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Honors Algebra 2
Summer Packet Answer Key
A.
Simplify/Evaluate – remember order of operation
1. -18
8. 7
11
30
2. 4
9.
3. 48
2
5
10.
4. -96
5
6
11.
5. -17
5
36
12.
Simplify using exact answers – no decimals
15
6
1. 4 2
2.
3.
4. 4 y 2 3xy
5
2
6.
9
2
7.
17
30
7
4
B.
5.
2
Simplify using rules of exponents
1
1
1.
2. x9
3. 6  411 a11 or 25,165,824a11
or
5
7776
6
6. 1
7. x6
8. -27y6
6. 7 6
7. 4ab a
4. 27
5.
C.
10. -216x21
11. -24x21
12. 324x10
D.
Simplify by adding, subtracting, multiplying or dividing
1. -x + 5
2. x2 - 5x – 1
3
2
4. 2.2x – 0.2x – 3.8x + 23
5. -1.8x4 - 0.6x2 – 1.8x + 4.6
7. x2 + 3x – 10
8. x4 – 1
4
2
10. x – 10x + 25
11. x3 + 15x2 + 75x + 125
13. -3x2 + 3x
14. 12x3 + 8x2 + 15x + 10
16. –u4 -2u + 1
19. -3t4 – 4t3 + 1
17. 50x4 – 7x3 + x
E.
Solve the following equations
1. a = 32
2. x = 9
3. No solution
 2
1 8  1 


8 0  3
7.
3. 13x – 1
6. -8x4 +24x3 + 20x2 – 4x
9. 4x2 -12x + 9
12. x2 – 13x + 13
12 x 5  2 x 3  5 x 2  8
15.
4
18. 5t2 + 3t - 6
4. x = 12
F.
Use the given matrices to solve the problems
1. 2 x 3
2. 3 x 2
3.  3  2 1
4. Not Possible
6.
9. 16a12b4
4  3
5.
 8  9 3 


 1 10  6
10  6


 0 4
 2 8 


G.
Solve each equation
1. r = -3
2. t = -12
3. x = 6
4. x = 7
5. x = 1.65
6. a = 2
1
x5
H.
Write the linear equation in slope-intercept form
2
1. y = x – 2
2. y = -4x + 3
3. y = -x – 1
3
6. x = 5
I.
7. y = -x + 5
8. y = 4
4. y =
4
2
x+ 5
3
3
5. y = -1
1
10. y =  x + 2
3
9. y = 2x + 3
Sketch the graph & state the domain and range
1. D: All Reals R: All Reals
2. D: {3} R: All Reals
4. D: All Reals R: All Reals
5. D: All Reals R: All Reals
6. D: All Reals R: y  1
7. D: All Reals R: y  8
8. D: All Reals R: y  0
9. D: All Reals R: y  0
10. D: All Reals R: y  3
11.
13.
3. D: All Reals R: {-1}
12.
14.
J.
Solve the system of equations (use graphing, substitution and/or elimination)
1. (2, -4) 2. (17/3, 16/3) 3. (17/3, 2/3) 4. (-12, 11) 5. (3, 0) 6.(4, -1) 7. All Reals 8. No Solution
K.
Factor the polynomial completely.
2 2
1. 8x (x – 3)
2. 17xy(x5y2 + 2x2y + 3)
4. (x + 3)(x + 2)
5. (x + 7)(x + 4)
7. (x + 12)(x – 6)
8. (x2 – 5)(x2 + 7)
10. (x + 10)(x – 10)
13. (x2 + 4)(x + 2)(x – 2)
16. (3x + 5)(x – 3)
19. 6(3x – 4y)(x + y)
11. (2x + 9)(2x – 9)
14. (x – 3y)(x + y)
17. (3x – 2)(3x + 4)
20. 5x(3x – 4)(x + 1)
3. 16xy2(x5y2 - 2x4y – 3)
6. (x – 3)(x – 5)
9. (x + 10)(x + 10)
or (x + 10)2
12. (x2 + y2)(x + y)(x – y)
15. (2x + 1)(x – 4)
18. (3x + 8)(3x – 2)
K.
Solve the equation. Use any method that will work: square roots, factoring, quadratic
Formula. Be sure to check your solutions.
1. x = 7, -3
2. x = 3
3. x = 4/3, 1
4. x = 3, -3
5. x = 1 3
6. x = 2  11
7. x = 
21
3
8. x = 0, 2
9. x =  2i,  2