Algebra 1 Online:

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Griffin Chapman
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2 Dear Algebra 2 Students, Within this packet you will find mathematical concepts and skills learned in Algebra 1 that are the foundation from which Algebra 2 is built. These concepts need to be reviewed and practiced throughout the summer. The Algebra 2 course has recently undergone course design and curriculum changes making such review work important and essential for your success in Algebra 2. The Algebra 2 prerequisite packet will be due the first day of school. The packet will be graded and will count as a test grade. Your test grade will reflect both your effort (50%), which is based on attempting all problems and showing work for all problems, and accuracy (50%). The Algebra 2 prerequisite packet contains sample examples that have been done out for each concept, followed by Try these problems for you to complete. Below are a few websites you may wish to visit for additional examples and support: Algebra 1 Online: Algebra 2 Online: Algebra Help: Khan Academy: Results from the summer prerequisite work will help guide skill and concept reinforcement lessons that will take place the first few weeks of school Have a nice summer, Lyman Math Department

3 Directions: Show all of your work in order to receive credit. Worked out examples have been provided for you to follow when completing problems. Section 1: Ordering and Comparing Numbers Try these: Graph the number on a number line and then write the numbers in order from least to greatest Section 2: Order of Operations

4 Try these: Evaluate the following expressions using order of operations Section 3: Combining Like Terms Try these: Simplify by combining like terms (x 2) + 5(x + 3) A: Simplifying or Reducing Fractions Section 4: Fractions Try these : Simplify = B: Adding or Subtracting Fractions

5 Try these: Add or subtract as indicated. 10. = C: Multiplying Fractions Try these: Multiply the fractions as indicated and simplify D: Dividing Fractions Try these: Divide the fractions as indicated and simplify =

6 Section 5: Solving Equations Try these: Solve for x Perimeter = 38

7 Section 6: Inequalities Try these: Solve and Graph Section 7: Graphing Try this: 23.

8 Example: Try this: Complete the table of value for the given function and then graph. 24. Try this: State the slope and y-intercept. Sketch the graph. 25. Slope: y-intercept:

9 Try this: Find the x and y intercepts then sketch the graph. 26. x-intercept: y-intercept: Section 8: Writing Equations of Lines Try this: Find the slope between the two given points. 27. (1, -5), (3, 7)

Try this: Write the equation of the line with the given information. 29.

10 Example: Write the equation of the line: Try this: Write the equation of a line with the given information. 28. Example: Write the equation of the line given the point (-3, -7) and slope 2. Try this: Write the equation of the line with the given information. 29. point (2, 3), m = -2 Example: Write the equation of the line given the two points (1, 1) and (5, 9). Try this: Write the equation of the line with the given information. 30. (-2, 1) and (-1, 5)

11 Example: Write the equation of the line parallel to y = 3x + 2 passing through (-1, -2). Try this: Write the equation of the line with the given information. 31. Parallel to y = -3x + 1 through (2, 1) Example: Write the equation of the line perpendicular to y = -1/2 x + 6 through (1, 1). Try this: Write the equation of the line with the given information. 32. Perpendicular to y = ¼ x 5 through (1, 1)

12 Try this: Write the equation of the vertical and horizontal line through the given point and sketch their graphs. 33. Through (-1, 4) Vertical: Horizontal:

13 Section 9: Solving Systems of Equations Solve the System by Graphing: Graph and find the point of intersection. Try this: Solve the system by graphing. 34. Solve the system by Substitution. Try this: Solve by substitution. 35.

14 Solve the system by Elimination. Try this: Solve by elimination. 36. Section 10: Multiplying Polynomials using FOIL Try this: Multiply the binomials 37. (2x + 3)(x + 1) = Try this: Multiply 38.

15 Section 11: Factoring Try this: Factor 39. 3x 4 y 2 6x 3 y x 2 y 2 Try these: Factor 40. x 2 + 4x x 2 27x + 50 _ x 2 64

16 Section 12: Solving Quadratic Functions Try this: Use the quadratic formula to find the solutions. 43. y = x 2 + 2x - 4

17 Section 13: Graphing Quadratic Functions without a Calculator General Form of a Quadratic: y = ax 2 + b x + c

18 Try this: Find the information and sketch the quadratic equation. 44. Section 14: Exponents Try this: 45. Complete the table by raising each value of x to the given power. You will be responsible for knowing the following values without a calculator.

19 Section 15: Absolute Value Equations Example: Solve 8 4 x = x = 12 Write the original equation. 8 4x = 12 or 8 4x = -12 Expression within Absolute Value Symbols can equal 12 or -12-4x = 12 or -4x = - 20 Subtract 8 from each side. x = -1 or x = 5 Divide each side by -4. The solutions are -1 and 5 Try these: Solve the Absolute Value Equations 46. x + 5 = 8 Section 16: Applications 47. The bill for the repair of a car was $420. The cost of parts was $210. If the repair took a total of 3 hours, how much money did the repair shop charge per hour for labor? 48. A new set of tires has a tread depth of 8 millimeters. The tread depth decreases 0.12 millimeters per thousand miles driven. Write an equation that gives the tread depth as a function of the distance driven. Then determine at what distance the tread depth will be 2 millimeters.

20 49. A nut wholesaler sells a mix of peanuts and cashews. The wholesaler charges $2.80 per pound for peanuts and $5.30 per pound for cashews. The mix is to sell for $3.30 per pound. How many points of peanuts and how many pounds of cashews should be used to make 100 pounds of the mix? 50. An adult pass at a carnival costs $2 more than a children s pass. When 378 adult and 214 children's passes were sold, the total revenue was $2384. Find the total cost for a family of two adults and two children.

Section 2.3 Task List

Summer 2017 Math 108 Section 2.3 67 Section 2.3 Task List Work through each of the following tasks, carefully filling in the following pages in your notebook. Section 2.3 Function Notation and Applications