South Brunswick Schools

Summer Packet For 

Rising Elements of Algebra 1 Students 

 

 

Directions: All students entering Algebra 1 are expected to be proficient in all their 

previously-learned skills. The following exercises are intended to provide a review of the skills 

needed to be successful in Algebra 1. Except for problems with an asterisk (*), complete all the 

problems without use of a calculator. Show all work – even for multiple choice problems!  If you need assistance with any topics, please refer to the following websites: 

● http://coolmath.com/algebra/Algebra1/index.html 

● http://www.algebra.com/ 

● http://www.classzone.com/books/algebra_1/index.cfm?state=NJ 

● http://mathforum.org/dr.math/ 

 

In addition, summer math help will be provided by honor society students during the summer. 

Please see the summer assignment description for dates and times. 

Answers to the exercises are provided on the last page – however, you must show all work to receive full credit. 

 

We highly recommend that students use a graphing calculator for success in mathematics. While our                             

math classrooms are equipped with graphing calculators for students to use during class, students are                             

encouraged to purchase their own graphing calculator for use at home. If you choose to purchase one,                                 

we recommend the TI-83+ or TI-84. Because these calculators are costly, students should permanently                           

mark the calculator with their name and keep them in a safe place if they bring them to school. These                                       

calculators can be used for all four years of high school mathematics as well as for other standardized                                   

tests such as the SAT so they are a worthwhile investment. 

 

*** Note: THIS PACKET SHOULD BE COMPLETED FOR TURN-IN ON THE FIRST DAY OF 

CLASS. YOU WILL TAKE A SKILLS QUIZ, BASED ON THIS PACKET, ON YOUR 3rd DAY OF 

CLASS   

 

 

 

 

Elements of Algebra I Summer Assignment 

 

Part I: Expressions and Equations 

 

Evaluate each expression for x = -2, y = 18, and z = 9.  

1. x • z 2. y − x 3. y ÷ z 

 

4. 5. xy 6. z − x 

 

 

 

Solve each equation. 

 

7. x + 10 = −6 8. −8 = x − 2  9. x − (−5) = −2 

 

 

10. −2x = −20 11. 5w = − 7 12. 6z = −42 

 

 

13. x 065 = 1 14. x6 = 5

315. x3

2 = − 53

 

 

 

16. 3x − 8 = 4  17.  62b − 4 = 2 18.

x2 + 8

3 = 1  

 

 

 

19. 3w + 5

2 = 115  20. 4x + 2 = 5(x + 10) 21. −10 + y + 3 = 4y − 13  

 

 

 

22. 3(t + 7) + 2 = 6t − 2 + 2t 23. 5x − 1 − 4x = x + 7 24. 2(f + 3) + 4f = 6 + 6f 

 

 

 

25. 3x + 7 − 2x =4x + 10 26. P = 4s for s 27. a + b + c = 180 for b 

 

 

28. 3ab = c; for a 29. y = x + for z 

Part II: Graphing Lines and Writing Equations of Lines 

 

 

Find the x- and y-intercepts of each graph.  

1. 2.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Find the x- and y- intercepts of each graph and use that to graph the line. 

 

3. 3x + 9y = 9 4. 4x + 6y = −12 5. 2x − y = 4 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The table shows the average retail price of cherries from 1986 to 1991. Find the rate 

of change in cost for each time interval. 

 

Year  1986  1988  1989  1991 

Cost per lb ($)  1.27  1.63  1.15  2.26 

   

6. 1986 to 1988  

 

 

7. 1988 to 1989  

 

 

  

Find the slope of each line.  

 

8. 9. 

 

 

 

 

 

 

 

 

 

 

 

 

 

10. 11. The line containing the points:   

(5 , -2) and (7 , 6). 

 

 

 

 

 

 

 

12. The line containing the points:  13. The line containing the points:   

(-1 , 3) and (0 , 5) (2 , 7) and (4 , 7)  

 

 

 

 

 

Find the slope of the line described by each equation. 

 

14. −2x − 5y = 10 15. 4x + 2y = 8 16. −6x + 2y = 12 

 

 

 

 

Write the equation that describes each line in slope-intercept form ( ).x y = m + b  

 

17. slope = 7, y-intercept = −2 __________________________________ 

 

18. slope is 3, ( 4, 6) is on the line.  __________________________________ 

19. slope is (−2, 8) is on the line.  __________________________________ 

 

20. slope = −3; (1, 2) is on the line __________________________________ 

 

21. slope = (8, 3) is on the line __________________________________ 

 

 

Write the following equations in slope-intercept form ( ).x y = m + b  

 

22. 5x + y = 30 23. x − y = 7 24. −4x + 3y = 12 

 

 

 

 

 

Graph the line with the given slope that contains the given point. 

25. slope = (−3, −3) 26. slope = (−2, 4) 27. slope = 3; (−2, −2) 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Identify which two lines are parallel. Then graph the parallel lines. 

 

28. y = 4x + 2 

 

y = 2x + 1 

 

y = 2x − 3 

 

 

 

 

 

 

 

Identify which two lines are perpendicular. Then graph the perpendicular lines. 

 

29. y = − x + 2 

y = x + 1 

y = x − 3 

 

 

 

30. Write an equation in slope-intercept form for the line that passes through (6, 5) and is 

parallel to y = −x + 4. 

 

 

 

 

 

31. Write an equation in slope-intercept form for the line that passes through (8, −1) and 

is perpendicular to y = −4x − 7. 

 

 

 

 

 

Elements of Algebra I Summer Assignment Answers 

 

Part I 

 

1. -18 2. 20 3. 2 

 

4. -9 5. 36 6. 11 

 

7. −16 8. −6 9. −7 

 

10. 10 11. −35 12. −7 

13. 12 14. −10 15. −  

16. 4 17. 60 18.  

 

19. −1 20. −48 21. 2  

 

22. 5 23. no solution 24. all real numbers 

25. −1 26. s = 27. b = 180 − a – c  

28. a = 29. z = 3(y − x)  

Part II 

1. x-int: 3; y-int: −3 2. x-int: −1; y-int: −2  

 

3. 3x + 9y = 9 4. 4x + 6y = −12 5. 2x − y = 4 

 

 

 

 

6.  

 

7.  

 

8. − 9. −5 10.  

 

11. 12. 2 13. 0  

 

14. − 15. −2 16. 3 

 

17. y = 7x − 2 18. y = 3x − 6 19. y= x + 9 

 

20. y = –3x + 5 21. y = x + 1 22. y = –5x + 30 

23. y = x – 7 24. y = x + 4 

 

 

 

25. 26. 27.  

 

 

 

 

 

 

 

 

 

 

 

 

 

28. y = 2x + 1; y = 2x – 3 29. y = − x + 2; y = x + 1 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

30. y = –x + 11 31. y = x – 3