OrmFulas for Final

Formulas for Final

You are not allowed to bring this formula sheet to exams. Only savings plan formula and loan payment are provided in exams

Chapter 3A

1. Describe changes

absolute change = new value - old/original value,

relative change

new value - old/original value

=

old/original value

.

2. Campare a value (compared value) to another (reference value).

absolute dierence = compared value - reference value,

Chapter 3B

relative

dierence

=

compared value - reference reference value

value

.

1.

Rules

of

exponents:

(a)

xnxm

= xn+m,

(b)

xn xm

= xn-m,

(c)

(xn)m

= xnm,

(d)

(xy)n

= xnyn.

Chapter 4

1. Compound interest formula for more than once a year:

2. Continuous compounding:

A = P ? (1 + APR )nY. n

A = P ? e(APR?Y).

3. Annual percentage yield (APY) for compounding more than once a year:

APY = (1 + APR )n - 1. n

4. Annual percentage yield (APY) for continuous compounding:

APY = eAPR - 1.

5. Savings plan formula:

A

=

PMT

?

(1

+

APR n

)nY

(

APR n

)

-

1

6. Loan payment formula:

PMT

=

[1

P

?

(

APR n

)

-

(1

+

APR n

)(-nY)]

Remark: In the above cases, n = 1 for annually, n = 4 for quaterly, n = 12 for monthly, n = 365 for daily.

Chapter 9B Linear Models

1. Rate of change:

rate

of

change

=

change in dependent variables change in independent variables .

Slope between two points (x1, y1) and (x2, y2):

slope

=

change change

in in

y x

=

y2 x2

- -

y1 x1

.

2. General equation for a linear function:

dependent variable = initial value + (rate of change ? independent variable).

Algebraic equation of a line:

y = mx + c,

m=slope and c=y-intercept.

1

2

3. Linear equation for given two points (x1, y1) and (x2, y2):

where

m=slope=

y2 x2

-y1 -x1

.

y = m(x - x1) + y1,

Chapters 8B & 9C Exponential functions

(1) For a quantity growing exponentially with a rate P %,

new quantity after time t = initial quantity ? (1 + P %)t.

(2) For a quantity decaying exponentially with a rate P %,

new quantity after time t = initial quantity ? (1 - P %)t.

Remark for (1) and (2): The units of time used for t and the rate P % have to be the same.

(3) If a quantity grows with the doubling time Tdouble,

new

quantity

after

time

t

=

initial

quantity

?

t

2 Tdouble

.

(4) If a quantity decays with the half-life Thalf,

new

quantity

after

time

t

=

initial

quantity

?

(

1

)

t Thalf

.

2

Remark for (3) and (4): The units of time used for t and Tdouble/Thalf have to be the same.

(5) Exact doubling time formula:

Tdouble

=

log10 2 . log10(1 + P %)

(6) Exact half-life formula:

Thalf

=

- log10 2 . log10(1 - P %)

Remark for (5) and (6): Make sure you know the units for Tdouble and Thalf in (5) and (6) respectively.

(7) Important property for log:

log10ax = x(log10a).

Chapter 10 Geometry and scaling Laws

(1) Area of a circle with a radius r = r2, Perimeter/circumference of a circle with a radius r =2r

Volume of a cylinder with a radius r in the circular base and height h = r2h, Curved surface area of a cylinder = 2rh

(2) If an object is scaled by a factor C, then scaled length = original length ? C scaled area = original length ? C2

scaled volume = original volume ? C3

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