DO NOT WRITE ON THIS PACKET Algebra 2 Unit 1 (Chapter 1) (CALCULATORS MAY NOT BE USED)

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DO NOT WRITE ON THIS PACKET Algebra 2 Unit 1 (Chapter 1)

(CALCULATORS MAY NOT BE USED)

1. Evaluate and simplify algebraic expressions.

Worksheet 1 1 – 24

2. Solve linear equations. Rewrite a formula solving for a specified variable.

Worksheet 2 1 – 33

3. Solve linear inequalities. Solve compound inequalities involving ‘and’ ‘or’

Worksheet 3 1 – 30

4. Solve absolute value equations.

Worksheet 4 1 – 22

5. Solve absolute value inequalities.

Worksheet 5 1 – 25 Review

Review Worksheet 1 1 – 37 Review Worksheet 2 1 – 24 UNIT 1 TEST

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Worksheet 1 Simplify:

1. − 5 2 + 1 2. 6 + 10 • 8 ÷ 4 – 2

3. – 10 4 + (– 3) 2 4. 6 − 2(12 − 15)

5. 10 (n2 + n) – 6 (n2 – 2) 6.

[ ]

2

2

18 ( 2) 9 (3 5) 2

− + + −

÷

7. 2

(6 9 27)

3 rs− − (8 − 3s) 8. 7 − 4(3k + 6)

9.

36 2 24 6

6 cc

10.

9 2 27 3 x +

11. 4 • 2 3 – 4 + 2 12. 36 12

3

x + − 24 40 8 x −

13. 12 54 2 2

x y

− + −

− 5 10 5

x + 14. 2 1

( 6 ) ( 20 )

5 y x  3

− −  

  Evaluate:

15. x2 + 7x when x = –9 16. n3 – 4n + 10 when n = –3

17. 2x4 – 4x3 when x = –1 18.

4

2

3( ) 2( )

y x y

x y

− −

+ if x = – 6, y = – 2 19. a + 10 ÷ c if a = -5, c = 1

2 20. c 2 + 3c if c = 0.3 21. 10

c − 4 + 1 if c = 1

5 22. 10 14

2 x

− +

− 4 8 4

x + if x = 6

23. The formula for the area of a trapezoid is A = ( 1 2) 2

h b +b . Find the area of a trapezoid given h = 6, b1 = 22, b2 = 17

24. Multiple Choice: What is the value of 2x2 – 6x + 15 when x = – 2 ? a. 11 b. 19 c. 35 d. 43

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Solve the following equations. If there is no solution, write no solution. If the equation is always true, write all real numbers .

1. 4 – 2(7 – x) = 8 – 4x 2. 3(1 − x) + 5 = 3(1 + x) − 7

3. 5

7 22

3x

− = 4. 12(x + 3) = 2(x + 5) – 3x

5. 5x +7 − 2x = 3x + 8 6. 1 1

2x + 3x = 10

7. 2 1 3 1

5x+6 = 10x+3 8. 1

3 (x − 2) = x + 46.

9. 6x + 12 = 3(x + 4) + 3x 10. 0.6 x + 0.5 = 2.9 11. 3.8x + 3.2 = 2.3(x + 4)

Solve the equation for y:

12. 3x + y = 26 13. 4y + 8x = 24

14. xy – 3x = 40 15. y – 2xy = 15

16. 9y + 6xy = 30 17. 4x + 7y + 5xy = 2

18. xy = x + y

Solve the equation for the specified variable:

19. 2x − 5y = 10 for x 20. y = mx + b for x 21. P = 2L + 2W for W 22. A = 2 πrw for w 23. K = 3(A + B) for B 24. S = π r (h + k) for h 25. 6xy + 7x = 4 + 5y for x 26. 3w + 2m – 5mw = 1 for w

27. D = 3 71

4x − 4 for x 28. 2K = 2 3

3y − 4 for y

In each formula, substitute the given values of the variables. Then find the value of the remaining variable.

29. Volume of a cylinder: V = πr h2 if V = 128, r = 8, find h 30. Volume of a cone: V = 1 2

r h if V = 48, r = 4, find h

31. Amount at simple interest: A = P(1 + r t) if A = 168, P = 150, r = 0.08 find t 32. Distance an object falls: d =

2

2 v

g if d = 40, v = 20, find g 33. Multiple Choice: Solve for K: D = 5(K – M)

a.

5 D M+

b. 5D + M c.

5

D + M d. D + 5M

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Worksheet 3 Solve the inequality and then graph the solution.

1. 4x – 8 > – 4 2. 13 > 4 + 3

2x

3. 15 – 3x > 3 4. 18 + 2x < 9x + 4

5. – 5 – (3 – 2x) > 6x – 2(x – 3) 6. 3

5 x – 2 3x > 4

7. 1

2x + 4 < 2 3 x + 1

2 8. 6.5 x + 1.5 < 4.3 x – 0.7

9. 1.7 (x + 5) < 2.1 x + 9.7 10. – 5 < x + 1 < 4

11. – 3 < 4 – x < 3 12. 2 < 3x – 1 < 6

13. – 4 < 2 + 4x < 0 14. – 20 <

2

x + 1 < – 10

15. x + 1 < – 3 or x – 2 > 0 16. 11 > 17 – 3

4 x > 5

17. x + 1 > – 3 and x – 3 < 2 18.

3

x + 1 < 9 and 4x – 2 > 10

19. x – 4 < – 6 or x + 2 > 5 20. 2x – 3 < – 4 or 3x + 1 > 4 21. 2 – 5x < – 8 or – x – 4 >1 22. 0.3 x – 0.5 < – 1.7 or 0.4 x > 2.4

23. 2

3 x

− – 7 < – 13 and 5x – 10 < 4x 24. 10 < 4 – 2x < 14

In problems 25 – 28 select the correct multiple choice.

25. Multiple Choice: Which is the graph of 7 < – x

a. • b. • c. • d. • 7 7 – 7 – 7

26. Which is equivalent to 0 > x > – 2 a. – 2 > x > 0

b. – 2 < x < 0

c. x > – 2 or x < 0 d. 2 < x < 0 27. Solve for x: 0 > x + 1 > – 7

a. – 8 > x > – 1 b. – 1 < x < – 8

c. x > – 8 or x < – 1 d. – 8 < x < – 1 28. Solve for x: 4 < 3 – x < 5

a. – 2 < x < – 1 b. – 2 > x > – 1

c. – 7 > x > – 8 d. – 1 < x < – 2

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Describe the error.

29. Problem: 2x + 8 < 6x – 4 Step 1: – 4x + 8 < – 4 Step 2: – 4x < – 12 Step 3: x < 3

30. Problem: 4x + 1 < – 15

Step 1: 4x > – 16 Step 2: x > – 4

Worksheet 4 Solve the equation. If there is no solution write ‘none’.

1. x −5 = 3 2. 6−x = 4

3. 2x −5 = 13 4. 3x +9 = 0

5. 1

4x −3 = 10 6. 20 9x− = 7

7. x +9 = – 11 8. 4 x −2 = 28

9. 1

7 6 3− x = 3 10. 5

2 7

6 x − = 30

11. 3 2x −5 = 0 12. 1

2 4

2x

− + = –12

13. 7 + 5 2x+ = 16 14. 8 – 4x +1 = 11

15. 3x +14 – 2 = 5 16. 2 7x −10 + 1 = 9 17. 7 – 3 3x −6 = – 14 18. 5 + 2 4x +7 = 1 19. 9 + 2 3

5 2x −6 = 15 20. 7 = 8x −1

21. 2

2 1

3 = x− 22. 1

2= 5 3− x

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Worksheet 5

In problems 1-5, use the definitions of absolute value equations and inequalities to determine if the statement is True or False.

1. True or False: 3x +7 =13 is equivalent to 3x+7 13= or x3 +7= −13 2. True or False: 9x + <1 19 is equivalent to 9x+ <1 19or 9x+ > −1 19 3. True or False: 2x −4 <12 is equivalent to 12− <2x−4 12<

4. True or False: 6x −4 = −10 is equivalent to 6x−4 10= or 6x−4= −10 5. True or False: 2x +5 > −1 has no solution

Solve the following inequalities and then graph the solution. If there is no solution write ‘none’. If the solution is all real numbers write ‘Reals’.

6. x < 5 7. x > 4

8. x > – 2 9. x −2 < 7

10. 3x −15 < 30 11. x < – 6

12. 2x +6 + 3 > 13 13. 4 4x −9 < 28

14. 1

5 1

2 x + > 7 15. −2 x+4 < 10

16. 16

2

x > 3 17. 24−x + 2 < 13

18. 2 7 2x− – 1 < 37 19. 17 – 3 4+x > 11

20. 1

7x +2 – 5 > 3 21. 4x +1 = 9

22. 5

6 x

− = 2 23. 3

3 4

7 x

− + < – 21

24. 5 – 6 1 2

x− > – 1

25. Multiple Choice: What is the solution of 6x −9 > 33?

a. – 4 < x < 7 b. – 7 < x < 4 c. x < – 4 or x > 7 d. x < – 7 or x > 4

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Simplify:

1. – 7 2 + 4 2. 18 + 2 − 13 + 4 3. 9(x2 + x – 1) – 2(3x2 – 4)

4. 1 3

( )( 15 )( 8 ) 5 4xyz 5.

15 3 5 5

5

x x

− − −

− 6. 10 − 2(3 + 1)

7. – 3 3 – 6 • 2 8. 12 + 18 ÷ 6 – 3(–2) 9.

3 3

(3 5 2 1) 9 (5 6) 6 2

− +

− +

• ÷

÷

10. 3 3 1

(10 ) ( 16 )

5 xy z −2   4

−    

    Evaluate:

11. x2 − y + 4 if x = − 5, y = 7 12. 5 – 3(x + 2) if x = 5 Solve the equation:

13. 3

15 2 11

8x+ = x− 14. 3 2 4 1

7x−9 = 9x+7 15. 6(x + 5) = 9x – 2 – 3x 16. 13 + 4(5 – 7x) = 5(2x – 5) – 18

Solve the equation and graph:

17. 1

4

x+ = 6 18. 5−x = – 7 19. 4 x −3 + 1 = 13

Solve the equation for y:

20. 6x + 5y = 30 21. 3xy – 28 = 16x 22. 6x + 2y + 3xy = 1

23. xy = 3x + 7y 24.

3

xy = d 25. x = 3(y + m)

26. Solve the formula for C: F = 9

5 C + 32 27. Find the value of h : A =

2

h

( b 1 + b 2) if A = 80 b 1 = 7 b 2 = 3

Solve the inequalities and graph:

28. 5 – 8x < 19 – 10x 29. 3(x – 2) > 5x + 14 30. – 7 < 2x + 1 < 11 31. x + 7 < – 5 or x – 2 > 0 32. – 2 < 5 – x < 8 33. 4x −2 < 6

34. 8

3

x > 1 35. 1 – x +9 < – 7 36. 8 > 5

7x −2

37. 3x + < −1 13

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Review 2 1. Evaluate: 2a2−3a+11when a =5

a. 16 b. 46 c. 71 d. 96

2. Evaluate: 6ab2−5cfor a=3, b= −2, and c=4

a. – 92 b. – 20 c. 52 d. 1276

3. Find the value of 3w2, if w = −5

a. – 225 b. – 75 c. 30 d. 55 e. 75

4. Solve: 2 3

(

r+4

)

−3

(

r+1

)

=11

a. – 2 b. – 1 c. 2 d. 3

5. What is the solution of 5 1 3

6 3 2

t− = −t ?

a. – 5 b. – 2 c. 2 d. 5 e. 7

6. If y mx b= + , then m =

a. y

x b+ b. y b

x

− c. y x

b

− d. x y b

(

)

e. b y

(

x

)

7. Solve for p in the equation A p prt= + a. p A r t= − −

b. A2

p=r t c.

1 p A

= rt

+ d. A r

p t

= −

8. Solve: w2 8

(

w

)

= −31

a. – 5 b. – 3 c. 15 d. 47

9. Solve: 2x+ <5 2 2

(

x+1

)

a. 3

x < −2 b. x >2

c. 3

x >2 d. x <2

10. Solve: 1 2

(

x+1

)

<3

(

x2

)

a. x <1

b. 5

x <4 c. 9

x <5 d. x >1

11. Which of the following is the graph of the compound inequality 1 2− ≤ x+ <5 13 a.

b.

c.

d.

e.

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12. Which of the following is the graph of the compound inequality 7 2+ x<1 or 13 5− x≤3 a.

b.

c.

d.

e.

13. Solve the compound inequality 9 4− < x− ≤1 9

a. 5

2 x 2

− < ≤ − b. 5

2 x 2

− ≤ < c. 5

2 x 2

− < ≤ d. 5

2 x 2

− < ≤ e. 5

2 x 2

− ≤ <

14. Solve: 4> −3m−7≥2

a. 11

3 m 3

− < ≤ − b. m ≤ −3 c. 11

m > − 3 d. 11

3 m 3

− ≤ < − e. 11

3 m 3

− ≤ ≤

15. Solve: 2y− +3 5y≥18 or 6 4− y−11> −1

a. y< −1 or y≥3 b. y ≥3 c. y < −1 d. y> −1 or y≤3 e. All real numbers 16. Solve: y −5 =6

a. {– 1, 11}

b. {– 11, 1} c. {– 11, – 1}

d. No solution 17. Solve: 7− +t 4 =15

a. t = – 12 or t = 4 b. t = 12 c. t = 4 d. t = 12 or t = 4 e. no solution exists 18. Which inequality correctly represents x <3

a. 3 < x < – 3 b. x > 3 and x < – 3 c. – 3 < x < 3 d. x < 3 or x < – 3 19. Solve the inequality 8x +4 <30

a. 17 13

4 x 4

− > > b. 13

x > 4 c. 17

x < − 4 d. 17 13

4 x 4

− < < e. No solution exists

20. Solve: 2x − <1 7

a. 3− <x<4 b. 4− <x<4 c. x>4 or x< −4 d. x>4 or x< −3 21. Solve: 4x +2 >10

a. x >2 b. x >3 c. x< −2 or x>3 d. x>2 or x< −3 22. Solve: 2x +7 >11

a. x >2 b. x < −9 c. x>2 or x< −9 d. x< −2 or x>9 e. No solution exists

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23. Solve for x: 2x −3 = −7

a. 5 or – 2 b. – 5 or 2 c. – 2 only d. 5 only e. No solution 24. The water temperature for a manufacturing process should be kept at 150° F. A computer program

uses the inequality t −150 <5

which describes the acceptable water temperature, t, in degrees. What is the range of acceptable temperature for the water?

a. 145 F < <t 155 F b. t<145 F or  t >155 F

c. t≥145 F or  t≤155 F d. t <145 F

e. t >155 F

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