Download EOCT Review Packet

UNIT 1: Use the following to review for you test. Work the Practice Problems on a separate sheet of paper.
What you need to
know & be able to
do
Things to
remember
A. Solve for x when
the angles are
supplementary.
Angles add to 180º
1.
2.
30°
B. Solve for x when
the angles are
complementary.
Angles add to 90º
2x – 50°
3.
One angle is 12 more than twice
its supplement. Find both
angles.
4.
2x - 10
3x + 10 and 2x – 5 are
complementary.
Solve for x.
x+5
C. Recognize and
solve vertical angles
Set vertical angles
equal to each other
5.
6.
x + 50
4x + 12
100°
D. Name and solve
problems involving
angles formed by 2
parallel lines and a
transversal.
Consecutive interior
angles are
supplementary.
Alternate interior,
alternate exterior, and
corresponding angles
are congruent.
7.
8.
9.
10.
2x - 20
E. Recognize and
solve midsegment of
a triangle problems
A midsegment
connecting two sides
of a triangle is parallel
to the third side and is
half as long.
11.
12.
F. Recognize and
solve triangle
proportionality
theorem problems
If a line parallel to one
side of a triangle
intersects the other
two sides of the
triangle, then the line
divides these two sides
proportionally.
13.
14.
The interior angles of
G.Solve for x in
a triangle sum to 180°.
problems involving
the sum of the interior
angles of a triangle.
15.
16.
3x
95°
x°
35°
(5x – 14)
H. Solve for x in
problems involving
the exterior angle
theorem.
The measure of an
exterior angle of a
triangle equals to the
sum of the measures
of the two remote
interior angles of the
triangle.
17.
18.
I. Recognize and
solve problems
involving the
congruent base
theorem.
If two sides of a
triangle are congruent,
then the angles
opposite those sides
are congruent.
19.
20.
25. ABC  FEG
26. ABC  FEG
CA  __________
GEF  __________
J. Name
Corresponding Parts
of Triangles.
K. Determine if two
triangles are
congruent.
Remember the 5
ways that you can
do this: SSS, SAS,
ASA, AAS, HL
27.
28.
UNIT 2: Use the following to review for you test. Work the Practice Problems on a separate sheet of paper.
What you need to
know & be able
to do
Things to remember
1. Dilate with k = ½.
A. Perform a
dilation with a
given scale factor
When the center of dilation
is the origin, you can
multiply each coordinate of
the original figure, or preimage, by the scale factor
to find the coordinates of
the dilated figure, or
image.
B. Find the
missing side for
similar figures.
Set up a proportion by
matching up the
corresponding sides. Then,
solve for x.
2. Dilate with k = 2.
3.
4.
5.
6.
7. ΔGNK ~ ______ by______
C. Determine if 2
triangles are
similar, and write
the similarity
statement.
8. ΔABC ~ ______ by______
Remember the 3 ways that
you can do this: AA, SAS,
SSS
9. Find sin A.
A
10. Find tan B.
D. Find sin, cos,
and tan ratios
Just find the fraction
using SOHCAHTOA
22
18
11. Find cos B.
12. Find tan A.
C
E. Know the
relationship
between the ratios
for
complementary
angles.
sin   cos(90   )
cos   sin(90   )
1
tan  
tan(90   )
14
B
13. Given Right ΔABC and sin   5 /13 , find
sin(90   ) and cos(90   ) .
15. Find m.
Set up the ratio and then
use your calculator.
F. Use trig to find
a missing side
measure
43
14. Find f.
85
25
If the variable is on the top,
multiply.
If the variable is on the
bottom, divide.
7
f
m
17. Find s.
16. Find p.
G. Use trig to
find a missing
angle measure
Set up the ratio and then
use the 2nd button on your
calculator.
32
p
40
s
13
17
Unit 2 – Right Triangle Trigonometry
46. A road ascends a hill at an angle of 6°.
For every 120 feet of road, how many
feet does the road ascend?
STANDARD: TRIGONOMETRIC RATIOS


Trig Ratios –
𝑂
𝐴
Sin 𝜃 = 𝐻 Cos 𝜃 = 𝐻
𝑂
Tan 𝜃 = 𝐴
47. Given triangle 𝐴𝐵𝐶, what is sin 𝐴?
Inverse Trig Ratios – Only used when
finding the angle measure of a right
triangle.
9
48. In a right triangle, if cos 𝐴 = 12, what is
43. What does it mean for two angles to be
complementary?
44. Angle 𝐽 and angle 𝐾 are complementary
angles in a right triangle. The value of
15
tan 𝐽 is . What is the value of sin 𝐽?
8
sin 𝐴?
49. In right triangle 𝐴𝐵𝐶, if  𝐴 and  𝐵
are the acute angles, and sin 𝐵 =
6
,
20
what is cos 𝐴?
45. Triangle 𝑅𝑆𝑇 is a right triangle with
right angle 𝑆, as shown. What is the
area of triangle 𝑅𝑆𝑇?
50. Find the measure of angle 𝑥. Round
your answer to the nearest degree.
51. Solve for 𝑥.
19
52. You are given that tan 𝐵 = 11. What is
the measure of angle 𝐵?
53. A ladder is leaning against a house so
that the top of the ladder is 18 feet
above the ground. The angle with the
ground is 47. How far is the base of
the ladder from the house?
Unit 3 – Circles and Spheres
54. What is the value of 𝑥 in this diagram?
y
55. Given 𝑇, with the inscribed
quadrilateral, find the value of each
variable.
2x
STANDARD: CIRCLES

Area – 𝜋𝑟 2

Circumference – 2𝜋𝑟

Parts of a Circle –
56. ̅̅̅̅
𝐴𝐵 is tangent to 𝐶 at point 𝐵. ̅̅̅̅
𝐴𝐶
̅̅̅̅ measures 7
measures 12 inches and 𝐴𝐵
inches. What is the radius of the circle?
57. Given 𝑄, the 𝑚𝐴𝐵𝐶 = 54° and the
𝑚𝐴𝑄𝐶 = (2𝑥 + 6)° find the value of
x.


Properties of Tangent Lines –
o Tangent and a radius form a
right angle
o You can use Pythagorean
Theorem to find the side
lengths
o Two tangents from a common
external point are congruent
Central Angles – 𝑚𝐴𝑛𝑔𝑙𝑒 = 𝑚𝐴𝑟𝑐

Inscribed Angles – 𝑚𝐴𝑛𝑔𝑙𝑒 =

Angles Outside the Circle –
𝑓𝑎𝑟 𝑎𝑟𝑐 − 𝑛𝑒𝑎𝑟 𝑎𝑟𝑐
𝑎𝑛𝑔𝑙𝑒 𝑥 =
2
Intersecting Chords –
𝑎𝑟𝑐 𝐴 + 𝑎𝑟𝑐 𝐵
𝑎𝑛𝑔𝑙𝑒 𝑥 =
2

58. If two tangents of 𝑋 meet
at the external point 𝑍, find
their congruent length.
𝑚𝐴𝑟𝑐
2
̂ is 64°. What is the
59. The measure of 𝐶𝐷
measure of 𝐵𝐷𝐶?
100
T
86
60. Isosceles triangle 𝐴𝐵𝐶 is inscribed in
̂ = 108°.
this circle. ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐵𝐶 and 𝑚𝐴𝐵
What is the measure of 𝐴𝐵𝐶?
61. In this diagram, segment ̅̅̅̅̅
𝑄𝑇 is tangent
to circle 𝑃 at point 𝑇. The measure of
̂ is 70°. What is 𝑚𝑇𝑄𝑃?
minor arc 𝑆𝑇
STANDARD: SPHERES

Surface Area – 4𝜋𝑟 2

Volume - 3 𝜋𝑟 3
4
62. A sphere has a radius of 8 cm. What is
the surface area? Answer in both
decimal and exact -form.
63. When comparing two
different sized bouncy balls,
by how much more is the
volume of larger ball if its
radius is 3 times larger than
the smaller ball?
64. Find the volume of the following
figures.
CCGPS Geometry
Unit 4 – Operations and Rules
Unit 4 Key Notes:

Combine like terms when adding and
subtracting polynomials

Use the distributive property when multiplying
polynomials

Perimeter: Add up all the sides

Area: length*width

Volume: Bh (remember B=area of the base)
Day 35 – Review
 Examples: 7 , 5 , 
Rational Numbers:
Can be expressed as the quotient of two integers (i.e.
a fraction) with a denominator that is not zero.
Many people are surprised to know that a repeating
decimal is a rational number.
Examples: -5, 0, 7, 3/2,




Imaginary Numbers: i × i = -1,
then -1 × i = -i,
then -i × i = 1,
then 1 × i = i (back to i again!)
i = √-1



i2 = -1
i3 = -√-1
i4 = 1

0.26
9 is rational - you can simplify the square
root to 3 which is the quotient of the integers 3
and 1.
i5 = √-1
The complex conjugate of a + bi is a – bi, and
similarly the complex conjugate of a – bi is a
+ bi. This consists of changing the sign of the
imaginary part of a complex number. The real
part is left unchanged.
Irrational Numbers:
Can’t be expressed as the quotient of two
integers (i.e. a fraction) such that the
denominator is not zero.
Unit 4 Test Review
Add or Subtract:
1. (5x2  8 x  6)  (7x2  9x  3)
2.
3x
Multiply:
3. 7 x 2  9xy 3  8 z 4 y  4y 3 
4.
 x  4
6.
 x  2   x2  4 x  6
5.
 x  6 x  7
7. Give the perimeter of the deck shown below.
2x + 4
x +3
x +3
10
2
 

 5 x  9  6 x 2  5 x  11
2
CCGPS Geometry
Unit 4 – Operations and Rules
8. Find the area of the figures
a)
Day 35 – Review
b)
x+3
x+2
4x+2
2x+6
9. Find the area of the white space.
(x + 2)
2x
x
(x + 3)
10. Find the volume of the rectangular prism.
x +3
x +6
x +1
Evaluate.
11. i12
12. i 27
13. i121
Perform the following complex operations.
14. (2  5i)  (4  12i)
15. (4  5i)(6  5i)
16.
9  2i
1  3i
17. 7i 2  3i 6
2
18. Rewrite in exponential form ( 4 x )9 .
19. Rewrite in radical form (4 x 2 ) 3
Simplify each expression completely.
21. 8
5
3
22.
4
256a16b20c13
23.
3
125 x3
8
CCGPS Geometry
1
3
1
4 2
24. (64  9 )
Unit 4 – Operations and Rules
4 2
2 3
5
5
25. 2 8 x y  8 x y
Day 35 – Review
26.
4 3 54 x4  x 3 16x
27.
43 x
2
2
28. 16x 5
3 6 3
29. (8 x y )
4
2
85
1
3
30.
x  x2
2
1
1
2
31. 2 x 3  4 x 2  8 x 3
x3
Review:
32. Find the volume of each figure below.
a)
b)
c)
CCGPS Geometry
Standard Form of a Circle
(Center at the Origin)
where r is the radius
Standard Form of a Circle (not
Centered at the Origin)
where
Unit 4 – Operations and Rules
Day 35 – Review
Characteristics of a Standard Equation of a Parabola (Vertex at
1. Write the
equation of the circle with
Origin)
center (3, -7) and radius
25 .
FOCUS
DIRECTRIX
AXIS
x2 = 4py
(0, p)
y = -p
x=0
y2 = 4px
(p, 0)
x = -p
y=0
EQUATION
is the center of the circle
Let us put that center at (a,b). So the circle
is all the points (x,y) that are "r" away from
the center(a,b).
2. Write the equation of the line tangent
to the circle x 2  y 2  40 at the point (6,
2).
Now we can work out exactly where all those
points are! We simply make a right-angled
triangle (as shown), and then
usePythagoras (a2 + b2 = c2):
3. What is the radius and center for the
2
2
circle  x  3   y  4   18 ?
4. Write the equation of the circle with
the center (3, -3) and Diameter 4 cm.
Then draw the circle.
Y
(x-a)2 + (y-b)2 = r2
Completing the Square:
x + y - 2x - 4y - 4 = 0
Put xs and ys together on left:
(x2 - 2x) + (y2 - 4y) = 4
Now to complete the square you take half of
the middle number, square it and add it.
Example:
2
2
(Also add it to the right hand side so the
equation stays in balance!)
Do it for "x"
(x2 - 2x + (-1)2 ) + (y2 - 4y) = 4 + (-1)2
And for "y":
(x2 - 2x + (-1)2) + (y2 - 4y + (-2)2 ) = 4 + (1)2 + (-2)2
Simplify:
(x2 - 2x + 1) + (y2 - 4y + 4) = 9
Finally: (x - 1)2 + (y - 2)2 = 32
X
CCGPS Geometry
5.
5.
6.
7.
8.
Unit 4 – Operations and Rules
Day 35 – Review
CCGPS Geometry
9.
10.
11.
12.
13.
Unit 4 – Operations and Rules
Day 35 – Review
CCGPS Geometry
Unit 4 – Operations and Rules
Day 35 – Review
14.
15.
16.
1. In a certain town, the probability that a person plays sports is 65%. The probability that
aperson is between the ages of 12 and 18 is 40%. The probability that a person plays
sports and is between the ages of 12 and 18 is 25%. Are the events independent? How do
youknow?
2. Terry has a number cube with sides labeled 1 through 6. He rolls the number cube twice.
a. What is the probability that the sum of the two rolls is a prime number, given that at
least
one of the rolls is a 3?
b. What is the probability that the sum of the two rolls is a prime number or at least one of
the rolls is a 3?
3. Mrs. Klein surveyed 240 men and 285 women about their vehicles. Of those surveyed,
155 men and 70 women said they own a red vehicle. If a person is chosen at random
from those surveyed, what is the probability of choosing a woman or a person that does
NOT own a red vehicle?
4. Bianca spins two spinners that have four equal sections numbered 1 through 4. If she
spins a 4 on at least one spin, what is the probability that the sum of her two spins is an
odd number?
5. Each letter of the alphabet is written on a card using a red ink pen and placed in a
container. Each letter of the alphabet is also written on a card using a black ink pen
and placed in the same container. A single card is drawn at random from the container.
CCGPS Geometry
Unit 4 – Operations and Rules
Day 35 – Review
What is the probability that the card has a letter written in black ink, the letter A, or
the letter Z?
6. In Mr. Mabry’s class, there are 12 boys and 16 girls. On Monday, 4 boys and 5 girls were
wearing white shirts.
a. If a student is chosen at random from Mr. Mabry’s class, what is the probability of
choosing a boy or a student wearing a white shirt?
b. If a student is chosen at random from Mr. Mabry’s class, what is the probability
ofchoosing a girl or a student not wearing a white shirt?
7. Assume that the following events are independent:
o The probability that a high school senior will go to college is 0.72.
o The probability that a high school senior will go to college and live on campus is
0.46.
What is the probability that a high school senior will live on campus, given that the person will
go to college?
8. Abdu, Reilly, Chandra, and Delroy are on a Student Council committee. For the January
meeting, they put their names in a hat and draw one name at random to decide who will
take notes. They do the same thing for the February meeting. What is the probability that
Abdu will be chosen at least once or Reilly will be chosen at least once?
9. Meadow Ridge High School has 820 students. There are 88 students in vocal music, 142
students in instrumental music, and 190 students in vocal or instrumental music. Which
option shows the approximate probability that a randomly chosen student at Meadow
Ridge High School is in both vocal and instrumental music?
a. 4.9% b. 6.6% c. 16.6% d. 29.8%
10.
CCGPS Geometry
11.
12.
Unit 4 – Operations and Rules
Day 35 – Review
CCGPS Geometry
13.
Unit 4 – Operations and Rules
Day 35 – Review