maths equations Flashcards
quadratic equation
x= -b± square root b^2 - 4ac / 2a
cosine rule
a^2 = b^2 + c^2 - 2bccosA
area of a triangle
1/2 absinC
midpoint
(x1x2)/2 , (y1+y2)/2
log(x) + log(y) =
log(xy)
log(x) - log(y) =
log(x/y)
log(a) = (when the base is a also)
1
log(1) =
0
log(1/x) =
-log(x)
1 + cot^2x =
cosec^2x
tan^2x + 1 =
sec^2x
sin2x
2sinxcosx
cos2x
cos^2x - sin^2x
2cos^2x -1
1 -2sin^2x
tan2x
(2tanx)/1-tan^2x
degrees to rad
(degree/180) x pi
rad to degrees
(rad/pi) x 180
arc length
r0
area of sector
1/2r^20
vector- AB =
OB - OA
mutually exclusive
P(A U B) = P(A) + P(B)
independent
P(A N B) = P(A) X P(B)
y’ (when differentiating with respect to x)
dy/dx
standard normal coding
Z = (X - mean) / standard deviation
for hypo testing normal distribution
X(x bar)~N(mean, standard deviation/square root of number in sample)
coding ( y = (x-a)/b)
(mean y) = (mean x - a)/b
(standard deviation y) = (standard deviation x)/b
chain rule (f(g(x))
g’(x) x f’(g(x))
product rule (f(x)g(x))
f(x)g’(x) + f’(x)g(x)
length
square root of x1-x2 squared + y1- y2 squared
equation of a straight line
y - y1 = m(x-x1)
equation of a circle
(x-a)^2 + (y-b)^2 = r^2
what are the 3 circle theorems
- the perpendicular bisector of a chord will pass through the centre of a circle
- a tangent to a circle is perpendicular to the radius of the circle at the point of intersection
- the angle in a semi circle is 90 degrees
