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Math Formula at Senior level, Study notes of Mathematics

Mathematics

Math Formula at Senior level ready recon

Typology: Study notes

2019/2020

Uploaded on 01/13/2020

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partho143 🇰🇼

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MATHS FORMULA SHEET
ALGEBRA
a ( b + c) = ab + ac
a
c
a
b
a
cb
22
22bababa
22 bababa
Binomial Expansion:
(a+b)n=an+ nC1an-1b+ nC2an-2 b2 + … + nCran-rbr +
…+bn
Index Laws:
DEF: an = a x a x a … n factors
an x am = an+m
an ÷ am = an-m
(an)m = anm
(ab)n = anbn
n
n
n
b
a
b
a
Meanings: a0=1
paa p
1
Logarithm Laws:
DEF:
NxaN a
xlog
p
aa
aaa
aaa
NNp
M
N
MN
NMMN
loglog
)(logloglog
)(logloglog
loga1 = 0
logaa = 1
a
N
N
b
b
alog
log
log
LINEAR FUNCTIONS
y= mx + c gradient = m, c = y-intercept
y – y1 = m(x – x1) gradient = m, Point= (x1,y1)
Gradient:
Parallel Lines: m1 = m2
Perpendicular Lines: m1 . m2 = -1
Distance:
2
12
2
12 )()( xxyyd
Mid-Point:
2
,
22121 yyxx
M
QUADRATICS:
General Form
y = ax2 + bx + c
x = 0 c = y-intercept
a
acbb
xy 2
4
02
Axis of symmetry:
a
b
x2
Completed square form
y= a(x – h)2 + k
Turning Point; (h,k)
TRIGONOMETRY:
180 – θ θ
π – θ
S A
T C -ө
180+ θ 360-θ
π + θ 2π -θ
Radian / Degrees: π radians = 1800
Graphing periodic functions:
y = a sin[b(x + c)] + d
y = a cos[b(x + c)] + d
Amplitude = a
Period =
b
2
Phase Shift = c +ve ← ; -ve →
Vertical Shift = d
Identities
cos
sin
tan
cos
1
sec
1cossin 22
sin
1
cos ec
cossin2)2sin(
tan
1
cot
n
n
a
a1
Mark Riley s2757729
pf2

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MATHS FORMULA SHEET

ALGEBRA

a ( b + c) = ab + ac

a

c

a

b

a

b c  

(^2 ) a b a  2 abb

2 2 a b ab a b

Binomial Expansion:

(a+b)

n =a

n

n C 1 a

n- b+

n C 2 a

n- b

2

  • … +

n Cra

n-r b

r

…+b

n

Index Laws:

DEF: a

n = a x a x a … n factors

a

n x a

m = a

n+m

a

n ÷ a

m = a

n-m

(a

n )

m = a

nm

(ab)

n = a

n b

n

n

n n

b

a

b

a   

Meanings: a

0

p a a

p 

1

Logarithm Laws:

DEF: N a x aN

x   log

p a a

a a a

a a a

p N N

M

N M N

N M NM

log log

log log log ( )

log log log( )

loga1 = 0

logaa = 1

a

N

N

b

b a log

log log 

LINEAR FUNCTIONS

y= mx + c gradient = m, c = y-intercept

y – y 1 = m(x – x 1 ) gradient = m, Point= (x 1 ,y 1 )

Gradient:

2 1

2 1

x x

y y m 

Parallel Lines: m 1 = m 2

Perpendicular Lines: m 1. m 2 = -

Distance:

2 2 1

2 d  ( y 2 y 1 ) (x x)

Mid-Point:  

x 1 x 2 y 1 y 2 M

QUADRATICS:

General Form

y = ax

2

  • bx + c x = 0 c = y-intercept

a

b b ac y x 2

2     

Axis of symmetry: a

b x 2

Completed square form

y= a(x – h)

2

  • k

Turning Point; (h,k)

TRIGONOMETRY:

180 – θ θ

π – θ

S A

T C - ө

180+ θ 360-θ π + θ 2π - θ

Radian / Degrees: π radians = 180

0

Graphing periodic functions:

y = a sin[b(x + c)] + d

y = a cos[b(x + c)] + d

Amplitude = a

Period = b

Phase Shift = c +ve ← ; -ve →

Vertical Shift = d

Identities

cos

sin tan 

cos

sec 

sin cos 1

2 2

 sin

cos ec 

sin( 2  ) 2 sincos

tan

cot 

n

n

a

a

Mark Riley

s

Right-Triangles

All triangles ABC:

Sine rule : sin( ) sin( ) sin(C)

c

B

b

A

a  

Cosine Rule :

Area ^12 absin(C)

FINANCE:

Compound Interest: FV=PV(1 + r)

n

Future Value Annuity: Present Value Annuity:

i

i FV p

n ( 1  )  1  i

i PV p

 n   

CALCULUS: DIFFERENTIATION

Definition:

h

f x h f x

dx

dy h

lim (^0)

Rules:

 constant  0 dx

dy y

( ) ( ) Af (x) Bg(x) dx

dy y Af x Bg x    

Power

 1  

n n nx dx

dy y x

1 n f x f x dx

dy y f x

n n   

Exponential

x x e dx

dy y e 

( ) () e f x dx

dy y e

f x fx   

Logarithm

dx x

dy y (^) xx

log 

log ( ) f x

f x

dx

dy y (^) xf x

Sine

cos( ) dx

sin( ) x

dy y  x 

cos[ ( )] ( ) dx

sin[ ( )] f x f x

dy y  f x   

Cosine

cos( ) sin(x) dx

dy y  x 

cos[ ( )] sin[f(x)] f(x) dx

dy y  f x   

Product Rule

uv uv dx

dy y uv    

Quotient Rule

2 v

uv uv

dx

dy

v

u y

INTEGRATION

 f x y f xdx dx

dy If ( )then ( )

Power

1

   

C n n

x xdx

n n

C

n

ax b

a

ax b dx

n n  

1

Exponential

e dx e C

x x

e C a

e dx

ax b axb  

 

dx x C x

 loge^ | |

ax b C a

dx ax b

 e   

log | |

Trigonometric

sin(x )dx cos(x)C

  axb C a

ax bdx cos( )

sin( )

cos(x )dx sin(x)C

  axb C a

ax bdx sin( )

cos( )

hypotneuse

opposite sinA 

adjacent

opposite tanA 

hypotenuse

adjacent cos A .

2 2 2

h a b

Pythagoras

2 cos( )

2 2 2 a b c  bc A

bc

b c a A 2

cos( )

2 2 2   