1. Strategic Math General Review of Algebra I By: Shirly Boots

2. Add/Subtract/Multiply/Divide Ex: -2 + 8 = Ex: -2 – 8 = Ex: 4(- 6) = Ex: -16/-2 Ex: (-3+33)/15 Ex: -2(-3)= Ex: x(x)Ex: x + 3x -3 -2 -1 0 1 2 3

3. Evaluate/PEMDAS PEMDAS _________ Evaluate means _________! Ex: - 4 + (3 – 5) 2 + 7(2) Ex: a = 4, b = -3 ab - 5a + b 2 Ex: a = -2, b = -5, c = 7 c 2 + ab – 3a

4. Combine Like Terms like terms What are like terms? What is perimeter? How do I find perimeter? Ex: 5a + 6ab + 7a – 8b + 3ab – 5a + 2b Ex: Ex: 2ab 2 + 3a 2 b + 7ab – 4a 2 b + 5ab 2 2x + 5 3x - 7

5. Multiply Polynomials Distribute: Ex: 5(x – 2) – 3(x + 7) + x(4 – x) FOIL: Ex: (2x + 3)(x – 5)

6. Solve 1 Variable Equations solve What does “solve” mean? How do I move something to the other side of the equation? Ex: 5x + 4 = 19Ex: ½ x – 7 = 11

7. Solve 1 Variable Inequalities 5 5 5 5 Remember Remember: when you multiply or divide by a negative, you must ______________

8. Discount/Tax – Find Cost Discount Discount: Cost = Price – (%)Price *change percent ______________________ Ex: John buys a $289.00 electronic device for 40% off. How much is the total costs? Tax Tax: Cost = Price + (%)Price Ex: Sarah is charged 7.25% tax on her purchase of $23.89. How much is the total costs?

9. Discount/Tax – Find Original Price Discount Discount: Ex: Mike’s purchase cost $58.24. There was a 20% discount. What was the original price? Tax Tax: Ex: Alex’s purchase cost $81.72. There is an 8% tax. What was the original price?

10. Slope from Equation m Y = mx + b Parallel lines have the ________________ Perpendicular lines ________________

11. Slope from Graph

12. Slope from 2 points Ex: (2,3)(-1,7) Ex: (-4,-3)(-17,-3)

13. Slope from Words Key Words Key Words: Ex: Carl gets paid $9.50 per hour at his job. Ex: Susan can make 2 birdhouses every 5 days.

14. Slope in Standard Form 3x + 2y = 6 Find x – int: y = 0 Find y – int: x = 0 Find slope: solve for y 3x - 4y = 24 Find x – int: y = 0 Find y – int: x = 0 Find slope: solve for y SLOPE SHORTCUT: _________________

15. Solve Proportions

16. Write proportions from figures Ex: 5 3 X-2 6 4 3 6 x+3

17. Write Proportions from Words Ex: The exchange rate is $3 for each rubel. How many rubels is $20? Ex: The exchange rate is 220 pesos for $1.50. How many pesos is $30?

18. Graph Linear Equations mb Y = mx + b Steps: 1. 2. 3. – 4.

19. Write Linear Equations from Graph

20. Write Linear Equations from Words Key Words: ___________ comes before the key word ___________ comes after the key word Ex: Walter gets paid $9.50 per hour. How much will he make in 22 hours? Ex: The taxi driver charges $2.50 for pickup and $1.35 for each mile. How much will it cost to go 7 miles?

21. Graph Linear Inequalities Steps: 1.Plot y intercept 2.Plot slope 3.Solid or dash line 4.Shade up or down >> >Shade up > Soliddash << <Shade < down

22. Write Linear inequality from Graph Steps: 1.Where is the shading? This determines 2.What kind of line? – This determines or 3.What is b? 4.What is the slope? 5.Plug into formula Y <> mx + b Ex:

23. Find the solution from the Graph Circle all solutions: Ex: (0,0) (-3,0) (-1,0) (0,5) (-4,6) (4,-6) (2,2) (5,0) Ex: (0,0) (-2,0) (-1,4) (0,-5) (-6,-6) (4,6) (2,2) (-5,0)

24. Match Graph to Equation Which one? A.Y = x – 1 B.Y= -x – 1 C.Y = x + 1 D.Y = -x + 1 What do you look for?

25. Match words to equation Ex1: Mr. Perkins took out a loan for $800. Each month he pays $50 on the loan. Ex2: Sam paid a one-time $800 connection fee for his commercial internet system. He pays $50 every month for service. What do you look for? Pick the Equation for each: Y = 50x + 800 Y = 800 – 50x Y = -50x – 800 Y= 800x + 50

26. Match Table to Equation A.Y = -2x – 7 B.Y = 5x + 7 C.Y = 2x + 7 D.Y = -5x + 7 E.Y = -2x + 7 F.Y = 5x - 7 Ex1: Ex2: Ex3:

27. Match Table to Graph Ex1: Ex2: Ex3: ABAB CDCD

28. Types of Scatterplots What is the correlation? Negative, positive, none What do you look for?

29. Scatterplots to Predict Domain: Range: What is the weight after 83 days? When will the animal weigh 5.8 lbs? How do you find each on the graph?

30. Types of Solutions for Systems Type: Type:Type: # of Solutions: # of Solutions : # of Solutions :

31. Solve by Graphing Steps: 1.Graph first line 2.Graph second line 3.Identify the point of intersection

32. Check the Answer Steps: 1. 2. 3. If either is false then ______________________

33. Solve Systems of Inequalities Steps: 1. 2. 3. 4. 5.

34. Solve by Substitution Steps: 1. Solve one equation for one of the variables (get x = ____ or y = ____) 2.SUBSTITUTE the expression for the variable into the other equation 3. Solve for the variable that’s left over 4. Plug in the value from the known variable into one of the original equations 5. Solve for the other variable

35. Solve by Elimination Steps: 1. 2. 3. 4. 5.

36. Write Equations for Systems Hint: Ex: John has $4.85 in quarters and dimes. There is a total of 32 coins. How many of each coin? Hint: Ex: Mark bought 2 bags of cookies and 3 dozen muffins for $9.81. Jenn bought 5 of each for $19.65. How much for each?

37. Check Solutions for Word problems One package of chocolates costs $8. Strawberries cost $5 per pound. She cannot spend more than $80 and must have at least 6 pounds of strawberries. Which solution gets her the most for her money? A.10 chocolate; 8 strawberries B.8 chocolate; 3 strawberries C.5 chocolate; 7 strawberries D.4 chocolate; 6 strawberries What is the money equation? What is another fact that we need to make a decision? How do you find the answer?

38. Parent Functions Lineary = Domain: Range: Quadratic y = Domain: Range:

39. Quadratic Transformations

40. Factor GCF What is a GCF? Ex: 7x + 28Ex: 5x 2 – 5x Ex: x 2 + 6xEx: 2x 2 + 6x - 8

41. Factor a = 1 Hints: 1) Find the possible factors of the last # 2) Find which pair of factors add up to the middle # Ex: x 2 + 12x + 36Ex: x 2 – 9x + 20 Ex: x 2 – x – 12Ex: x 2 + 4x – 12

42. Factor by grouping What is grouping? Ex: 12a 3 – 9a 2 + 20a – 15 Ex: 6x 3 + 12x 2 + x + 2

43. Factor and Solve Hint: Ex: 4x 2 + 6x = 0Ex: x 2 + 16x + 55 = 0

44. Quadratics – Vertex and AOS Axis of Symmetry – A vertical line which divides the parabola in half Vertex (Min/Max) – The point on the curve where the parabola changes direction X-Intercepts – Any point where the curve touches the x-axis (where y = 0)

45. Quadratic Example Opens: Up or Down Vertex:_______________ Max/Min AOS: _________________ Roots: ________________ ______________________ Equation: ______________

46. Quadratics – Roots XY -40 -31 -24 9 04 11 20 Which way does the parabola open (up or down)? What are the x-intercepts? What is the vertex? Is the vertex a maximum or a minimum? What is the axis of symmetry?

47. Domain/Range from Graph

48. Domain/Range from Equation

49. Domain/Range from Words Key Words: Ex: An airplane at 5,000 feet descends at a rate of 100 feet per minute to land. Ex: Joshua earns $8 per hour working a 10 hour shift. Ex: A beach ball falls from a 100 ft platform onto a table 4 feet off the ground over the span of 10 seconds.

50. Add/Subtract Fractions

51. Multiply Fractions

52. Divide Fractions

53. Direct Variation Formula: Ex: If a is directly proportional to b, and a = 30 when b = 5, find b when a = 40. Ex: If r varies directly as s + 1, and r = 18 when s = 5, find r when s = 8.

54. Absolute Value on Number Lines Ex: What 2 numbers are 4 away from 3? Ex: What 2 numbers are 6 away from -2? Ex: How far away are -3 and 5 from ________?

55. Solve Absolute Value Equations