ALGEBRA 2 / TRIGONOMETRY 1
Name: _____________________________
ALGEBRA 1 REVIEW PACKET
Part I. Solving Linear Equations
Solve:
2
1.
x 1  x  7
3
2. 5x  2(3  x)  (4  x)
3. 6(2 x  1)  3  6(2  x)  1
4.
2
3
x2  x5
3
4
5. A stockbroker earns a base salary of $40,000 plus 5% of the total value of the stocks, mutual funds, and other investments that the
stockbroker sells. Last year, the stockbroker earned $71,750. What was the total value of the investments the stockbroker sold?
Part II. Solving Inequalities
Solve & graph on a number line:
6. 6  x  7 x  12
7. 5(2 x  3)  15  20 x
8. You have $50 and are going to an amusement park. You spend $25 for the entrance fee and $15 for food. You want to play a game
that costs $0.75. Write and solve an inequality to find the possible number of times you can play the game. If you play the game
the maximum number of times, will you have spent the entire $50? Explain.
Part III. Solving Absolute Value Equations and Inequalities
Solve:
9.
2x  5  4  5
10.  3
2
x  9  54
3
Solve & graph on a number line:
11. 4 10  3x  5  73
12.
1
x  10  4  18
4
Part IV. Graphing Linear Equations
Graph on graph paper:
13. y  3x  6
14. 4x  6 y  5
15. y  2x  2
16. 3 y  2x  3
17. The cost C (in $) of placing a color advertisement in a newspaper can me modeled by C  7n  20 where n is the number of
lines in the ad. Graph the equation. What do the slope and C-intercept represent?
Part V. Graphing Linear Inequalities
Graph on graph paper:
18. y  2 x  3
19. x  3 y  15
20.
x y 3
 
4 2 2
21. 2 x  6
22. You have relatives living in both the U.S. and Mexico. You are given a prepaid phone card worth $50. Calls within the U.S. cost
$0.16 per minute and calls to Mexico cost $0.44 per minute.
(a) Write a linear inequality in two variables to represent the number of minutes you can use for calls within the U.S. and for
calls to Mexico.
(b) Graph the inequality and discuss three possible solutions in the context of the real-life situation.
Part VI. Writing Equations of Lines
23. Give the slope and the y-intercept of y  2 x  4
24. Give the slope and y-intercept of 2x  3 y  12
Write the equation of the line in the form: y  mx  b
25. With a slope of 4 and y-intercept of -3
26. With m  2 and passing through the point (-2, 6).
27. Through the points (0, 2) and (2, 0).
28. Parallel to the line y  2x  3 and contains the point (-2, -1).
29. Perpendicular to the line y  2x  3 and contains the point (-2, -1).
30. With a slope of 0 and contains the point (-10, 17).
31. The table below gives the price p (in cents) of a first-class stamp over time where t is the number of years since 1970. Plot the
points onto a coordinate plane. State whether the correlation is positive or negative. Write the equation of the best-fitting line.
Part VII. Relations and Functions
32. Given { (-5, 5), (-5, -5), (0, 3), (0, -3), (5, 0)} (a) State the domain. (b) State the range. (c) Is the relation a function? Explain.
33. Given { (-4, 2), (-3, -3), (-2, 0), (4, 2), (2, 4)} (a) State the domain. (b) State the range. (c) Is the relation a function? Explain.
34. If f ( x) 
6
x 4
2
 1 
35. If g ( x)  x 2  5 , evaluate g (6) and g  
 2 
, evaluate f (4) and f (7)
Part VIII. Solving Systems of Equations and Inequalities
  4 x  y  1
36. Solve by graphing: 
 3 x  3 y  12
 5 x  6 y  16
38. Solve by elimination: 
 2 x  10 y  5
 3x  y  4
37. Solve by substitution: 
 5x  3 y  9
  2x  y  6
39. Solve by substitution or elimination: 
 4x  2 y  5
40. You are selling tickets for a high school concert. Student tickets cost $4 each and general admission tickets cost $6 each. You sell
450 tickets and collect $2,340. How many of each type of ticket did you sell? (Set up and solve a system to answer this question).
 x y4
41. Graph the solution: 
 2x  y  3
 3x  2 y  6
42. Graph the solution: 
 y  x  3
Part IX. Simplifying Exponential Expressions
Leave no negative exponents in your final answer.
43. 3( x 2 y 3 ) 4
44.
3xy 2
45.
4 x 2 y 3
40 x 3 y
 3xy 6
46.
(3x 3 y 4 )( 2 x 2 z 5 )
4 x 4
Part X. Polynomial Addition & Subtraction
47. (2x 2  1)  (3x 2  6x  2) 
48. (2x 2 y  6 y)  (4x 2  2 y) 
Part XI. Polynomial Multiplication
49. 3x( x 3  6 x  7) 
50. x( x  2)(x 2  1) 
51. (2 x  6)(3x  4 y  6) 
Part XII. Polynomial Factoring
Factor completely:
53. x 3  x 2  4 x  4
54. 4 x  28 x 2
55. x 4  5 x 2  6
56. 3x 2  2 x  8
57. x 2  64
58. x 2  25
52. ( x 2 y  3 y)(2 xy  3 y) 