Algebra 1 Name: _____________________________ Date: ______________________________ Class #: ____________________________

Final Exam Review 12-13 Chapter 2: Solving Linear Equations Solve the equations. 1. 5 – 6 2 –14x x x+ = 2. 12 – 4 18 11x x= − +

3. 2 703w− = − 4. 27 1

3x+ = −

5. ( ) ( )9 4 – 7 5 3 – 2x x x− = 6. ( )6 – 3 – 6 5 – 4y y y= Rewrite the formula for the specified variable. 7. 3 27 for m p m+ = 8. ( )5 32 for

9C F F= −

Chapter 3: Solving Inequalities Solve and graph each of the inequalities. 9. 5 3 4 19x− < + < 10. 3 8 17 or 2 5 7x x+ > + ≤

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

11. 4x + 3 ≤19 12. 3 7 13x− − >

Solve the absolute value equation. 13. | 2 4 | 8 10x − − = 14. | 6 4 | 2x − = 15. Julie has $100 to spend on groceries. She wants to buy chicken that is $7.50 per package, hamburgers that are

$8.25 per package, and hotdogs that are $3.25 per package. Write an inequality that represents the number of packages of chicken, c, hamburgers, h, and hotdogs, f, that Julie can buy.

Chapter 4: Intro to Functions Evaluate. 16. ( ) 3 2 Find ( 3).f x x f= + − 17.

g x( ) = −4x + 9 Find g(5). Chapter 5: Linear Functions 18. Graph the triangle that is formed by the intersections of the x-axis, the y-axis, and the line 5x + 4y = 40 .

What is the area of this triangle?

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Use the given information to (a) write an equation in point-slope form. Then, (b) rewrite the equation into slope-intercept form and then (c) standard form.

19. (5, 12) (6, -2) 20. (2, 12) (7, 2) a. Point Slope Form: a. Point Slope Form: b. Slope-Intercept Form: b.

Slope-Intercept Form:

c. Standard Form: c. Standard Form: Write the equation for a vertical line passing through the point. 21. (-53, 72) 22. (5, 11)

23. Write the equation of a line in slope-intercept form through the point (-8, 5) and is parallel to the line y = 2x − 3 .

24. Your gym charges 80 dollars to become a member and an additional 25 dollars per month that you are a member.

a. Write an equation representing the cost of your gym membership for x months.

b. If you spent $230 on the gym, for how many months were you a member?

c. If you become a member for an entire year, you get a 15% discount on your year’s bill. How much would you spend?

Chapter 6: Systems of Linear Equations and Inequalities Solve the system using substitution or elimination. Check your solution! 25. 3 4 5

1y xx y

+ =+ =

26. 2 3 73 5

x yy x

− = −= − −

Solve the system by graphing. Check your solution!

27.

−3x + y = 24x −8y = 0

28. 2 41 12

y x

y x

= −

= +

Check: Check: Graph the inequality.

29. −3x − y ≤ 2 30. y > − 2

3x + 4

Graph the system of inequalities.

31. 2 53

y xx≤ −>

32. 2 4

2x yy

− >≤

Write the equations that would represent the situation described. Do NOT solve!! 33. You are selling tickets for a high school play. Student tickets cost $4 and general admission tickets cost $6.

You sell 525 tickets and collect $2876. Write the system of equations that would solve the problem. 34. A store is selling compact discs for $10.50 and $8.50. You buy 10 discs and spend a total of $93. Write the

system of equations that would solve the problem. Chapter 7: Exponents Simplify.

35. 3 342x yxy

36. 5 8

2 10

164x yx y−

37. 0

8

42x−

38. ( )22 3 45a b c− 39. 2 7 3(3 )(4 )x x− 40. ( ) ( )3 22 4 22 3x y x y Write each number in scientific notation. 41. 0.00000748 42. 4,017,000 43. 0.00009021

Chapter 8: Polynomials and Factoring For #44-49, (a) perform the indicated operation. Then, (b) classify each polynomial by degree and the number of terms. 44. 2 2(2 6 3) ( 3 3)x x x x− − + − + 45. 2 2( 3 5 8) ( 5 8)x x x x− + − − − − a. Simplify: a. Simplify: b. Classify by Degree:

b. Classify by Degree: c. Classify by # of Terms: c. Classify by # of Terms: 46. (2 3)(2 3)p p− + 47. 2( 9)( 3 2)t t t− − + a. Simplify: a. Simplify: b. Classify by Degree:

b. Classify by Degree: c. Classify by # of Terms: c. Classify by # of Terms: 48. 2( 10)(4 3 9)x x x+ + + 49. 2(2 3)x+ a. Simplify: a. Simplify: b. Classify by Degree:

b. Classify by Degree: c. Classify by # of Terms: c. Classify by # of Terms: Factor. 50. 6 218 6 3d d d− + 51. 2 46 3x x+ 52. 2 9 14x x− + 53. 2 5 14x x+ − 54. 215 33 6x x+ + 55. 28 18 4x x+ +

Chapter 9: Quadratic Equations and Functions Solve using square roots. Simplify each radical completely. 56. 29 16 0x − = 57. 2121 25 0x − = Simplify. 58. 16 i 23 59. 9 i 2 60. 72 61. 20 62. 49

36− 63.

− 75

6

How many solutions will each of the following quadratic equations have? Show your work. 64. The name of the calculation that can help you to determine the number and type of solutions a quadratic has is

called the: __________________ whose formula is: ________________________. 65. 24 3 2 0x x− + − = 66. 29 12 4 0x x− + = Graph the quadratic function. Identify the vertex and the equation of the axis of symmetry. 67. 2( ) 4f x x= − 68. g(x) = −x2 − 2x − 3

Vertex: ________ LOS: _________ Vertex: ________ LOS: _________

69. You are standing on a bridge over a creek, holding a stone 20 feet above the water. *Hint*: use the formulas 216h t s= − + and

216h t vt s= − + +

a. You release the stone. How long did it take the stone to hit the water?

b. You take another stone and toss it straight up with an initial velocity of 30 feet per second. How long will it take the stone to hit the water?

Family of Functions For #70-72,

a) Write the equation in standard form. b) To what family of functions does each equation belong? c) Sketch the shape of the graph (include the effect of the a).

70. 2 33 8 155

y x x= + − 71. ( ) 5 19g x x= − − 72. 1( ) 64

x

f x ⎛ ⎞= −⎜ ⎟⎝ ⎠

73. Write the parent equation for each type of function. You do not need to include a, h, and k.

a) Linear function ______________________________________

b) Quadratic function ____________________________________

c) Cubic function ________________________________________

d) Absolute-value function ________________________________