Damascus High School
Honors Algebra II
Summer Review Packet
THIS PACKET IS DUE THE FIRST DAY OF SCHOOL
This assignment should serve as a review of the Algebra skills necessary for success in Honors Algebra 2. Our hope is that this review will keep your mind mathematically active during the summer, identify weaknesses in Algebra, if they exist, and prepare you for the fun and challenging year ahead.
All the work should be completed and ready to turn in on the first day of school. You might be assessed on the content of this material during the first week of school.
Enjoy your summer! We look forward to meeting you and working with you when you return in the fall.
Be sure to show all work for full credit. Circle your final answer for each question.
A. Simplify/Evaluate – remember order of operation
1. -3 – – 12
2. (-4)2 -
3. - 42 + 82
4. 2x3 – 3x2 + 5x when x = -3
5. 3ab2 + 5a2b -1 when a = 2 and b = -2
6.
7.
8.
9.
10.
11.
12.
B. Simplify using exact answers – no decimals
1.
2.
3.
4.
5.
6.
7.
C. Simplify using rules of exponents
1.
2.
3.
4.
5.
6.
7. (x3)2
8. (-3y2)3
9. (2a3b)4
10. (3x2)3(-2x5)3
11. 3(x2)3(-2x5)3
12. (2x)2(-3x2)4
D. Simplify by adding, subtracting, multiplying or dividing
1. (3x + 2) + (-4x + 3)
2. (-6x + 2) + (x2 + x – 3)
3. (6x + 1) – (-7x + 2)
12. (x2 – 5x + 4) – (8x – 9)
13. -3x(x – 1)
4. (1.2x3 + 4.5x2 – 3.8x) + (-3.4 x3 - 4.7x2 + 23)
5. (0.5x4 - 0.6x2 + 0.7) – (2.3x4 + 1.8x – 3.9)
6. -4x(2x3 - 6x2 – 5x + 1)
7. (x + 5)(x – 2)
8. (x3 + x2 + x + 1)(x – 1)
9. (3 – 2x)2
10. (x2 – 5)2
11. (x + 5)3
14. (3x + 2)(4x2 + 5)
15.
16.
17.
18.
19.
E. Solve the following equations
1.
2.
3.
4.
F. Use the given matrices to solve the problems
1. State the order of
2. State the order of
3. C - A
4. A + B
5. 2C – 3A
6. A + C
7. 2B
G. Solve each equation
1. 3(r – 6) + 2 = 4(r + 2) – 21
2. 5(t + 3) + 9 = 3(t – 2) + 6
3.
4.
5. 0.7(3x + 6) = 1.1 – (x + 2)
6. a + (a – 3) = (a + 2) – (a + 1)
H. Write the linear equation in slope-intercept form
1. 4x – 6y = 12
2. 8x + 2y = 6
3. through (0, -1), m = -1
4. through (-2, 3), m = 4/3
5. through (3, -1), m = 0
6. vertical, through (5, 4)
7. through (2, 3) & (7, -2)
8. through (3, 4) & (-2, 4)
9. parallel to y = 2x + 1 through (1, 5)
10. perpendicular to y = 3x – 2 through (12, -2)
I. Sketch the graph & state the domain and range
1. y = ½ x – 4
2. x = 3
3. y = -1
4. x – 2y = -4
5. 2x + 3y = 12
6. y = (x – 2)2 + 1
7. y = x2 + 6x + 1
8. y = |x|
9. y = |x + 2|
10. y = |x| + 3
11.
12.
13.
14. x>-2
J. Solve the system of equations (use graphing, substitution and/or elimination)
1. x - y = 6
x + y = -2
2. y – 2x = -6
2y – x = 5
3. x – y = 5
x + 2y = 7
4. x + 2y = 10
3x + 4y = 8
5. 3x – y = 9
2x + y = 6
6. 3x – 4y = 16
5x + 6y = 14
7. x + y = 3
2x + 2y = 6
8. x – y = 5
x – y = 6
K. Factor the polynomial completely.
1. 8x4 – 24x2
2. 17x6y3 + 34x3y2 + 51xy
3. 16x6y4 - 32x5y3 - 48xy2
4. x2 + 5x + 6
5. x2 + 11x + 28
6. x2 - 8x + 15
7. x2 – 72 + 6x
8. x4 + 2x2 - 35
9. x2 + 20x + 100
10. x2 - 100
11. 4x2 - 81
12. x4 – y4
13. x4 – 16
14. x2 – 2xy – 3y2
15. 2x2 – 7x - 4
16. 3x2 – 4x - 15
17. 9x2 + 6x - 8
18. 9x2 + 18x - 16
19. 18x2 – 6xy – 24y2
20. 15x3 – 5x2 – 20x
K. Solve the equation. Use any method that will work: square roots, factoring, quadratic
Formula . Be sure to check your solutions.
1. x2 - 4x = 21
2. x2 = 6x - 9
3. 3x2 - 7x + 4 = 0
4. x2 - 9 = 0
5. x2 - 2x - 2 = 0
6. x2 - 4x – 7 = 0
7. 3x2 – 5 = 2
8. x3 - 4x2 + 4x = 0
9. x4 - 16 = 0