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MAT0022 DEVELOPMENTAL ALGEBRA
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PRACTICE FINAL
Simplify each expression.
Solve each equation for the specified variable.
1.
9  3  42 • 2  10
14. Solve for p: 6p − 5q = 3
2.
24  2(3  9)2  32
15. Solve for y: 3x + 4y = 7
3.
Solve each inequality.
9  16   8
16. 4x + 6  3(3x  5)
4.
 17  16  24
17. 24 − 5x > −3x + 18
Evaluate the expressions for the given values of x
and y.
5.
5xy  x2; x = 4 and y = 2
6.
x2 − 2xy + 3y2; x = −2 and y = −1
Translate and solve.
18. Eight times the difference of some number and
5 is 32. Find the number.
19. Twelve subtracted from three times a number is
6 more than the number. Find the number.
Simplify each expression.
7.
3x – 2(5x + 5) + 4
20 The product of five and a number is the same as
the number increased by 44. Find the number.
8.
−2(5y + 3) – 9y – 13
Solve each problem.
9.
5x – 3 − 4(x – 5)
21. The perimeter of a rectangle is 28 feet. Find the
length of the rectangle if the length is 4 feet less
than two times the width.
Solve each equation.
10. 8  2(a  1)  9  a
11. 7(2 x  3)  6 x  1  7 x
12.
13.
1
3
y  2  y 1
3
4
3
x  2  1  3x
7
©Palm Beach State College
22. The number of women attending a conference
was three less than twice the number of men. If
51 people attended the workshop, how many
were women?
Simplify each expression.
23. (2r 3 s 2t )(5st 6 )
24. ( x3 y5 z 0 )( x4 y 2 )
Page 1 of 4
Developmental Algebra – Practice Final
Simplify each expression.
Factor each expression completely.
25. (a 7b2c0 )3
38. 5x2y3 − 15x3y + 10xy2
39. 16 x4 y 2  8x3 y 2  4 x2 y 2
26. ( x3 y 2 z )5
40. 25x2 − 16y2
2 6 3
27.
28.
x y z
x11 yz 4
41. 64a4 − 9b2
x6 y  5
x 2 y3
Factor each expression completely.
2
42. 9y − 3x + 3y − xy
Write the number in scientific notation.
29. 0.0000415
43. ax − a + bx − b
Write the number in standard form.
44. 4x2 − 11x + 6
30. 6.102 × 106
45. 5x2  13x  6
Add the polynomials.
Solve each equation.
31. (2x2 − 3x − 5) + (−8x2 + 5x − 2)
46. 3y2 − 4y − 15 = 0
Subtract the polynomials.
2
2
32. (x + 2x − 5) − (6x − 4x − 1)
47. 4a2  9a  5  0
2
Multiply the polynomials.
48. x + 7x − 60 = 0
33. 6x3 (3x2 − 5)
49. x2 − 2x − 48 = 0
34. −4x2y (5x3y2 − 2x2y + 3x)
Simplify each expression.
35. (3x − 2)(4x + 1)
50.
2 x2  7 x  4
x 2  16
51.
x2  4x  3
x2  1
36. (4x − 5y)2
37. (2x − 7)(2x + 7)
©Palm Beach State College
Page 2 of 4
Developmental Algebra – Practice Final
Simplify each expression. Assume the variable
represents a non-negative number.
Graph each linear equation.
59. y = −4x − 5
52.
60a6
53.
144 x7 y 4
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1
Simplify each expression.


54.
3 2 3  21
55.
3  2 75  27
y
x
1 2 3 4 5 6
-1
-2
-3
-4
-5
-6
60. 2x + y = 4
6
5
4
3
2
1
56. 4 5  6 45  80
Find the x-intercept for the given line.
-6 -5 -4 -3 -2 -1
57. 2x + 5y = 15
Find the y-intercept for the given line.
-1
-2
-3
-4
-5
-6
y
x
1 2 3 4 5 6
58. x + 3y = 2
©Palm Beach State College
Page 3 of 4
Developmental Algebra – Practice Final
ANSWER KEY
1.
25
27.
53. 12 x3 y 2 x
y5
x9 z
x8
y8
2.
−57
3.
−1
4.
23
5.
24
29. 4.15 × 10−5
56. 10 5
6.
3
30. 6,102,000
 15 
57.  , 0 
 2 
28.
54. 6  3 7
55. 12 3
2
7.
7x  6
31. −6x + 2x − 7
8.
19y  19
32. −5x2 + 6x − 4
9.
x + 17
10. a  1
4
11. x  
3
36
12. y  
5
7
13. x  
6
5q  3
14. p 
6
7  3x
15. y 
4
5
33. 18x − 30x
5 3
4 2
2
37. 4x2 − 49
2
2
38. 5xy(xy − 3x + 2y)
40. (5x − 4y)(5x + 4y)
45. (x − 3)(5x + 2)
5
46. y   , y  3
3
43. (x − 1)(a + b)
5
47. a  , a  1
4
49. x = −6, x = 8
y7
24.
x
b6
25.
a 21
50.
2x  1
x4
51.
x3
x 1
y10
x15 z 5
©Palm Beach State College
60.
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1-1
-2
-3
-4
-5
-6
y
x
1 2 3 4 5 6
48. x = −12, x = 5
10
23.  3 5
r st
26.
x
1 2 3 4 5 6
41. (8a2 + 3b)(8a2 − 3b)
18. 8(x  5) = 32; x = 9
22. 33 women
y
-6 -5 -4 -3 -2 -1-1
-2
-3
-4
-5
-6
39. 4x2y2(4x2 − 2x + 1)
44. (x − 2)(4x − 3)
21. 8 ft
6
5
4
3
2
1
36. 16x2 − 40xy + 25y2
17. x < 3
20. 5x = x + 44; x = 11
59.
35. 12x − 5x − 2
42. (3 + y)(3y − x)
19. 3x  12 = x + 6; x = 9
3
34. −20x y + 8x y − 12x y
16. x  21
5
 2
58.  0, 
 3
3
52. 2a3 15
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Developmental Algebra – Practice Final