Dear 2008-2009 student,

Congratulations on your promotion to **Pre-Calculus
and/or
Pre-Calculus Honors. **

This packet is due on the first day you return to class in
September.

You will have the opportunity to ask questions about anything in it

when you come back. By the end of the first week of school you will

be given a test on the material from this packet. The test will count

as a first quarter grade and will be used to plan your review and after

school remediation as necessary.

If you need more review over the summer, there are many resources

to be found at the county library and on the Internet. If you find that

you have questions, you can ask them and get additional practice

from “Ask Dr. Math”. You can also view lists of questions previously

asked by other students, with answers provided.

Pre-Calculus Honors, or AP Stats continue the

foundation for our advanced math courses, and we expect a high

level of performance from all students over the coming year. We

expect you to take the initiative to find out about things that you don’t

understand including any information in this packet. The algebra 2

team hopes you enjoy your summer vacation and looks forward to

seeing you in the fall!

Enjoy,

May 2009

**DOMAIN & RANGE**

Domain: The possible x-values of a function

Range: The possible y-values of a function

Example:

D: all real numbers

R: all real numbers

Give Domain and Range of the following

**FACTORING POLYNOMIALS**

When factoring, always try to pull out a greatest common
factor first. Then look for certain patterns

such as the ones shown below:

Type of factoring: | Examples: |

Greatest Common Factor: | |

Difference of squares: | |

Perfect square trinomials: | |

x-squared trinomials: | |

To fill in these blanks, find two numbers whose product is ‘b’ and whose sum is
‘a’.

Other trinomials:

When there is a coefficient other than one

in front of the x^{2} term, all possibilities need

to be taken into account. These possibilities

are then evaluated by guess and check.

FACTOR COMPLETELY:

**RADICAL REVIEW**

EXAMPLES:

In order to simplify a radical, look for the highest perfect square
that

is a factor of the radicand ( the number under the radical sign)

SIMPLIFY:

**Solve the equations for x:**

**FUNCTIONS
FUNCTION NOTATION: f(x)
To be written as f(x) means the represented expression satisfies the definition
of a function
--- for each x-value, there is an unique corresponding y-value
Example of function notation:
EVALUATION OF FUNCTIONS:
f(3) means replace each ‘x’ in f(x) with ‘3’ to find the function’s y-value
**

**ADDITION, SUBTRACTION AND MULTIPLICATION OF FUNCTIONS:
Functions can be added, subtracted and multiplied just as any other expressions:
**

**COMPOSITION OF FUNCTIONS:
Composition of functions means instead of replacing ‘x’ in a function with a
number, an entire
function is inserted instead.
EXAMPLE:
The composition of f(x) and g(x) is written: f (g(x))
To evaluate, simply plug in g(x) wherever an ‘x’ appears in f(x).**

**PRACTICE PROBLEMS:**

**Use these functions:**

**30-60-90 TRIANGLES**

**Hypotenuse = twice the short leg
Long Leg = short leg ***

**Find the missing sides of the triangles. Each
triangle measures 30-60-90° . Leave answers in
simplified radical form.**

**45-45-90º TRIANGLES**

Hypotenuse = leg *

**Find the missing sides of the triangles. Each triangle
measures 45-45-90º.
Leave answer in simplified radical form.**

**SOH-CAH-TOA
Basic Trigonometry Review**

**Solve each triangle for the indicated side x.**

**Arithmetic Review
Evaluate without a calculator. Put answers in simplest form.**