Download Third Nine Weeks Benchmark Review 2010

Third Nine Weeks Benchmark Review 2010-2011
1. A and B are two vertices of a square.
a. What could the coordinates of the other two vertices be? Add the points to the grid, and label their coordinates.
b. What is the side length of the square you have identified?
c. What is the area of the square you have identified?
2.
3.
a.
On the dot grid below, draw and label a line segment with length
b.
Draw and label a line segment with length
c.
Which is greater,
+
or
? Explain how you know.
Arrange the following numbers on a number line.
,
4.
.
Is
the same as
a.
Use estimation.
b.
Simplify the radicals
,
,
,
, 1.5,
? Prove your answer in two ways:
.
5.
For each number sentence below, decide if it is true (T) or false (F):
a. 7 =
6.
b. 7 = –
c. –7 =
d. –7 = –
List all the whole numbers that could be substituted for x so that the expression is true.
a. 4 <
<5
b. 8 <
<9
c. 0 <
<1
7.
Simplify -
?
8.
Simplify
?
9.
Simplify
10.
The area of a square is 289 sq ft. What is the length of the side?
11.
Sally carpeted her square room with 400 square yards of shag carpet. If she wants to buy baseboards to go
around the carpet’s edges, how many linear feet should she buy?
12.
Without using a calculator, choose the number that could be a representation of
a. 4.1231056
13.
on a calculator.
b. 5.2915026
Between what two consecutive whole numbers does
lie?
a. 4 and 5
c. 5 and 6
b. 6 and 7
d. 7 and 8
14.
A square board has an area of 5 square feet. To the nearest tenth of a foot, what is the length of one side of the
board?
a. 2.2 ft
15.
b. 1.3 ft
Evaluate the expression
a.
c. 34
b. 2
d. 8
16.
Evaluate 5
17.
a.
c. 14
b.
d. 61
Evaluate
18.
a. -
c.
b. 7
d. already simplified
Simplify
19.
a.
c.
b.
d. 0
Simplify
20. a.
a. 7
c.
b.
d.
81  _____ b.  81  ______ c.
81  _____ d.  81  ___
21. The length of the side of a square is 18 feet. What is the area of the square?
22. The area of a square is 625 square feet. What is the length of the side of the square?
23. John has a square yard. The area of the yard is 169 sq meters. John is putting a fence around the
perimeter of the yard. How many meters of fence will he need to purchase to go around the yard??
24. x 2  4  85
Solve for x.
25.  27  4 48
26. 5 6  2  7 2  4 6
27.
28. 
32x2
16
25
29. 2 63a 2

30. 7 30  2 3
31.

12
2
32. Estimate
24 to the nearest tenth.
3 Rational/Irrational
34. 0.7283975… Rational/Irrational
9
35.
Rational/Irrational
13
36. 0.132132… Rational/Irrational
33.
37. Between what two consecutive whole numbers does
35 lie?
38. Between what two consecutive whole numbers does 18 lie?
39. Arrange the numbers from least to greatest (small to large).
2
 ,
3
7, - 13, -3.5, 5,
25
40. Arrange the following numbers on the number line.
1
,
4
10,
22, - 8, 2, 0,  4
41. In the given right triangle, find the missing length to the nearest tenth.
a. 20.2 ft
b. 7.5 ft
c. 11.7 ft
d. 17.3 ft
42. The length of two sides of a right triangle are leg: 20 m and hypotenuse: 25 m. Find the length of the third
side. Round to the nearest tenth if necessary.
a. 10.5 m
b. 8.9 m
c. 32 m
d. 15 m
43. In the given right triangle, find the missing length to the nearest tenth.
a. 4.2 ft
b. 2.8 ft
c. 3.5 ft
d. 4.5 ft
44. The length of two sides of a right triangle are leg: 22 m and hypotenuse: 37 m. Find the length of the third
side. Round to the nearest tenth, if necessary.
a. 38.1 m
b. 21.4 m
c. 43 m
d. 29.7 m
45. The length of two sides of a right triangle are leg: 26 m and hypotenuse: 50 m. Find the length of the third
side. Round to the nearest tenth if necessary.
a. 56.4 m
b. 42.7 m
c. 47.3 m
d. 27.6 m
46. In the given right triangle, find the missing length to the nearest tenth.
a. 23.4 ft
b. 9.3 ft
c. 30.5 ft
d. 20.6 ft
47. In the given right triangle, find the missing length to the nearest tenth.
a. 24.6 ft
b. 22.2 ft
c. 8.1 ft
d. 12 ft
48. In the given right triangle, find the missing length to the nearest tenth.
a. 18.6 ft
b. 9.1 ft
c. 23.4 ft
d. 29.2 ft
49. The length of two sides of a right triangle are leg: 28 m and hypotenuse: 33 m. Find the length of the third
side. Round to the nearest tenth if necessary.
a. 14.6 m
b. 17.5 m
c. 43.3 m
d. 21.9 m
50. Find the length of the hypotenuse. Round to the nearest tenth if necessary.
a. 20.8 ft
b. 8.5 ft
c. 24 ft
d. 17 ft
51. The legs of an isosceles right triangle are 11 cm long. Find the length of the hypotenuse. Round to the
nearest tenth if necessary.
a. 15.6 cm
b. 22 cm
c. 7.8 cm
d. 19.1 cm
52. Find the length of the hypotenuse. Round to the nearest tenth if necessary.
a. 12 ft
b. 10.4 ft
c. 4.2 ft
d. 19.1 cm
53. Find the length of the hypotenuse. Round to the nearest tenth if necessary.
a. 9.9 ft
b. 19.8 ft
c. 28 ft
d. 2 ft
54. Find the length of the hypotenuse. Round to the nearest tenth if necessary.
a. 6.9 ft
b. 2.8 ft
c. 5.7 ft
d. 8 ft
55. Ingrid is making a quilt using squares that measure 20 in. on a side. What is the length of a diagonal of one
of the quilt squares? Round to the nearest tenth.
a. 14.1 in.
b. 34.6 in.
c. 28.3 in.
d. 56.6 in.
56. Find the length of the hypotenuse. Round to the nearest tenth if necessary.
a. 18 ft
b. 12.7 ft
c. 15.6 ft
d. 6.4 ft
57. The legs of an isosceles right triangle are 7 cm long. Find the length of the hypotenuse. Round to the
nearest tenth if necessary.
a. 14 cm
b. 4.9 cm
c. 9.9 cm
d. 12.1 cm
Find the length of AB to the nearest hundredth centimeter. All measurements are in centimeters, but figures may be
drawn to different scales. Show how you find the length.
58.
59.
60.
A surveyor determined the distance between two docks on opposite sides of a lake. Which is the closest
estimate of the distance between the two docks?
a. 2 miles
b. 1 mile
c. 2.3 miles
d. 3 miles
61.
In triangle ABC below, side AB has a length of 6 cm and side BC has a length of 10 cm. What is the length of side
AC?
a. 4 cm
62.
b. 6 cm
c. 11.66 cm
d. 8 cm
What is the length in centimeters of the hypotenuse of the right triangle below?
a.
b.
c. 8 – 2
d.
In the given right triangle, find the missing length to the nearest tenth.
63.
17 ft
11 ft
x
Not drawn to scale
a. 20.2 ft
b. 7.5 ft
c. 11.7 ft
d. 17.3 ft
64.
y
7 ft
14 ft
Not drawn to scale
a. 3.7 ft
b. 15.7 ft
c. 5.9 ft
d. 12.1 ft
The lengths of two sides of a right triangle are given. Find the length of the third side.
Round to the nearest tenth if necessary
65.
Leg: 20 m; hypotenuse: 25 m
a. 10.5 m
66.
b. 8.9 m
c. 32 m
d. 15 m
Find the length of the hypotenuse. Round to the nearest tenth if necessary.
x
4 ft
4 ft
a. 6.9 ft
b. 2.8 ft
c. 5.7 ft
d. 8 ft
67.
The Peachtree Ridge High School Marching Band sold gift wrap for a trip to Hawaii. The gift wrap for solid colors
sold for $4 per roll and the printed gift wrap sold for $6 per roll. The total number of rolls sold was 480 and the
total amount of money collected was $2340. Write a system of equations to represent the situation.
68.
Which of the following ordered pairs is a solution of the given system of linear equations?
3x + 5y = 21
x – y = –1
a. (–2, 1)
b. (2, 3)
c. (3, –2)
d. (1, -1)
69. Rosa has some $2 bills and $5 bills. In all, she has 10 bills worth $41. Which linear system represents the given
situation?
a. x + 9y = 9 and x + 3y = 25
c. x + y = 10 and x + 5y = 41
b. x + y = 10 and 2x + 5y = 41
d. x + y = 10 and 2x + y =41
70. What is the solution of the system of linear equations in the given graph?
a. (1, 0)
c. (3, 0)
b. (0, 3)
d. (2, 1)
71. Select the following system of linear equations that has the solution (7, 3)?
A.
B.
C.
D.
72. Solve
a. This system has exactly one solution.
b. This system has infinitely many solutions.
c. This system has no solution.
d. (1, 1) and (0, 0)
73. Select the graph that models the system of linear inequalities.
3
x5
4
4
y   x3
3
y
A.
B.
C.
3
x  2 and x + 2y = 4?
2
75. Determine the solution of the system of linear equations 3x = 9 and –x + 2y = 9.
74. Which point represents the solution of the system of linear equations? y 
76. Which point lies on the point of intersection of the system? 3x + 5y = -3 and -3x + y = -15
77. The ordered pair (2, 1) is the solution of which system of equations?
a. x + y = 1
2x + y = 7
b. -x + 5y = -11
3x + 2y = – 18
c. 2x + y = 5
3y = 4x – 5
d. 4x + 5y = -2
5x = 2 – 10y
78. What is the x- coordinate of the solution to the system y = -2x - 2 and 2x – y = -3?
79. Solve the system of linear equations. x + y = 4 and -5x + 2y = -6
80. Determine the solution to the system of linear equations: x + y = 7 and y = -2x + 8
81. How many solutions does the linear system have? -5x = y + 8 and 5x + y = 8
82. How many solutions does the linear system have? 2x – y = 4 and 1 - y = -2x + 5
83. Graph the following system and Label the Solution: y = -x + 3 and y = -½x + 3
84. Solve the following linear system. 6x +y = 12 and -4x - 2y = 0
85. Solve the following linear system. x + y = 10 and 2x + 5y = 41
Problems 86 through 88 - Classify the following systems as consistent and independent, consistent and dependent or
inconsistent and tell how many solutions each system has (one solution, many solutions or no solutions).
86. y= -2x + 6
2x + y = -3
87. 3x + y = -1
y = -2x + 1
88. y = 2(x+1)
y – 2x = 2
Problems 89 through 93 - Graph the following Systems of Inequalities and shade the region of the solution
89.
and
3y > -6x + 9
90.
x>7
1
y  x2
3
and
x + y > -3
91.
3x – 2y < 8
and
y 1 
92.
y>x+1
3
y  x5
4
and
y < -2x
4
y   x3
3
93.
and
3
x
2
Answer Key:
1. If AB is a side of the square, the other points could be (3, 2) and (2, –1) or (–4, 1) and (–3, 4). If AB is a diagonal of the
square, the other points are (–2, 2) and (1,1).
2.
b.
If AB is a side,
. If AB is a diagonal,
.
c.
If AB is a side, 10 square units. If AB is a diagonal, 5 square units.
a and b.
c.
must be greater than 1 but less than 2, as
and therefore greater than
and
So,
+
must be greater than 2
.
3.
4. a. Possible answer:
b. Possible answer:
5.
6.
7.
8.
,
so their sum is approximately 6. But 8 + 10 = 18.
simplifies to
a.
True
b.
False
c.
False. Recall that
d.
True
a.
17, 18, 19, 20, 21, 22, 23, 24
. This is not the same as
which simplifies to
indicates the positive square root of x.
b. 65 through 80
c. none
9.
5
10.
17 ft
11.
240 feet
12.
B
13.
B
14.
A
15.
D
16.
B
17.
A
18.
C
19.
D
20.
a.
21.
The length of the side of a square is 18 feet. What is the area of the square? Area = 324 square feet
22.
The area of a square is 625 square feet. What is the length of the side of the square? Side = 25 feet
23.
John has a square yard. The area of the yard is 169 sq meters. John is putting a fence around the
perimeter of the yard. How many meters of fence will he need to purchase to go around the yard??
52 feet of fence needed
24.
x 2  4  85
25.
 27  4 48  9 3
26.
5 6  2 7 2 4 6  6 9 2
81  9 b.  81  9 c.
81  no _ rea l_n umber d.  81  9
Solve for x. x = 9
32 x2  4 x 2
27.
16
4

25
5
28.

29.
2 63a2  6a 7
30.
7 30  2 3  42 10
31.
12
6 2
2


32.
Estimate
33.
36.
3 Rational/Irrational
0.7283975… Rational/Irrational
9
Rational/Irrational
13
0.132132… Rational/Irrational
37.
Between what two consecutive whole numbers does
34.
35.
24 to the nearest tenth. 4.9
35 lie? Between 5 and 6
38.
39.
Between what two consecutive whole numbers does 18 lie? Between 4 and 5
Arrange the numbers from least to greatest (small to large).
2
 ,
3
7, - 13, -3.5, 5,
25
2
- 13, -3.5,  , 7,5, 25
3
40.
Arrange the following numbers on the number line.
 4
0
41. A
42. D
43. D
44. D
45. B
46. C
47. A
48. D
49. B
50. D
51. A
52. D
53. B
54. C
55. C
56. B
57. C
58. 1.44 cm
59. 10.00 cm
60.
C
61.
D
62.
A
63.
A
1
4
2
8 10
22
64.
D
65.
D
66.
C
67.
250 solid colored rolls and 230 printed rolls
68.
B
69.
B
70.
D
71.
A
72.
B
73
B
74. (2, 1)
75. (3, 6)
76. (4, -3)
77. C
78. 
5
4
79. (2, 2)
80. (1, 6)
81. No solution ( 0  8 )
82. Infinite solutions (0 = 0)
83. Solution: (0, 3)
84. (3, -6)
85. (3, 7)
Classify the following systems as consistent and independent, consistent and dependent or inconsistent and tell how
many solutions each system has.
86. Inconsistent
87. Consistent and independent
88. Consistent and dependent
No solution ( 0  9 )
One Solution (-2, 5)
Infinite solutions (2 = 2)
Graph the System of Inequalities and shade the region of the solution
89.
91.
93.
90.
92.