2U Formula Sheet

8/10/2019 2U Formula Sheet

1/8

Actual Formula Test #1 Test #2 Formula

(a + b)(a2ab +b

2) a

3+b

3=

(ab)(a2

+ ab +b2) a

3 b

3=

x= b b

2

4ac2a

Quadratic Formula

f(x) = f( x) Test for even

functions

f( x) = f(x) Test for odd

functions

(xh)2

+ (yk)2

= r2

General equation

of a circle

y= r2x

2

Equation of a

semi-circle

0 limx

1x

=

1

2 sin

4

=

1

2 cos

4

=

1 tan

4

=

3

2

sin

3

=

1

2 sin

6

=

1

2 cos

3

=

32

cos 6

=


2/8

3 tan

3

=

1

3 tan

6 =

sincos

tan =

cossin

cot =

1 sin2 + cos2 =

1 +cot2 = cosec2 Other trig identity

tan2 + 1 = sec2 Other trig identity

sinAa

= sinBb

Sine rule

a2

=b2

+c2 2bccosA

Cosine rule forside

cosA = b2

+c2 a

2

2bc

Cosine rule for anangle

A = 12absinC

Area of a triangle

using trig

Graphs

d = (x2x1)2

+ (y2 y1)2 Distance formula

P =x1 +x2

2,y1 +y2

2

Midpoint Formula

m = y2y1x2x1

Gradient Formula

m = tan Gradient using trig


3/8

yy1 = m(xx1) Point-gradient

formula

y y1x x1

= y2y1x2x1

Two-point formula

m1 = m2 Parallel lines proof

m1m2 = -1 Perpendicular linesproof

d =|ax1 +by1 +c|

a2

+b2

Perpendiculardistance formula

tan = m1 m2

1 +m1m2

Angle between two

lines

x=mx2 +nx1m +n

y = my2 +ny1m +n

Dividing interval in

ratio m:n

dydx

= limh 0

f(x+h) f(x)h

First principledifferentiation

nxn 1

d

dxx

n

f'(x)n[ f(x)]n 1

d

dx[f(x)]

n=

vu' + uv' d

dxuv

vu' u v'

v2

d

dx

u

v

x = b2a

Axis of symmetryin quadratic

= b2 4ac The discriminant

ba

Sum of roots


4/8


5/8

12xy

Area of rhombus

A = 12h(a + b)

Area of trapezium

A = r2 Area of circle

S = 2(lb +bh +lh) Surface area of arectangular prism

V = lbh Volume of a

rectangular prism

S = 6x2

Surface area of a

cube

V = x3

Volume of a cube

S = 2r2 + 2rh Surface area of a

cylinder

V= r2h Volume of a

cylinder

S = 4r2 Surface area of a

sphere

V = 43r3

Volume of asphere

S = r2 + rlSurface area of a

cone

V = 13r2h

Volume of a cone

xn + 1

n + 1 + c

x

ndx

h2[ (y0 +yn) + 2(y1 +y2 +. .. + yn 1)]

whereh = b an

Trapezoidal rule


6/8

h3

[ (y0 +yn) + 4(y1 +y3) + 2(y2 +y4)]

whereh = b an

Simpsons Rule

(ax+ b)n + 1

a(n + 1) + c

(ax+ b)

ndx

V =

y

2

dx

Volume about the

x-axis

V = x

2dy

Volume about they-axis

ex

d

dxe

x

f'(x) ef(x)

d

dxe

f(x)

ex + c

exdx

1a

eax +b + c

eax +bdx

logax + logay loga(xy)

logax logay logax

y

nlogax logaxn

logax =logexlogea

Change of baserule

1x

ddx

logex

f'(x)f(x)

ddx

logef(x)

logex+c 1

xdx


7/8

logef(x) + c f'(x)

f(x)dx

180 radians =

C = 2rCircumference of a

circle

l = r Length of an arc

A = 12r

2

Area of a sector

A = 12r

2( sin)

Area of a minorsegment

sinx xtanx xcosx 1

Small Angles

f'(x) cos [ f(x)]

d

dxsin [ f(x)]

f'(x) sin [ f(x)] d

dxcos [ f(x)]

f'(x) sec2

f(x) d

dxtan f(x)

1a

sin(ax+b) + c

cos(ax+b) dx

1a

cos(ax+b) + c

sin(ax+ b) dx

1atan(ax+b) + c sec

2

(ax+b) dx

1

2x + 1

4asin 2ax + c

cos

2axdx

1

2x 1

4asin 2ax +c

sin

2axdx


8/8

r = T2T1

Common ratio ingeometric series

Tn = arn 1

Term of a

geometric series

Sn =a(r

n 1)

r 1 for|r| > 1

Sn =a(1 rn)

1 r for|r| < 1

Sum of a

geometric series

S =a

1 r

Sum to infinity of ageometric series

A = P1 + r

100n

Compound interestformula

Iffa +b

2

= 0

Halving the intervalmethod

a1 = a f(a)f'(a)

Newtons methodof approximation

n!(nr)!

nPr =

n !s! t!...

Arrangementswhere some are

alike

(n 1)! Arrangements in a

circle

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