Upload
others
View
1
Download
0
Embed Size (px)
Citation preview
Math Geometry FAIM 2015 Form 1-B [1530459]StudentClassDate
InstructionsUse your Response Document to answer question 21.
1. In the figure below,
Which relationship can be proven knowing that
A.
B.
C.
Math Geometry FAIM 2015 Form 1-B Page 1/73
D.
2. is translated to form as shown on the coordinate plane.
What are the translations applied to to form
3. How many square inches is the area of parallelogram MNOP, shown on the coordinate plane below?
Math Geometry FAIM 2015 Form 1-B Page 2/73
4. Which statement must be true?
A.
B.
C.
D.
5. Isabella graphed a quadrilateral with coordinates and on a coordinate plane.
Part A. Use the coordinates of the points to prove that WXYZ is a parallelogram.
Part B. Isabella thinks that quadrilateral WXYZ is a also rectangle. Is she
Math Geometry FAIM 2015 Form 1-B Page 3/73
correct? Explain.
Use words and/or numbers to show your work.
6. Dwayne considers a square drawn in the xy-coordinate plane with vertices
Dwayne finds squa
Math Geometry FAIM 2015 Form 1-B Page 4/73
re
by dilating TUVW with a scale factor of 2, and with a center of dilation at
What is the slope of
A.
Math Geometry FAIM 2015 Form 1-B Page 5/73
B.
C.
D.
7. Alex needs to bisect
using a compass and straightedge. He starts by perfo
Math Geometry FAIM 2015 Form 1-B Page 6/73
rming the following steps.
Step 1: Place the compass on vertex B of the angle.Step 2: Draw an arc that intersects bo
Math Geometry FAIM 2015 Form 1-B Page 7/73
th sides of the angle.Step 3: Label these intersections as point D and point E.Step 4: Place the compass at poi
Math Geometry FAIM 2015 Form 1-B Page 8/73
nt D and draw an arc in the interior of the angle.
What are the next steps Alex should take in his construction?
Math Geometry FAIM 2015 Form 1-B Page 9/73
A. Adjust the compass width to be half the distance between pointBand pointEand then place the
Math Geometry FAIM 2015 Form 1-B Page 10/73
compass on pointEand draw an arc in the interior of the angle that crosses the other arc.
B. Withou
Math Geometry FAIM 2015 Form 1-B Page 11/73
t adjusting the compass width, place the compass at pointEand draw an arc in the interior of the angle
Math Geometry FAIM 2015 Form 1-B Page 12/73
that crosses the other arc.
C. Adjust the compass width to be half the distance between pointB
Math Geometry FAIM 2015 Form 1-B Page 13/73
and pointEand then place the compass on pointEand draw an arc on the exterior of the angle.
D. Wi
Math Geometry FAIM 2015 Form 1-B Page 14/73
thout adjusting the compass width, place the compass at pointEand draw an arc on the exterior of the
Math Geometry FAIM 2015 Form 1-B Page 15/73
angle that is opposite the other arc.
8. Given points
and
what is the value of the ratio
Math Geometry FAIM 2015 Form 1-B Page 16/73
9. Kayla measured the distances surrounding a lake, as shown in the diagram below.
Math Geometry FAIM 2015 Form 1-B Page 17/73
Kayla used the diagram to determine the distance across the lake. If
Math Geometry FAIM 2015 Form 1-B Page 18/73
what is the distance across the lake?
A. 75
ft
B. 95
ft
C. 112.5 ft
D. 165.8 ft
10.
Quadrilateral AB
Math Geometry FAIM 2015 Form 1-B Page 19/73
CD is considered a cyclic quadrilateral because there is a circle passing through all four of its vertices.
Math Geometry FAIM 2015 Form 1-B Page 20/73
What is the sum, in degrees, of
Explain your answer.
Math Geometry FAIM 2015 Form 1-B Page 21/73
11.
Consider the diagram and angle measurements shown below.
Math Geometry FAIM 2015 Form 1-B Page 22/73
What is
A.
B.
C.
D.
12.
A flat, rectangular television
Math Geometry FAIM 2015 Form 1-B Page 23/73
screen has a height of 25 inches and a diagonal of 32 inches. What is the width of the television screen? Round yo
Math Geometry FAIM 2015 Form 1-B Page 24/73
ur answer to the nearest hundredth of an inch.
13.
The figure below shows the circles and
Which of thes
Math Geometry FAIM 2015 Form 1-B Page 25/73
e statements can be used to prove that the circles are similar?
A. Th
Math Geometry FAIM 2015 Form 1-B Page 26/73
e circles and
are similar because
can be mapped onto
by a translation two units to the right an
Math Geometry FAIM 2015 Form 1-B Page 27/73
d three units up followed by a dilation about its center by a scale factor of
B. The circles and
are
Math Geometry FAIM 2015 Form 1-B Page 28/73
similar because
can be mapped onto
by a translation two units to the right and three units up followed
Math Geometry FAIM 2015 Form 1-B Page 29/73
by a dilation about its center by a scale factor of 2.
C. The circles and
are similar because
can
Math Geometry FAIM 2015 Form 1-B Page 30/73
be mapped onto
by a translation two units to the left and three units down followed by a dilation about its
Math Geometry FAIM 2015 Form 1-B Page 31/73
center by a scale factor of
D. The circles and
are similar because
can be mapped onto
by
Math Geometry FAIM 2015 Form 1-B Page 32/73
a translation two units to the left and three units down followed by a dilation about its center by a scale fac
Math Geometry FAIM 2015 Form 1-B Page 33/73
tor of 2.
14.
In the figure below,
Write a proportion using the sid
Math Geometry FAIM 2015 Form 1-B Page 34/73
e lengths of the triangles that can be used to prove that
15.
Part A. A cone is carved from a cylinder
Math Geometry FAIM 2015 Form 1-B Page 35/73
so that the cone has a volume of
and a diameter of 4 ft. If the cylinder has the same height and base as the co
Math Geometry FAIM 2015 Form 1-B Page 36/73
ne, find the height and the volume of the cylinder. Show your work.
Part B. A cone is carved from a cylinder. If
Math Geometry FAIM 2015 Form 1-B Page 37/73
the cylinder has the same height and base as the cone, explain how to determine the volume of the cylinder wit
Math Geometry FAIM 2015 Form 1-B Page 38/73
hout determining the height or the size of the base.
Use words and/or numbers to show your work.
16 In
Math Geometry FAIM 2015 Form 1-B Page 39/73
. the figure below, Circle C has tangent lines
and
and diameter
Math Geometry FAIM 2015 Form 1-B Page 40/73
Angle QSR measures
What is the measure of
A.
B.
Math Geometry FAIM 2015 Form 1-B Page 41/73
C.
D.
17.
In the diagram below,
What is the
Math Geometry FAIM 2015 Form 1-B Page 42/73
most precise classification for quadrilateral ADEF?
18.
The radius and slant height of a right cone are 3 cm an
Math Geometry FAIM 2015 Form 1-B Page 43/73
d 5 cm, respectively. To the nearest tenth of a cubic centimeter, what is the volume of the cone?
19.
The
Math Geometry FAIM 2015 Form 1-B Page 44/73
figure below shows isosceles triangle ABC, with
and
bisecting
Which is a valid
Math Geometry FAIM 2015 Form 1-B Page 45/73
proof that shows
?
A.
B.
C.
Math Geometry FAIM 2015 Form 1-B Page 46/73
D.
20.
Soda cans are made out of aluminum and are shaped like a cylinder. The formula for the
Math Geometry FAIM 2015 Form 1-B Page 47/73
surface area of a cylinder can be used to find the amount of aluminum, in square centimeters, that is needed to ma
Math Geometry FAIM 2015 Form 1-B Page 48/73
ke a soda can. The formula is provided below:
A typical soda can measures 12 centimeters tall and has a vol
Math Geometry FAIM 2015 Form 1-B Page 49/73
ume of 235.5 cubic centimeters. To the nearest whole number, how many square centimeters of aluminum are require
Math Geometry FAIM 2015 Form 1-B Page 50/73
d to make a can?
A. 39 square centimeters
B. 188 square centimeters
C. 208 square centimeters
Math Geometry FAIM 2015 Form 1-B Page 51/73
D. 228 square centimeters
21.
Mark is planting a garden in a corner of his backyard. He wants to divide the
Math Geometry FAIM 2015 Form 1-B Page 52/73
garden into different sections for different vegetables, and he wants the sections to be congruent to each ot
Math Geometry FAIM 2015 Form 1-B Page 53/73
her so that he is sure that the different types of plants have the same amount of space.
Math Geometry FAIM 2015 Form 1-B Page 54/73
Part A. Sketch one segment that would divide the garden to produce two co
Math Geometry FAIM 2015 Form 1-B Page 55/73
ngruent triangles. Part B. Use a paragraph proof to explain how you know that the two triangles are co
Math Geometry FAIM 2015 Form 1-B Page 56/73
ngruent. Part C. Now, Mark wants to divide each of the two triangular sections in half so the garden will ha
Math Geometry FAIM 2015 Form 1-B Page 57/73
ve a total of four congruent triangles. Sketch one possible way Mark can do this, and label the side lengths an
Math Geometry FAIM 2015 Form 1-B Page 58/73
d angle measures. Part D. Explain how you know that all four triangles are congruent, using a paragraph
Math Geometry FAIM 2015 Form 1-B Page 59/73
proof and a different congruence postulate than used in part A. Part E. How does the side length of the ori
Math Geometry FAIM 2015 Form 1-B Page 60/73
ginal garden relate to the side length of the four small triangles? Explain, using a paragraph proof and geometric
Math Geometry FAIM 2015 Form 1-B Page 61/73
postulates to support your answer. Place an "X" in the answer box below.Answer the question on the Resp
Math Geometry FAIM 2015 Form 1-B Page 62/73
onse Document provided.Click next.
22.
What is the center of a circle given by the equation:
Math Geometry FAIM 2015 Form 1-B Page 63/73
23.
Line segment
is drawn in the first quadrant. Its image, line segment
is formed by reflecting
ov
Math Geometry FAIM 2015 Form 1-B Page 64/73
er the x-axis. Which statement will always be true?
A. Line segments
and
are parallel to each othe
Math Geometry FAIM 2015 Form 1-B Page 65/73
r.
B. Line segments
and
are perpendicular to each other.
C. Corresponding points on
and
Math Geometry FAIM 2015 Form 1-B Page 66/73
are equidistant from the xaxis.
D. Corresponding points on
and
can be connected to form a
Math Geometry FAIM 2015 Form 1-B Page 67/73
line segment perpendicular to both
and
24.
Which words correctly complete the statement below?
Math Geometry FAIM 2015 Form 1-B Page 68/73
is dilated with the center of dilation at the origin and a scale factor of 0.5 to obtain
The triangles’ corresponding
Math Geometry FAIM 2015 Form 1-B Page 69/73
angles are
and their corresponding sides are
therefore, the triangles are
A. congruent; proport
Math Geometry FAIM 2015 Form 1-B Page 70/73
ional; similar
B. congruent; congruent; congruent
C. proportional; proportional; similar
D. proport
Math Geometry FAIM 2015 Form 1-B Page 71/73
ional; congruent; congruent
25.
What is the y-intercept of the line perpendicular to the line
th
Math Geometry FAIM 2015 Form 1-B Page 72/73
at includes the point
Math Geometry FAIM 2015 Form 1-B Page 73/73