MATHS FORMULA SHEET ALGEBRA

a ( b + c) = ab + ac

a

c

a

b

a

cb

2222 bababa

22 bababa

Binomial Expansion:

(a+b)n=an+ nC1an-1b+ nC2a

n-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

nn

b

a

b

a

Meanings: a0=1

p

aa p 1

Logarithm Laws:

DEF: NxaN a

x log

p

aa

aaa

aaa

NNp

MNMN

NMMN

loglog

)(logloglog

)(logloglog

loga1 = 0 logaa = 1

a

NN

b

ba

log

loglog

LINEAR FUNCTIONS y= mx + c gradient = m, c = y-intercept y – y1 = m(x – x1) gradient = m, Point= (x1,y1)

Gradient: 12

12

xx

yym

Parallel Lines: m1 = m2 Perpendicular Lines: m1 . m2 = -1

Distance: 2

12

2

12 )()( xxyyd

Mid-Point:

2,

2

2121 yyxxM

QUADRATICS: General Form y = ax2 + bx + c x = 0 c = y-intercept

a

acbbxy

2

4 0

2

Axis of symmetry: a

bx

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 = 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

sintan

cos

1sec

1cossin 22

sin

1cos ec

cossin2)2sin(

tan

1cot

n

n

aa

1

Ma

rk R

iley s

275

772

9

Right-Triangles

All triangles ABC:

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

c

B

b

A

a

Cosine Rule:

)sin(21 CabArea

FINANCE:

Compound Interest: FV=PV(1 + r)n

Future Value Annuity: Present Value Annuity:

i

ipFV

n 1)1(

i

ipPV

n

)1(1

CALCULUS: DIFFERENTIATION Definition:

h

xfhxf

dx

dyh

)()(lim 0

Rules:

0 constant dx

dyy

)()( )()( xgBxfAdx

dyxBgxAfy

Power

1 nn nxdx

dyxy

)()( )(1

xfxfndx

dyxfy

nn

Exponential

xx edx

dyey

)( )()( xfedx

dyey xfxf

Logarithm

xdx

dyxy x

1 log

)(

)( )(log

xf

xf

dx

dyxfy x

Sine

)cos(dx

)sin( xdy

xy

)()](cos[dx

)](sin[ xfxfdy

xfy

Cosine

)sin( )cos( xdx

dyxy

)()](sin[ )](cos[ xfxfdx

dyxfy

Product Rule

vuvudx

dyuvy

Quotient Rule

2

v

vuvu

dx

dy

v

uy

INTEGRATION

dxxfyxfdx

dyIf )( then )(

Power

1 1

1

nCn

xdxx

nn

Cn

bax

adxbax

nn

)1(

)(1)(

1

Exponential

Cedxe xx

Cea

dxe baxbax

1

Cxdxx

e ||log1

Cbaxa

dxbax

e ||log

11

Trigonometric

Cxdxx )cos()sin(

Cbaxa

dxbax )cos(1

)sin(

Cxdxx )sin()cos(

Cbaxa

dxbax )sin(1

)cos(

hypotneuse

oppositeA sin

adjacent

oppositeA tan

hypotenuse

adjacentA .cos

222 bah

Pythagoras

)cos(2222 Abccba

bc

acbA

2)cos(

222