MCF3M1 Formula Sheet

MCF3M1
Formula
Sheet
 This
is
a
list
of
formulas
you
should
know
for
the
exam.

You
are
NOT
allowed
to
use
this
sheet
during
the
exam.
 
 Quadratic
Functions


Exponents
and
Exponential
Functions


Standard
form


 f ( x ) = ax 2 + bx + c 


Exponent
laws








x m ⋅ x n = x m +n 





(x )

Y‐intercept:
 c 


Vertex
form




€




2

f ( x ) = a( x − h ) + k 
 Vertex:
 ( h,k ) 


€ Factored
form


 f ( x ) = a( x − s)( x − t ) 
 € 
 Zeros:
 s and t 
 € Mapping
notation


( x, €y) → ( x + h, ay + k ) € (−1, 1) 
 (0, 0) (1, 1)







x=

€




€

−b ± b 2 − 4ac 
 2a

€

I 


 interest
 r 


 interest
rate
 
 P 


 principal
 t 


 time
(in
years)
 € n Compound
interest




 A = P (1+ i) 
 € € 
 A 


 amount
 P 


 principal
 € € 
 i 


 interest
rate
per
compounding
period
 € 
 n 


 number
of
compounding
periods
 € Annuities
 € € n R (1+ i) −1 €
 Amount




 A = 
 i 
 i, n 


 as
above
 A 


 amount


[

€

€

n

m

x = x =

€ x

( ) n

m







n Logarithms




 log x€ = n log x 



 


P ( x ) = Pob x 
 €
 


Po 

 initial
amount
 b 



 growth/decay
factor


Doubling
period
( k )



 P ( x ) = Po 2 


€ x €  1h Half‐life
( h )




 P ( x ) = Po   
 2 € €




Trigonometry
 Right
triangles
( 90° 
angle)
 € 


€

[

−n

]


i i, n 


 as
above





P 


 present
value





R 


 regular
withdrawal
or
payment
 €




opp 
 hyp

cosθ =

adj 
 hyp

tan θ =




sin A sin B sinC = = 
 a b€ c a b c = = 
 
 sin A sin B sinC

Sine
law






€




]

R 1− (1+ i)

sin θ =

€ Non­right
triangles


€ Cosine
law




 a 2 = b 2 + c 2 − 2bc cos A 


Trigonometric
functions
 


R 


 regular
deposit


€

m n

1 
 xn

€




Present
value




€P =

x −n =




€ Simple
interest




 I = Pr t 


€


=x y 


x k

Finance


€

 x n x n   = n
 y  y −n  x  y n =   

    x  y

€

n

Exponential
growth
and
decay







Discriminant

 b 2 − 4ac 





n

€ 





€

( xy )

n

€

2

€







€

Given

 ax + bx + c = 0 


x 0 = 1



= x mn 


€

€

Quadratic
formula
 


m n

xm = x m−n 
 n x




f€( x ) = asin( x − c ) + d 
 € f ( x ) = acos( x − c ) + d 





€ €

Domain

 D : { x ∈ R state restrictions} 
 Range


€

R : { f ( x ) ∈ R state restrictions} 


opp 
 adj