Formula Not Given Flashcards
Quadratic formula
Minus b plus or minus the square root of b squared minus 4ac all over 2a
The discriminant
B squared -4ac
Discriminant > 0 2 real roots
Discriminant = 0 1 repeated root
Discriminant < 0 0 real roots
Modulus ( |x| )
|x| means the positive value of x
a^m multiplied by a^n
a^m+n
a^m divided by a^n
a^m-n
a^0
1
a^-m
1/a^m
a^1/n
n root of a
(a^m)^n
a^mn
Gradient
Change in y over change in x
Equation for a circle with centre (a,b) and radius r
(x-a)^2 + (y-b)^2 = r^2
Log(x) + log(y)
Log(xy)
Log(x^n)
nLog(x)
Log(x) - log(y)
Log(x/y)
Log(n root x)
1/nLog(x)
Log(1)
0
Sin(x)/cos(x)
Tan(x)
Sin^2(x) + cos^2(x)
1
Area of a triangle
1/2abSin(C)
Sine rule
a/SinA = b/SinB = c/SinC
Flip for angles
2 pi in degrees
360 degrees
Arc length (for radians)
r times theta
Area of a sector (for radians)
1/2 r^2 times theta
Differentiation from first principles
F’(x) = lim (h->0) = f(x+h) - f(x)
——————
h
Differential of e^kx
ke^kx
Differential of ln(x)
1/x
Differential of sin(kx)
kcos(kx)
Differential of cos(kx)
-ksin(kx)
Product rule
VU’+UV’
Quotient rule
VU’-UV’
————
V^2
Chain rule
Multiply the bracket by the old power and the differential of the inside of the bracket and bring the power down by one.
Integral of e^kx
1/k e^kx
Integral of 1/x
ln|x|
Integral of sin(kx)
-1/k cos(kx)
Integral of cos(kx)
1/k sin(kx)
Sec^2(x) is exactly equal to
1 + tan^2(x)
Cosec^2(x) is exactly equal to
1 + cot^2(x)
Sin(2x) =
2sin(x)cos(x)
Cos(2x) =
Cos^2(x)-sin^2(x)
OR
2cos^2(x) - 1
OR
1 - 2sin^2(x)
Tan(2x) =
2tan(x)
——————
1- tan^2(x)
SUVAT constant acceleration equations
s = ut + 1/2at^2
s = 1/2(u + v)t
s = vt - 1/2at^2
v = u + at
v^2 = u^2 + 2as
Non-constant acceleration
a differentiates to v and v differentiates to s
s integrates to v and v integrates to a
Individual data -> mean
X bar = sum of all x values
——————————
n
Grouped data -> mean
X bar = the sum of fx
———————
n
sin 2A ≡
2sin A cos A
cos 2A ≡
cos^2(A) – sin^2(A)
OR
2cos^2(A) – 1
OR
1 – 2sin^2A
tan 2A ≡
1 – tan^2(A)
arc length (for degrees)
theta/360 x 2(pi)r
area of sector (for degrees)
theta/360 x pi(r^2)
area of a segment (for radians)
1/2r^2 ( theta - sin(theta) )
area of a segment (for degrees)
1/2r^2 [ (pi/180)theta - sin(theta) ]
length of a chord
(cosine rule)
a^2 = b^2 + c^2 - 2bcCos(A)
cosine rule
(for sides)
a^2 = b^2 + c^2 - 2bcCos(A)
(for angles)
cos(A) = b^2 + c^2 - a^2
———————-
2bc
small angle approximation of sin(x)
sin(x) = x
small angle approximation of cos(x)
cos(x) = 1 - 1/2 x^2
small angle approximation of tan(x)
tan(x) = x
