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Math 40
Cumulative Review
Miller/O’Neill Text
1. Perform the indicated operations:
-12 + 5 – (-3)
2. Perform the indicated operations:
−
3. Perform the indicated operations:
19.8 ÷ (-7.2)
4. Perform the indicated operations:
5 – 2[3 – (4 – 7)]
5. Perform the indicated operations:
2 ⎛ 1⎞
− +⎜ ⎟
3 ⎝2⎠
6. Perform the indicated operations:
− 3 2 + (− 5 )
2
2
5 − ( −20) − 3 2
7. Perform the indicated operations:
8. Perform the indicated operations:
1 7
+
5 10
− 3.5 + 2 .8 ÷ 0.4
− 1 + 2 ( −8) + 4 (3 − 5) 2
[
]
9. Place the numbers in the appropriate location in the diagram:
3
{ 7 , -2, 2, , π , 0.25, 0.7 }
5
10. Translate the mathematical expressions and simplify the results:
a.
One-third of three-fourths
b.
The square root of the difference of five squared and nine
11. Write the reciprocal of each number, if possible.
2
a. −
5
b. 3
c. 0
12. List the terms of the expression:
-7x2y + 4xy – 6
13. Identify the coefficient of the term:
ab
14. Simplify:
-4[2x – 3(x + 4)] + 5(x – 7)
15. Solve for x:
-2.5x – 5.2 = 12.8
16. Solve for p:
-5(p – 3) + 2p = 3(5 – p)
17. The sum of two consecutive odd integers is 156. Find the integers.
18. The total bill for a man’s three-piece suit (including sales tax) is $374.50. If the tax rate
is 7%, find the cost of the suit before tax.
19. The area of a triangle is 48 cm2. Find the height of the triangle if the base is 12 cm.
20. Rachel invests twice as much money in an account earning 9% simple interest as she
does in an account earning 4% simple interest. If the total interest is $792 after one
year, find the amount originally invested in each account.
21. An athlete bicycles an average of 12 mph faster than she runs. She runs 0.8 hours and
bicycles for 1.2 hours for a total distance of 30.4 miles. Find her average rate bicycling.
22. (a) Solve the inequality. (b) Graph the solution set on a number line.
(c) Express the solution in interval notation.
-2x – 3(x + 1) < 7
23. What number represents the opposite of the absolute value of –10?
24. Translate to an algebraic expression and simplify:
3
7
a. The quotient of and −
4
8
b. The product of –2.1 and –6
25. Solve:
2
1
4
y− =y+
3
6
3
26. Solve for a:
3a + b = c
27. Find the x- and y-intercepts of –2x + 4y = 4.
28. Complete the ordered pairs for the equation 2y + x = 7
a. (1, ?)
b. (?, -3)
29. Given: 3x + 2y = -12
a. Write the equation in slope-intercept form.
b. Identify the slope.
c. Identify the y-intercept.
1
and y-intercept (0, -5).
30. Write an equation of the line with slope
2
31. Translate to a mathematical expression and evaluate:
The difference of the square of five and the square root of four.
32. Solve for x:
1
1
2
x −3 = x −
2
4
3
33. Solve for y:
-2y – 3 = -5(y – 1) + 3y
34. For a point in a rectangular coordinate system, in which quadrant are both the x- and ycoordinates negative?
35. For a point in a rectangular coordinate system, on which axis is the x-coordinate zero
and the y-coordinate nonzero?
36. In a triangle, one angle is 23 degrees more than the smallest angle. The third angle is
10 degrees more than the sum of the other two angles. Find the measures of each
angle.
37. A salesperson makes 3% commission on the sale of merchandise. If his total
commission at the end of a week is $360, what was the value of the merchandise that
he sold?
38. A farmer wants to enclose a rectangular lot that is five times as long as it is wide. One
of the shorter sides of the lot is adjacent to the barn and does not require fencing. The
farmer plans to fence the other three sides. If the farmer has 264 ft of fencing available,
what should the dimensions of the lot be?
39. Solve the inequality and express the solution in interval notation:
2 – 3(2x + 4) < -2x – (x – 5)
40. Simplify: (2x2 + 3x – 7) – (-3x2 + 12x + 8)
41. Simplify: (2y + 3z)(-y – 5z)
42. Simplify: (4t – 3)2
1 ⎞⎛ 2
1⎞
⎛2
43. Simplify: ⎜ a + ⎟⎜ a − ⎟
3 ⎠⎝ 5
3⎠
⎝5
44. Simplify: (7x – 8) – (x + 3)2
45. Simplify: (12a4b3 – 6a2b2 + 3ab) ÷ (-3ab)
46. Simplify:
47. Simplify:
4m 3 − 5m + 2
m−2
(x 2 )3 (x 4 x − 6 )
x5
⎛ 2 c 2 d4 ⎞
⎟
48. Simplify: ⎜
⎜ 8 c d6 ⎟
⎝
⎠
49. Simplify:
2
10 a −2 b −3
5 a0 b − 6
50. Write in scientific notation:
a. 752,000
b. 0.03478
51. Solve and write the answer in interval notation:
0
⎛ 1⎞
⎛ 1⎞
52. Simplify: ⎜ ⎟ − ⎜ ⎟
⎝2⎠
⎝4⎠
−2
53. Factor completely:
w4 – 16
54. Factor completely:
2ax + 10bx – 3ya – 15yb
55. Factor completely:
4a2 – 12a + 9
56. Factor completely:
4x2 – 8x – 5
57. Factor completely:
12x3 + 14x2 – 6x
58. Factor completely:
9x3y4 – 6x5y3 + 3x3y2
−5
5
x <
3
12
59. Solve:
4x(2x – 1)(x + 5) = 0
60. Solve:
x(x + 2) = 35
61. Simplify:
( x −1 ) 2 x 5
x3
62. What is the domain:
x +3
(x − 5)(2x + 1)
63. Simplify:
x2 − 9
x 2 + 8 x + 15
64. Simplify:
2x − 6
10 x 2 − 90
÷
x 2 − 16 x 2 − x − 12
65. Simplify:
x 2 − 6x
−9
−
x −3
x −3
66. Simplify and write the answer in scientific notation: (2.8 x 10-2)(1.8 X 10-6)
67. Simplify and write the answer in scientific notation:
8 .2 × 10 −2
2 .0 × 10 − 5
Answers
1.
–4
14. 9x + 13
2.
1
2
15. x = -7.2
24. a.
b. (-2.1)(-6) = 12.6
16. All real numbers
3.
–2.75
4.
–7
5.
−
5
12
6.
16
7.
4
8.
–3.5
17. The numbers are 77
and 79
18. The cost was $350.
19. The height is 8 cm.
20. She invests $3600 in
the 4% account and
$7200 in the 9%
account.
3
7
6
÷− = −
4
8
7
25.
−9
2
c −b
3
27. (-2,0) and (0,1)
26. a =
28. a. 3 b. 13
3
x −6
2
3
b. slope is −
2
c. (0,-6)
29. a. y = −
9.
30. y =
1
x −5
2
31. 5 2 − 4 = 23
32.
10. a.
b.
1 3 1
⋅ =
3 4 4
5 −9 = 4
2
5
2
b. 1/3
c. not possible;
undefined
11. a. −
12. –7x2y, 4xy, -6
13. 1
21. Her average running
rate is 8 mph and
her average biking
rate is 20 mph.
22. a. x > - 2
b.
28
3
33. no solutions
34. III
35. y-axis
36. 31o,54o,95o
37. $12,000
c. ( −2, ∞ )
23. -10
38. 24 ft x 120 ft
39. [-5, ∞ )
40. 5x2 – 9x - 15
59. {-5, 0, ½}
41. –2y2 - 13yz -15z2
60. {-7, 5}
42. 16t2 - 24t + 9
61. 1
43.
4 2 1
a −
25
9
1⎫
⎧
62. ⎨ x | x ≠ 5, x ≠ − ⎬
2⎭
⎩
44. –x2 + x - 17
63.
x −3
x +5
64.
1
5( x + 4)
45. –4a3b2 + 2ab - 1
46.
4m2 + 8m + 11 +
47.
24
m−2
1
x
65. x - 3
66. 5.04 x 10-8
2
48.
c
16d 4
49.
2b 3
a2
50. (a) 7.52 x 105
(b) 3.478 x 10-2
51. [-4,∞)
52. –15
53. (w-2)(w+2)(w2+4)
54. (a+5b)(2x-3y)
55. (2a – 3)2
56. (2x-5)(2x+1)
57. 2x(2x + 3)(3x – 1)
58. 3x3y2(3y2 – 2x2y + 1)
67. 4.1 x 103