Algebra 2 Review Packet Name
Trigonometry
Algebra 2 Review
On the following pages you will find a review of the Algebra 2 concepts needed to successfully complete
Trigonometry. Concepts such as fractions, proportions, factoring, solving polynomials, simplifying square
roots, complex numbers, the quadratic formula, rational exponents, and rational expressions are contained in
this packet. You are expected to have full function of these concepts, because they will not be reviewed
throughout the year.
The completed packet will be turned in the first day of school. On the second day of school a test will be
administered to assess basic Algebra 2 concepts. A minimum of 70% is required to remain in Trigonometry.
Students who do not attain a 70% will be removed from the roster and rescheduled.
Although all of you have taken Algebra 2, not all of you have learned or remember the concepts in this packet.
I recommend using your Algebra 2 notebook as a resource to complete the packet. If you do not have your
notebook, then refer to Khan Academy (www.khanacademy.org ) for video instruction.
The packet should take about 3 hours to complete. I recommend waiting until August to complete the packet, in
order to ensure the concepts are easily recalled for the test.
Mrs. Amoriello
Algebra 2 Review Packet Name
Fractions No Calculator! Show all your work for each problem.
Add or Subtract.
1. 12
5
8
3 2.
12
1
4
7 3.
2
1
4
3 4.
2
1
8
7
5. 3
1
5
2 6.
6
5
9
8 7.
14
2
7
6 8.
6
1
8
3
Multiply or Divide.
9. 5
4
3
2 10.
15
4
8
5 11.
6
5
4
3 12.
6
58
\
13. 2
1
12
5 14.
10
3
8
7 15.
12
7
16
21 16.
16
15
24
25
Complex Fractions: take the reciprocal of the denominator and multiply. Ex: 10
3
5
2
4
3
2
54
3
17. 3
9
5
18. 7
3
6
19.
15
146
7
20.
10
97
6
21.
23
13
1
22.
9
7
81
7
23.
5
16
36 24.
8
19
32
1
Algebra 2 Review Packet Name
Proportions
Ex: Solve the proportion. x
10
6
5
1065 x Cross Multiply.
605 x
12x
Solve the proportion. Write the answer in simplified fraction form.
1. x
4
2
6 2.
3
84
x 3.
10
7
5
x
4. x5
2
5
6 5.
6
6
8
9
x 6.
3
4
10
2
x
7. 3
4
2
10
x 8.
1
8
3
2
x 9.
9
7
8
xx
10. x
x 10
4
9 11.
4
7
5
9
x
x 12.
5
4
9
6
xx
2
Algebra 2 Review Packet Name
Factoring Special Products
Greatest Common Factor
Factor out the greatest common factor found in each term.
Ex: 93 x Ex: xx 164 2 Ex: 1068 2 xx
333 x 444 xxx 523242 2 xx
33 x 44 xx 5342 2 xx
1. 4035 x 2. 144 x 3. 69 2 x
4. xx 52 5. xx 1812 2 6. 24 246 xx
7. 4164 2 xx 8. 234 24183 xxx 9. 15305 2 xx
Difference of Two Squares
bababa 22 Ex: 44162 xxx 5353259 2 xxx
10. 42 x 11. 642 x 12. 812 x
13. 1625 2 x 14. 19 2 x 15. 3649 2 x
Factor the Greatest Common Factor then factor the expression. Ex: 33292182 22 xxxx
16. 44 2 x 17. 546 2 x 18. 246 2 x
19. 322 2 x 20. 728 2 x 21. 5424 2 x
3
Algebra 2 Review Packet Name
Factoring Trinomials To factor a quadratic expression means to write it as the product of two linear expressions.
Standard Form: cbxax 2
1. Factoring when b is positive and c is Positive
Ex: Factor 862 xx . 862 xx
)4)(2( xx Check: by multiplying.
)4)(2( xx = 8242 xxx FOIL
= 862 xx
2. Factoring when b is Negative and c is Positive
Ex: 652 xx . 652 xx
)3)(2( xx Check: )3)(2( xx = 6232 xxx
= 652 xx
3. Factoring when b is negative and c is Negative
Ex: 1032 xx . 1032 xx )5)(2( xx
4. Factoring when b is Positive and c is Negative
Ex: Factor 1872 xx . 1872 xx )9)(2( xx
Factor the trinomial.
1. 1272 xx 2. 16102 xx 3. 2452 xx
4. 202 xx 5. 982 xx 6. 21102 xx
7. 36132 xx 8. 1832 xx 9. 4062 xx
10. 3072 xx 11. 32122 xx 12. 4472 xx
13. 1452 xx 14. 1892 xx 15. 3692 xx
4
Algebra 2 Review Packet Name
Factoring Trinomials a>1
cbxax 2 Need to find the factors of a and the factors of c.
factors of a (m and n) -first positions in each binomial(always positive)
factors of c ( p and q) -second position in each binomial
qnxpmx
Ex: 5112 2 xx factors of a 1 and 2
factors of c 1 and 5
)12)(5( xx -Arrange both sets of factors so that the middle term equals 11x.
-This process can take a couple of attempts before you find the right combination.
Check by using FOIL: 51125102)12)(5( 22 xxxxxxx
Ex: 823 2 xx factors of a 1 and 3
factors of c 1 and 8 and 2 and 4
432 xx
Check by using FOIL: 8238643432 22 xxxxxxx
Factor.
1. 5163 2 xx 2. 295 2 xx 3. 673 2 xx
4. 328 2 xx 5. 5112 2 xx 6. 743 2 xx
7. 992 2 xx 8. 372 2 xx 9. 143 2 xx
10. 8103 2 xx 11. 384 2 xx 12. 6117 2 xx
13. 968 2 xx 14. 4146 2 xx 15. 15520 2 xx
5
Algebra 2 Review Packet Name
Solving Polynomial Equations by Factoring
Zero Product Property
Let A and B be real numbers or expressions. If 00,0 BorAthenBA .
Ex: Solve 024102 xx 064 xx Factor.
0604 xx Zero product property.
64 xx Solve for x.
Solve the equations by factoring.
1. 01072 xx 2. 01452 xx 3. 0962 xx
4. 01492 xx 5. 0442 xx 6. 062 xx
7. 40132 xx 8. 1032 xx 9. 2762 xx
10. 010173 2 xx 11. 05136 2 xx 12. 09188 2 xx
13. 372 2 xx 14. 01073 2 xx 15. 72512 2 xx
Factor out the GCF and solve.
16. 0243543 2 xx 17. 060288 2 xx 18. 02482 2 xx
6
Algebra 2 Review Packet Name
Square Roots
Square Root of a Number If ab 2 , then b is a square root of a. bba 2
Ex: 932 therefore 39
Product Property of Radicals baab where 0a and 0b .
Ex: 52545420
Simplify the expression.
1. 16 2. 64 3. 49 4. 121
5. 12 6. 75 7. 18 8. 200
9. 32 10. 192 11. 54 12. 84
13. 72 14. 132 15. 288 16. 117
Quotient Property of Radicals b
a
b
a where 0a and 0b
Ex: 3
2
9
4
9
4
Rationalizing the Denominator No radicals are in the denominator of a fraction.
2422
Ex: Simplify2
1.
2
1
2
1
2
1 no radicals in denominator.
2
2
2
2
2
1 rationalize the denominator.
Simplify the expression.
17. 25
1 18.
64
9 19.
100
49 20.
32
18
21. 81
11 22.
4
5 23.
7
1 24.
3
2
25. 5
8 26.
14
18 27.
5
12 28.
8
27
7
Algebra 2 Review Packet Name
Solving Quadratic Equations by finding square roots: 1. Isolate x
2 on one side of the equation.
2. Find the square root of each side.
Ex: Solve the equation. 42 x 82 x 182 2 x
42 x 82 x 92 x
2x 8ix 9x
22ix 3x
1. 12 x 2. 162 x 3. 72 x 4. 122 x
5. 812 x 6. 5005 2 x 7. 63 2 x 8. 324 2 x
9. 2203 2 x 10. 2752 2 x 11. 9307 2 x 12. 41132 2 x
Ex: Solve 36162x . 1. Isolate the squared binomial 61
2x
2. Take the square root of both sides. 612
x
3. Add/Subtract value to both sides. 61 x
61x
4. Separate into two solutions, one + and one – . 6161 xorx
13. 2522x 14. 5015
2x 15. 832
2x 16. 2824
2x
Use a calculator to solve the equation. (Round to the nearest hundredth)
17. 5734 2 x 18. 34226 2 x 19. 10142 2 x 20. 612432
x
8
Algebra 2 Review Packet Name
Complex Number System
The Square Root of a Negative Numbers
Imaginary unit: 1i and 12 i :
If r is a positive real number, then rir .
Ex: 55 i Ex: i24 Ex: 228 i
Ex: Solve 26103 2 x . 363 2 x
122 x
12x
32ix
Simplify.
1. 64 2. 25 3. 100 4. 144
5. 27 6. 75 7. 72 8. 45
Solve.
9. 492 x 10. 813 2 x 11. 1372 x
12. 4192 2 x 13. 1442 x 14. 1332 2 x
15. 1622
x 16. 120562 x
9
Algebra 2 Review Packet Name
The Quadratic Formula
The Quadratic Formula: The solutions of the quadratic equation 02 cbxax are:
a
acbbx
2
42
Use the quadratic formula to solve the equation. Place the equation in standard form.
1. 0342 xx 2. 012 xx 3. 01452 xx
4. 0532 2 xx 5. 0135 2 xx 6. 0386 2 xx
7. 182 xx 8. xx 619 2 9. 263 2 xx
10
Algebra 2 Review Packet Name
Real nth Roots: Odd index : one real solution
Ex: 51253 Ex: 51253
Even index : two real solutions
Ex: 3814 Ex: solutionrealno4 81
Rational Exponents: mnmnnm aaa 1
Ex: 2739993332123
Ex: 4232323222
525152
Evaluate the expression.
1. 121 2. 3 64 3. 4 16 4. 5 243 5. 3 216
6. 4 625 7. 5 1 8. 196 9. 3 343 10. 169
11. 316 12. 23 27 13. 34 256 14. 25 1024 15. 525
Evaluate the expression.
16. 2149 17. 5132 18. 21144 19. 41256 20. 31125
21. 254 22. 348 23. 4381 24. 32512 25. 56
1
11
Algebra 2 Review Packet Name
Rational expression: a fraction whose numerator, denominator, or both are nonzero polynomials.
Ex: 4
3
x
9
22 x
x
1
132
x
x
Simplifying Fractions: b
a
cb
ca
bc
ac
Ex:
226
6
12
6 2 x
x
xx
x
x
-Factor the numerator and denominator completely.
-cancel out like factors.
Ex: Simplify xx
xx
x
xx
32
)3(2
6
622
2
Ex: Simplify: 12
22
2
42
2
xx
xx
xx
x
Note: When you simplify rational expressions, you can only cancel out factors, not terms.
Incorrect: Ex: 66
2
2
x
x NO!!
1. x8
20 2.
4
7
63
21
x
x 3.
x
xx
36
642 3 4.
2
22
x
xx
5. xx
x
2410
1252
6.
102
252
x
x 7.
158
52
xx
x 8.
6
6112 2
x
xx
9. 152
202
2
xx
xx 10.
4
1492
23
x
xxx 11.
xxx
xx
65 23
3
12.
xxx
xxx
3662
4828423
3
13. 1
432
2
x
xx 14.
823
18112
2
xx
xx 15.
1892
151962
2
xx
xx
12
xx
xx
32
32
x
x
3
3
1
2
x
x
Algebra 2 Review Packet Name
Answer Key
Page 1 Fractions
Odd Answers:
1. 24
19 3.
4
5 5.
15
1 7. 1 9.
15
8 11.
8
5 13.
6
5 15.
4
9 17.
3
5 19.
4
5 21. 2
23. 45
Page 2 Proportions
Odd Answers:
1. 3
4x 3.
2
7x 5.
4
3x 7.
2
11x 9. 56x 11.
3
71x 12. 3x
Page 3 Factoring Special Products
Odd Answers:
1. 875 x 3. 233 2 x 5. 326 xx 7. 144 2 xx 9. 365 2 xx 11. 88 xx
13. 4545 xx 15. 6767 xx 17. 336 xx 19. 442 xx 21. 32326 xx
Page 4 Factoring Trinomials
Odd Answers:
1. 43 xx 3. 83 xx 5. 19 xx 7. 94 xx 9. 104 xx 11. 84 xx
13. 27 xx 15. 123 xx
Page 5 Factoring Trinomials a > 1
Odd Answers:
1. 513 xx 3. 323 xx 5. 512 xx 7. 332 xx 9. 113 xx
11. 3212 xx 13. 3234 xx 15. 1345 xx
Page 6 Solving Polynomial Equations by Factoring
1. 5,2x 2. 7,2 x 3. rootdoublex 3 4. 7,2x 5. ..2 rdx 6. 2,3x
7. 5,8 x 8. 5,2x 9. 3,9x 10. 5,3
2x 11.
3
5,
2
1x 12.
4
3,
2
3x
13. 3,2
1x 14. 1,
3
10x 15.
4
1,
3
7x 16. ..9 rdx 17. 5,
2
3x 18. 6,2 x
Page 7 Square Roots
Odd Answers:
1. 4 3. 7 5. 32 7. 23 9. 24 11. 63 13. 26 15. 212
17. 5
1 18.
8
3 19.
10
7 20.
4
3 21.
9
11 22.
2
5 23.
7
7 24.
3
6 25.
5
102 26.
7
73
27. 5
152 28.
4
63
Algebra 2 Review Packet Name
Page 8 Solving Quadratic Equations by Finding Square Roots
1. 1x 2. 4x 3. 7x 4. 32x 5. 9x 6. 10x 7. 2x
8. 22x 9. 6x 10. 4x 11. 3x 12. 14x 13. 7,3x
14. 101x 15. 5,1x 16. 72x 17. 87.3x 18. 41.1x 19. 46.3x
20. 55.1,45.6 x
Page 9 Complex Number System
Odd Answers:
1. i8 3. i10 5. 33i 7. 26i
9. ix 7 10. 33ix 11. 52ix 12. ix 5 13. 23ix 14. 22ix
15. ix 42 16. 525 ix
Page 10 The Quadratic Formula
1. 3,1x 2. 2
51x 3. 7,2x 4.
4
313 ix
5.
10
293x 6.
6
2
3
2 ix
7. 154x 8. 3
1x 9.
3
31x
Page 11 Rational Exponents
Odd Answers:
1. 11 3. 2 5. –6 7. –1 9. 7 11. 64 13. 64 15. 3,125 17. 2 19. 4 21. 32
23. 27 25. 1
Page 12 Rational Expressions
1. x2
5 2.
3
3x 3.
6
7 2x 4. x 5.
x2
1 6.
2
5x 7.
3
1
x 8. 12 x 9.
3
4
x
x
10.
2
7
x
xx 11.
6
1
x
xx 12.
6
42
x
x 13.
1
43
x
x 14.
43
9
x
x 15.
6
53
x
x