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Algebra I & Concepts

Algebra I & Concepts. Ch. 1 Notes. Section 1-1: Variables and Expressions. Algebraic Expression- Variable- Term- Exponent- Base-. Section 1-1. Ex1) Write the verbal expression for each algebraic expressions a) b). Section 1-1.

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Algebra I & Concepts

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  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)

  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

  9. Section 1-3: Addition and Multiplication Properties

  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

  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) -2 -3 0 6 3 9 c) {(2,1), (3,-2), (3,1), (2,-1)} 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)

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