Download PC-P.1

Day 1 of Pre-Calculus! Wohoo!
Bain’s Daily Procedures:
Homework: review from the night before,
and turn it in (HW worth 2 pts)
Notes: will be given in the form of power
points. You can print these out from my
teacher page and bring them to class with
you if you would like – choosing a format
that works best for note taking.
Extended Periods: we will proceed with
the next days notes, then add some mindstretching activities!
Let’s begin exploring (reviewing?!?!)
the info in P.1
Interval Notation,
Properties of Algebra
& Exponents, Scientific
Notation
Recall the real number line:
Coordinate of a point
Origin
-6 -5 -4 -3 -2 -1 0
Neg. real
numbers
13
3
1
2
3
4
Pos. real
numbers
5
6
We can use inequalities to describe
intervals of real numbers
<
(recall the symbols?)
<
>
>
Ex: Describe and graph the interval of real
numbers for the inequality given
1. x > –2
All real numbers greater than
or equal to negative two
–2
–1
0
1
–2 –1
0
1
Closed bracket – value included in solution.
We can use inequalities to describe
intervals of real numbers
<
(recall the symbols?)
<
>
>
Ex: Describe and graph the interval of real
numbers for the inequality given
2. 0 < x < 3
All real numbers between zero
and three, including zero
–1
0
1
2
3
–1
0
1
2
3
Interval Notation
Bounded Intervals of Real Numbers
(let a and b be real #s with a < b;
a and b are the endpoints of each interval)
Interval
Notation
Interval
Type
Inequality
Notation
[a, b]
closed
a<x<b
a
b
(a, b)
open
a<x<b
a
b
[a, b)
half-open a < x < b
a
b
(a, b]
half-open a < x < b
a
b
Graph
Interval Notation
Unbounded Intervals of Real Numbers
(let a and b be real #s)
Interval
Interval
Inequality
Graph
Notation
Type
Notation
)
closed
x>a
(a,
)
open
x>a
, b]
closed
x<b
, b)
open
x<b
8
[a,
8
8
(
8
(
a
a
b
b
More Examples…
Convert interval notation to inequality notation or vice
versa. Find the endpoints and state whether the
interval is bounded, its type, and graph the interval.
[–3, 7]
3. –3 < x < 7
Endpoints: –3, 7
Bounded, closed interval
–3
0
7
More Examples…
Convert interval notation to inequality notation or vice
versa. Find the endpoints and state whether the
interval is bounded, its type, and graph the interval.
8
4. (–
x < –9
, –9)
Endpoint: –9
Unbounded, open interval
–9
0
Some new/old info…
Consider the magically appearing expression below:
Constants
2x   p  3b
3
Variables
Algebraic
Expression
3
y

z
c

  yc  z c
3
Factored
Form
Expanded
Form
a z  a w  a  z  w
3
3
Expanded
Form
3
Factored
Form
Additive inverses are two numbers
whose sum is zero (opposites?)
Example:
Multiplicative inverses are two numbers
whose product is one (reciprocals?)
Example:
Other Properties from Algebra
Let u, v, and w be real numbers, variables,
or algebraic expressions.
Commutative Property
Addition: u + v = v + u
Multiplication: uv = vu
Associative Property
Addition: (u + v) + w = u + (v + w)
Multiplication: (uv)w = u(vw)
Inverse Property
Addition: u + (– u) = 0
Multiplication:
Identity Property
Addition: u + 0 = u
Multiplication: (u)(1) = u
Distributive Property
u(v + w) = uv + uw
(u + v)w = uw + vw
Exponential Notation
Let a be a real number, variable, or algebraic
expression and n is a positive integer. Then:
n
a =a
a
a … a,
n factors
n is the exponent, a is the base, and a n is the
nth power of a, read as “a to the nth power”
Properties of Exponents
(All bases are assumed to be nonzero)
1. u
m
u
n
=u
um
2. n = u
u
0
3. u = 1
4. u
–n
1
= n
u
m+n
m–n
Properties of Exponents
(All bases are assumed to be nonzero)
5. (uv)
6. (u
7.
m
u
v
m
=u
m
v
n
mn
m
um
vm
) =u
( )=
m
Scientific Notation
c x 10
m
Where 1 < c < 10,
and m is any integer
Let’s do some practice problems…
Guided Practice
1. Proctor’s brain has approximately 102,390,000,000
Neurons (at least before the rugby season). Write this
number in scientific notation
1.0239 x 10
11
2. Write the number 8.723 x 10
–9
0.000000008723
in decimal form
Guided Practice
For #3 and 4, simplify the expression.
3.
2
2
( )
ab
b
3
a
2
b
2
4.
2
3
–1
5
(3x) y
12x
3
3x
4y
2
y
Guided Practice
Use scientific notation to multiply:
5.
–7
6
(3.7 x 10 )(4.3 x 10 )
2.5 x 10
7
6.364 x 10
6
Homework: p. 11-12 5-31 odd, 37-63 odd
Note: Name and assignment should be
written on the top line of you paper.