bethlehem central high school algebra 2 review algebra 2

BethlehemCentralHighSchool Algebra2Review

1

Algebra 2 Review for Pre-Calculus

"To accomplish anything of significance comes with a cost. Are you willing to pay the price?"

Table of Contents

Section Topic Page #s 1. Inequalities 1 – 3 2. Exponents and Radicals 4 – 7 3. Algebraic Expressions 8 – 11 4. Rational Expressions 12 – 15 5. Solving Equations 16 – 19 6. Answers 20

Summer Reading Each student taking Regular Pre-Calculus or Pre-Calculus AB next fall at Bethlehem Central High School is responsible for reading this material and completing all of the practice problems at the end of each section. Each set of problems are to be completed on a separate sheet of paper (blank electronic sheet), showing all work. All student work should be submitted electronically via google classroom, by the first day of class. You will receive your schedule and assigned pre-calculus teacher by the end of August. If this is not possible bring the completed work to the first day of class. Although these concepts will not be directly assessed they lay the foundation for the topics we study in the first semester of the year.


2

10) Solving an Absolute Value Inequality

If X is an algebraic expression and c is a positive number,

a. The solutions of X c< are the numbers that satisfy c X c- < < .

b. The solutions of X c> are the numbers that satisfy or X c X c< - > . These rules are valid if < is replaced by £ and > is replaced by ³ . 11) Solve: 2 3 5x + ³

x c³ means or x c x c£ - ³ 2 3 5x + ³ means 2 3 5x + £ - or 2 3 5x + ³

We solve each of these inequalities separately.

2 3 5x + £ - or 2 3 5x + ³

2 8x £ - or 2 2x ³

4x £ - or 1x ³

The solution set is ,

that is, all in .


3

Problem Set #1:

4) 4 3 2 126 12x x- -

+ ³

5) 2 6 8x - < 6) 3 8 7x - >

7) 2 6 23y +

<

8) 33 94x- >

9) 3 1 2 8x- + ³ 10) 2 4 4x- - ³ -


4


5


6

4) Rationalizing a Denominator Containing Two Terms

Example: Rationalize the denominator: 75 3+

.

Solution: If we multiply the numerator and denominator by 5 3- , the denominator will not

contain a radical. (Remember ( )( ) ( ) ( )2 2a b a b a b a b+ - = - = - ) Therefore, we

multiply by 1, choosing 5 35 3--

for 1.

75 3+

= 75 3+

( )( )

( )2

2

7 5 3 7 5 35 325 35 3 5 3

- --× = =

-- -

= ( )7 5 3 35 7 3 or

22 22

- -

In either form of the answer, there is no radical in the denominator.


7

Problem Set #2:

11) 75 2-

12) 117 3-


8


9


10


11

Problem Set #3:

For problems 1 – 3, perform the indicated operations. For problems 4 – 15 factor the polynomial. Simplify completely whenever possible.

11) 3 64x +

12) 327 1x -

13) 42 162x -

14) 26 17 12x x- +

15) Challenge: 2 212 36 49x x y- + -


12


13


14

Problem Set #4: Simplify or perform the indicated operation.


15

9) 2 22 24 7 6x x

x x x x-

- - - + 10)

2

2

4 6 3 53 2 1 2

x x xx x x x

+ -- +

+ + + +

11) 2 2

2 2 2

12 5 6 330 2 3 7 6

x x x x xx x x x x x+ - + + +

× ÷+ - - - + +

12) 2

3 42 274

x x

x

-- +

-

13) 2

11

1 12 3 3

x

x x x

+

+- - -


16

Check to verify the solutions!


17


18

D) Solving an Equation Involving Absolute Value

Solve: 3 2 3 8 25x- - =

3 2 3 8 25x- - = We need to isolate 2 3x-

3 2 3 33x- = Add 8 to both sides.

2 3 11x- = Divide both sides by 3.

2 3 11x - = or 2 3 11x - = - Rewrite the equation without absolute value bars.

2 14x = 2 8x = - Add 3 to both sides of each equation.

7x = 4x = - Divide both sides of each equation by 2.

Check to verify the solutions!

The solution set is {-4, 7}.

Problem Set #5:

8) 3 5 13 2 6 2x x x= +

+ + -


19

9) 2

6 5 203 2 6x x x x

-- =

+ - + -

10) 2 2 1 5 9x- - =

11) 3 3 13 7 8x- - + = -

12) 22 3 4x x= -


20

6. Answers:

Problem Set #1 Problem Set #2

Problem Set #3 Problem Set #4 Problem Set #5

1. 112,æ ö¥ç ÷

è ø

1. 212x- 1. 26 13 12x x- - 1. 26xz y- 1. 127

x = -

2. [ ]1 7, 2. 6

15

27ab

- 2. 4 3 22 9 3 14 6x x x x- - + + -

2. 2

55 25x

x x+

+ +

2. All real #s

3. ( ]1 2,- 3. 5

12y

3. 3 2 2 39 27 27x x y xy y+ + +

3. 6 73 1 3 1( )( )

xx x

-+ +

3. 5 34 2,x = -

4. 196,é ö- ¥÷êë ø

4. 3 2

3x y

4. – 15. Answers will be provided when classes begin.

4. 2 2a bb a+-

4. 13

x = -

5. ( )1 7,- 5. 1 5. 1

( )x x h-+

5. 74

x = ±

6. ( )1 or 53, ,æ ö-¥ ¥ç ÷

è ø 6.

22ab

6. 2

2

13 12( )xx--

6. 4 31x = - ±

7. ( )6 0,- 7. 2

62xyy

7. 2

2

2 41

x xx x- ++ +

7. 3 2 3x = ±

8. ( ) ( )8 or 16, ,-¥ - ¥ 8.

3 63

xy y

8. 2

2

3 212 13

x xx x- - -+ -

8. 8x = -

9. ( ] [ )1 or 3, ,-¥ - ¥ 9. 2 2 236 2xz x y

9. 5

1 4 6( )( )( )x

x x x-

- + -

9. 7x =

10. [ ]2 6, 10. 32 93x

x-

10. 1

2xx-+

10. 3 4,x = -

11. 7 5 14+ 11. 4 2

5( )( )x x

x+ +

- 11. 8 6

3,x =

12. 11 7 11 3

4+

12. 14

7x- +

12. 2 102

x - ±=

13. 3

2xx-+

bethlehem central high school algebra 2 review algebra 2

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