1. Algebra I & Concepts
Ch. 1 Notes

2. Section 1-1: Variables and Expressions
Algebraic Expression- Variable- Term- Exponent- Base-

3. Section 1-1
Ex1) Write the verbal expression for each algebraic expressions a) b)
Operation
Verbal Phrases
Addition
Subtraction
Multiplication
Division

4. Section 1-1
Ex2) Write the algebraic expression for the verbal expression
A number t more than 6
10 less than the product of 7 and f
Two thirds of v

5. Section 1-2: Order of Operations
Parenthesis and brackets
Exponents
Multiplication & Division
Addition &Subtraction

6. Section 1-2
Ex1) Evaluate the expression Ex2) Evaluate each expression a) b)

7. Section 1-2
c) d) Ex3) Evaluate when x = 4, y = 5, z = 3 a) b)

8. Section 1-3: Properties of Numbers
Property
Words
Symbols
Examples
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

9. Section 1-3: Addition and Multiplication Properties
Property
Words
Symbols
Example
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
Symbols
Example
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

10. Section 1-3
Ex1) Evaluate the expressions a) b) Commutative Property (add. & mult.)- Associative Property (add. & mult.)-

11. Section 1-4: The Distributive Property
Distributive Property – Ex1) Rewrite using the Distributive Property a) 7(3w – 5) b)

12. Section 1-4
Like Terms – Simplest Form – Ex2) Simplify a) 17u + 25u b) c) d)

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}

14. Section 1-5
Ex2) Apply Order of Operations to solve for the variable a) b) One solution, no solutions, all real numbers

15. Section 1-5
Ex3) Determine if the equation has one, no, or all real solutions a) b)

16. Section 1-5
Ex4) Determine if the given number is a solution to the equation
12 + y = 26; 14 b) 2t – 10 = 4; 3
c) d)

17. Section 1-6: Relations
Coordinate Plane

18. 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, y-axis, origin). A(3, 5) B(-2, 4) C(-1, -7) D(5, -8) E(3, 0) F(0, -6)

19. Section 1-6 Ordered Pair- X-coordinate- Y-coordinate Relation
Domain- Range- Mapping

20. Section 1-6: Vocabulary
Ordered Pair- set of numbers of coordinates written in the form (x, y) X-coordinate- the horizontal placement of the point Y-coordinate- the vertical placement of the point Relation- a set of ordered pairs
Domain- first number in the ordered pair (typically x), also called the input Range- second number in the ordered pair (typically y), also called the output Mapping- shows how each element of the domain is paired with an element in the range

21. Section 1-6: All the Same!
Ordered Pairs: (1, 2), (-2, 4), (0, 3) Table
Graph Mapping Domain Range X Y

22. 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!

23. Section 1-6 Independent Variable – Dependent Variable –
Ex2) Identify the dependent and independent variables
The dance committee is selling tickets to the Fall Ball. The more tickets they sell, the more money they can spend on decorations.
Generally, the average price of movie tickets had increased over time.

24. 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
The dance committee is selling tickets to the Fall Ball. The more tickets they sell, the more money they can spend on decorations.
Generally, the average price of movie tickets had increased over time.

25. 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
Dom. Range b)
0 6
c) {(2,1), (3,-2), (3,1), (2,-1)} 4
Domain 1 3 5
Range 4 2 -4

26. Section 1-7
Discrete Function – Continuous Function – Vertical Line Test -

27. Section 1-7
Ex2) Determine if whether -3x + y = 8 is a function Function Notation -

28. Section 1-8: Interpreting Graphs of Functions
Intercepts – Y – intercept – X – intercept – Line of Symmetry –

29. 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

30. Section 1-8 Ex1) For each graph: Identify as linear or nonlinear
Estimate the intercepts
Find symmetry (if possible)