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Study Guide
Semester 2: 2nd 4.5 Exam
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Vocabulary words to know! Write a short definition in your own words for each vocabulary word.
Word To Know
Definition
Word To Know
Definition
Sample Space
Sample Space shows all possible Probability
The chance that an event
outcomes.
will occur
Compound Probability
The probability of more than 1
event
Scalene Triangle
A triangle with no
congruent sides
Acute Angle
A angle less than 90 degrees
Isosceles Triangle
A triangle with at least two
congruent sides
Equilateral Triangle
A triangle where all sides
are congruent
Acute Triangle
A triangle with three acute
angles
Complementary Angles
2 angles who have a sum
equal to 90 degrees
Right Angle
An angle which measures
exactly 90 degrees
Obtuse Angle
Supplementary Angles
An angle which measures more
than 90 degrees
2 angles who have a sum equal
to 180 degrees
Right Triangle
A triangle with one right angle
Obtuse Triangle
A triangle with one obtuse
angle
Cross-section
The 2d shape that is formed
when a 3D figure is sliced by a
plane
Fundamental counting
Principle
A 3D figure composed of two
congruent polygon faces, all
other faces are rectangles
Circumference
A method for determining
the number of possible
outcomes by multiplying
the total outcomes for each
event
The distance around the
outside of a circle
Prism
Part 1: Geometry
Find the circumference and area of each circle. C= πd
1
C= 3.14(18)= 56.52 cm
A= 3.14(9²)=254.34 cm²
A=πr²
2.
C= 3.14(12)=37.68 cm
A= 3.14(6²)=113.04cm²
3.
C= 3.14(16)=50.24 cm
A= 3.14(8²)=200.96cm²
Find the volume and surface area for each figure: Formulas- Prisms- V= (area of the base)x(height)
1.
2.
3.
V= _200 cm³_
V= _972 cm³__
4.
V= __192 cm³___
V= __12 inches ³_____
SA= 220 cm²____
SA= _208 cm²___
Find the area for the composite figure:
Formulas: Rectangle- a= lw
Triangle a=½bh Circle a= πr²
Trapezoid a= ½h(b1 + b2)
1.
a=_31.73 mi²_
2.
a= 160 m²_
Find the missing angle for each triangle and classify the
triangle by its angles.
<1
<2
<3
Classification by angles:
Right, Acute or Obtuse
44⁰
68⁰
68⁰
acute
121⁰
7⁰
52⁰
obtuse
56⁰
103⁰
21⁰
obtuse
72⁰
18⁰
90⁰
right
Name the Faces, Vertices and Edges
for each 3-D figure.
Shape
Faces
Vertices Edges
Rectangular 6
12
8
Prism
Triangular
4
4
6
pyramid
Hexagonal
8
12
16
Prism
Classify the triangle by the sides and the angles. Congruent sides and angles are indicated.
Right, Isosceles
Obtuse, Scalene
Acute, Equilateral
Acute, Scalene
Right, Scalene
Name each 3-D figure & Sketch the cross-section for each slice.
Figure(name each)
Cut by a plane
parallel to the base
Circle
Cut by a plane
perpendicular to the base
Triangle
Cut by a plane
diagonal to the base
Ellipse/Oval
Rectangle
Square/Rectangle
Parallelogram
Circle
Rectangle
Ellipse/Oval
Rectangle
Triangle
Parallelogram
_____Cone______
______Right Prism _____
___Cylinder______
____Rectangular Pyramid______
Find the value of x and find the missing angles.
3x
5x+20
3x + 5x + 20 = 180
8x + 20 = 180
8x = 160
X = 20
Part 2: Probability
City
Athens
Berlin
London
Paris
Rome
2x-6
X
2x – 6 + x = 90
x – 6 =90
x= 96
x
3x
x-12
3x + x + x – 12 = 180
5x – 12 = 180
5x = 192
X = 38.4
1. Keisha’s family is planning a trip to Europe. If they want to visit each of the cities
listed in the table at the right, in how many different orders can they visit the cities?
(Use fundamental counting principle)
5 x 4 x 3 x 2 x 1 = 120 possible orders
2. Employees at a company are given a three digit employee identification code. If each digit cannot be repeated, how
many different codes are possible? 9 x 8 x 7= 504 different id codes are possible
3. There are 26 students in Mr. Everly’s social studies class. Mr. Everly will randomly select one student as
spokesperson and a second student as an alternate spokesperson for an upcoming presentation. In how many different
ways can they be chosen? 26 x 25= 650 different ways
4. Drew spun a spinner with 5 equal sections 75 times. Each section of the spinner was a different color. One of the
colors was blue. The outcome of “blue” occurred 30 times. Compare the theoretical to the experimental probability of
spinning blue. (Show both fractions and compare them using the words greater than or less than. Give a reason the
probabilities may be different.
Theoretical P = 1/5 Experimental P= 2/5 The experimental probability was greater than the theoretical probability, a
reason for the discrepancy is the frequency of the experiment. If the frequency of the experiment was increased the
experimental probability would be closer to the theoretical probability.
5. A coin is flipped then a spinner with 3 equal sections that are yellow, blue
and red is spun. Draw a tree diagram to show the sample space for the events.
HR
Sample Space- HR, HY, HB, TR, TY, TB
Y
B
TR
Y
B
Permutations:
For 6 and 7, find the total number of outcomes that will be in each sample space.
6. buying bedroom furniture if you can select one each from 7 dressers, 4 beds, 6 lamps, and 9 night tables
7 x 4 x 6 x 9 = 1512
7. tossing a dime, a quarter, a penny, a nickel, and rolling a number cube
2 x 2 x 2 x 2= 16
8. How many ways can 4 friends sit together at the movies in 4 seats? 4 x 3 x 2 x 1= 24
Use the spinner to find each probability. Write each probability as a fraction, decimal and percent. Round to the
nearest percent.
9. P(even number)
4/8 = ½
10. P(2 or 3)
2/8 = ¼
11. P(not 4)
7/8
12. The spinner is spun twice. Find P(5, then 8)
1/8 x 1/8 = 1/64
A bag contains 4 white beads, 6 red beads, 5 yellow beads, and 5 blue beads. One bead is selected, kept, and
another bead is selected. Write the probability as a simplified fraction.
13. Find P(blue, then blue)
5/20 x 4/19 = 4/76 = 1/19
14. Find P(white, then red)
4/20 x 6/19= 6/95
15. Find P(red, then red)
6/20 x 5 / 19 = 3/38
Permutations: Find each value.
(Remember the first number is the starting number, the second tells you how many times it is permutated!)
16. P(8, 5)
17. P(10, 2)
18. P(11, 4)
8 x 7 x 6 x 5 x 4= 6720
10 x 9 = 90
11x10x9x8= 7920
19. Explain the difference in independent and dependent events?
In independent events the outcome of the first event does NOT affect the outcome of the second event. In dependent
event the outcome of the first event does affect the outcome of the second event.
20. Explain the difference in theoretical and experimental probability. Experimental probability can only be determine
if an experiment has taken place and the results have been recorded. Theoretical probability is the number of
favorable outcomes over the number of total possible outcomes.