Download ALGEBRA 1 1st SEMESTER FINAL

ALGEBRA 1 1st SEMESTER FINAL REVIEW
Simplify the expression.
1. (c 2 )3 (3c5 )4
2. (2a3 )5 (3ab2 )3
3. (6mn)3 (5m3 )2
4.
 4 


 7nt 
3
Solve the equation.
5.
2
x + 7 = -10
3
6. 5(y-3)=19
7. -3z+8+(-2z)=-12
8. -2y+5+5y=14
9. m+5(m-1)=7
10. Graph using intercepts : -3x+y=6
11. Graph using intercepts: 5x-3y=15
12. Find the x and y intercepts of each equation:
A. x+2y=18
B. 3x-y=0
C. -5x+y=30
13. Write an equation of a line with the given slope and y-intercept.: m = –
2
,b= 3
9
2
x + 5 in standard form using integers.
3
3
15. Write y =  x -4 in standard form using integers.
4
14. Write y =
16 . Write an equation in point-slope form for the line through the given point with the given slope:
(3,-4); m = 6
17.
Write an equation in point-slope form for the line through the given point with the given slope:
(4,2); m = 
5
3
18. Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y=5x = 3
y=-5x +7
19. Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
3x – 5y = 3
-5x +3y = 8
20. Solve the inequality: 4d+7 < 23
21. Solve the inequality: -2(h+2) <-14
22. -3(v-3)  5-4v
23. -4(3m-1)  2(m+3)
Write a compound inequality that represents each situation. Graph your solution.
24. all real numbers that are between -4 and 6
25. all real number that are at least 2 and at most 9
Solve the compound inequality. Graph your solution.
26. 2d+5 < –1 or -2d + 5< 5
Solve the equation. If there is no solution, select “no solution”.
27. –2c-4 = –8
28. 4c+1 = 16
29. Solve the inequality. Then graph your solution: –1  4m+7 < 11
30. Solve the inequality. Then graph your solution: 3 w+2 < 7
31. In which quadrant or on which axis would you find the point (–12, 0)?
32. In which quadrant or on which axis would you find the point (8, -18)?
33. Evaluate f(x) = -3x – 10 for x = 6.
34. Evaluate f(x) = -3x +5 for x = -3.
35. Find a solution to the following system of equations.
3x -10 y = –25
4x +40 y = 20
36. Find a solution to the following system of equations.
24x +2 y = 52
6x -3 y = -36
37. What is the solution of the system of equations?
y = 2x
y=x–1
38. Graph the function: y = -4x – 1
39. Graph the function: y = 2/3x +5
40. Graph the system of inequalities: y> 1/4x
y<-x+4
41. The length of a rectangle is 6 inches more than its width. The perimeter of the rectangle is 24 inches. What are
the dimensions of the rectangle?
Find the length and width of each rectangle with the given conditions.
42. The length is 3 in more than the width. The perimeter is 30 in.
43. The width is one half the length. The perimeter is 54 cm.
44. The length is 3 yd more than twice the width. The perimeter is 36 yd.
45. A chemist has a 40% acid solution and a 80% acid solution. How many liters of each solution does the chemist
need to make 300 L of a solution that is 64% acid?
46. A chemist has a 10% acid solution and a 60% acid solution. How many liters of each solution does the chemist
need to make 200 L of a solution that is 50% acid?
Determine each sequence is an arithmetic sequence and if so, explain.
47. 4,7,9,12…
48. 15,13,11,9…
49. 10,15,25,40…
50. -10,-5,0,5…
51. Find the function that represents the relationship.
X
y
1
5
2
6
3
7
4
8
53. Find the function that represents the relationship.
X
y
1
1
3
9
6
36
9
81
54. In 2008, there were 2,000 students at La Quinta High. In 2010, there were 2,250. What is the rate of
change in the number of students?
55. Write an example of a linear, quadratic equation.
56. Write an equation that describes the nth term of the arithmetic sequence 7,13,19,25…
57. Write an equation that describes the nth term of the arithmetic sequence 30,26,22,18….
58. Write an equation for the nth term of the geometric sequence -2,10,-50….
59. Write an equation for the nth term of the geometric sequence 6,-54,486…
60. What is exponential growth?
61. Graph y  2(4) x
62. Find the third term of the sequence in which
63. Find the 4th term of the sequence in which
= -11 and
= 14 and
64. Find the first 5 terms of the sequence in which
= -3 and
-7, if n ≥ 2.
=
+6.5, if n ≥ 2.
=
=3
65. Find a recursive formula for the geometric sequence 7,28,112,448….
66. Find a recursive formula for the arithmetic sequence -37,-15,7,29…
67. Find a recursive formula for the arithmetic sequence 73,52,31,10…..
+10, if n ≥ 2.