Quiz #2 Name Date 1.

Transcription

Quiz #2
Name
1.
Date
The total number of Algebra students who completed the four assignments in the last week before the
Semester nal is shown in the bar graph below. Which statement is statistically correct about this graph?
a) Twice as many students completed the 4th assignment compared to the rst.
b) Only half as many students completed the 3rd assignment compared to the second.
c) Only few students did the rst assignment.
d) The scale on the horizontal axis in the graph does not show equal increments.
2.
Kelly Burger, who was a candidate for the president of the student council, drew the following graph to
show how she has become more popular during the last few months. Which statement is not correct?
a) The title of the graph does not correspond to the purpose.
b) The change from September to October is exaggerated.
c) The graph shows only 10–12% range on the vertical axis.
d) Kelly's popularity increased greatly from July to October.
Page 1
Quiz #2
3.
The ages of residents in a certain community are shown in the histogram below. What is misleading about
the display?
a) The intervals are too small
b) The interval 1–10 is not same as the interval 11–20
c) The intervals are too large
d) The interval 21–40 is twice as large compared to the rest of the intervals.
4.
The graph is misleading because the ratio of the height of the bars does not re ect the actual ratio. What
is the correct ratio of the bars?
a) 1:36 : 1
b) 3:25 : 1
c) 3:18 : 1
Page 2
d) 1:25 : 1
Quiz #2
5.
The pictograph compares the company pro ts between 1999 and 2000. If the two pictures are compared
how many times greater will the pro ts be in 2000 than in 1999?
a) 2 times
6.
b) 4 times
c) 5 times
d) 8 times
The sales of a store for di erent months are represented on the graph below. Which graph is misleading
and why?
a) The second graph; It changes rapidly.
b) The rst graph; The vertical axis does not start at zero.
c) The second graph; The scale on the vertical axis is not correct.
d) The second graph; The sale has varied a lot over the months.
Page 3
Quiz #2
7.
8.
Which graph could make you feel as if Total Cars has sold a lot of cars?
a)
b)
c)
d)
Select the reason(s) why the graph is misleading?
I. the little bar within the larger bar
II. the y-axis does not start at 0
III. there is no title on the graph
a) I only
b) III only
c) I and III only
d) I, II and III only
Page 4
Quiz #2
9.
The pictograph compares the house sales of two companies. The Fosbo company sold twice as many
houses in 1999 as the Acme company. What part(s) of the graph could lead to a misinterpretation.
I. The vertical axis is not labeled correctly.
II. The horizontal axis is not labeled correctly.
III. The title is incorrect.
IV. The picture is not drawn correctly.
10.
a) I only
b) I and III only
c) I, II and IV only
d) IV only
Select the reason(s) why the graph is misleading.
I. the pie chart is tilted
II. the 3-D e ect causes a distortion
III. some of the segments appear to be the wrong size
a) I only
b) II only
c) I and III only
d) I, II and III
Page 5
Problem-Attic Sample Document
all items from CCSS Math Database
copyright (c) 2013 EducAide Software
Pre-Algebra
1.
Answer:
Objective:
d
N.Q.01
2.
Answer:
Objective:
d
N.Q.01
3.
Answer:
Objective:
d
N.Q.01
4.
Answer:
Objective:
a
N.Q.01
5.
Answer:
Objective:
b
N.Q.01
6.
Answer:
Objective:
c
N.Q.01
7.
Answer:
Objective:
d
N.Q.01
8.
Answer:
Objective:
a
N.Q.01
9.
Answer:
Objective:
d
N.Q.01
10.
Answer:
Objective:
d
N.Q.01
Quiz #2
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Complex Number Review
Name
1.
Name the imaginary part of the following complex
number:
p
25
3+
A.
5
B.
5
C.
5i
7.
8i
B.
p
2i 2
C.
p
2i 4
4.
0
16
B.
C.
1
C.
8
i
12i
C.
12
D.
12
p
3 2
B.
p
3 2
p
6 and
C.
p
D.
9
3?
9
Express the product of 3 + 2i and 2i in the form
a + bi.
A.
D. 2
C.
16
D.
10.
8
Find the sum of this pair of complex numbers:
6 + 4i, 3
A.
6.
1+i
18
4 + 6i
B.
4 + 6i
3 + 4i
D. 3
4i
Find the value of ( 4i)2 .
A.
5.
B.
B.
p
D. 8i
Simplify: i38 + i104
A.
12i
8 i11
What is the product of
A.
9.
3.
p
D. 5i
When
expressed in terms of the imaginary unit i,
p
8 can be represented as
.
A.
Simplify: i7
A.
8.
2.
Date
9
3i
Express 8i4
A.
9 + 9i
Find the product of 7 i and the additive inverse
of 3 5i in a + bi form.
A.
16 + 38i
B.
26 + 38i
C.
26
D.
16
38i
38i
7i
B.
9 + 3i
C.
3
3i
D. 3 + 3i
11.
A.
3i3 + 3i2 + 6i + 4 in the form a + bi.
B.
8 + 9i
C.
7 + 6i
Express
C.
D. 10 + i
Page 1
1
5
2i
5 10i
+
3
3
1 + 2i
in the form a + bi.
B.
5 + 2i
D. 5 + 10i
12.
Express the following complex number in standard
form.
p
3 i 2
p
2+i 2
A.
2
3
C.
5
6
p
5 2
i
6
p
2
i
6
B.
1
6
D.
2
3
15.
p
The point n = 15 is graphed pon the complex
15 ?
plane. Which point represents
p
5 2
i
6
p
2
i
6
A.
13.
14.
A
B.
B
C.
C
D. D
Write the multiplicative inverse of 3 + 2i in
standard form.
A.
3
13
C.
3
5
2
13 i
2
5i
B.
3
13
D.
3
5
+
2
13 i
16.
+ 25 i
The number 3 + 4i is represented by which of
the following points on the complex plane?
Express in the form a + bi the reciprocal of 2 + i.
A.
2
5
1
5i
B.
2
5
+ 15 i
C.
2
3
1
3i
D.
2
3
+ 13 i
A.
Page 2
A
B.
B
C.
C
D. D
17.
Which of the following graphs represents the
number 2 + 3i in the complex plane?
18.
A.
Which of the following graphs represents the
number i(3 4i) in the complex plane?
A.
B.
B.
C.
C.
D.
D.
Page 3
19.
A and B represent complex numbers on a
coordinate plane.
22.
Express the complex number represented by the
5
coordinates (4; ) in a + bi form.
6
A.
p
2 3
Find A
B.
A.
7 + 2i
B.
3 + 8i
C.
7
D.
3
2i
21.
32
B.
16
C.
8
24.
4(cos 120 + i sin 120 )
B.
4(cos 150 + i sin 150 )
C.
4(cos 140 + i sin 140 )
Express the complex number represented by the
coordinates (18; 300 ) in a + bi form.
p
9i 3
A.
9
C.
p
9 2
B.
p
9i 2
D.
p
9 + 9i 3
p
p
9 2 + 9i 2
Find the amplitude of the complex number
1
[1(cos 40 + i sin 40 )] 2 which, when represented
graphically, lies in he third quadrant.
A.
D. 4
Express in polar form the root of x3 64 = 0
which if plotted, would lie in quadrant II.
A.
p
2i 3
D. 2
2i
p
20. Find the value of r when ( 3 + i)5 is expressed in
the form r(cos + i sin ).
A.
p
2 + 2i 3
B.
p
2 3 + 2i
C.
23.
2i
25.
Page 4
B.
220
C.
240
D. 260
In the complex number plane, points P and
Q represent i and 1 + i, respectively. If O
represents the origin, how many degrees are there
in angle POQ ?
A.
D. 4(cos 135 + i sin 135 )
200
45
B.
30
C.
50
D. 60
Numbers
1.
Answer:
Objective:
D
N.CN.01
13.
Answer:
Objective:
A
N.CN.03
2.
Answer:
Objective:
B
N.CN.01
14.
Answer:
Objective:
A
N.CN.03
3.
Answer:
Objective:
A
N.CN.02
15.
Answer:
Objective:
A
N.CN.04
4.
Answer:
Objective:
A
N.CN.02
16.
Answer:
Objective:
D
N.CN.04
5.
Answer:
Objective:
A
N.CN.02
17.
Answer:
Objective:
A
N.CN.04
6.
Answer:
Objective:
A
N.CN.02
18.
Answer:
Objective:
D
N.CN.05
7.
Answer:
Objective:
C
N.CN.02
19.
Answer:
Objective:
A
N.CN.05
8.
Answer:
Objective:
A
N.CN.02
20.
Answer:
Objective:
A
N.CN.04
9.
Answer:
Objective:
A
N.CN.02
21.
Answer:
Objective:
A
N.CN.04
10.
Answer:
Objective:
A
N.CN.02
22.
Answer:
Objective:
C
N.CN.04
11.
Answer:
Objective:
C
N.CN.03
23.
Answer:
Objective:
A
N.CN.04
12.
Answer:
Objective:
A
N.CN.03
24.
Answer:
Objective:
A
N.CN.04
Numbers
25.
Answer:
Objective:
A
N.CN.04
Your school newspaper ran a mock election in 2008 in order to see who the students would have picked for
president in the election. They were also interested in getting information like the exit polls do on election
day. They gathered the following data:
Candidate Females
2
66 832
Obama
6
McCain 666 282
4
Unknown
60
Males
Whites
Blacks
Hispanics
Mixed Race
535
584
124
560
355
77
506
320
75
191
121
17
110
70
15
3
77
77
77
5
From the matrix above, how many voters were undecided?
A
_
368
B
_
184
C
_
60
D
_
2,417
The matrix below displays the average percentages that your math teacher had on the last three tests for 1st,
2nd, and 3rd period classes.
Unit 1
2
1st Period 6 72
6
2nd Period 666 76
4
3rd Period
68
Unit 2
Unit 3
78
74
74
84
80
86
3
77
77
75
Based on this matrix, what was the percentage gain for 2nd period from the Unit 1 test to Unit 3 test and for
3rd period from the Unit 2 test to Unit 3 test.
A
_
2nd period had a 6% gain while 3rd period had a 12% gain
B
_
C
_
D
_
You are interested in purchasing a new cellular phone, but in order to buy one, you have to decide which
company you want to go with for cellular service. Each company has a basic plan that o ers up to
200 minutes for free.
Verizon is o ering a plan for $39.95 with each additional minute costing you $.06.
T-Mobile is o ering a similar plan for $29.95 with each additional minute costing you $.07.
AT&T has a basic plan that includes a monthly fee of $24.95 with each additional minute costing you $.08.
Finally, Cricket is o ering you a plan for $42.25 with each additional minute costing you $.02.
Which matrix below expresses this data.
A
_
$42:25
$0:02
$24:95
$0:06
$39:95
$0:07
$29:95
$0:08
B
_
$39:95
$0:08
$24:95
$0:06
$29:95
$0:02
$42:25
$0:07
C
_
$24:95
$0:06
$42:25
$0:07
$39:95
$0:08
$29:95
$0:02
D
_
$24:95
$0:08
$29:95
$0:07
$42:25
$0:02
$39:95
$0:06
At a local department store, a pair of slacks cost $36.99, a dress costs $85.99 and a pair of shoes cost $45.99.
Create a 3 2 matrix that represents the discounted cost of each item on Friday and Saturday if there is a
store-wide discount of 25% on Friday and 30% on Saturday.
A
_
2
3
66 27:18 25:89 77
66 63:20 60:19 77
4
5
33:77 32:19
B
_
2
3
66 27:74 25:89 77
66 64:49 60:19 77
4
5
34:49 32:19
C
_
2
66 27:74
66 64:49
4
34:49
3
19:42 7
7
45:14 775
24:14
D
_
2
3
66 11:99 6:99 77
66 60:99 55:99 77
4
5
20:99 15:99
Matrix A lists the calories and fat grams per serving for the given foods.
Matrix A
Calories
Fat Grams
" Teddy Grams Triscuits Mu ns Raisins #
130
120
160
130
4:5
3
6
0
If you had 12 a serving of Triscuits, a serving of raisins, and 2 servings of Teddy Grams, which matrix would
represent the calories and fat you would be taking in?
Matrix A
A
_
Calories
260
60
160
130
Fat Grams
9
1:5
6
0
B
_
Matrix A
C
_
Calories
260
60
160
130
Fat Grams
4:5
1:5
3
0
Matrix A
Calories
260
60
0
130
Fat Grams
9
1:5
0
0
Matrix A
D
_
Calories
260
60
160
130
Fat Grams
9
3
12
0
The matrix represents the number of CDs purchased by two students over the weekend.
4
2
0
3
0
1
If the retail price of a CD is $14.99, write a matrix that would represent the amount of tax paid for each
purchase. (Assume that sales tax is 6%).
A
_
0:24
0:12
C
_
35:98
17:99
0:00 0:00
0:18 0:06
0:00 0:00
26:98 8:99
B
_
3:60 0:00 0:00
1:80 2:70 0:90
D
_
63:56 0:00
31:78 47:67
0:00
15:89
The number of boat sales for July 2001 at Southside Watercrafts are:
2 Ski Boat
66 15
Bob
6
Joseph 666
5
64
William
13
Bass Boat
4
12
10
Sail Boat 3
77
4
77
77
3
75
8
If the salesmen get a $300 commission on any boat they sell, which matrix shows the amount in commission
each earns?
A
_
C
_
2 Ski Boat
66 315
Bob
6
Joseph 666 305
64
William
313
Bass Boat
304
312
310
Sail Boat 3
304 777
303 777
75
308
2 Ski Boat
66 4500
Bob
6
Joseph 666 1500
64
William
3900
Bass Boat
1200
3600
3000
Sail Boat 3
1200 777
900 777
75
2400
B
_
D
_
2 Ski Boat
66 285
Bob
6
Joseph 666 295
64
William
287
Bass Boat
296
288
290
Sail Boat 3
296 777
297 777
75
292
2 Ski Boat
66 1680
Bob
6
Joseph 666 840
64
William
1440
Bass Boat
960
1560
1200
Sail Boat 3
960 777
120 777
75
960
The matrix below contains the vertices of the hexagon in the picture. Which matrix would represent tripling
the size of this object?
2
2
A
_
C
_
3
0
4
2
2
2
3
0
2
2
6
0
4
4
4
4
4
0
4
4
1
1
0
3
1
5
5
5
4
4
6
3
5
1
B
_
5
5
6
3
D
_
6 9
6 0
5
1
6
6
1
1
0
3
1
5
6
6
9
0
6
6
Which matrix expression dilates ^LMN
A
_
5
2
8 3
+
2 0
5
C
_
3
2
2
0
2
0
5
2
8
2
2
0
8 3
2 0
3
so that N 0 is at (1; 0)?
0
B
_
5
2
8 3
2 0
D
_
1 5
3 2
2
0
2
0
2
0
8 3
2 0
Scalar multiplication can be used to nd the coordinates of a triangle whose perimeter is n times that of
a given triangle. If the original gure has coordinates (x1 ; y1 ), (x2 ; y2 ) and (x3 ; y3 ), then the new gure's
coordinates can be found by the following scalar product.
"
#
x1 x2 x3
n y y y
1
2
3
Which matrix contains the coordinates of a matrix whose perimeter is 4 times that of ^ABC whose
coordinates are A(2; 5), B(3; 1), and C( 4; 6) ?
A
_
8
12
20 4
16
24
B
_
8
20
12
4
8
2
C
_
8
12
20 4
16
24
D
_
1 7
1 5
0
2
^MNO has vertices at M(3; 7), N(8; 2), and O( 5; 2) .
If ^MNO is to be translated by the rule (x0 ; y0 ) = (x + 4; y
3), which matrix expression models this translation?
A
_
3
7
8
2
5
+
2
4
3
4
3
4
3
B
_
3
7
8
2
5
2
4
3
4
3
4
3
C
_
3
7
8
2
5
+
2
3
4
3
4
3
4
D
_
3
7
8
2
5
2
3
4
3
4
3
4
Matrix A contains the vertices of kite in the picture. You would like to move this kite ve units to the right
and six units down represented by Matrix B. Which of the following matrices would represent the new
vertices of the kite?
2 7
2
6
5
5
5
5
Matrix A
Matrix B
3 0
3 0
6
6
6
6
A
_
7
3
2
6
7
3
11
6
B
_
7
9
12
6
7
9
11
6
C
_
3
3
12
6
3
9
1
6
D
_
3
9
12
6
3
9
1
6
The United States Congress consists of the Senate and the House of Representatives. The matrices below
show the number of men and women in the Senate and the House at the beginning of the 109th Congress.
HOUSE
2 Men
Democrat 666 157
Republican 666 208
64
Other
1
Women 3
45 777
23 777
75
0
SENATE 2 Men
Democrat 666 35
Republican 666 49
64
Other
1
Women 3
77
9
77
77
5
75
0
Select the matrix which shows the number of men and women in Congress in 2005.
A
_
C
_
CONGRESS 2 Men
Democrat 666 192
Republican 666 247
64
Other
2
Women 3
54 777
28 777
75
0
CONGRESS 2 Men
Democrat 666 182
Republican 666 247
64
Other
2
Women 3
54 777
28 777
75
0
B
_
D
_
CONGRESS 2 Men
Democrat 666 202
Republican 666 231
64
Other
1
Women 3
44 777
54 777
75
1
CONGRESS 2 Men
Democrat 666 192
Republican 666 257
64
Other
2
Women 3
54 777
28 777
75
0
A car rental company rents four di erent types of cars, Ford, Dodge, Honda, and Toyota from three di erent
rental locations. The company's rentals for March are summarized in the table.
Ford Dodge Honda
Toyota
Location I
177
88
622
0
Location II
355
266
355
0
Location III
355
355
355
266
The car rental company charge for one day is $14 for a Ford, $16 for a Dodge, $17 for a Honda, and $20 for
a Toyota.
The data could be summarized using the
2
2
3
66 177
0 7
66 177 88 622
66 88
7
M = 664 355 266 355
0 775 N = 666
64 622
355 355 355 266
0
following matrices:
3
355 355 7
7
266 355 777
7 A = [ 14
355 355 775
0
266
16
17
20 ]
2 3
66 14 77
66 16 77
B = 666 777
64 17 75
20
Which of the following matrix products could be used to nd the total revenue at each location in March?
A
_
MB
B
_
BM
C
_
BN
D
_
NA
Which matrix calculation was used to transform ^XYZ to ^X 0 Y 0 Z0 ?
A
_
C
_
0
1
1
0
1
0
0
1
4
2
4
2
7
4
1
6
7
4
1
6
B
_
1
0
0
1
4
2
7
4
1
6
D
_
0
1
1
0
4
2
7
4
1
6
Quadrilateral LMNO was transformed using the matrix multiplication
2
3
66 1 0 77 3 3 7 7
66 2
77
.
64
17
5 0 3 3 0
0
2
Which of the following describes this transformation?
A
_
re ection over the x-axis then a dilation by a scale factor of
1
2
B
_
re ection over the y-axis then a dilation by a scale factor of
1
2
C
_
90 cc rotation about the origin then a dilation by a scale factor of
1
2
D
_
180 cc rotation about the origin then a dilation by a scale factor of
1
2
To nd the new coordinates of "a triangle that
# has been rotated 90
x1 x2 x3
multiply the coordinate matrix y y y by the rotation matrix
1
2
3
A (5; 7), B ( 4; 3), and C ( 6; 8), use this information to determine
has been rotated 90 counterclockwise about the origin.
counterclockwise about the origin, you
0
1
. If the coordinates of ^ ABC are
1 0
the new coordinates for ^ A0 B0 C0 after it
A
_
A0 (7; 5), B0 (3; 4), C0 (8; 6)
B
_
A0 ( 7; 5), B0 ( 3; 4), C0 ( 8; 6)
C
_
A0 ( 7; 5), B0 (3; 4), C0 (8; 6)
D
_
A0 ( 7; 5), B0 ( 3; 4), C0 (8; 6)
The area of a triangle with vertices (x1 ; y1 ), (x2 ; y2 ), and (x3 ; y3 ) can be found by the following formula.
A=
1
2
x1
x2
x3
y1
y2
y3
1
1
1
Find the area of triangle whose vertices are (3; 1), ( 2; 6), and (4; 8).
A
_
52
B
_
26
C
_
26
D
_
52
Matrices Problem-of-the-Day
1.
Answer:
Objective:
B
N.VM.06
13.
Answer:
Objective:
D
N.VM.08
2.
Answer:
Objective:
D
N.VM.06
14.
Answer:
Objective:
A
N.VM.08
3.
Answer:
Objective:
D
N.VM.06
15.
Answer:
Objective:
B
N.VM.12
4.
Answer:
Objective:
B
N.VM.06
16.
Answer:
Objective:
B
N.VM.12
5.
Answer:
Objective:
B
N.VM.06
17.
Answer:
Objective:
B
N.VM.12
6.
Answer:
Objective:
B
N.VM.07
18.
Answer:
Objective:
C
N.VM.12
7.
Answer:
Objective:
C
N.VM.07
8.
Answer:
Objective:
D
N.VM.07
9.
Answer:
Objective:
D
N.VM.07
10.
Answer:
Objective:
A
N.VM.07
11.
Answer:
Objective:
A
N.VM.08
12.
Answer:
Objective:
C
N.VM.08
3/26/13 In Class Practice
Mr. Wright, Pre-ALG I
1.
2.
Use synthetic division to divide 3x4
by x 3.
$ Q(x) = 3x3 + 9x2
22x
$ Q(x) = 3x3 + 112
18x + 9 R 20
$ Q(x) =
x3
$ Q(x) =
3x3
+ 11x
+ 9x2
$
295
16
5.
5
72 R 201
1 R0
+ 22x + 72 R 211
What is the remainder when 3x4
divided by x 4?
$ 1
3.
+ 9x2
5x2 + 6x
$ 39
Name
Write the division statement for
2x3 5x2 10x 6
.
x 4
$ (x
4)(2x2 + 3x + 2) + 2
$ (x
4)(2x2 + 3x + 2)
2
$ (x + 4)(2x2 + 3x + 2)
2
$ (x + 4)(2x2 + 13x
6.
x2 + 3x + 1 is
$ 765
Find the polynomial Q(x) and the constant R if
2x3 7x2 9 = (x 4)Q(x) + R.
7.
Simplify:
1
2a
$
$
1
2
$ does not simplify
Simplify:
3
6
$
x
x
$ Q(x) = x2 + 2x + 4 R 4
$
(x 4)(x + 3)
(x + 4)(x 6)
2x + 4 R 37
8.
Find k so that when x3 + kx2 4x + (3
divided by x 2, the remainder is 0.
$ 3
$ 1
$
1
Simplify:
k) is
$
x+3
x+6
$
x+4
x 6
x2 + 7xy + 12y2
x2 16y2
$
x + 3y
x 4y
$
x + 3y
x + 4y
$
x
x
3y
4y
$
x + 4y
x 3y
$ 10
Page 1
1
a
x2 x 12
x2 + 2x 24
x + 4 R7
$ Q(x) = x2
4.
a 4
2a 8
$
$ Q(x) = 2x2 + x + 4 R 7
$ Q(x) = 2x2
42) + 174
9.
Simplify:
14.
2a3 + a2 6a 3
6a2 + 13a + 5
10.
a2
12.
3
3a + 5
$
$
a 3
3a + 5
$ does not simplify
Simplify: (2x2
6)
x
$ 2x2
2a + 3 2a4
9a3
24
7
(2x + 3)
$ x
2
1
$
$ x
3
x2 25
x2 + 6x + 5
x+1
x 5
$ x+1
$ 1
Simplify:
2
(2x
y)
8x
1
$
1
2(2x y)
$
x4
2(2x y)3
$
x2
2(2x y)
$
4(x4 )
2x y
12a2 + 29a + 30
6a2 + 3a + 1
$ a3
$ 2a3
8a2 + 2a
$ a3 + 6a2
1
What is the remainder when 3x4
divided by 2x 3?
$
15.
x2 + 2x + 1
x 5
2x(2x y)
4x 2
$ 2a3
$ 39
13.
$ x
$
$ x+3
11.
2a2
Multiply:
125
16
$
295
16
6a2 + 3a + 10
16.
Simplify:
3a + 1
x2 + 3x + 1 is
x2 x 2
x2 + 6x + 5
2x2 3x 2
4x2 1
$
(x + 1)(2x 1)
(x + 3)(x + 2)
$
2x 1
x+5
$
x+5
2x 1
$
1
(x + 2)(x + 3)
$ 753
17.
3x2 6x 3x2 + 5x 2
Simplify:
4 x2
27x2 3
Simplify:
7x2 y
21x2 6x
14x
49x2 4
$
x
3x + 1
$
x(x 2)
(3x 1)(x + 2)
$
6
7xy + 2y
$
7xy + 2xy
6y
$
x(x 2)
(3x 1)(x + 2)
$
x(x + 2)
(3x 1)(x + 2)
$
6
7xy + 2x
$
7xy + 2y
6
Page 2
x
18.
Subtract and simplify:
$
$
x 8
2x 4
x 8
(x + 4)(x + 6)
2x + 8
x2 + 6x + 8
x + 16
x2 + 8x + 12
$
x 4
(x + 2)(x + 6)
$
x 14
(x + 2)(x + 6)
Page 3
1.
Answer:
Objective:
d
A.APR.02
13.
Answer:
Objective:
a
A.APR.07
2.
Answer:
Objective:
d
A.APR.02
14.
Answer:
Objective:
c
A.APR.07
3.
Answer:
Objective:
a
A.APR.02
15.
Answer:
Objective:
d
A.APR.07
4.
Answer:
Objective:
c
A.APR.02
16.
Answer:
Objective:
b
A.APR.07
5.
Answer:
Objective:
a
A.APR.02
17.
Answer:
Objective:
d
A.APR.07
6.
Answer:
Objective:
c
A.APR.06
18.
Answer:
Objective:
b
A.APR.07
7.
Answer:
Objective:
b
A.APR.06
8.
Answer:
Objective:
a
A.APR.06
9.
Answer:
Objective:
a
A.APR.06
10.
Answer:
Objective:
c
A.APR.06
11.
Answer:
Objective:
b
A.APR.06
12.
Answer:
Objective:
c
A.APR.06
Assignment #23
Name
1.
Date
Diana's bookcase has 3 shelves. Each shelf is the same length (`) and width (w). If she measures the
shelves in inches, which of the following shows how many square feet of liner-paper (A) Diana needs to
cover the shelves?
a) A = 3 +
2.
`w
144
b) A =
3+`+w
12
c) A =
3
`w
12
d) A =
3
`w
144
The scoring for a particular math contest that is all multiple choice is as follows:
The student starts with an automatic 40 points.
For each correct answer the student receives 5 points.
For each incorrect answer the student loses 2 points. (This is done to prevent guessing.)
Jonathon participates in the contest. He answers C questions correctly and I questions incorrectly. Which
of these equations could be used to calculate his nal score, M ?
a) M = 40 + 5C
3.
2I
b) M = 40 + 5C + 2I
2I
d) M = 40 + C
2I
Frank's Doughnut shop has a special deal. The rst dozen doughnuts cost $3.50. For every doughnut
after that the price is 15c/ . Which formula best describes the cost C in dollars of buying D doughnuts
(assuming the D 12)?
a) C = 0:15(D
12) + 3:50
b) C = 0:15D + 3:50D
c) C = 0:15 + 3:50D
4.
c) M = 5C
d) C = 3:65D
12
If you are caught shing with an expired license, the ne is $35 (the cost of a new license), plus $2.00
per day for each day over the expiration date, plus $5.00 for each pound of sh in your possession.
Which equation will best determine the ne F for shing d days after your license expires and having p
pounds of sh in your possession?
a) F = 35 + 2d + 5p
b) F = 35(d)(p)
c) F =
Page 1
105p
2d
d) F = 35(2d)(5p)
Assignment #23
5.
Translate into an equation.
An ice cube with a surface area of 60 in.2 is placed in the sun. As it melts, it loses 15% of its
surface area each minute. Let y be the surface area of the ice cube x minutes after it is placed in
the sun.
a) y = 60(1 + 0:15)x
6.
7.
b) y = 60(1
0:15)x
c) x = 60(1
0:15)y
d) y = x(1
0:15)60
Use an absolute value function to represent the following. Five less than the distance from point A to
point B is 12 more than the distance from point C to point B.
a) j5j
A
B = j12j + C
c) jA
Bj
5 = jC
B
B j + 12
b) j5
Aj + B = j12 + C j + B
d) 5
jA + B j = 12 + jC + B j
The average cost of an item is de ned as the total cost to produce it divided by the number of units
produced. A shoe company that pays $240,000 in rent and employee salaries per year gures it also
must pay $3.50 in materials per shoe set it produces.
About how many shoe sets would the company need to produce for the average cost per shoe set to be
$7.50?
a) 21,800
8.
b) 32,000
c) 41,200
d) 60,000
The height of a rocket can be approximated by relating it to the number of seconds it has been in the air.
The rocket's height is approximately the sum of fty times the number of seconds s it has been in the
air and the height of the launch pad p. How long has a rocket launched from a 100 ft pad with current
height of 1,500 ft been in the air?
a) 28 sec
b) 36 sec
c) 40 sec
Page 2
d) 44 sec
Assignment #23
9.
By driving 10 miles per hour faster, Goldie was able to shave 2 hours and 30 minutes o her 50-mile trip
to visit her grandmother who lives in the mountains. Select the equation that could be used to solve this
problem. Use x to represent her faster driving rate.
a)
10.
50
x
50
5
=
x + 10 2
c)
50
x + 10
50 5
=
x
2
d)
50
x
50
5
=
x 10 2
b) (20
300 = 74
2x)(15
2x) + 74 = 300
d) (20 + 2x)(15 + 2x) = 74
A population of insects can double in 40 days. After 125 days, how many times greater will the population
be than after 40 days?
a) 0.25 times
b) 4.17 times
c) 4.29 times
d) 4.36 times
A plane leaves an airport at 1pm traveling at 400 mph. One hour later, another plane leaves on the same
course traveling at 440 mph. At what time will they be 50 miles apart?
a) 9:45 pm
13.
50 5
=
x
2
(20 + 2x)(15 + 2x) = 74
c) (20 + 2x)(15 + 2x)
12.
50
x 10
Martin has a ower garden that is 20 ft long and 15 ft wide. He wants to put a uniform walk around the
garden and increase the area by 74 ft2 . Which equation best represents the situation if x is the width of
the walk?
a) 300
11.
b)
b) 10 pm
c) 10:45 pm
d) 11 pm
Maria can paint a room twice as fast as her daughter Rosaria. Together, they painted a room that
measures 200 square feet in 17 hours. How long would it have taken Rosaria to paint the same room if
she worked alone?
a) 11 hours
b) 25.5 hours
c) 51 hours
Page 3
d) 102 hours
Assignment #23
14.
Corey invested $57 000. He invested part of it at 8% interest per year and the rest at 10% interest per
year. If his total interest income for the year was $5 000, then how much was invested at 8%?
a) $17 000
15.
d) $40 000
69 + 67 + 70
+ S > 68
3
b)
69 + 67 + 70
+S
3
68
69 + 67 + 70
3
d)
69 + 67 + 70 + S
4
68
c) S
It costs ve dollars to get into the local skating rink. The video games there cost 75c/ each to play. If
all you have to spend on skating and video games is twelve dollars, what is the most number of video
games you can play?
a) 6 games
17.
c) $35 000
Tiger is playing for the USPG Championship. His goal for the week is to average at most 68 for his four
rounds of golf. During his rst three rounds he scores 69, 67, and 70. Which inequality best represents
the situation if S represents the score for his fourth round?
a)
16.
b) $22 000
b) 7 games
c) 9 games
d) 16 games
A school club sells candy bars for a fundraiser. If the club makes a pro t of 25c/ on each candy bar and
spends $25 on advertising, how many candy bars must be sold to make a pro t of at least $100?
a) 40 candy bars
b) 400 candy bars
c) 500 candy bars
Page 4
d) 1000 candy bars
Assignment #23
18.
Which graph represents the solution to the system of inequalities?
x +2>4
x 5
a)
!
4
3
2
1
0
1
2
3
4
5
6
7
4
3
2
1
0
1
2
3
4
5
6
7
4
3
2
1
0
1
2
3
4
5
6
7
4
3
2
1
0
1
2
3
4
5
6
7
b)
!

c)
!

d)
19.
!
Which inequality has this graph for a solution?
!
5
4
3
a) jx + 2j < 3
20.
2
1
0
1
b) jx
2
3
4
5
2j < 3
c) jx
1j < 2
d) jx + 1j > 2
Bill has an 8 in: 10 in. picture of his family. He wants to hang it in a frame that encloses an area of
224 in2 . How wide must the picture border, x, be to cover this area?
a) 3 in.
b) 5 in.
c) 9 in.
Page 5
d) 12 in.
Assignment #23
21.
In a collection of nickels, dimes, and quarters the value of the collection is $12.85. If the number of
nickels is 6 less than twice the number of dimes and the number of quarters is 5 more than twice the
number of dimes, how many quarters are there?
a) 17
22.
b) 16
c) 36
d) 80
b) 15 cm
c) 18 cm
d) 36 cm
Farmer Joe has a garden that covers 1032 yd2 . He wants to reduce his garden 366 yd2 by cutting 6 yds
o both the length and the width. The length of the original garden is 5 less than twice the width. What
is the width of the new garden?
a) 18 yd
25.
d) 39
A piece of wire 90 cm long is bent into a right triangle whose hypotenuse is 39 cm. How long is the
shorter leg of the triangle?
a) 12 cm
24.
c) 37
The length of a rectangle is 5 times the width. If the length and width are both increased by 2 the new
area would be 132. What is the original area?
a) 4
23.
b) 28
b) 24 yd
c) 30 yd
d) 37 yd
Fred and Barney go to a baseball game on Friday. They buy four hot dogs and 8 bronto burgers and
spend no more than $40. On Saturday they return to the same ballpark and purchase only 2 hot dogs
and 5 bronto burgers and spend more than $20. Which of the following cannot be a solution?
a) hotdogs cost $4 and burgers are $3
b) hotdogs cost more than bronto burgers
c) hotdogs cost $2 and bronto burgers are $5
d) hotdogs and bronto burgers are the same price
Page 6
Assignment #23
26.
Write the constraints and objective function for the following problem.
A manufacturer makes two kinds of televisions monitors, lcd and plasma. He has equipment to
manufacture any number of lcd monitors up to 400 per month or any number of plasma monitors up to
500 per month, but he can manufacture at most 600 monitors of both kinds per month in all. It takes 50
man-hours to manufacture either an lcd monitor or a plasma monitor, and the manufacturer has available
30,000 man-hours per month. If the manufacturer realizes a pro t of $70.00 on each lcd monitor and
$50.00 on each plasma monitor, nd the number of each type he should manufacture to realize the
greatest pro t. (Let x represent the number of lcd monitors and let y represent the number of plasma
monitors.)
a) P(x; y) = 50x + 70y
0 x 400
0 y 500
x + y 600
50x + 50y 30; 000
b) P(x; y) = 50x + 70y
0 x 400
0 y 500
x + y 600
50x + 50y 30; 000
Page 7
c) P(x; y) = 70x + 50y
0 x 400
0 y 500
x + y 600
50x + 50y 30; 000
d) P(x; y) = 70x + 50y
0 x 400
0 y 500
x + y 600
50x + 50y 30; 000
Assignment #23
E Lethume
1.
Answer:
Objective:
d
A.CED.02
13.
Answer:
Objective:
c
A.CED.01
2.
Answer:
Objective:
a
A.CED.02
14.
Answer:
Objective:
c
A.CED.01
3.
Answer:
Objective:
a
A.CED.02
15.
Answer:
Objective:
d
A.CED.01
4.
Answer:
Objective:
a
A.CED.02
16.
Answer:
Objective:
c
A.CED.01
5.
Answer:
Objective:
b
A.CED.02
17.
Answer:
Objective:
c
A.CED.01
6.
Answer:
Objective:
c
A.CED.02
18.
Answer:
Objective:
a
A.CED.03
7.
Answer:
Objective:
d
A.CED.02
19.
Answer:
Objective:
a
A.CED.03
8.
Answer:
Objective:
a
A.CED.02
20.
Answer:
Objective:
a
A.CED.03
9.
Answer:
Objective:
b
A.CED.01
21.
Answer:
Objective:
d
A.CED.03
10.
Answer:
Objective:
c
A.CED.01
22.
Answer:
Objective:
d
A.CED.03
11.
Answer:
Objective:
d
A.CED.01
23.
Answer:
Objective:
b
A.CED.03
12.
Answer:
Objective:
a
A.CED.01
Assignment #23
24.
Answer:
Objective:
a
A.CED.03
25.
Answer:
Objective:
c
A.CED.03
26.
Answer:
Objective:
d
A.CED.03
E Lethume
Which graph represents 2x
3y
9?
Which of the following graphs represents 5x
A.
B.
A.
B.
C.
D.
C.
D.
Which of the following is the graph of the solution set of the system?
y
y
2?
Which of the following is the graph of the solution set of the system?
2
x
y
y
y
3
x
2
2x 2
A.
B.
A.
B.
C.
D.
C.
D.
Given the graphs of y = 3x 1 and y = 2x + 1, determine which
ordered pair is a solution to
Given the graphs of y = 34 x 1 and y = 12 x + 1, determine which
ordered pair is a solution to
y < 3x 1
y > 2x + 1
y
y
A.
( 4; 2)
B.
(4; 2)
C.
(0; 4)
D.
(2; 4)
3
4x
1
2x
1
+1
A.
( 2; 1)
B.
(13; 2)
C.
(4; 4)
D.
(13; 8)
What is the inequality represented by the graph?
What is the inequality represented by the graph?
A.
y > 3x
2
B.
y < 3x
2
A.
y
3
2x
4
B.
y
3
2x
4
C.
y
2
D.
y > 3x + 2
C.
y
2
3x
4
D.
y
2
3x
4
3x
The solution that is graphed belongs to which of the systems below?
Which system represents the graph?
A.
A.
B.
x
y
2
3x + 1
x>2
y > 3x + 1
C.
x<2
y < 3x + 1
D.
y>2
y > 3x + 1
x
y
1
y
2
3x
x
y
2y
C.
A 50 Ha farm is planted with tomatoes and potatoes. At most $8000
can be spent on planting costs. Planting cost for potatoes is $100/Ha
and for tomatoes $200/Ha. Choose the best graph that shows the area
of each crop that can be planted.
A.
B.
C.
D.
3
2x
B.
3x
x
y
2y
2
1
6
3x
x
y
2y
2
2
8
+3
1
D.
2
3
Which point does not belong to the solution set of the given system?
4x + y < 8
5x y
5
A.
( 3; 4)
B.
( 2; 1)
C.
( 1; 0)
D.
(0; 8)
Which quadrant is the solution to the following system?
Select the system of inequalities whose solution is all of quadrant III,
but not the x- or y-axis.
y>0
x<0
A.
A.
I
B.
II
C.
IV
D.
V
x>0
y>0
B.
x<0
y>0
C.
x<0
y<0
D.
What shape best describes the intersection of the following system?
Find the area of a triangle de ned by the given system.
x + 2y
x + 2y
x 2y
x 2y
7x 2y + 14 > 0
7x + 4y 28 < 0
y>0
6
4
4
x>0
y>x
6
A.
A.
parallelogram
B.
square
C.
rectangle
D.
rhombus
12 units2
B.
18 units2
C.
21 units2
D.
42 units2
HS-A-3
Mrs. Bethamy
1.
Answer:
Objective:
A
A.REI.12
9.
Answer:
Objective:
A
A.REI.12
2.
Answer:
Objective:
B
A.REI.12
10.
Answer:
Objective:
D
A.REI.12
3.
Answer:
Objective:
D
A.REI.12
11.
Answer:
Objective:
D
A.REI.12
4.
Answer:
Objective:
B
A.REI.12
12.
Answer:
Objective:
D
A.REI.12
5.
Answer:
Objective:
B
A.REI.12
13.
Answer:
Objective:
B
A.REI.12
6.
Answer:
Objective:
C
A.REI.12
14.
Answer:
Objective:
C
A.REI.12
7.
Answer:
Objective:
A
A.REI.12
15.
Answer:
Objective:
D
A.REI.12
8.
Answer:
Objective:
A
A.REI.12
16.
Answer:
Objective:
C
A.REI.12
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Standard HS-F-1
Period
1.
2.
3.
Name
What is the y-intercept of the graphed line?
A.
4
B.
5 12
C.
6
D.
6 12
Which of the following best describes the line
y = 12 x + 8?
A.
goes down to the right at a steep angle;
crosses y-axis at 21 .
B.
goes up to the right at more than a 45
angle; crosses y-axis at 8.
C.
goes down to the right about a 30 angle;
crosses y-axis at 8.
D.
goes up to the right at about a 30 angle;
crosses y-axis at 8.
4.
5.
The table below contains values for x and y
in a quadratic function.
x
y
3
2
1
0
1
2
3
12
0
8
12
12
8
0
Which of the following are neither even nor
odd?
A.
I only
B.
II only
C.
III only
D.
II and III
The graph of y = x 2
1 is shown below.
What is the maximum y-value graphed?
A.
0
B.
1
C.
2
D.
5
6.
What are the roots of this quadratic function?
A.
C.
0 and
12
12, 0 and 1
B.
12,
2 and 3
D.
2 and 3
What are the roots of the function whose
graph is shown?
A.
f5g
B.
C.
f1; 5g
D.
f3; 2g
Page 2
7.
Standard HS-F-1
Given the graph, determine the number of
distinct real solutions.
10.
Which graph has lines of symmetry of x = 3
and y = 4?
A.
8.
A.
no solution
B.
one solution
C.
two solutions
D. not enough information
B.
In the diagram, is the vertex a maximum or
minimum point? What are the coordinates of
the vertex?
C.
9.
A.
maximum; (5; 3)
B.
minimum; ( 3; 5)
C.
maximum; (5; 3)
D.
minimum; (5; 3)
Identify the line(s) of symmetry for the conic
graphed below.
A.
x = 5; y = 4
B.
x = 10; y = 4
C.
x = 2; x = 8
D.
y =4
D.
Page 3
11.
Standard HS-F-1
The grid shows the coordinates of one point
on the graph of y = csc .
14.
Write the x-coordinates of four other points on
the graph that have the same y-coordinate as
this point.
What would be a possible phase shift for the
graph shown if we consider the graph to be a
cosine function of the form y = a cos (x c) ?
A.
3
4
left
B.
3
4
right
C.
1
4
left
D.
12.
13.
A.
330 ,
210 , 210 , 330
B.
150 ,
30 , 210 , 330
C.
330 ,
210 , 150 , 390
D.
150 ,
30 , 150 , 390
15.
2
right
The period of the sinusoidal graph shown is:
A.
2
B.
C.
2
D.
1
2
Using the graph below, the sine of which
angle(s) is(are) equal to approximately 0.5?
A.
0.5 and 2.6
B.
1.1 only
C.
1.1 and 5.2
D.
0.5 only
16.
The grid shows the coordinates of one point
on the graph of y = sin x.
Write the x-coordinates of four other points on
the graph that have the same y-coordinate as
this point.
Find the amplitude for the sinusoidal graph
shown below.
A.
9
B.
3
C.
1.5
D.
0
A.
30 , 30 , 150 , 330
B.
390 ,
150 ,
C.
210 ,
150 , 150 , 330
D.
390 ,
150 , 150 , 390
30 , 330
Standard HS-F-1
Dr. Branson
1.
Answer:
Objective:
B
F.IF.04
13.
Answer:
Objective:
B
F.IF.04
2.
Answer:
Objective:
D
F.IF.04
14.
Answer:
Objective:
C
F.IF.04
3.
Answer:
Objective:
D
F.IF.04
15.
Answer:
Objective:
B
F.IF.04
4.
Answer:
Objective:
B
F.IF.04
16.
Answer:
Objective:
B
F.IF.04
5.
Answer:
Objective:
B
F.IF.04
6.
Answer:
Objective:
C
F.IF.04
7.
Answer:
Objective:
C
F.IF.04
8.
Answer:
Objective:
D
F.IF.04
9.
Answer:
Objective:
A
F.IF.04
10.
Answer:
Objective:
C
F.IF.04
11.
Answer:
Objective:
C
F.IF.04
12.
Answer:
Objective:
A
F.IF.04
The graph of f (x) = 2x + 3 is sketched below. Which graph represents f
A
_
B
_
1 (x)?
C
_
D
_
C
_
D
_
Which graph is the inverse of the graph shown?
A
_
B
_
Which of the following graphs is the inverse of y = (x
A
_
B
_
Which graph is the inverse of y =
A
_
B
_
1
x
3
2)2
3?
C
_
D
_
C
_
D
_
?
Which of the following tables gives the values for f
A
_
x
f
3
2
1
6
1 (x)
0
1
2
3
B
_
x
0
1
2
3
f
1 (x)
3
4
7
12
1 (x)
C
_
if f (x) =
x
0
1
2
3
f
p
x + 3?
1 (x)
3
2
1
6
D
_
x
0
1
2
3
The data below is for a certain function h(x).
x
3
1
4
8
h(x)
21
3
1
5
Through which of the following points would the inverse function h 1 (x) have to pass?
A ( 21; 3)
_
B (1; 4)
_
C (5; 8)
_
D (3; 1)
_
f
1 (x)
9
16
25
36
Which graph is the inverse of f (x) = x3 + 6x ?
A
_
B
_
C
_
D
_
p
Which graph is the inverse of y = 2 + x ?
A
_
B
_
C
_
D
_
What is the inverse function of the given parabola?
2)2
3
B y = (x + 3)2 + 2
_
C y = (x + 3)2
_
2
D y = (x + 2)2
_
A y = (x
_
3
Which of the graphs best represents the inverse of the function y =
A a
_
B b
_
C c
_
D none of these
_
1 x
2 ?
The graph of f (x) is shown below. Find the equation for f (x) and f
1 (x).
A f (x) = 2x ; f 1 (x) = log2 x
_
B f (x) = ( 1 )x ; f 1 (x) = log 1 x
_
2
C f (x) = log2 x; f 1 (x) = 2x
_
D f (x) = log8 x + 1; f 1 (x) = 8(x
_
2
1)
What is the inverse of y = 3x2 + 4?
r
A y=
_
x
3
4
r
B y=
_
x
3
4
r
C y=
_
x
3
r
4
D y=
_
x
3
4
HS-F-2
1.
Answer:
Objective:
B
F.BF.04C
2.
Answer:
Objective:
A
F.BF.04C
3.
Answer:
Objective:
D
F.BF.04C
4.
Answer:
Objective:
A
F.BF.04C
5.
Answer:
Objective:
C
F.BF.04C
6.
Answer:
Objective:
B
F.BF.04C
7.
Answer:
Objective:
C
F.BF.04C
8.
Answer:
Objective:
A
F.BF.04C
9.
Answer:
Objective:
C
F.BF.04C
10.
Answer:
Objective:
C
F.BF.04C
11.
Answer:
Objective:
D
F.BF.04C
12.
Answer:
Objective:
B
L.24
Ms. Kostos
Exercise #13
Ms. Ocampo, Pre-Calculus
1.
2.
Simplify:
+ tan
B.
sec
+ cot
C.
csc
+ cot
D.
sec
+ csc
The expression
tan + cot
sec sin
sec2
1
B.
1
cos2
D.
1
1
cos2
1
B.
0
C.
tan4 x
D.
cot2 x
A.
cos2
C.
1 + sin2
cos2
+ tan2
B.
p
sec2 x
Simplify: p
csc2 x
sec2
sec + 1
A.
8.
9.
2
2 sec2
1
sin2 x
B.
tan2 x
C.
tan4 x
D.
cot4 x
sec4
sec + 1
1
B.
1
1 + cos2 A
1
1
2 cos2 A
D.
1
1 + 2 cos2 A
0.4
B.
0.64
C.
0.8
as a
D.
The statement
x
2
+ cos2
x
2
=
1
2
is true for—
1
A.
D.
1
cos2 A
sin2
D.
sec2
sec + 1
Given cos2 x = 0:6, express sin2 x
decimal.
A.
+ cos2
B.
Express csc2 A in terms of cos A.
C.
A.
3
sec
sec + 1
C.
7.
1)
+ sec2
A.
cot
1
sin
sin
can be reduced
Simplify: (csc x + 1) (csc x
Simplify: sin2
Express in terms of sec :
tan
sec
C.
5.
6.
A.
A.
4.
Name
cos
1 sin
to
3.
Period
Page 1
A.
x=2
only
B.
some but not all real values of x
C.
all real values of x
D.
no real value of x
1
Exercise #13
Period
Name
10.
12.
For the given diagram, point P is 1 unit
away from the origin. If sin2 = 12 , nd the
coordinates of point P.
A.
p p
(2 2; 2)
B.
(
C.
( 21 ; 12 )
D.
(
13.
p
2
2
;
)
2
2
cos
A.
sin
B.
sin
C.
cos
D.
cos
can be expanded to:
4
cos
4
cos
4
4
4
cos
4
4
cos
cos
+ cos
sin
4
+ sin
4
The expression sin(x
p
A.
p
2 1
; )
2 2
+
4
C.
p
3 sin x cos x
2
p
cos x
3 sin x
2
4
4
4
4
sin
sin
sin
sin
4
4
4
4
30 ) equals
p
3 cos x sin x
2
p
sin x
3 cos x
2
B.
D.
11.
14.
sin
A.
C.
15.
Which of the following statements is true for
the given diagram?
cos2
B.
k cos2
C.
k cos
D.
k 2 (cos
+ sin2
= 5k
+ k sin2
+ k sin
2 sin
p
4
2 cos x
Simplify:
sin(90
) cos(
A.
A.
+ x + sin
4
C.
4
x
is equivalent to:
B.
p
2 sin x
D.
p
2 2 + sin x
) + cos(90
1
B.
cos 2
) sin(
)
cos 2
D.
sin 2
=5
=
p
16.
5
+ sin )2 = 52
Express sin(2 ) cos 6 cos(2 ) sin 6 as a
trigonometric function of a single angle and
simplify.
A.
Page 2
1
2
B.
1
2
p
C.
3
2
D.
p
2 3
2
Exercise #13
Period
17.
Name
Write as a single trigonometric function:
22.
Express as a integer:
cos 56 sin 56
18.
A.
1
2
sin 112
B.
cos 28
C.
1
2
cos 56
D.
1
2
B.
2
C.
1
D.
0
23.
1
A.
sin 15:6
B.
sin 7:8
C.
cos 15:6
D.
cos 15:6
Determine the exact value of cos
p
2
2
A.
20.
sin 56
1
)
270)
Write as a single trigonometric function:
2 cos2 7:8
19.
A.
cos(270
tan sin(
B.
p
2
2
C.
1
2
Along with the given diagram, the following
are steps which show that the identity
cos2 (x) + sin2 (x) = 1 is equivalent to the
Pythagorean theorem.
1
15
4
.
1) cos2 (x) + sin2 (x) = 1
p
D.
3
2
Find tan 80 to four decimal places.
2)
cos x
sin x
1
+
=
cos x
sin x
cos x sin x
3)
a c b c
c c
=
+
c b c a
a b
4) a2 + b 2 = c 2
21.
A.
0.1736
B.
0.9848
C.
5.6713
D.
89.2838
Which of the following statements best
describes how to go from step 1 to step 2?
If sin A = 23 , cos B = 34 , OA is in quadrant II,
and OB is in quadrant IV, evaluate cos(A B).
(Answer in radical form and put everything
over a common denominator.)
A.
C.
p
35
12
p
p
3 5 2 7
12
6
B.
D.
p
p
3 5 2 7
12
p
p
5 2 7
12
Multiply both sides by
B.
Divide both sides by cos x sin x.
C.
Let cos2 (x) =
sin2 (x) =
D.
Page 3
1
.
csc2 x
A.
1
1 + cos(2x)
and
2
cos(2x)
.
2
Use the identity 1
simplify.
sin2 x = cos2 x and
Exercise #13
Mr. Ocampo
1.
Answer:
Objective:
A
F.TF.08
13.
Answer:
Objective:
A
F.TF.09
2.
Answer:
Objective:
D
F.TF.08
14.
Answer:
Objective:
C
F.TF.09
3.
Answer:
Objective:
D
F.TF.08
15.
Answer:
Objective:
B
F.TF.09
4.
Answer:
Objective:
D
F.TF.08
16.
Answer:
Objective:
A
F.TF.09
5.
Answer:
Objective:
B
F.TF.08
17.
Answer:
Objective:
A
F.TF.09
6.
Answer:
Objective:
B
F.TF.08
18.
Answer:
Objective:
C
F.TF.09
7.
Answer:
Objective:
A
F.TF.08
19.
Answer:
Objective:
B
F.TF.09
8.
Answer:
Objective:
A
F.TF.08
20.
Answer:
Objective:
C
F.TF.09
9.
Answer:
Objective:
D
F.TF.08
21.
Answer:
Objective:
B
F.TF.09
10.
Answer:
Objective:
B
F.TF.08
22.
Answer:
Objective:
C
F.TF.09
11.
Answer:
Objective:
B
F.TF.08
23.
Answer:
Objective:
B
F.TF.08
12.
Answer:
Objective:
C
F.TF.09
Unit 4 Practice Test
Geometry, Mrs. Hodgins
Name
1.
2.
Given that triangle ABC is similar to triangle DEC,
OABC corresponds to:
a) OCDE
b) ODEC
c) OACB
d) OECD
5.
^RST. Find RT.
^MNO
Period
Date
Triangle ABC is a right triangle. DE is
perpendicular to AC and bisects AC. If AB = 6
and BC = 8, then how long is DE ?
a) 4
b) 8 31
c) 7 23
d) 3 34
6.
a) 4 cm
b) 12 cm
c) 20 cm
d) 24 cm
Determine the length of MN if ST is (3x + 2)
units.
3.
Using the similar gures shown, what is the
relationship between x and y?
a) 6x + 4
a) x = 2y
7.
b) y = 2x
c) x
d) y =
4.
y=1
1
2x
In the accompanying diagram, ^ PQR is similar to
^P0 Q0 R0 , P0 R0 = 7, P0 Q0 = 4, R0 Q0 = 9, PQ = 6,
and RQ = y. Find the value of y.
a) 16
b) 15
c) 13.5
d) 12
Page 1
b) 6x + 2
c) 3x + 1
d)
3x + 2
2
Polygon ABCD is similar to polygon EFGH.
Using the values in the diagram, nd x.
a) 15
b) 14
c) 12
d) 8
8.
Period
Mary says, “All rectangles are similar.” Bob says,
“All rectangles are congruent.” Who, if either, is
correct?
12.
a) Bob is correct
b) Mary is correct
c) Both Bob and Mary are correct
Many photographic devices use similar triangles to
reproduce images as shown in the gure. The nal
image is 9 cm tall and a = 72 cm and b = 8 cm.
What is the size of the original object?
a) 16 cm
b) 36 cm
c) 45 cm
d) 81 cm
d) Neither Bob nor Mary is correct
13.
9.
In the gure, k k ` k m k n. If AB = 4, AC = 10,
and EF = 6, then nd EG.
Campsites P and Q are on opposite sides of a
lake. A survey crew made the measurements
shown on the diagram.
What is the distance between the 2 campsites?
a) 15
10.
b) 18
c) 12
d) 14
a) 500 m
Referring to the diagram, select the statement that
is incorrect.
a)
EF
DE
=
AB
AC
b)
AC
3
=
DF 2
c)
AB
DE
=
BC
EF
14.
15.
11.
Corresponding sides of two similar triangles are 6
and 15. If the perimeter of the smaller triangle
is 22, what is the perimeter of the larger triangle?
a)
44
5
b) 15
c) 42
d) 55
Page 2
c) 300 m
d) 250 m
A streetlight casts a shadow 20 feet long. A
nearby billboard casts a shadow 80 feet long. The
distance from the top of the streetlight to the end
of the shadow is 40 feet. How far is it from the
top of the billboard to the end of the shadow?
a) 20 ft
d) ÂBC is similar to ^DEF
b) 380 m
b) 40 ft
Find the length of side x.
a) 10
b) 12
c) 14
d) 194
c) 120 ft
d) 160 ft
16.
17.
18.
19.
Period
20.
In ÂBC, AC = 10, BC = 8, mO B = 90 and
mOBDA = 90 . How long is AD ?
a) 3.6
b) 4
c) 5.4
d) 9
p
9 3
a)
2
p
c) 6 3
21.
In the diagram, AB = 15, DB = 6, and BC = 8.
If mOB = 90 , what is the perimeter of triangle
ADC ?
a) 24
b) 36
c) 42
d) 60
Find the area of the triangle.
22.
What is the length of side BC to one decimal
place?
b) 9
p
d) 9 3
Which of the following equations can be used to
nd the length of x ?
a) sin 35 =
x
14
b) cos 35 =
x
20
c) cos 35 =
20
x
d) tan 55 =
x
30
To the nearest degree, nd the measure of OA
given a = 6 and b = 11.
a) 6.7
b) 7.4
a) 15
b) 29
c) 9.0
d) 14.9
c) 33
d) 56
Solve for the altitude a in terms of x.
p
a) 3 x
p
3 2
c)
2
23.
x
2
p
x 3
d)
2
b)
Page 3
Two sides of a rectangle are 5 00 and 15 00 . What is
the approximate measure of O1?
a) 18.43
b) 24.18
c) 20
d) 30
24.
Period
Which trigonometric ratio can be used to nd the
measure of OT using only the lengths shown?
25.
p
A 6 2 meter long wire is attached to the top of a
telephone pole 6 meters tall. What is the exact
measure of the angle the wire makes with the
ground?
a) 25
b) 45
c) 60
d) 90
a) cosine only
b) tangent only
c) all of the ratios above
26.
d) no ratios
Page 4
Two towers are 32.2 m apart. From the top of the
shorter one, the angle of elevation to the top of
the other is 26.9 , while the angle of depression
to the base is 78.7 . Find the sum of the heights
of each tower to the nearest tenth of a meter.
a) 16.3 m
b) 161.1 m
c) 249.0 m
d) 338.6 m
Geometry
Mrs. Hodgins
1.
Answer:
Objective:
b
G.4
13.
Answer:
Objective:
b
G.SRT.05
2.
Answer:
Objective:
b
G.SRT.05
14.
Answer:
Objective:
d
G.SRT.05
3.
Answer:
Objective:
b
G.4
15.
Answer:
Objective:
b
G.SRT.08
4.
Answer:
Objective:
c
G.SRT.05
16.
Answer:
Objective:
a
G.SRT.08
5.
Answer:
Objective:
d
G.SRT.05
17.
Answer:
Objective:
b
G.SRT.08
6.
Answer:
Objective:
a
G.SRT.05
18.
Answer:
Objective:
c
G.SRT.08
7.
Answer:
Objective:
b
G.SRT.05
19.
Answer:
Objective:
d
G.SRT.08
8.
Answer:
Objective:
d
G.4
20.
Answer:
Objective:
a
G.SRT.08
9.
Answer:
Objective:
a
G.SRT.05
21.
Answer:
Objective:
b
G.SRT.08
10.
Answer:
Objective:
a
G.SRT.05
22.
Answer:
Objective:
c
G.SRT.08
11.
Answer:
Objective:
d
G.SRT.05
23.
Answer:
Objective:
a
G.SRT.08
12.
Answer:
Objective:
d
G.SRT.05
Geometry
24.
Answer:
Objective:
c
G.SRT.08
25.
Answer:
Objective:
b
G.SRT.08
26.
Answer:
Objective:
d
G.SRT.08
Mrs. Hodgins
1.
Lines r and s are cut by a transversal, as shown. If you know that the lines
are parallel, then which of the following angle pairs must be supplementary?
I. O1, O4
II. O3, O5
III. O1, O6
IV. O2, O8
A
_
I only
B
_
II and IV only
C
_
II, III and IV only
D
_
all of them
2.
The measure of each interior angle of a regular polygon is 150 . Tandra used the fact that the
sum of the exterior angles of any polygon is 360 to show that the polygon has 12 sides. Her
steps are as follows:
1) The sum of the exterior angles = 360
2) Each exterior angle =
3)
360
= 180
n
4)
360
= 30
n
360
n
150
5) 360 = 30n
6) 12 = n
If the teacher asks Tandra to justify her reasoning for the third step, what should Tandra
answer?
A
_
Each exterior angle is supplementary with an interior angle.
B
_
The sum of the angles is 180 .
C
_
Each exterior angle is complementary with an interior angle.
D
_
180 is half of 360 .
3.
In hexagon DRAGON the diagonals RO and AN bisect each other. Jared's geometry class is
writing a proof to show that RA = ON.
Statement
Reason
1. RO bisects AN
1. given
2. RS = SO; AS = SN
2. De nition of segment bisector
3. OOSN = OASR
3.
4. ^NOS = ÂRS
5. RA = ON
4. SAS
5. CPCTC
The teacher asks Jared to justify step three. What should he answer?
A
_
Adjacent angles are congruent.
B
_
Vertical angles are congruent.
C
_
Alternate Interior angles are congruent.
D
_
De nition of angle bisector.
4.
Given:
AC is the median to BE
EC is the median to AD
Prove:
AB k ED
statement
1.
2.
3.
4.
5.
6.
7.
8.
reason
AC is the median to BE
BC = CE
mO1 = mO2
EC is the median to AD
AC = CD
ÂCB = ^DCE
mO3 = mO4
AB k ED
In the proof, what is the reason for line 8?
A
_
alternate interior angles are congruent
B
_
de nition of parallel
C
_
isosceles triangle theorem
D
_
CPCTC
5.
Given:
CF = EF
FD is a median of ^CFE
FD bisects OCFE
Prove:
statement
reason
FD is a median of ^CFE
(1)
CD = ED
(2)
(3)
given
(4)
(5)
^CFD = ÊFD
(6)
(7)
(8)
FD bisects OCFE
(9)
In the above proof, what is reason (6)?
A
_
CPCTC
B
_
SAS
C
_
SSS
D
_
angles opposite equal sides are congruent
6.
Using the given diagram, Thomas writes a proof to show that if EN = LN, then ONEA = ONLG.
Statement
Reason
1. EN = LN
2. ÊNL is isosceles
Given
De nition of an isosceles triangle
3. ONEL = ONLE
Base angles of an isosceles triangle are =
De nition of = angles
4. mONEL = mONLE
5. mONLG = mONEL + mOENL
mONEA = mONLE + mOENL
6. mONEA = mONEL + mOENL
Substitution Property
7. mONEA = mONLG
Transitive Property
8. ONEA = ONLG
De nition of congruent angles
What reason should Thomas use to justify the fth step?
A
_
Triangle Angle-Sum Theorem.
B
_
Linear Pair Postulate.
C
_
Angle Addition Postulate.
D
_
Triangle Exterior Angle Theorem.
7.
Here is a proof that the sum of the angle measures of a triangle is 180.
Statement
!
1. Given ÂBC, draw XY through B and
parallel to AC.
Reason
There is exactly one line through a point
not on a given line that is parallel to the
given line.
2. OXBA and OABY form a linear pair
de nition of a linear pair
3. mOXBA + mOABY = 180
The sum of the measures of the angles in
a linear pair is 180 .
4. mOABC + mOCBY = mOABY
angle addition postulate
5. mOXBA + mOABC + mOCBY = 180
6. OCBY = OBCA and OXBA = OBAC
substitution
7. mOCBY = mOBCA and mOXBA = mOBAC
de nition of congruent angles
8. mOBAC + mOABC + mOBCA = 180
substitution
In the proof, what is the reason for statement 6?
A
_
Alternate interior angles formed by parallel lines and a transversal are congruent.
B
_
Alternate exterior angles formed by parallel lines and a transversal are congruent.
C
_
Vertical angles formed by parallel lines and a transversal are congruent.
D
_
Corresponding angles formed by parallel lines and a transversal are congruent.
8.
Given the diagram as marked ÂBC is scalene and CD is an angle bisector.
To prove that CD cannot be perpendicular to AB the steps are given but not
necessarily in the correct order, and one step is missing. Find the missing step.
I. Therefore mOA = mOB and ÂBC is isosceles.
II. ^CDA = ^CDB by ASA.
III. CD = CD.
IV. Therefore assumption is false and CD is not perpendicular to AB.
V. OACD = OBCD
A
_
Assume mOCDA = mOCDB = 90.
B
_
Let AD = DB.
C
_
Assume CA = CB.
D
_
There is no missing step.
9.
ABCDEF is a regular hexagon. Which of these statements would be most helpful in
proving that triangle FGE is isosceles?
A
_
All sides of ABCDEF are equal in length by the de nition of a hexagon.
B
_
O3 = O4, because supplements of congruent angles are congruent.
C
_
If you draw AD, then you create isosceles triangle AGD, and this triangle is
similar to triangle FGE.
D
_
O1 = O4 and O2 = O3, because they are alternate interior angles, so O3 = O4 by
transitivity.
10.
Which of the following
Pythagorean theorem?
gures involve using similarity to prove the
A
_
B
_
C
_
D
_
11.
Given the diagram as marked. To prove that PS and QR bisect each other
using indirect proof, what assumption should be made?
A
_
quadrilateral PQRS is not a rhombus.
B
_
mOSMP = mOQMP = 90 .
C
_
mOSMP 6= mOQMP 6= 90 .
D
_
PQ is not parallel to RS.
12.
Quadrilateral PARK is a parallelogram with OPAK complementary to OKAR.
Which of the following statements is true?
I. Quadrilateral PARK is a rhombus
II. Quadrilateral PARK is a square
III. Quadrilateral PARK is a rectangle
A
_
II
B
_
III
C
_
I and II
D
_
II and III
Geometry
1.
Answer:
Objective:
Geometric Proofs - Overheads
C
G.CO.09
9.
Answer:
Objective:
B
G.CO.10
A
G.CO.09
10.
Answer:
Objective:
C
G.SRT.04
B
G.CO.09
11.
Answer:
Objective:
C
G.CO.11
4.
Answer:
Objective:
A
G.CO.10
12.
Answer:
Objective:
B
G.CO.11
5.
Answer:
Objective:
C
G.CO.10
6.
Answer:
Objective:
D
G.CO.10
7.
Answer:
Objective:
A
G.CO.10
8.
Answer:
Objective:
A
G.CO.10
2.
Answer:
Objective:
3.
Answer:
Objective:
The 3-dimensional gure is a triangular pyramid. What would the pyramid look like if it
were viewed from directly above?
A.
B.
C.
D.
Here is a picture of an angle. The distance from A to C is the same as the length of
segment BC.
Suppose points B and C are xed, but segment AB can rotate in space around
segment BC. If OABC is always 45 , what 3-dimensional shape is created by the rotating
segment?
A.
a circle
B.
a cone
C.
a cylinder
D.
a spiral
The sketch represents a rectangular house with a hip roof. Which diagram best represents
the top view of the house?
A.
B.
C.
D.
The sketch represents a 3-dimensional gure. Which diagram best represents the top view
of the gure?
A.
B.
C.
D.
Which solid is represented by the pro le views shown?
A.
B.
C.
D.
The drawing shows a solid gure built with cubes. Which 2-dimensional gure could be
the top view of this solid?
A.
B.
C.
D.
Which pentacube is not congruent to the others?
A.
B.
C.
D.
The solid gure is composed of cubes. Which diagram could represent the top view of the
solid?
A.
B.
C.
D.
The 3 3 square shows the top view of a solid, with the numbers corresponding to the
number of cubes in each stack. Which solid matches the 3 3 square?
B.
A.
C.
D.
Top View
The side, front, and top views of an object built from cubes are shown. How many cubes
are needed to construct this object?
A.
20
B.
16
C.
12
D.
9
Geometry
1.
Answer:
Objective:
B
G.GMD.04
2.
Answer:
Objective:
B
G.GMD.04
3.
Answer:
Objective:
C
G.GMD.04
4.
Answer:
Objective:
C
G.GMD.04
5.
Answer:
Objective:
C
G.GMD.04
6.
Answer:
Objective:
A
G.GMD.04
7.
Answer:
Objective:
B
G.GMD.04
8.
Answer:
Objective:
B
G.GMD.04
9.
Answer:
Objective:
A
G.GMD.04
10.
Answer:
Objective:
C
G.GMD.04
Group Discussion Cards - Spatial Reasoning
Benchmark 4-4 Exam
Mr. von Duchowitz
Name
1.
Statistics
Date
The following table shows SAT scores for the past 5 years since a new experimental math program was
introduced.
Year
1
Average SAT score
2
3
440 432 410
4
5
415 405
If a linear regression line is used, then what is the predicted SAT score 3 years from now (to the nearest
whole number)?
a) 377
2.
b) 420
c) 385
d) 361
Sam is jogging slowly on a football eld. He records his position at various times in the table below.
Time
measured
in seconds
Position
measured
in yards
0.2
48
1.1
41
1.9
37
2.5
33
3.6
27
4.4
19
5.2
13
Use a linear regression and predict the time Sam will cross the goal line. Round your time to the nearest
tenth of a second.
a) 6.8 sec
b) 6.9 sec
c) 7.3 sec
Page 1
d) 49.6 sec
Benchmark 4-4 Exam
Mr. von Duchowitz
3.
Statistics
Select the statement(s) that is(are) true.
I. If the points on a scatter plot form a strong negative correlation the mean t line will certainly
miss all the points.
II. A scatter plot is required for constructing the mean t line.
III. The mean coordinates of the scatter plot do not always lie on the mean t line.
a) I only
b) II only
c) III only
d) II and III only
4.
What are the mean coordinates shown by this mean t line?
a) (4:5; 5:5)
5.
b) (6:0; 5:0)
c) (6:0; 5:5)
d) (6:5; 6:5)
A baskeball player was practicing for a skills competition. She stayed a certain distance away from the
basket and shot 12 shots each time. A scatter plot was made using the distance from the basket as the
independent variable and the number of baskets made as the dependent variable. The mean coordinates
of this data were (8; 5). Select the statement that is true about the data.
a) On average, 5 baskets were made in 8 tries.
b) On average, if she took 12 shots from 8 feet out, she will be successful 5 times.
c) On average, from 8 ft out, she made 12 baskets.
d) On average, from 8 ft out, she she makes 5 baskets.
Page 2
Benchmark 4-4 Exam
Mr. von Duchowitz
6.
Statistics
In a study to determine the relationship between a person's weekly income and the amount a person
spends per week for recreation the following data was obtained.
Income
Amount
700
230
500
150
1100
250
1400
120
1500
240
A scatter plot is drawn using Income as the independent variable. What are the mean coordinates?
a) (1240; 198)
b) (1420; 126)
c) (1440; 168)
d) (1640; 208)
7.
The temperature change in degrees Celsius over a time in minutes is given for a liquid in this table of
values:
Time in mins
0
2
5
6
Temp in degrees Celsius 85 72 60 55
Determine the median point by using the graph to plot the points.
a) (3:5; 66)
b) (2; 66)
c) (3:25; 65)
Page 3
d) (5; 60)
Benchmark 4-4 Exam
Mr. von Duchowitz
8.
Statistics
A teacher is interested in nding the relationship between grades in mathematics and grades in english.
She records the nal grades in percentage for both courses. She then plots the scatter plot of the data
using mathematics as the independent variable. Use your calculator to determine the equation of the
linear regression line for the data.
Mathematics English
69
71
71
73
90
86
100
96
75
91
a) y = 0:65x + 30:67
9.
b) y = 0:45x + 14:32
c) y = 0:53x + 17:53
d) y = 0:45x + 15:12
The graph show the population of cyotes in a certain area for the years 1981 to 1987. The years are
coded so that 1981 = 1, 1982 = 2, etc.
Use the exponential regression equation for the data to estimate the population in 2005.
a) 1321
b) 1158
c) 620
Page 4
d) 598
Benchmark 4-4 Exam
Mr. von Duchowitz
10.
A
B
C
Statistics
x
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
D
?
y
G
F
!
E
Use a calculator to nd the quadratic regression equation for the data points in the graph. Answer
accurate to one decimal place.
Note: Each horizontal and vertical line represents 1 unit.
a) y = 1:0x2 + 0:9x
11.
5:9
b) y = 2:3x2 + 0:9x
6:0
c) y = 1:1x2 + 1:9x
5:7
d) y = 1:0x2 + 1:9x
5:7
A scientist is studying the number of bacteria that are growing in a culture in the biology lab. From a
graph of the data she determines that the bacteria is increasing exponentially. Using the data and your
graphing calculator what is the exponential regression equation?
Time in hours Number of bacteria
1
230
2
520
3
1210
4
2790
5
6430
a) y = 99
2:3x
b) y = 91
2:8x
c) y = 95
Page 5
2:0x
d) y = 500
2:1x
Benchmark 4-4 Exam
Mr. von Duchowitz
12.
Statistics
Choose the reason(s) that explain why the line shown is not the line of best t for the scatter plot.
I. The line does not show the direction of the points.
II. There is a disproportionate number of points above the line.
III. There is a disproportionate number of points below the line.
IV. The points above or below the line are all concentrated at one end of the line.
a) II only
13.
b) III only
d) I and IV only
Albert has described the line of best t for a set of data as y = 1:5x + 1. The actual linear regression line
is y = 1:5x + 2:42. Which of the following graphs could be a set of residuals for the data with respect to
Albert's line?
b)
a)
14.
c) IV only
c)
d)
Using the data in the table, rst nd the linear regression line y1 for the data. Then use the equation to
nd the value of g in the table.
x
y
y1 (x)
Residual
-4
21
a
f
2
20
b
g
3
18
c
h
4
17
d
i
11 16
e
j
a) 0.066202090592
b) 1.177700348432
c)
Page 6
1.118466898955
d) 0.344947735192
Benchmark 4-4 Exam
Mr. von Duchowitz
15.
Using the data in the table, rst nd the linear regression line y1 for the data. Then use the equation to
nd the sum of the absolute values of the residuals.
x
y
y1 (x)
Residual
0
4
a
f
2
2
b
g
3
-5
c
h
6
-6
d
i
12 -9
e
j
a) 11.215596
16.
Statistics
b) 17.547475
c) 10.531674
d) 12.307393
The median-median line for a set of data is y = 3:1x + 2:4. Find the residual for the point ( 4; 15:2).
a) 0.4
b)
0.5
c)
Page 7
0.3
d) 0.8
Benchmark 4-4 Exam
Mr. von Duchowitz
17.
Statistics
The table shows health care expenditures during a seven-year period.
Health Care Expenditures
(billions of dollars)
Year
Expenditure
1990
1992
1994
1997
1.8
2.2
2.6
3.2
Graph the data below.
Select the point through which the graph passes.
a) A
18.
b) C
c) D
d) E
The gure is a scatter plot of ordered pairs gathered by measuring the body length of a child and the
circumference of the child's head. What is the equation of the linear regression line for this data?
a) y = 5:446x + 5:084
b) y = 0:747x
3:138
c) y = 5:462x + 0:430
d) y = 3:573x + 1:758
Page 8
Benchmark 4-4 Exam
Mr. von Duchowitz
19.
F
G
Statistics
x
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
D
?
?
?
?
?
?
?
?
?E
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
y
A
B
!
C
For the graph of the data points, nd the equation of the linear regression line for this data.
Note: Each horizontal and vertical line represents 1 unit.
a) y = 0:841x
20.
1:451
b) y = 0:630x
0:857
c) y = 0:619x
1:088
d) y = 1:573x
1:058
In a linear regression, which of the following explain why we need to be concerned with the range of the
independent (x) variable?
I. The precision of the estimate of the y variable depends on the range of the independent (x)
variable explored.
II. If the range of the x variable is very small, then the regression line will not be of much use.
III. If the range of the x variable is very small, then extrapolation is not recommended.
a) I and II only
b) I and III only
c) I, II and III
Page 9
d) II and III only
Benchmark 4-4 Exam
Mr. von Duchowitz
1.
Answer:
Objective:
a
S.ID.06A
13.
Answer:
Objective:
c
S.ID.06B
2.
Answer:
Objective:
c
S.ID.06A
14.
Answer:
Objective:
b
S.ID.06B
3.
Answer:
Objective:
d
S.ID.06A
15.
Answer:
Objective:
a
S.ID.06B
4.
Answer:
Objective:
a
S.ID.06A
16.
Answer:
Objective:
a
S.ID.06B
5.
Answer:
Objective:
b
S.ID.06A
17.
Answer:
Objective:
b
S.ID.06C
6.
Answer:
Objective:
a
S.ID.06A
18.
Answer:
Objective:
b
S.ID.06C
7.
Answer:
Objective:
a
S.ID.06A
19.
Answer:
Objective:
b
S.ID.06C
8.
Answer:
Objective:
a
S.ID.06A
20.
Answer:
Objective:
c
S.ID.06C
9.
Answer:
Objective:
b
S.ID.06A
10.
Answer:
Objective:
a
S.ID.06A
11.
Answer:
Objective:
a
S.ID.06A
12.
Answer:
Objective:
d
S.ID.06B
Statistics Extra Credit
Ms. Maceda
1.
Two particular kinds of locks have 3 or
4 number combinations. If they can only
use the numbers 1, 2, 3, 4, 5, or 6 and
must start with the number 3, then how many
combinations are possible?
A
252
_
2.
C
B
216
7776 _
_
5.
D
5040
_
In how many ways can 3 letters from the word
SENIOR be arranged?
A
12
_
3.
Name
B
20
_
C
_
120
6.
D
720
_
A delivery truck has to go from point X to
point Y and make a stop at point O. How
many di erent routes are possible, assuming
the driver never wants to go out of her way?
Each employee at a large company is to be
issued a computer ID code that consists of
three letters followed by two digits (0 to 9).
How many ID codes are possible if letters
may not repeat, but digits may repeat?
A
1,757,600
_
B
1,560,600
_
C
_
D
2,600,000
_
2,000,000
The menu of a Thai restaurant lists ve
vegetable dishes, eight seafood dishes and
ve noodle dishes. A group of customers
eating together decides to order three
vegetable dishes, four seafood dishes and
three noodle dishes. What is the number of
selections that the customers can make?
C
A
B
D
7000 _
5200 _
5100 _
6220
_
7.
A
60
_
4.
B
150
_
C
_
700
D
11
_
What is the number of di erent arrangements
of the word `CAPTURED' if the arrangements
begin and end in a vowel?
A
12
_
8.
A
40320
_
B
5040
_
C
_
D
84605
_
4320
How many paths are there from A to B if each
path must be as short as possible and follow
the edges of the grid?
B
30
_
C
_
14
D
25
_
In how many ways can ve men and four
women be seated on a bench if the men and
women must alternate seats?
C
A
B
D
2880 _
2328 _
2540 _
2100
_
Page 1
9.
Eight people from a list of ten are being
chosen to participate on a TV show about
survival. If Roger is chosen then Amber must
be chosen and vice versa. If Gerry is chosen
then Keith must not be chosen and vice versa.
In how many ways can the eight people be
chosen?
A
25
_
10.
B
35
_
C
_
18
13.
B
35
_
C
_
140
D
13
_
14.
D
210
_
B
7
_
C
_
8
D
10
_
15.
12.
A ball is dropped from the opening at the top
of the board shown. What is the probability
that the ball will exit through C or D?
A
_
5
8
B
_
1
16
C
_
5
16
D
_
A
.0476
_
B
.0397
_
C
_
D
.1056
_
.2381
A computer store has a sales bin that has
50 zip-drives in it. There are 15 that are
made in the USA, 12 that are made in Japan,
14 that are made in China and 9 that are
made in Germany. You are going to choose
3 zip-drives at random with replacement.
What is the probability that only two of the
three are from Germany?
Tara has the same number of skirts, pairs of
shoes, and tops. She won't wear the same
out t twice in a year. How many of each
clothing item does she have?
A
6
_
A Faculty-Student committee is to be selected
at random from 3 students and 6 faculty
members. The committee is to consist of
5 individuals.
What is the probability that no students are
on the committee?
The band will choose a new uniform for this
year. They can choose from 4 styles, 7 colors,
and 5 di erent types of material. In how many
ways can they select their uniforms?
A
16
_
11.
Ms. Maceda
7
16
Page 2
A
.0175
_
B
.0058
_
C
_
D
.54
_
.0116
In the game of blackjack, a 2-card hand
consisting of an ace and either a face card
or a 10 is called a blackjack. If a player
is dealt 2 cards from a standard deck of
52 well-shu ed cards, what is the probability
that the player will receive a blackjack?
A
_
0.0483
B
_
0.0631
C
_
0.0111
D
_
0.0524
1.
Answer:
Objective:
A
S.CP.09
13.
Answer:
Objective:
A
S.CP.09
2.
Answer:
Objective:
C
S.CP.09
14.
Answer:
Objective:
A
S.CP.09
3.
Answer:
Objective:
A
S.CP.09
15.
Answer:
Objective:
A
S.CP.09
4.
Answer:
Objective:
C
S.CP.09
5.
Answer:
Objective:
B
S.CP.09
6.
Answer:
Objective:
A
S.CP.09
7.
Answer:
Objective:
A
S.CP.09
8.
Answer:
Objective:
A
S.CP.09
9.
Answer:
Objective:
D
S.CP.09
10.
Answer:
Objective:
C
S.CP.09
11.
Answer:
Objective:
C
S.CP.09
12.
Answer:
Objective:
A
S.CP.09
A game is played by rolling a fair six-sided die once. If
the die lands on a 1 the player wins $8 otherwise the
player loses $1.50. What is the value of the game?
A
_
$0.30
B
_
$0.08
C
_
$0.10
In a game that costs $3 to play, a fair die is rolled. If a
ve or a six is rolled the player receives $6. If any
other number is rolled, the player receives nothing.
What is the expected value of the game?
D
_
$0.18
A
_
A game consists of throwing a dart at a target. Assume
the dart must hit the target and land inside one of the
squares. The player pays $24 to play the game. If
the dart hits the shaded region, the player wins $44,
otherwise the player receives nothing. What is the
expected value of the game?
$0.50
B
_
$0.25
C
_
$0.75
D
_
$0.10
B
_
$1.00
C
_
$5.00
D
_
$1.00
A man wins $2.00 if a Head comes up and loses $3.00
if a Tail comes up when a coin is tossed. If he wins
on the rst toss he quits. If he loses on the rst toss
he tries once more. What is the expected amount of
money he can win?
A
_
A
_
$0.50
$0.75
B
_
$2.50
C
_
$1.50
D
_
$2.00
In a game there is a 1 in 5 chance of winning the
game and a 4 in 5 chance of losing. The game costs
$1 to play. If the game is won the winner receives $4.
If the game is lost the player receives nothing. What is
the expected value of the game?
A game costs $3 every time it is played. There is a
1 in 10 chance of winning $25, a 1 in 5 chance of
winning $5, and a 7 in 10 chance of winning nothing.
What is the expected value of the game?
A
_
A
_
$0.20
B
_
$0.20
C
_
$2.00
D
_
$0.75
C
_
$0.75
D
_
C
_
$0.50
D
_
$5.00
A game consists of tossing 2 coins. If they are both
Heads you win $4, if they are both Tails you win $6,
and if one of each comes up then you lose $8. What
are your expected winnings?
A
_
B
_
$0.00
B
_
$0.00
$2.00
In a game there is a 1 in 4 chance of winning the game
and a 3 in 4 chance of losing. The game costs $2 to
play. If the game is won the winner receives $5. If the
game is lost the player receives nothing. If you play
the game 10 times, what is the expected gain or loss?
A
_
$0.50
$7.50
$1.50
B
_
$2.00
C
_
$2.00
D
_
$0.75
A particular carnival game allows you to roll 3 dice. If
your number comes up on all 3 dice you win 4 times
the amount you payed to play. If your number comes
up on 2 of the dice then you win 3 times the amount
you payed to play. If your number comes up on only
one die, then you win double the amount you payed to
play. Finally, if your number doesn't come up then you
lose whatever amount you payed to play. If you pay
$1.00 to play, then what are your expected winnings?
A local high school runs the following game at an
annual fundraising event. In this game, marbles are
randomly picked from a bag. The bag contains four red
marbles, three white marbles, and one black marble. If
you pick the black marble, you win $5. If the one you
pick is white, you win $2. If you pick a red one, you
do not win anything. The game costs $2 to play. What
is the expected value of the game?
A
_
A
_
$0.08
B
_
$1.42
C
_
$1.42
D
_
$0.32
Use geometric probabilities to determine the expected
value of a game where the player turns the spinner to
determine the amount she will win, if the player pays
$8 to play.
A
_
C
_
$0.50
C
_
$1.50
$1.50
B
_
$0.125
D
_
$0.50
The odds that Allison will beat Sarah are 9 to 5. How
much money must be bet in order to win $25 if Allison
wins?
A
_
$45.00
$0.50
B
_
$0.50
D
_
$0.625
B
_
$38.89
C
_
$20.00
D
_
$31.11
A school casino has a game that pays $2.00 if an even
number comes up on the single roll of a die and pays
$4.00 if an odd number comes up on that roll. If this
is to be a fair game, how much should a player be
charged to play?
A
_
$3.00
B
_
$3.50
C
_
$2.75
D
_
$3.75
The odds of winning a ra e are 1 : 3. If the winning
prize is $12, then how much should a ticket cost if the
ra e is fair?
A
_
$4.00
B
_
$3.00
C
_
$6.00
D
_
$2.00
You invent a game where a single die is rolled. If a 4
comes up you pay out $12, if an odd number comes up
you pay out $8, and you pay nothing for anything else.
If this is to be a fair game, then how much should you
charge a player to play?
A
_
$6.00
B
_
$20.00
C
_
$4.50
D
_
$4.00
You invent a game where a single die is rolled. If a 4
comes up you pay out $12, if an odd number comes up
you pay out $8, and you pay nothing for anything else.
If this is to be a fair game, then how much should you
charge a player to play?
A
_
$6.00
B
_
$36.00
C
_
$4.50
D
_
$4.00
CCSS Math HS-S-3
Ms. Rodriguez
1.
Answer:
Objective:
B
S.MD.05A
9.
Answer:
Objective:
A
S.MD.05A
2.
Answer:
Objective:
D
S.MD.05A
10.
Answer:
Objective:
A
S.MD.05A
3.
Answer:
Objective:
C
S.MD.05A
11.
Answer:
Objective:
A
S.MD.05A
4.
Answer:
Objective:
A
S.MD.05A
12.
Answer:
Objective:
A
S.MD.05A
5.
Answer:
Objective:
A
S.MD.05A
13.
Answer:
Objective:
A
S.MD.06
6.
Answer:
Objective:
C
S.MD.05A
14.
Answer:
Objective:
A
S.MD.06
7.
Answer:
Objective:
D
S.MD.05A
15.
Answer:
Objective:
A
S.MD.06
8.
Answer:
Objective:
A
S.MD.05A
16.
Answer:
Objective:
A
S.MD.06

Quiz #2 Name Date 1.

Transcription

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