South Brunswick Schools · 2019. 6. 21. · South Brunswick Schools Summer Packet For Rising...
Transcript of South Brunswick Schools · 2019. 6. 21. · South Brunswick Schools Summer Packet For Rising...
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