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Do Now!!

Do Now!!. In your composition notebook THOROUGHLY explain how you would solve the equation below: -3(x – 3) ≥ 5 – 4x. EOC Review. Objective. SWBAT make connections with content from Chapters 1 – 4. 1-1 Variables and Expressions.

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Do Now!!

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  1. Do Now!! In your composition notebook THOROUGHLY explain how you would solve the equation below: -3(x – 3) ≥ 5 – 4x

  2. EOC Review

  3. Objective SWBAT make connections with content from Chapters 1 – 4.

  4. 1-1 Variables and Expressions A variable is a symbol, usually a letter, that represents values of a variable quantity. For example, d often represents distance. An algebraic expression is a mathematical phrase that includes one or more variables. A numerical expression is a mathematical phrase involving numbers and operations symbols, but no variables.

  5. 1-1 Variables and Expressions What is an algebraic expression for the word phrase 3 less than half a number x? You can represent “half a number x” as x/2. Then subtract 3 to get: x/2 – 3.

  6. 1-4 Properties of Real Numbers You can use properties such as the ones below to simplify and evaluate expressions. Commutative Properties: -2 + 7 = 7 + (-2) 3 × 4 = 4×3 Associative Properties: 2× (14×3) = (2×14) × 3 3 + (12 + 2)= (3 + 12) + 2 Identity Properties: -6 + 0 = -6 21 × 1 = 21 Zero Property of Multiplication: -7 × 0 = 0 Multiplication Property of -1: 6 ∙ (-1) = -6

  7. 2-1 and 2-2 Solving One- and Two-Step Equations To solve an equation, get the variable by itself on one side of the equation. YOU can use properties of equality and inverse operations to isolate the variable. For example, use multiplication to undo its inverse, division.

  8. 2-1 and 2-2 Solving One- and Two-Step Equations What is the solution of _y_ + 5 = 8 2 _y_ + 5 – 5 = 8 – 5 Subtract to undo + 2 _y_ = 3 Simplify 2 2 * _y_ = 3*2 Multiply 2 y = 6 Simplify

  9. 2-3 Solving Multi-Step Equations To solve some equations, you may need to combine like terms or use the Distributive Property to clear fractions or decimals.

  10. 2-3 Solving Multi-Step Equations You do! What is the solution of 12 = 2x + _4_ – _2x_ ? 3 3 8 = x

  11. 2-4 Solving Equations With Variables on Both Sides When an equation has variables on both sides, you can use properties of equality to isolate the variable on one side. An equation has no solution if no value of the variable makes it true. An equation is an identity if every value of the variable makes it true.

  12. 2-4 Solving Equations With Variables on Both Sides What is the solution of 3x – 7 = 5x + 19 ? 3x – 7 – 3x = 5x + 19 – 3x Subtract 3x -7 = 2x + 19 Simplify -7 – 19 = 2x + 19 – 19 Subtract 19 -26 = 2x Simplify -26 = 2x Divide by 2 2 2 -13 = x Simplify

  13. 2-5 Literal Equations and Formulas A literal equation is an equation that involves two or more variables. A formula is an equation that states a relationship among quantities. You can use properties of equality to solve a literal equation for one variable in terms of others.

  14. 2-5 Literal Equations and Formulas You Do!What is the width of a rectangle with area 91 ft2 and length 7 ft? 13 = w

  15. 3-1 Inequalities and Their Graphs A solution of an inequality is any number that makes the inequality true. You can indicate all the solutions of an inequality on the graph a closed or dot indicates that the midpoint is a solution. An open dot indicates that the midpoint is not a solution.

  16. 3-1 Inequalities and Their Graphs What is the graph of x ≤ - 4? -4

  17. 3-2 Solving Inequalities Using Addition or Subtraction You can use the addition and subtraction properties of inequality to transform an inequality into a simpler, equivalent inequality.

  18. 3-2 Solving Inequalities Using Addition or Subtraction What are the solutions of x + 4 ≤ 5 ? x + 4 ≤ 5 x + 4 – 4 ≤ 5 – 4 Subtract 4 x ≤ 1 Simplify

  19. 3-3 Solving Inequalities Using Multiplication or Division You can use the multiplication and division properties of inequality to transform an inequality. When you multiply or divide each side of an inequality by a negative number you have to reverse the inequality symbol.

  20. 3-3 Solving Inequalities Using Multiplication or Division What are the solutions of -3x > 12 ? -3x > 12 -3x <12 Divide each by -3 -3 -3 Reverse Inequality Symbol x < -4 Simplify

  21. 3-4 Solving Multi-Step Inequalities When you solve inequalities, sometimes you need to use more than one step. You need to gather the variable terms on one side of the inequality and the constant terms on the other side.

  22. 3-4 Solving Multi-Step Inequalites You do! What are the solutions of 3x + 5 > -1 ? x > -2

  23. 3-5 Working With Sets The complement of a set A (A’) is the set of all elements in the universal set that are not in A.

  24. 3-5 Working With Sets Suppose U = {1, 2,3,4,5,6} and Y = {2,4,6}. What is Y’? The elements in U that are not in Y are 1, 3, and 5. So Y’ = {1, 3, 5}

  25. 3-8 Unions and Intersections of Sets The union of 2 or more sets is the set that contains all elements of the sets. The intersection of 2 or more sets is the set of elements that are common to all the sets. Disjointsets have no elements in common.

  26. 4-4 Graphing a Function Rule A continuous graph is a graph that is unbroken. A discrete graph is composed of distinct, isolated points. In real-world graph, show only points that make sense.

  27. 4-4 Graphing a Function Rule The total height h of a stack of cans is a function of the number n of layers of 4.5-in. cans used. This situation is represented by h = 4.5n. Graph the function.

  28. 4-5 Writing a Function Rule To write a function rule describing a real-world situation, it is often helpful to start with a verbal model of the situation.

  29. 4-5 Writing a Function Rule At a bicycle motocross (BMX) track, you pay $40 for a racing license plus $15 per race. What is the function rule that represents your total cost? Total cost = license fee + fee per race ∙ # of races C = 40 + 15 ∙ r A function rule is C = 40 + 15r

  30. 4-6 Formalizing Relations and Functions A relation pairs numbers in the domain with numbers in the range. A relation may or may not be a function.

  31. 4-6 Formalizing Relations and Functions Is the relation [(0,1), (3,3), (4,4), (0,0)] a function? The x-values of the ordered pairs form the domain, and the y-values form the range. The domain value 0 is paired with two range values, 1 and 0. So the relation is not a function.

  32. 4-7 Sequences and Functions A sequence is an ordered list of numbers, called terms, that often forms a pattern. In an arithmetic sequence, there is a common difference between consecutive terms.

  33. 4-7 Sequences and Functions Tell whether the sequence is arithmetic. 5 2 -1 -4…… -3 -3 -3 The sequence has a common difference of -3, so it is arithmetic

  34. Summary Our Objectives were that: SWBAT make connections with content from Chapters 1 – 4.

  35. HomeworkIn TEXTbook NC EOC Test Practice Chapter 1 pg. 74 – 76 Problems 1 – 20 even Chapter 2 pg. 158-160 Problems 1 – 18 even Chapter 3 pg. 228 – 230 Problems 1 – 20 even Chapter 4 pg. 286-288 Problems 1 – 14 even

  36. Class Assignment In the paper back NC Algebra 1 EOC Test Workbook Complete Problems: 1-9; 11-12; 14-22; 24-26; 28-29; 31 – 34 On pages 1-7 SHOW ALL WORK If there is no computation to answer the question, EXPLAIN your reasoning for getting your answer choice. YOU MAY write in the text book.

  37. EARLY BIRDS Review Released EOC test booklet and choose questions from the booklet you need to go over. Have these questions ready for Thursday’s review.

  38. Objective SWBAT make connections with content from Chapters 5 – 8.

  39. Do Now!! Factor each expression: • h2 + 8h + 16 • d2 – 20d + 100 • m2 + 18m + 81

  40. 5-1 Rate of Change and Slope Rate of change shows the relationship between two changing quantities. The slope of a line is the ratio of the vertical change (the rise) to the horizontal change (the run). slope = rise = y2 – y1 run x2 – x1 The slope of a horizontal line is 0, and the slope of a vertical line is undefined.

  41. 5-1 Rate of Change and Slope What is the slope of the line that passes through the points (1, 12) and (6, 22)? Slope = y2-y1= 22 – 12 = 10 = 2 x2-x1 6 – 1 5

  42. 5-2 Direct Variation A function represent a direct variation a direct variation if it has the form y = kx, where k ≠0. The coefficient k is the constant of variation.

  43. 5-2 Direct Variation Suppose y varies directly with x, and y = 15 when x = 5. Write a direct variation equation that relates x and y. What is the value of y when x = 9? y = kx 15 = k(5) 3 = k y = 3x The equation y = 3x relates x and y. When x = 9, y = 27

  44. 5-3, 5-4, and 5-5 Forms of Linear Equations The graph of a linear equation is a line. You can write a linear equation in different forms. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. The point-slope form of a linear equation is y – y1 = m(x – x1), where m is the slope and (x1,y1) is a point on the line. The standard form of a linear equation is Ax+By = C, where A, B, and C are real numbers, and A and B are not both zeros.

  45. 5-6 Parallel and Perpendicular Lines Parallel lines are lines in the same plane that never intersect. Two lines are perpendicular if they intersect to form right angles.

  46. 5-6 Parallel and Perpendicular Lines Are the graphs of y = 4/3 x + 5 and y = -3/4x + 2 parallel, perpendicular, or neither? Explain. The slope of the graph of y = 4/3x + 5 is 4/3 The slope of the graph of y = -3/4x + 2 is -3/4 (4/3)∙(-3/4) = -1 The slopes are opposite reciprocals, so the graphs are perpendicular. What type of slopes do parallel lines have? The same slope

  47. 5-7 Scatter Plots and Trend Lines A scatter plot displays two sets of data as ordered pairs. A trend line for a scatter plot shows the correlation between the two sets of data. The most accurate trend line is the line of best fit. To estimate or predict values on a scatter plot, you can use interpolation or extrapolation.

  48. 6-1 Solving Systems by Graphing One way to solve a system of linear equations is by graphing each equation and finding the intersection point of the graph, if one exists.

  49. 6-1 Solving Systems by Graphing What is the solution of the system? y = -2x + 2 y = -0.5x – 3 The solution is (2, -2)

  50. 6-2 Solving Systems Using Substitution6-3 Solving Systems Using Elimination • You can solve a system of equations by solving one equation for one variable and then substituting the expression for that variable into the other equation. • You can add or subtract equations in a system to eliminate a variable. Before you add or subtract, you may have to multiply one or both equations by a constant to make eliminating a variable possible.

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