formulas Flashcards
area of a triangle
0.5 x b x h
the sum of a two triangles is more or less the other side
more
the difference of two sides is more or less the other side
less
what is the exterior angle rule of a triangle
two angles opposite to the exterior angle is equal
angle opposite to the largest side is the ___
largest
angle opposite to the smallest side is the ____
smallest
when the power goes to the other side it becomes
the reciprocal
d1 + d2
———— av speed?
T1 + T2
d1+d2/T1+T2
S1 + S2
———— av speed?
T1 + T2
(s1 x t1) + (s2 x t2) / T1 + T2
d1 + d2
———— av speed?
s1 + s2
d1 + d2 / (x1/v1) (x2/v2)
when two objects move in same direction you ___ the speeds
subtract
when two objects move in different direction you ___
the speeds
add
mean
sum of all observations/ number of observations
weighted mean eg: if in one class 10 students get 90% and in second class 20 students gets 70% what would be the average of two classes
(10 x 90) + (20 x 70) / 30
( (average x number of students) + (average x number of students) ) / total number of students
median
middle term - arrange in consecutive order. it is the (n+1)/2 th term if odd
if even it is the (n/2) and (n+1)/2 th terms average
mode
most frequently repeated term
circle formula if centre is (0,0)
A^2 + B^2 = R^2
circle formula with any centre (h,k)
(x-h)^2 + (y-k)^2 = R^2
area of circle
pi 2 squared
circumference of circle
2 pi r
when a tangent is drawn next to a circle the radius is…
perpendicular
If two tangents are drawn by a circle and intersect at one point they are….
equal
in a circle two lines are drawn (a+b) and (c+d), they intersect. What is the relation
a x b = c x d
arc length in degrees
theta/360 x 2 pi r
sector area in degrees
theta/360 x pi r square
from centre of a circle (a,b) a line is drawn that hits the circumference at (x,y) what is the relation?
x = a + r cos theta
y = b + r sin theta
(theta is taken from positive x axis in anti-clockwise direction)
distance formula
root ( x2 - x1 )^2 + (y2- y1)^2
mid point
coordinate is ( ( x1 + y2) / 2 , (y1 + y2) /2 )
slope
y2-y1/x2-x1
gradients of two perpendicular lines
negative reciprocal
area of rectangle
lb
perimeter of rectangle
2(l+b)
in a rectangle are diagonals equal and bisect
yes at 90
parallelogram area
b x h
parallelogram perimeter
2 (b + h )
do diagonals bisect and are they equal in parallelogram
bisect (not a 90) but are not equal
rhombus perimeter
4a
rhombus area
p x q / 2
trapezium area
(a + b)2 x h
sum of interior angles
(n-2) x 180
one angle in a regular polygon
180(n-2)/n
sum of exterior angles
360
volume and sa of cuboid
volume= l x b x h sa = 2(lb+bh+hl)
diagonal of cuboid from top left vertex to bottom right
root of l^2 + b^2 + h^2
volume and sa of cube
volume = a^3 sa = 6a^2
sa of cone
pi r (slant height x radius)
sa of sphere
4 pi r squared
if a sphere is inscribed in a cube what is the diameter of a sphere
the length of the side of the cube
if a cuboid is inscribed in a sphere what is the diagonal fo the cuboid
diameter of sphere
volume of object immersed in water
base area of container x h (water amount rises)
i =
root - 1
i squared =
-1
i cubed =
-i
i ^ 4 =
1
how do you conjugate a complex number
change sign of imaginary number
when are two complex numbers equal
when both imaginary and real numbers are equal
how to find magnitude of complex number
root of imaginary squared + real squared
radian to degree
multiply by 180/pi
degree to radian
multiple by pi/180
length of arc in radians
theta into radius
area of sector in radians
theta/2 pi x pi r squared
cosec theta
1/sintheta
sec theta
1/cos theta
cot theta
1/ tan theta
unit circle order
CAST and SECACOSCOT
sin 90 - theta
cos theta
cos 90 - theta
-sin theta
adding c to all observations
mean median mode increase by c, SD and range is same
multiplying c to all observations
everything multiples by c
what is mean, sd, median and mode on calculator
x̅, σ, med, mod
best fit line on calculator ?
F6
geometric progression
nth term = ar ^ (n-1)
a= first term n = number of terms r = common ratio
exponential growth equation
final - initial (growth multiplier) ^ (time required/time period)
arithmetic progression
a + (n-1) d
a= first term n= number of terms d = common difference
quadratic formula
-b plus minus root b squared - 4ac / 2a
how to complete the square
a (x+d) squared + e = 0
d = b/2a
e = c - (b square/ 4a)
