[DIRECTIONS: FOR EACH ROUND, YOU WILL COMPLETE 4 PROBLEMS WITH AN ASSIGNED
PARTNER.ONCE TIME IS CALLED, YOU WILL THEN BE INSTRUCTED TO ROTATE TO THE
SPEED DATING:
Final Exam Review
NEXT PERSON. DURING THE ROTATION, YOU WILL CHECK ANSWERS FOR THE PREVIOUS
ROUND AND THEN WORK ON A NEW SET OF 4 PROBLEMS. PROCESS WILL REPEAT AS
DEEMED NECESSARY. NOTE: THIS ACTIVITY IS NOT A COMPETITION, BUT RATHER
SHOULD BE VIEWED AS AN OPPORTUNITY TO COLLABORATE AND UNDERSTAND YOUR
CLASSMATES’ METHODS OF SOLVING. A TIME WILL BE LEFT AT THE END OF CLASS TO
ADDRESS QUESTIONS AS A WHOLE CLASS.]
Round One Questions
2. Find the counter-clockwise angle of rotation about O that maps
.
F
1. Find the image of C(-7, 2) under the translation
described by the translation rule
.
R
G
Q
H
P
I
O
N
J
M
3. A microscope shows you an image of an object that is 80
K
L
4. What is the value of x?
times the object’s actual size. An insect has a body length
of 7 millimeters. What is the body length of the insect
38°
under the microscope?
21
21
xº
Drawing not to scale
Round Two Questions
1. Use the information in the diagram to determine the
measure of the angle formed by the line from the point on
the ground to the top of the building and the side of the
building. The diagram is not to scale.
2. For the triangle represented by the above drawing, what is the
exact length of
?
46º
15
3. Given
length of QS and TV.
, QS=3v+2 and TV=7v-6, find the
4.
State whether the two triangles are congruent and how?
Round Three Questions
1. Joe and Sara were standing on a pier sailing a toy sail
2. The ratio of a pair of corresponding sides in two similar
boat. The boat was 6 feet from the base of the pier and
triangles is 5:3. The area of the smaller triangle is 108 cm2. What
the pier was 4 feet above the water.
is the area of the larger triangle?
Determine the angle of depression to the nearest tenth
from the pier to the toy sail boat.
3.
Solve for x and then find all the angle measurements.
4.
A mountain climber stands on level ground 300m from the base
of a cliff. The angle of elevation to the top of the cliff is 58˚.
What is the height of the cliff to the nearest tenth of a
meter?
Round Four Questions
1.
Find the product: (n2 + 6n − 4)(2n − 4)
2.
Simplify the rational expression:
9 x 2  81x
x 3  8x 2  9 x
State any restrictions on the variable.
3.
Solve the quadratic equation by using the quadratic
formula: 10n2 – 9= 5n
4.
If
which statement represents a correct value of
x?
A)
B)
C)
D)
Round Five Questions
2. Translate the image up 4 and right 2. Provide the image
coordinates.
1.
What is the rule that maps the pre-image to the
image?
3.
Translate the figure ABCD (x, y)→(x+2, y-1) and then
reflect it across y=2. Where A(-5, -2), B(-4,1), C(0, -1),
D(-2, -4). Provide the image coordinates.
4.
What are the coordinates of the image when reduced by
Round Six Questions
1.
Given: A trapezoid.
perpendicular to
and
.
and
.
Prove: EGF HFG
.
S
R
V
U
T
W
4. Given:
Given:
X
and
Prove:
Prove:
V
W
Z
Given: E H; HFG EGF
perpendicular to
Prove:
3.
2.
.
Y
Statements
1.
and
Reasons
1. Given
2.
3.
2. Vertical angles are
congruent
3. ?
4.
4. ?
.
1.
3.
1.
Round Seven Questions
A 20 foot ladder is leaning against a wall. The foot of
2. What is the ratio of the surface areas of two spheres with
the ladder is 7 feet from the base of the wall. What is
volumes of 64 cm3 and 125 cm3?
the measure of the angle the ladder forms with the
ground? Round to the nearest hundredth?
A sign is shaped like an equailateral traingle. If one
side of the sign is 40 inches what is the area of the
sign?
4.
A spherical paintball measures 1.5 centimeters in diameter.
How much paint can the paintball hold, in terms of π?
Round Eight Questions
A cylinder with a height of 6 inches and a radius of 3
2. When standing upright, Gary knows his eyes are 6 feet above
inches is inside a rectangular prism, as shown below.
ground level. To determine the depth of a well, he stands in
the position shown.
A point inside the rectangular prism will be chosen
randomly. What is the probability that the point will also be
How deep is the well?
inside the cylinder?
3.
A circle is inscribed in a square, as shown below.
If a point is randomly chosen inside the square, what is
the chance that the point lies outside the circle?
Round answer to nearest whole percent.
4.
A cube is painted as shown. The three faces that are not
seen are not painted.
If a point on the surface of the cube is randomly chosen,
what is the probability that it will lie in the painted area?
Round Nine Questions
1.
Determine the length of the side of a square in simplest
2.
radical form if the diagonal of the square is 7 cm.
Determine the length of the rectangular prism using the
given information. The volume is 2,187 in3.
9in
9in
3.
Find the area of the figure.
4.
A box with no top is to be made from an 8 inch by 6 inch
piece of metal by cutting identical squares from each
corner and turning up the sides. The volume of the box is
modeled by the polynomial 4x3 – 28x2 + 48x. Factor the
polynomial completely. Then use the dimensions given on
the box and show that its volume is equivalent to the
factorization that you obtain.
Round Ten Questions
3
1.
Simplify:
 3x 5 


 y 
3.
Simplify:
9
9

x2 x
State any excluded values.
2.
Simplify:
4.
Simplify:
12
3
x 2  49 x 2  14 x  49
 2
2x  2
x  6x  7
State any excluded values.