Review: Spring Final Exam Pre-AP Geometry

Review: Spring Final Exam
Pre-AP Geometry
1.
Find the midpoint of the segment with
endpoints (-6, 3) and (2, -3).
2.
The midpoint A of ̅̅̅̅
𝑆𝑀 has coordinates
(-9, 5). Find the coordinates of S if point
M is at (9, -3).
3.
Find the length of the segment with
endpoints (-2, -5) and (3, 7).
4.
The length and width of a rectangle are
quadrupled. How do the perimeter and
area of the new rectangle compare with
the perimeter and area of the original
rectangle?
5.
The figure below shows two squares. The
2
area of square I is 36 in and the area of
2
square II is 196 in . Find a and b.
6.
Space alien Google-eyed Goreki spent a
year observing life on our planet. When
autumn came, Google-eyed Goreki
notices that the leaves on the trees
surrounding his spacecraft turned golden
brown and fell from their branches. He
observes other trees in the area, and he
notices that their leaves also turned
brown and fell to the ground. When he
makes a conjecture based on his
observations, what type of reasoning is
space alien Google-eyed Goreki using?
9.
Find the value of 𝑥.
a
II
I
b
7.
Referring to the information in Q6, space
alien Google-eyed Goreki conjectures
“Porve simp torkdom feek”. Translate his
conjecture into English.
8.
What counterexample does space alien
Google-eyed Goreki need to see to
disprove his conjecture?
A
D
A'
3
C
x 3
B
x+2
B'
C'
10. As a coordinate mapping, write a
composition of transformations that
would map figure 𝐴 to figure 𝐴’.
11. If an angle is an obtuse angle, then its
measure is greater than 90° but less than
180°. The 𝑚∠𝐴 = 125°. Using the Law of
Detachment, what conclusion can be
made?
6
A
4
2
5
2
A'
4
2x + 4
12. If I go to my friend’s house, then I will use
his portable matter transportation unit to
instantaneously travel to a planet in the
general vicinity of Betelgeuse. If school is
canceled, then I will go to my friend’s
house. If I end up on a planet in the
vicinity of Betelgeuse, then my
dematerialized body will rematerialize so
that my left arm is attached to center of
my forehead. Using the Law of Syllogism,
what conclusion can be made?
13. Find the value(s) of 𝑥 that make 𝑙 ∥ 𝑚.
14. Find the value of 𝑥 so that 𝑚 ∥ 𝑛.
15. Find the equation of the line through the
points (−5, −1) and (−8, 4). Write your
answer in standard form.
For Q17-Q19, determine which triangles, if
any, are congruent. State the congruence
postulate or theorem that supports the
congruence statement. If the triangles cannot
be shown to be congruent from the given
information, write “Cannot be determined.”
17. WHY  _______ by ________
19. ADB  _______ by ________
20. Find the value of 𝑥.
l
(90 10x)°
(x2+3x)°
n
m
16. Find the values of x, y, and z.
60°
92°
z
48°
y
x
18. STP  _______ by ________
58°
x
21. Find the value of x.
22. Find the value of y.
11
y
x
23. x =
24
7
10
24. x =
25. x =
y=
26. The earth has a circumference of
approximately 24,900 miles. Find its
volume and surface area.
27. Solve the right triangle.
28. Solve the right triangle.
29. Find the value of x.
30. In the diagram, ABCDE ~ FGHJK. Find the
perimeter of ABCDE.
31. Find the value of x.
32. Find the values of x and y.
33. Using slope, how can you determine if
two lines are parallel, perpendicular, or
neither?
34. Write the equation of the line through
(-9, 4) that is parallel to the line with the
1
equation 𝑦 = 𝑥 − 2.
35. Write the equation of the line through
(-9, 4) that is perpendicular to the line
1
with the equation 𝑦 = 𝑥 − 2.
36. Find the value of x.
37. ABC is on the coordinate plane with A(3, 3), B(6, 3), and C(3, 6). Find the
coordinates of A’B’C’ if the triangle is
dilated by a scale factor of 2/3 with the
origin as the center of dilation.
15
F
G
9
A
10
H
B
C
18
12
E
D
K
15
J
68°
(2x+20)°
38. Classify the type of quadrilateral below.
3
39. Find the area of the regular hexagon.
10
3
40. Find the perimeter of the sector below.
41. Find the area of the shaded sector.
42. The area of a regular polygon is 14 square
units. If the side length is tripled, what is
the area of the new polygon?
43. Find the exact perimeter and area of the
rectangle below.
6 5 in.
4 in.
44. A square pyramid with the largest
possible volume is cut out of a cube with
a side length of 12 cm. Find the volume
of the square pyramid.
45. A cone with the largest possible volume is
cut from a cube with side length of 12 cm.
Find the volume of the cone.
46. A sphere with the largest possible volume
is cut out of a cube with a side length of
12 cm. Find the volume of the sphere.
47. In the diagram, the circle is inscribed in a
equilateral triangle. Find the area of the
shaded region.
48. Find the area of the shaded region.
49. To use the machine below you turn the
crank, which turns the pulley wheel,
which winds the rope and lifts the box.
Through how many rotations must you
turn the crank to lift the box 10 feet?
24
50. Find the volume and surface area of the
sphere with section removed.
51. Find the volume and surface area of the
solid.
52. The radius of Earth is about 6378 km, and
the radius of Mercury is about 2440 km.
About how many times greater is the
volume of Earth than that of Mercury?
53. A rectangular prism aquarium holds 64
gallons of water. A similarly shaped
aquarium holds 8 gallons of water. If a 1.5
2
ft cover fits on the smaller tank, what is
the area of a cover that will fit on the
larger tank?
54. Solid I is similar to Solid II. Find the value
of 𝑥.
56. x =
57. One group of carbon compounds, called
hydrocarbons, consists of combinations of
carbon (C) and hydrogen (H). In a
hydrocarbon compound, all carbon atoms
must be linked to each of the other
carbons in a chain. Hydrocarbons in
which all the bonds between the carbon
atoms are single bonds are called alkanes.
The first four alkanes are modeled below.
The dash between letters represents
single bonds.
What is the function for alkanes (CnH?)?
In other words, if there are n carbons (C),
how many hydrogen atoms (H) are in the
alkane?
55. Find the area of the shaded region,
rounded to the nearest tenth.
58. At a particular party, everyone shakes
hands with each other. This situation can
be modeled using geometry. Let points
represent people, and let the segments
that connect them represent handshakes.
At a party of 25 people, how many
handshakes will there be?
59. A plane intersects a double-napped cone
as shown below. What 2-D shape is
formed by the intersection?
60. How many more faces, edges, and
vertices does a pentagonal prism have
than a pentagonal pyramid?
61. Draw the indicated orthogonal views
and mat plan for the 3-D solid shown.
FRONT View
RIGHT view
62. Plot N’O’E’L’ if it is the image after
translating NOEL under the vector (10, -2)
and then reflecting it across the x-axis.
64. Classify the 3-D figure based on its net.
TOP View
63. Classify the 3-D figure based on its net.
65. Let’s say you are throwing beans at the
circular target shown. The radii of the
concentric circles are 3 inches, 6 inches,
and 12 inches respectively. What is the
probability that you will earn 15 points on
one throw of a bean, assuming that any
point on the target is equally likely to be
hit by a thrown and bouncing bean?
20
15
5
66. Find the volume of the right cone shown
below.
67. A traffic cone can be approximated by a
right cone with radius 5.7 inches and
height 18 inches. To the nearest tenth of
a square inch, find the approximate
lateral area of the traffic cone.
68. Find the lateral and total surface area.