Sequences and Series
A. Arithmetic Growth
The following is an arithmetic sequence: 15, 25, 35, . . . , 125. Why ?
To find the general term of an arithmetic sequence one must use the formula tn = a + (n 1)d
where, a =
d=
n=
tn =
To find the sum of an arith
Pre-Calculus Math 11
Quadratic Functions & Equations
Example 1: Solve the following by factoring.
a) x3 + 7x2 + 10x = 0
(b) 7x2 68 = -5
Example 2: Factor the following.
a) (x 3)2 + 2(x 3) 15
(b) 6(x 1)2 + (x 1) 1
Example 3: Solve using the quadratic formu
Rational Expressions
A. Simplifying Expressions
Step 1: Factor everything fully
Step 2: Cancel if there is a common factor on the top and on the bottom
Example 1: Simplify the following.
3x
(x + 7)(x + 4)
2
a) 3x 9
(b) x 49
(x 1)
(c)
2
x + 2x 3
B. Adding
Absolute Values, Reciprocals, and Systems of Equations
A. Absolute Values
Example 1: Given the following graph, graph the absolute value of each of the following.
Example 2: Solve.
a) |7x 3| = x + 1
b) 3x 1 = |4x2 x 4|
B. Reciprocal Functions
Example 3: G
PRE-CALCULUS 11
Unit 7 Day 1: EXPONENT LAWS AND SEQUENCES
EXPONENT LAWS (review)
Rules for rewriting expressions with powers, the exponent laws:
(a )(a ) = a
m
n
(ab )
m
m
=a b
mn
= amn
m
m
a = a ,b0
b
bm
m
a m = 1 , a 0
am
a 0 = 1, a 0
example: Simplify
PRE-CALCULUS 11
Unit 6 Day 1: ABSOLUTE VALUE
ABSOLUTE VALUE
The absolute value of a real number a is the distance from a to 0 on a number line;
an absolute value cannot be negative.
0
The absolute value of a is written as | a | .
The absolute value of 7 i
PRE-CALCULUS 11
Unit 5 Day 1: RATIONAL EXPRESSIONS (Part 1)
RATIONAL EXPRESSIONS
A rational number is any number that can be written as a quotient of two integers, b
a
where the denominator cannot equal zero; a 0 .
A rational expression is any expression
PRE-CALCULUS 11
Unit 1 Day 1: POLYNOMIALS REVIEW
POLYNOMIALS
A monomial is a number, a variable, or a product of a number and variables.
A monomial that is just a number is also called a constant.
The number multiplied to the variables is called the coe
PRE-CALCULUS 11
Unit 2 Day 1: GRAPHICAL SOLUTIONS OF QUADRATIC EQUATIONS
QUADRATIC EQUATIONS
A quadratic equation is a second degree equation which can be written in the form,
ax2 + bx + c = 0, where x is the variable and a, b, and c are real numbers and
PRE-CALCULUS 11
Unit 3 Day 1: SOLVING SYSTEMS OF EQUATIONS GRAPHICALLY
SYSTEMS OF EQUATIONS
A system of equation is a collection of two or more equations with the same variables.
A system of equations with two variables will usually have two equations.
T
PRE-CALCULUS 11
Unit 4 Day 1: WORKING WITH RADICALS
RADICALS
n
Radicals are expressions in the form
a , which is the "nth root of a".
is the radical symbol; n is the index; and a is the radicand.
n
= a number
such that
=
8=
because
81 =
because
25
3
4
(th