Intro to Algebra Intro to Algebra Arithmetic Questions: 1) Calculate the following expressions: a. 61 b. 61 c. 61 d. 61 e. 9 f. 1 g. 7 ... Simplify the following by taking out a Common

College Algebra 2

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Intro to Algebra

Arithmetic Questions:

1) Calculate the following expressions:

a. 6 1+ b. 6 1− c. 6 1− −

d. 6 1− + e. 5 13 9− − + f. 5 7 23 1+ − +

g. 5 8 12 17− − +


a. 2 5 b. ( )2 5− − c. 2 5−

d. ( )2 5 − e. 2 0− f. ( ) ( ) ( )2 3 4− − −

g. ( ) ( )2 3 4− −


a. 8: 4 b. 50 : 10− − c. 15:3−

d. ( ) ( )25 : 5− − e. ( ) ( )30 : 3− f. ( ) ( )0 : 5

g. 32

4−


a. 22 b. 42 c. 62

d. 42− e. ( )4

2− f. ( )42−

g. 32−


a. 64 b. 3 64 c. 5 32

d. 16− e. 4 64 f. 4 64−

g. 4 33 8− + − h. i.

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College Algebra 2




a. 169 b. 24− c. ( )3

3−

d. 3 27− e. 4 625 f. 4 16−

g. 5 32− h. i.


a. 2196 5 2 20 : 2+ − b. ( ) ( )4 3

2 : 2 10 2− − −

c. ( )23 4 5 4 7 2 900− − + − + d. ( ) ( )2 264 : 4 2 4 3 10− + − − +

e. ( )2

144 20 : 4 3 2− + − f. ( )3 4 3 4 2 10 6+ − + − + +

g. ( ) ( ) ( )4 3

3 : 9 5 2− − − −

Answer Key:

1) a. 7 b. 5 c. -7 d. -5

e. -9 f. -10 g. 2 2) a. 10 b. 10 c. -10 d. -10

e. 0 f. -24 g. 24 3) a. 2 b. 5 c. -5 d. 5

e. -10 f. 0 g. -8 4) a. 4 b. 16 c. 64 d. -16

e. 16 f. -16 g. -8 5) a. 8 b. 4 c. 2 d. No solution.

e. 2.828 f. No solution. g. -83 6) a. 13 b. -16 c. -27 d. -3

e. 5 f. No solution. g. -2 7) a. 24 b. 88 c. -79 d. -20

e. 19 f. -37 g. 31



College Algebra 2



Fractions Questions:

1) Write the following improper fractions as mixed numbers:

a. 3

2 b.

8

5 c.

13

2 d.

18

4

2) Write the following mixed numbers as improper fractions:

a. 3

28

b. 2

125

c. 1

62

d. 1

84

3) Which fraction is bigger?

a. 5 3

7 7 or b.

3 3

5 7 or c.

3 4

4 5 or

4) Convert the following decimals to fractions: a. 0.3 b. 0.02 c. 1.012 d. 2.75

5) Convert the following fractions to decimals:

a. 1

10 b.

1

100 c.

3

1000 d.

12

1000

6) Convert the following fractions to decimals:

a. 12

11000

b. 3

50 c.

7

20 d.

12

25

7) Convert the following percentages to fractions: a. 50% b. 25% c. 75% d. 15%

8) Convert the following fractions to percentages:

a. 4

10 b.

5

20



College Algebra 2




a. 1 3

4 4+ b.

5 7

2 4+ c.

3 1 5

2 4 8+ − d.

2 5 1

3 9 6+ −


3 5 7

4 6 5− +

1 111

8 12−

1 231 2

9 27− +

2 31 3

21 14− −


2 2

3 5

24

5

1 12 1

3 4

1 23 2

3 5


2 5

:3 6

2

: 45

3

6 :4

2 1

2 :13 5


5 1

:39 3

33

4

33

4

9 1 1 11 1 :

20 3 4 2 +


4 2

3 7

1 15 :

3 6

6 2 9

2 3 4

1 23 4

2 5


5

:36

3 5

3 :54 8

3 12

8 :2 20



College Algebra 2



Answer Key:

1) a. 1

12

b. 3

15

c. 1

62

d. 1

42

2) a. 19

8 b.

62

5 c.

13

2 d.

33

4

3) a. 5

7 b.

3

5 c.

4

5

4) a. 3

10 b.

1

50 c.

31

250 d.

32

4

5) a. 0.1 b. 0.01 c. 0.003 d. 0.012

6) a. 1.012 b. 0.06 c. 0.35 d. 0.48

7) a. 1

2 b.

1

4 c.

3

4 d.

3

20

8) a. 40% b. 25%

9) a. 1 b. 1

44

c. 1

18

d. 1

118

10) a. 19

160

b. 5

24 c.

72

27 d.

62

42−

11) a. 4

15 b.

31

5 c.

112

12 d. 8

12) a. 4

5 b.

1

10 c. 8 d.

22

9

13) a. 1

6 b.

27

64 c.

36

4 d.

13

10

14) a. 8

21 b. 32 c.

41

5 d.

215

5

15) a. 5

18 b.

2

3 c. 20



College Algebra 2



Algebraic Expressions Questions:

1) Evaluate the following algebraic expressions using substitution:

( )3, 5, 4 x y x y+ = = − 5 4 33 7, 1 a a a a− − + = −

2 2 1 116 9 , ,

2 3 m n m n− = = −

24 3, 1, 2, -4

a ba b c

c

− = − = =


( )

4

22, 2, 2

a ca a c

a

−− = = − 2 22 , 3, 5+ + = = −a ab b a b

( )2 23 3 , 5, 1x x b x b− + = = − 3 42 , 2, 1x xy y x y− − + = − = −

3) Combine [collect] like terms:

5 3 12x x x+ − 5 5a a+

7 11 9 2m m+ − − 2 21 2 3 2b b b+ − − −


2 24 3 3 5ab a b b a ab− + − 2 2 23 9 5x y xy y x xy xy− + + −

2 2 210 3 2 5m n mn m n m − − − 2 2 28 10 5 11a a a a a+ − − +

2 2 2 25 8 20 14a b ab a b ab− + −

5) Expand the brackets:

( )2 4x + ( )5x x + ( )7 3a − ( )2 2b x− −


( )2 3 2x x x+ − ( )2

6 33

x y−

( )5 7y− − ( )3 2 5x y+


( )3 2x x y− − ( )5 2 1x x+ −

( )( )4 5x x+ + ( )( )3 5x x+ −




College Algebra 2



( )( )3 1 3x x− − ( )( )2 5 2 5x x− +

( ) ( )( )4 3 2 2 1 3 5x x x− − − + ( )2a a b c− +

Answer Key:

1) a. 1 b.4 c. 3 d. 1

2

2) a. 644 b. 4 c. -71 d. 5

3) a. 4x− b. 22a c. 2 9m− + d. 2 2 2b b− − −

4) a. 2 23 3ab a b b a− − + b. 2 28 2x y xy xy+ − c. 2 215 3 10m n mn m− −

d. 24a a− e. 2 225 22a b ab−

5) a. 2 8x + b. 2 5x x+ c. 7 21a − d. 2 4b x− +

6) a. 3 23 2x x x+ − b. 4 2x y− c. 5 7y− + d. 15 10x y+

7) a. 26 3x xy− + b. 11 5x − c. 2 9 20x x+ + d. 2 2 15x x− + +

8) a. 23 12 9x x− + b. 24 25x − c. 26 5 3x x− + − d. 2 2a ab ac− +



College Algebra 2



Special Binomial Products Questions:

1) Expand the following Square Binomials:

( )2

2x + ( )2

3a + ( )2

1b + 2

1

4c

+

2) Expand the following Square Binomials:

( )2

2 5m + ( )2

5 4y t+ ( )2

2 11x y +

3) Expand each of the following as a Difference of Squares:

( )( )7 7x x− + ( )( )9 9x x− + ( )( )3 4 3 4x x− +

4) Simplify the following by taking out a Common Factor. 2 4x − 3 6x − 80 4x− 64 8a+

5) Simplify the following by taking out a Common Factor:

2 3x x+ 3x x− 5 22x x− 3 24 12x x+

6) Factorize the following as Square Binomials:

2 6 9x x+ + 29 12 4a a+ +

212 60 75x x+ + 2 16 64x x− +

7) Factorize the following as Special Binomial Products: [Difference of Squares or Square Binomials]

2 10 25a a− + 22 36 162x x− +

2 16x − 2 9a −

8) Simply the following by using Special Binomial Products: [Difference of Squares or Square Binomials]

281 x− 2100 49x − 349x x−

3x x− 2 9m −



College Algebra 2



Answer Key:

1) a. 2 4 4x x+ + b. 2 6 9a a+ + c. 2 2 1b b+ +

d. 2 1 1

2 16c c+ +

2) a. 24 20 25m m+ + b. 2 225 40 16y yt t+ + c. 4 2 222 121x y x y+ +

3) a. 2 49x − b. 281 x− c. 29 16x −

4) a. ( )2 2x − b. ( )3 2x − c. ( )4 20 x−

d. ( )8 8 a+

5) a. ( )3x x + b. ( )2 1x x − c. ( )2 3 2x x −

d. ( )24 3x x +

6) a. ( )2

3x + b. ( )2

3 2a + c. ( )2

3 2 5x +

d. ( )2

8x −

7) a. ( )2

5a − b. ( )2

2 9x − c. ( )( )3 3a a+ −

d. ( )( )4 4x x+ −

8) a. ( )( )9 9x x+ − b. ( )( )10 7 10 7x x+ − c. ( )( )7 7x x x+ −

d. ( )( )1 1x x x+ − e. ( )( )3 3m m+ −



College Algebra 2



Rational Expressions Questions:

1) In problems a-c, reduce the rational expressions to lowest terms:

2

2

4

2 5

x x

x x

+

−

2

1

2 3

x

x x

−

+ −

2

2

2 8

4

x x

x

− −

−

2) In problems a-d perform the indicated operation and reduce the answer to lowest terms:

2 2

2 2

2 2 15

6 3 4

x x x x

x x x x

+ − + −

− − + −

2 2

2 2

9 6 27

4 21 14 45

x x x

x x x x

− + −

+ − + +

2 2

2 2

4 3 6 27

4 5 14 45

x x x x

x x x x

− + + −

+ − + +

2

2

3

45

8 20

xx

x x

−+

+ −

Answer Key:

1) a. 4

2 5

x

x

+

− b.

1

3x + c.

4

2

x

x

−

−

2) a. 5

4

x

x

+

+ b.

2

1

x

x

+

− c. 1 d.

( )

( ) ( )

3 10

2 5

x

x x

+

+ +



College Algebra 2



Complex Numbers Questions:

1) Evaluate each of the following and write your answers in standard form:

( ) ( )4 3 2i i+ + − ( ) ( )2 3 4 5i i− + − − ( ) ( )3 2 5 6 2i i+ − +

( ) ( )4 3 5 2i i i i+ + − + ( ) ( )2 3 4 2 3i i i+ + −

2) Perform the following multiplications and write your answers in standard form:

( ) ( )4 3 2i i+ − ( ) ( )2 3 4 5i i− + − ( ) ( )4 2 2 3i i− − − +

( ) ( )2 4 1 3i i− − ( ) ( )4 2 4 2i i− +

3) Compute the following powers [exponents] and write your answer in standard form:

8i 15i ( )6

i− ( )9

i−

( )2

2 3i + ( )2

5 13i i−

4) Perform the following divisions and write your answers in standard form:

5

2 i+

2 3

5 2

i

i

+

−

6

4

i

i

−

−

4 2

4 2

i

i

+

−

( )

2

1 2

2 3

i

i

−

+

5) Write with i , ( )1i = − :

4− 9− 5−

6) Solve the following equations:

2 36 0x + = 2 2 5 0x x− + = 2 4 5 0t t− + =

24 12 25 0z z+ + = 24 16 25 0z z+ + = ( ) 21 2 1 0i z z i+ + + − =



College Algebra 2



Answer Key:

1) a. 7 i− b. 6 8i− + c. 24 7i− − d. 7 11i− −

e. 6 6i−

2) 1. 14 5i− b. 7 22i+ c. 14 8i− d. 10 10i− −

e. 20

3) a. 1 b. i− c.-1 d. i−

e. 5 12i+ f. 0

4) a. 2 i− b. 4 19

29 29i+ c.

1 3

4 2i+ d.

3 4

5 5i+

e. 19 22

169 169i− −

5) a. 2i b. 3i c. 5 i

6) a. 6i b. 1 2i c. 2 i d. 3

22

i−

e. 3

22

i− f. i , -1



Documents

Intro to Algebra Intro to Algebra Arithmetic Questions: 1) Calculate the following expressions: a. 61 b. 61 c. 61 d. 61 e. 9 f. 1 g. 7 ... Simplify the following by taking out a Common