Download Chapter-1-Notes - Windsor C

Algebra I & Concepts
Ch. 1 Notes
Section 1-1: Variables and Expressions
Algebraic ExpressionVariableTerm-
ExponentBase-
Section 1-1
Ex1) Write the verbal expression for each
algebraic expressions
a)
b)
2
4
3x
Operation
Addition
Subtraction
Multiplication
Division
5z +16
Verbal Phrases
Section 1-1
Ex2) Write the algebraic expression for the
verbal expression
a) A number t more than 6
b) 10 less than the product of 7 and f
c) Two thirds of v
Section 1-2: Order of Operations
arenthesis and brackets
xponents
ultiplication &
ivision
ddition & ubtraction
Section 1-2
Ex1) Evaluate the expression
5
3
Ex2) Evaluate each expression
a) 16 -8¸ 22 +14
b) 4 ¸ 2 + 5(10 - 6)
Section 1-2
c) 6 éë32 - (2 + 3)2 ùû
d)
23 - 5
15 + 9
Ex3) Evaluate when x = 4, y = 5, z = 3
a) 3x 2 + (2y + z3 )
b) 3xy + z
x
2
Section 1-3: Properties of Numbers
Property
Words
Reflexive
Property
Any quantity is equal to
itself
Symmetric
Property
If one quantity equals a
second quantity, then the
second quantity equals the
first
Transitive
Property
If one quantity equals a
second quantity and the
second equals a third, the
the first and third are equal
Substitution
Property
A quantity may be
substituted for its equal in
any expression
Symbols
Examples
Section 1-3: Addition and
Multiplication Properties
Property
Words
Additive Identity
For any number a, the sum of
a and 0 is a
Additive Inverse
A number and its opposite are
additive inverses of each other
Property
Words
Multiplicative Identity For any number a, the
product of a and 1 is a
Multiplicative
Property of Zero
For any number a, the
product of a and 0 is 0.
Multiplicative Inverse
(Reciprocal)
The product of any number
and its reciprocal is 1
Symbols
Example
Symbols
Example
Section 1-3
Ex1) Evaluate the expressions
a)
b) 2 ×3+ (4 × 2 -8)
1
7(4 - 3) -1+ 5×
5
Commutative Property (add. & mult.)Associative Property (add. & mult.)-
Section 1-4: The Distributive Property
Distributive Property –
Ex1) Rewrite using the Distributive Property
a) 7(3w – 5)
b) (6v2 + v - 3)4
Section 1-4
Like Terms –
Simplest Form –
Ex2) Simplify
a) 17u + 25u
c)
4y3 + 2y -8y + 5
b) 6t 2 + 3t - t
d) b2 +13b +13
Section 1-5: Equations
Equations vs. Expressions:
Solving and the Solution:
Ex1) Find the solution set of the equation
2x + 5 = 13 if the replacement set is {2, 3, 4, 5, 6}
Section 1-5
Ex2) Apply Order of Operations to solve for the
variable
a) 6 + (52 - 5) ¸ 2 = p
b) 7 - (42 -10) + n =10
One solution, no solutions, all real numbers
Section 1-5
Ex3) Determine if the equation has one, no, or
all real solutions
a) n(3+ 2)+ 6 = 5n + (10 - 3)
b) (2 × 5-8)(3h + 6) = [(2h + h)+ 6]2
Section 1-5
Ex4) Determine if the given number is a solution
to the equation
a) 12 + y = 26; 14
b) 2t – 10 = 4; 3
c) x = 20;10
2
d) w - 4 = -3;-11
5
Section 1-6: Relations
Coordinate Plane
Section 1-6: Plotting Points
Plot and label the following points on the graph, and
identify the location of the point (I, II, III, IV, x-axis, yaxis, origin).
A(3, 5)
B(-2, 4)
C(-1, -7)
D(5, -8)
E(3, 0)
F(0, -6)
Section 1-6
Ordered Pair-
Domain-
X-coordinate-
Range-
Y-coordinate
Mapping
Relation
Section 1-6: Vocabulary
Ordered Pair- set of numbers
of coordinates written in the
form (x, y)
Domain- first number in the
ordered pair (typically x), also
called the input
X-coordinate- the horizontal
placement of the point
Range- second number in the
ordered pair (typically y), also
called the output
Y-coordinate- the vertical
placement of the point
Relation- a set of ordered pairs
Mapping- shows how each
element of the domain is
paired with an element in the
range
Section 1-6: All the Same!
Ordered Pairs: (1, 2),
(-2, 4), (0, 3)
Table
X
Graph
Y
Mapping
Domain
Range
Section 1-6
Ex1) Express [(2,5), (-2,3), (5,-2), (-1,-2)] as a
table, a graph, and mapping
TABLE
GRAPH
MAPPING
Determine the domain and range!
Section 1-6
Independent Variable –
Dependent Variable –
Ex2) Identify the dependent and independent variables
a) The dance committee is selling tickets to the Fall Ball. The
more tickets they sell, the more money they can spend on
decorations.
b) Generally, the average price of movie tickets had increased
over time.
Section 1-6
Independent Variable – the variable that determines the output
Dependent Variable – the variable whose value is dependent on the
independent variable
Ex2) Identify the dependent and independent variables
a) The dance committee is selling tickets to the Fall Ball. The more
tickets they sell, the more money they can spend on decorations.
b) Generally, the average price of movie tickets had increased over
time.
Section 1-7: Functions
Function – a relationship between input and output.
For each input there is one output
Ex1) Determine if the relationships are functions
a) Dom. Range
b)
-2
0
3
4
-3
6
9
Domain
1
3
5
1
Range
4
2
4
-4
c) {(2,1), (3,-2), (3,1), (2,-1)}
Section 1-7
Discrete Function –
Continuous Function –
Vertical Line Test -
Section 1-7
Ex2) Determine if whether -3x + y = 8 is a
function
Function Notation -
Section 1-8: Interpreting Graphs of
Functions
Intercepts –
Y – intercept –
X – intercept –
Line of Symmetry –
Section 1-8: Interpreting Graphs of
Functions
Intercepts – the points on a graph that intersect
with an axis
Y – intercept – the point where a graph crosses the
y-axis
X – intercept – the point where a graph crosses the
x-axis
Line of Symmetry – a vertical line the cuts a graph
in half
Section 1-8
Ex1) For each graph:
a) Identify as linear or nonlinear
b) Estimate the intercepts
c) Find symmetry (if possible)