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Hello Future Algebra 2 Honors Student,

This assignment must be completed and handed in to your teacher on the first day of class. NO EXCEPTIONS! The summer homework is a review of Algebra I skills that are necessary for success in Algebra II. This assignment will serve as the main review for a test to be given during the first week of school, which will count toward your first quarter grade.

You must complete the entire packet showing sufficient evidence of effort in mathematical reasoning, use of computational skills, understanding of concepts, and communication of appropriate math processes and terms. In other words, show all your work or explain how you got your answer, label when necessary, and answer word problems in a complete sentence. Work should be neatly organized with complete steps and done only in pencil. Do not write on booklet. Calculators may be used and are recommended. When using calculators, show your work by writing down steps needed to solve the problem. The TI 83, TI 83 plus or TI 84 graphing calculators are strongly recommended and will be used extensively in class.

If you have access to the internet, you may find the web site for our text book helpful. This site is provided by the publishers of our textbook series, Prentice Hall.

Web address: www.PHSchool.com. Click on Course Content Click on Math.

Click on “Textbook Companion Sites”. Click “PH Mathematics 2004”. Click on Algebra II under the picture of the textbook. Click on “Homework Video Tutors.” Choose the appropriate chapter, lesson, and then objective. Enjoy the lesson. The video clip can be repeated as necessary.

You will also find a study packet on the math department website. If you need a hard copy, please contact the guidance office at WHHS.

Remember that if this assignment is not completed to the specifications stated above, you may not be eligible to remain in the Honors Mathematics Program.

If you have any questions, feel free to email [email protected].

All WHHS students taking an Honors or Advanced Placement (AP) course in the fall must show proof that they have successfully completed the plagiarism tutorial and correctly answered all ten questions on the plagiarism post-test at the following website: http://www.lib.usm.edu/legacy/plag/plagiarismtutorial.php. At the end of the tutorial, you will print out the page that states that you answered all ten questions correctly and attach it to your summer assignment.

Have a great summer!

Good luck and enjoy!

The WHHS Math Department

Algebra 2 Honors Summer Homework 1

mailto:[email protected]

Algebra 2 Honors Summer Packet

Directions: Find the slope of the line that passes through the following points.1. (3, 7) and (-2, -3) 2. (-2, 6) and (1, 7)

Find the slope and y – intercept of the following lines.

3. −9 x+3 y=15 4. −5 x+6 y=12

Find the rate of change and explain what it means for the situation.5. 6.

Write equation of the line in slope-intercept form based on the given information.

7. m=1

2;b=−5

8. m=−3 ;b=8


Identify the slope and y – intercept of the following equation. Then, graph.

9. y=23x−4

Identify the slope and y – intercept in the following graphs. 10. 11.

Determine the slope of the following.12. 13.

Determine the x – intercepts and y – intercepts.14. 3 x+9 y=18 15. 6 x+4 y=24


Write the following in standard form using integers.

16. y=23x−7

17. y=12x+5

Graph.

18. y−1=( x−2 ) 19. ( y+2 )=2

3(x−1 )

20. Write the equation of the line that passes through the points (2, -5) and (-3, 5).

21. The table shows the amount of money an employee makes given the number of hours worked.

a) Model the data with an equation.

b) Predict the salary for an employee who works 7 hours.


Determine whether the graphs of the following equations are parallel, perpendicular, or neither.

22.

y=−3x+1

y=13x−2

23.

y=12x+1

y=12x−3

24.

y=4 x+7y=−2 x−1

25. Write the equation of the line that is perpendicular to the line y=12x+6

and passes through the point (1, 5).

26. Write the equation of the line that is parallel to the line y=3 x−1 and passes through the point (-2, 7).

27. Graph the system of equations

y=x+3y=2x+2 . Label the solution clearly.


Determine the number of solutions: one solution, no solutions, or infinitely many solutions. Explain your reasoning.

28.

y=13x+4

y=13x+4

29.

y=2x−4y=2x+5 30.

y=x+4y=−2x−9

Determine if the point (2, 5) is a solution of the following systems of equations.

31.

y=−2 x−1y=2 x+1 32.

y=4 x−3y=−x+7

Solve each system of equations.

33.

y=−2x+3y=4 x+9 34.

2 x+3 y=11y=4 x−1


35.

3 x+5 y=142 x−5 y=6 36.

3 x−4 y=−24x+ y=1

37. How do we know when to solve by elimination or substitution?

Graph the following.

38. y<2 x−1 39. y≥12x−3

Solve the system of equations by graphing.

40.

y<−2 x+3

y≥13x−1


Explain how each of the following graphs changes from the parent function y=x2

.

41. y=3 x2

42. y=3 ( x−2 )2

43. y=12x2

44. y= (x+4 )2+1

45. The sum of two numbers is 59. Their difference is 11. What are the two numbers?

46. The West Haven High School band is selling tickets for their spring concert. Adult tickets cost $5.00 and student tickets cost $2.00. There were 150 tickets sold for a total of $450.00. How many adult tickets were sold and how many student tickets were sold?

Decide whether the data shown in each graph is linear. Explain your reasoning. 47. 48.

`Determine whether the following are linear or quadratic.


49. f ( x )=3 x+4 50. f ( x )=4 x2−5x+9 51. f ( x )=x2+8 x−1 52. f ( x )=2x+5

Find the GCF of the following algebraic expressions.

53. 4 x2−16 x+8 54. 5 x+30 55. 2 x

7+5 x9 56. 6 x5−7 x3

57. Find a quadratic function to model the values in the table. Predict the value of y for x=6 .

58. For the parabola to the right, find the following.

A) Vertex: _______________

B) Axis of Symmetry: _______________

C) Coordinates of point P': _______________

D) Coordinates of point Q': _______________

E) Coordinates of the Minimum (if any): __________

F) Coordinates of the Maximum (if any): __________

59. The equation to model the height (h) of an arrow shot into the air is h (t )=−14 t2+56 t+9where t is the time and h is the height. a) How long does it take (t) for the arrow to reach the maximum height?

b) Find the maximum height (h) of the arrow.


Write the following quadratic equations in vertex form.

60. y=3 x2−12x+2 61. y=x

2+4 x−6

Identify the vertex and the y-intercept of the following quadratic equations.

62. y=−5 (x+1 )2+17 63. y=4 ( x+1 )2−3

Factor the following. (FIRST TRY TO FACTOR OUT A GCF.)

64. 15 x2+6 x 65. 64 x

2−100 66. x2+15 x+50

Solve.

67. ( x−2 ) ( x+5 )=0 68. (2 x−6 ) ( x−8 )=0

69. (2 x+5 )2=0 70. (3 x−9 )2=0


Solve by factoring.

71. x2−9 x+18=0 72. x

2+7 x+21=9

Solve without factoring or using the quadratic formula.

73. x2=36 74. 2 x

2=32 75. 3 x2−1=26

Multiply.

76. ( x−4 ) ( x+2 ) 77. (3 x−1 ) (4 x+5 ) 78. ( x−3 ) (2 x+1 )

Graph. Identify the vertex and axis of symmetry.

79. y=x2+1 80. y=x

2−3


81. Solve the equation x2+14 x−15=0by completing the square.

Use the quadratic formula to solve the equation. Round to the nearest hundredth, if necessary.

82. x2+4 x+3=0 83. 2 x

2+2x−12=0

FormulasLinear Equations

Slope: m=

y2− y1x2−x1 Slope – Intercept Form: y=mx+b Point – Slope Form: y− y1=m (x−x1)

Quadratic Equations

Vertex Form: y=a ( x−h )2+k Vertex: (h , k ) or (−b2a , f (−b2a ))

Axis of Symmetry: x=−b2a

Standard Form: y=ax2+bx+c y – intercept: (0, c) Quadratic Formula:

x=−b±√b2−4 ac2a

Exponent Properties Radical Properties

an⋅am=an+m (an)m=anm n√a=a1n n√an=a

nn=a


(ab )n=an bnam

an=an−m n√ab=n√a⋅n√b

n√ ab=n√an√b

a−n= 1an a0=1


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