negatives in front of b and c, and divide everything by the determinant (ad-bc).)
A = a b = A=d -b
c d. -c a
Determinant
The determinant is:
|A| = ad − bc
“The determinant of A = a X d -b X c”
Cramer’s rule (2x2)
method for solving linear simultaneous equations. It makes use of determinants and so a knowledge of these is necessary before proceeding.
If we are given a pair of simultaneous equations
a1x+b1y = d1
a2x+b2y = d2
then x, and y can be found from
X = d1 b1 Y= a1 d1
d2 b2 a2 d2
------------------------------------
a1 b1 a1 b1
a2 b2 a2 b2
a⌃2-b⌃2
(a-b)x(a+b)
(a+b)⌃3
a⌃3+3a⌃2b+3ab⌃2+b⌃2
(a-b)⌃3
a⌃3-3a⌃2b+3ab⌃2-b⌃3
a⌃3+b⌃3
(a+b)⌃3-3ab(a+b)
a⌃3-b⌃3
(a-b)⌃3+3ab(a-b)
Acceleration
vf-vi/t
vf = final velocity Vi = initial velocity t = yime
Mean
Mean(x̄) =∑x/n
add up all the numbers, then divides by how many numbers there are
Mean of grouped data
Mean(x̄) =Z(m+f)/N
m = midpoint f = frequency N = total number of values
To calculate the mean of grouped data, determine the midpoint of each interval, midpoints must then be multiplied by the frequencies of the corresponding interval. The sum of the products divided by the total number of values will be the value of the mean.
Range
the difference between the highest and lowest values in a set of numbers
Position of median
(n+1)/2
To find the median, order your data. Then calculate the middle position based on;
n = the number of values in your data set.
If n is an odd number, the median lies at the position (n + 1) / 2.
If n is an even number, the median is the mean of the values at positions n / 2 and (n / 2) + 1.
Relative frequency
f/Zf
Relative frequency or experimental probability is calculated from the number of times an event happens, divided by the total number of trials in an actual experiment.
Cumulative frequency
Cumulative frequency is a running total of the frequencies. This can be represented on a graph by plotting the upper boundary of the groups.
Class width
Highest value - smallest value.
difference between the upper and lower boundaries of any class (category). sometimes used more specifically to mean:
Frequency density
frequency/total frequency
lower quartile
0.25xn
upper quartile
0.75xn
interquartile range
upper quartile-lower quartile
simple interest
invest =PxRxT
compound interest
A=p(1+r/n)
how do you know if two functions are inverse
f(g(x))=x g(f(x))=x
total sum of exterior angles of a polygon
360°
each exterior angle of an equiangular polygon
360/n
perimeter of a polygon
sum of sides
triangle (A)
BxH/2
area of a triangle is one half of base times height.
Circle (SA)
sa= surface area
πr⌃2
Cylinder (V)
v=volume
πr⌃2h
cone
πr⌃2h/3
slope/gradient
M=(y2-y1)/(x2-x1)
Pythagorean theorem
asdf
a2 + b2 = c2
c is the longest side of the triangle
a and b are the other two sides
c=hypotenuse
a2=b2+c2 triangle is right angled
a2b2+c2 triangle is obtuse
Sin(A)
The Law of Sines (or Sine Rule) is very useful for solving triangles:
a/sin A = b/sin B = c/sin C
relates the ratios of side lengths of triangles to their respective opposite angles.
Cos(A)
The Law of Cosines (also called the Cosine Rule) says:
c2 = a2 + b2 − 2ab cos(C)
used to find the remaining parts of an oblique (non-right) triangle when either the lengths of two sides and the measure of the included angle is known (SAS) or the lengths of the three sides (SSS) are known.
Tan(A)
tan(a + b) = (tan a + tan b)/(1 - tan a·tan b)
Tangent rule gives the relationship between the sum and differences of the sides and angles of a triangle
Sohcahtoa”!
Soh... Sine = Opposite / Hypotenuse cah... Cosine = Adjacent / Hypotenus toa Tangent = Opposite / Adjacent
