Download Quarter 2 Benchmark Review - Oak Park Unified School District

Name: ______________________ Class: _________________ Date: _________
Algebra Intro - Quarter 2 Benchmark Review
Short Answer
Solve the equation. Then check your solution.
1. −6z + 13 = −11z − 7
2. 6 + 17z = 13z + 18
3.
4
5
2
k – 5 = –7 + 5 k
4. − 45 w +
1
4
=
1
5
1
+ 3w
5. 15(−42x + 40) = 15(−8x + 244)
6. 4 – 35 (3a + 4) = 7
7.
1
2
d
(15 + 7d) = − 4
Solve the proportion. If necessary, round to the nearest hundredth.
8.
6
7
9.
104
b
=
p
42
=
13
10
Graph the points given below.
10. {(3, 1), (2, –5), (2, 4), (3, 3)}
Express the ordered pairs below as a graph and a table.
11. {(4, 0), (3, 2), (3, 0), (–3, –2), (4, –1)}
1
ID: A
Name: ______________________
ID: A
12. The table below shows the yearly sales of a CD player in a particular store.
Year
Sales
1
55
2
100
3
145
4
490
5
235
6
280
Find an equation for the table above.
13. The table below shows the number of copies a copier can make related to the number of minutes the
machine has been running.
Time (min)
Number of
Copies
2
15
4
30
6
45
8
60
10
75
Find the number of copies the copier can make in 20 minutes.
14. Jordan is 3 years less than twice the age of his cousin. If their ages total 48, how old is Jordan?
15. Joji earns 3 times as much as Masao. If Joji and Masao earn $4500.00 together, how much money does
Masao earn?
16. One line segment is 5 cm more than 4 times the length of another. The difference in their lengths is
35 cm. How long are they?
Write an algebraic expression for each verbal expression.
17. the product of 5 and twice a number
18. the sum of one-third of a number and 27
19. 42 decreased by twice some number
Write a verbal expression for each algebraic expression.
20. 4n 3 + 6.
21. 7 + t = 11
2
Name: ______________________
ID: A
Evaluate each problem below.
22. 1 • 4 • 9 • 1
3
2
23. 6 • 8 + 29 + 7 + 3 • 7
24. 2 3 [(15 – 7) ÷ 2].
3
2
25.
5•2 −4•3
.
1+3
26.
6 + 3 (4 )
.
7−1
2
2
27.
2
6 + (3 + 4) − (21 ÷ 3 + 4 • 2)
4
3
14 − 3 • 1 + 2 − (5 − 1) • 2
.
Substitute and Evaluate
28. 3w + (8 – v)t if w = 4, v = 5 and t = 2.
29. w2 + n(v2 – t) if w = 4, n = 8, v = 5, and t = 2.
30. 3nw − w 2 + t 3 if w = 4, n = 8, v = 5, and t = 2.
Name the set or sets to which each number below belongs.
31.
21
3
32. − 49
33.
36
4
34. 0
3
Name: ______________________
ID: A
35. -0.33333....
Simplify completely
36. 3x2 y(2x2 y – 5xy2 + 8y3 x2 )
37. 5hk2 (2h 2 k – hk3 + 4h 2 k2 )
38. (11m 2 – 2m n + 8n 2 ) + (8m 2 + 4m n – 2n 2 )
39. (x2 + 5y) – (2x2 + 6y)
40. 5n 2 (n – 6) – 2n(3n 2 + n – 6) + 7(n 2 – 3).
41. (7u 2 v – 3uv + 4uv2 ) – (4uv – 3u 2 v – 2uv2 )
42. (8w2 + 4w – 2) + (2w2 – w + 6)
43. 15w – 6w + 14w2
44. 7(2y + 1) + 3y
45. 3x + 4(5x + 2)
46. 3 + 6(5a + 4an) + 9na
Solve
47. 1 = y − 5
9
9
48. 14 = − s
5
49. –8x = –56
50. − 7 y = −6
9
4
Name: ______________________
ID: A
51. 1 = x − 2
5
5
52. 31 = − n
6
53. − 5 w = −9
8
54. –6n = 16
55. −13 = − n
4
56. w + (–8) = –21
Use the table that shows 2006 airmail letter rates to Greenland.
Weight (oz)
5.0
6.0
7.0
8.0
Rate ($)
4.20
5.05
5.90
6.75
57. Write the data as a set of ordered pairs.
58. Draw a graph that shows the relationship between the weight of a letter sent airmail and the total cost.
Use the graph.
59. State the location of each point above as an ordered pair.
5
Name: ______________________
ID: A
Use the graph.
60. What Quadrant is the point (-3, 3) located in?
61. Katherine is 6 inches taller than Emily. If Katherine is 68 inches tall, write and use an equation to find
Emily’s height.
62. A potted tree weighs 21 pounds. The pot weighs 3 pounds. If w represents the weight of the tree
without the pot, write an equation to find the weight of the tree without the pot.
63. David had $350. After shopping, he was left with $235. If c represents the amount he spent, write an
equation to represent this situation. Then use the equation to find the amount of money David spent.
64. Jack’s school is 20 miles from his house. He has already traveled 13 miles. If d represents the distance
he still needs to travel to reach his school, write an equation to represent this situation. Then use this
equation to find the distance Jack still needs to travel to reach his destination.
65. A candle is 4 inches tall and burns at the rate of 0.6 inch per hour. If the height of the candle after x
hours is 1.5 inches, write an equation to represent the situation. Then use this equation to find the
expected number of hours in which the candle melted to 1.5 inches.
66. In a random sample of 2000 bolts, 350 were found to be defective. If there are 5500 bolts, how many
bolts are expected to be defective? Write and solve an equation to find the answer.
67. In a random sample of 400 customers at a fast food restaurant, it was determined that 124 customers
ordered a salad. If the restaurant typically has 1200 customers in a day, how many of these customers
will probably order a salad?
6
ID: A
Algebra Intro - Quarter 2 Benchmark Review
Answer Section
SHORT ANSWER
1. –4
2. 3
3. −5
4. 683
5.
6.
7.
8.
9.
–6
–3
–2
36
80
10.
1
ID: A
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
x
y
4
0
3
2
3
0
−3
−2
4
−1
y = 45x + 10
150
31
$1125.00
10 cm and 45 cm
5(2x)
1
n + 27
3
42 –2n
4 times n cubed plus 6
Seven plus a number is equal to eleven.
6
105
32
1
7
35
11
18
200
88
natural numbers, whole numbers, integers, and rational numbers
integers and rational numbers
2
ID: A
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
natural numbers, whole numbers, integers, and rational numbers
Rational numbers, integers, whole numbers
Rational Numbers
6x4 y2 – 15x3 y3 + 24x4 y4
10h 3 k3 – 5h 2 k5 + 20h 3 k4
19m 2 + 2m n + 6n 2
–x2 – y
–n 3 – 25n 2 + 12n – 21
10u 2 v – 7uv + 6uv2
10w2 + 3w + 4
2
55.
56.
57.
9w + 14w
17y + 7
23x + 8
3 + 30a + 33an
2
3
–70
7
5
7
7
3
5
–186
2
14
5
2
−2
3
52
–13
(5.0, 4.20), (6.0, 5.05), 7.0, 5.90), (8.0, 6.75)
58.
59.
60.
61.
62.
63.
(-3, -1), (-3, 2), (0, 1), (4, 3)
Quadrant II
6 + y = 68; 62 inches
3 + w = 21
$350 − c = $235; $115
47.
48.
49.
50.
51.
52.
53.
54.
3
ID: A
64. 13 + d = 20; 7 miles
65. 1.5 = −0.6x + 4; about 4.17 hour
66. 2000 d = 5500; about 963 bolts
350
67. 372
4