Name: __________

Lyman Memorial High School

Algebra 2

Prerequisite Packet

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: http://teachers.henrico.k12.va.us/math/hcpsalgebra1/modules.html

Algebra 2 Online: http://teachers.henrico.k12.va.us/math/hcpsalgebra2/modules.html

Algebra Help: http://www.algebrahelp.com/

Khan Academy: https://www.khanacademy.org

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

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.

1. _______________

2. _______________

Section 2: Order of Operations

Try these: Evaluate the following expressions using order of operations.

3. __________ 4. __________

Section 3: Combining Like Terms

Try these: Simplify by combining like terms.

5. _______________

6. 3(x – 2) + 5(x + 3) _______________

Section 4: Fractions

A: Simplifying or Reducing Fractions

Try these: Simplify.

7. ______ 8. ________ 9. = ________

B: Adding or Subtracting Fractions

Try these: Add or subtract as indicated.

10. = _____ 11. _____ 12. _____

C: Multiplying Fractions

Try these: Multiply the fractions as indicated and simplify.

13. ________ 14. ________

D: Dividing Fractions

Try these: Divide the fractions as indicated and simplify.

15. _____ 16. = _____

Section 5: Solving Equations

Try these: Solve for x.

17. __________

18. __________

19. __________

20. Perimeter = 38 __________

Section 6: Inequalities

Try these: Solve and Graph

21. 22.

__________ __________

Section 7: Graphing

Try this:

23.

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: __________

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) _______________

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) __________

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)

__________

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: __________

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. __________

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. __________

Section 11: Factoring

Try this: Factor

39. 3𝑥4𝑦2 − 6𝑥3𝑦2 + 15𝑥2𝑦2 _______________

Try these: Factor

40. 𝑥2 + 4𝑥 − 21 41. 𝑥2 − 27𝑥 + 50

__________ ___________

42. 𝑥2 − 64

__________

Section 12: Solving Quadratic Functions

Try this: Use the quadratic formula to find the solutions.

43. 𝑦 = 𝑥2 +2x - 4

__________

Section 13: Graphing Quadratic Functions without a Calculator

General Form of a Quadratic: 𝒚 = 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄

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.

Section 15: Absolute Value Equations

Example:

Solve |8 − 4𝑥| = 12

|8 − 4𝑥| = 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.

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.