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Transcript
Name _____________________________________________
Period ________________
Pre-Algebra Final Review Part II
GEOMETRY
Vocab: Fill in the blank with one of the following: line, point, line segment, ray, plane, angle
a) A ___line segment__ is part of a line between 2 endpoints.
b) A flat surface made up of points, extended infinitely in 2 directions is a __plane______________.
c) A ___ray_________ is made up of points extended infinitely in one direction.
d) The intersection of two rays at a common endpoint is an ___angle______________.
e) A ___point________ is a location without shape or size.
f) Points that are ___collinear________ are on the same line.
g) Points that are on the same plane are called ___coplanar____________.
h) In order for two rays to be the same, they must share the same ___endpoint______ and extend
infinitely in the __same______ direction.
Use the diagram to answer questions 26-30. Use the vocabulary words above to help you.
26. FH names a ___ray________.
27. < EFH names a ___(right) angle_____.
28. Name a ray that is the same as GF:
⃗⃗⃗⃗⃗ ________
___
H
E
F
G
⃗⃗⃗⃗⃗ _________.
⃗⃗⃗⃗⃗ ________ and ____
29. Name two different rays from the diagram: ____
30. Are EF and FG the same ray? ____no______ Why or why not? ______do not share same endpoint_
Line Relationships:
Fill in the blank.
a) ___parallel____________ lines share no points and are in the same plane.
b) ___skew_______________ lines share no points and are NOT parallel.
c) ___intersecting_________ lines share ONE point ONLY.
e) ___coincidental_________ lines share ALL points. (lie on top of one another)
31) Name the line relationship of the following:
Y
D
A
VX
E
C
B
a) XB and BC ___intersecting________________
c) XY and DE ___skew_____________________
d) RA and AR ____coincidental_________
e) XY and BE ____parallel_____________
ANGLE CLASSIFICATION:
a) ___vertical____________ angles are formed by intersecting lines.
b) ___adjacent___________ angles are next to each other, share a common vertex, common ray
and do not overlap.
c) ___complementary_____ angles are angles whose measures add up to 90 degrees.
d) ___supplementary_____ angles are angles whose measures add up to 180 degrees. (hint—“s”
straight angle)
32. Find the measure of <B if <C is equal to 47 degrees and <B and <C are complementary.
90-47 = 43o
Use the diagram to the right to answer questions 33-36.
33. Name two vertical angles:
___∠6&∠3___or _∠1&∠4___or __∠2&∠5___
34. If the measure of <1 is 42 degrees, what is
the measure of <2? _____________
35. Name two angles that are adjacent:
______________ and ____________
36. What is the measure of <3? ________
How do you know? Angle 3 and 6 are vertical
angles. Since vertical angles have the same
measure and angle 6 measures 90o, angle 3
measures 90o.
ANGLE PAIRS:
a) Angles that are on the opposite side of the transversal and inside the lines are
____________________ ___________________ angles.
b) Angles that are on the same side of the transversal in the same position are
___________________ __________________ angles.
c) Angles that are on the opposite side of the transversal outside the lines are
___________________ __________________ angles.
Use the diagram to the right to answer the following questions.
37. Name an angle pair that are alternate exterior:
_______ , ______
38. Name an angle pair that are corresponding:
________, ________
39. Name an angle pair that are alternate exterior:
______, _______
40. If the measure of <3 is 78 degrees, what is the
measure of <7? ______ <4?_______ <2? ________
1 2
3 4
5 6
7 8
CLASSIFYING TRIANGLES:
a) The sum of all the angles of a triangle are equal to _________ degrees.
b) You can classify triangles by their _______________ and/or their ________________.
c) An ___isosceles________________ triangle has 2 equal sides and 2 equal angles.
d) A ____scalene_____________ triangle has all different sides and angles.
e) An ______equilateral_______ triangle has all equal sides and angles.
f) An _______acute__________ triangle has 3 angles less than 90 degrees.
g) A ________right___________ has one angle that measures 90 degrees.
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be
_______greater_________ than the measure of the 3rd side.
41. The angles of a triangle measure 90 degrees, 38 degrees and x degrees. Find the value of x.
180-128=52 degrees
42. Could the following measures be the sides of a triangle? Why or Why not? 2 , 2, 4
____No because 2+2=4, which is not greater than 4.
42. The angles of a triangle measure 90 degrees, 45 degrees and 45 degrees. The sides measure 6 cm, 4
cm and 4 cm. Classify the triangle: _____right (angles)________ and ______isosceles (sides)________
PROBABILITY:
**We just completed this unit in class. Use your NOTES and/or your TEXTBOOK to help you.
43. In a bag of Sour Patch Kids, 6 are red, 4 are yellow, 5 are green and 2 are purple. What is the
probability of choosing the following? Answer in a simplified fraction, decimal and percent. Total - 17
2
a) a purple: 17 ≈.12 ≈12%
5
b) a green: 17 ≈.29 ≈29%
c) a red or a yellow:
6+4
17
=
d) a yellow then a green:
10
17
4
∙
≈.59 ≈59%
5
17 16
=
5
68
≈.07 ≈ 7%
44. In Mrs. Ellwood’s closet, she has 6 pairs of shoes, 4 skirts and 9 shirts. How many possible outfits
are possible?
6*4*9 = 216 outfits
45. In a package of M and M’s , Jennifer found that 15% of the candies were yellow. There are 200 M
and M’s in the package. How many M and M’s can be expected to be yellow?
15
P(red) = .15
OR
P(red) = 100

= .15
x = .15(200)
x = 30
200

15
= 100
100x = 3000
x = 30
200
Pre-Algebra Final Study Guide continued
Name: ________KEY___________________
1) Solve and check the following equations algebraically.
Example: 5a  9  a  21
5a  9 ( a)  21
4a  9  21
9  9
4a  12
44
a 1
Change subtraction to adding the opposite
Combine like terms
Undo addition by subtracting 9 on each side
Simplify
Undo multiplication by dividing by 4 on each side
Simplify
a. x + 4x + 6 = 31
5x + 6 = 31
-6 -6
5x = 25
5
5
x=5
b. 5r + 3r – 6 = 10
5r + 3r + (-6) = 10
8r + (-6) = 10
+6 +6
8r = 16
8
8
r=2
c. 1 – 3y + y = 5
1 + (-3y) + y = 5
1 + (-2y) = 5
-1
-1
-2y = 4
-2 -2
y = -2
5r  3r  6  10
5(2)  3(2)  6  10
10  6  6  10
10  10
1 3y  y  5
1  3(2)  (2)  5
1  (6)  (2)  5
1  6  (2)  5
7 (2)  5
55
Check:
x  4 x  6  31
(5)  4(5)  6  31
5  20  6  31
25  6  31
31  31
2) Use the percent proportion or the percent equation to solve each problem.
Example: What is 5% of 224?
Percent Proportion
is
%
Percent Equation

of 100
part  (% as decimal)( whole)
x
5

x  (.05)(224)
224 100
x  11.2
100 x  1120
x  11.2
a. What is 16% of 36.2?
x = .16 (36.2)
x = 5.792
OR
x
16

36.2 100
100 x 579.2

100
100
x  5.792
b.
60 is 28% of what number? c. What percent of 48 is 0.6?
60 = .28 (x)
p (48) = 0.6
.28 .28
48
48
214.29 = x
p = 0.0125
= 1.25%
60 28

x 100
28 x 6000

28
28
x  214.29
0.6
x

48 100
48 x 60

48 48
x  1.25%
3) A dress originally priced at $75 is on sale for 30% off. What is the discount? What is the sales
price?
d  %(op)
d  .30(75)
sp  75  22.50
sp  $52.50
d  $22.50
4a) Graph y = -2x + 1 by first completing the table below and then graph on the coordinate plane.
x
Work
y
(x, y)
-2
y = -2(-2) + 1 = 4 + 1 =
5
(-2, 5)
-1
y = -2(-1) + 1 = 2 + 1 =
3
(-1, 3)
0
y = -2(0) + 1 = 0 + 1 =
1
(0, 1)
1
y = -2(1) + 1 = -2 + 1 =
-1
(1, -1)
2
y = -2(2) + 1 = -4 + 1 =
-3
(2, -3)
b) Is the graph increasing or decreasing? (1 pt) ___decreasing_____________
c) Is the graph proportional? Explain why or why not. (2 pts)
__No, the graph is not proportion because it does not pass through the origin._____________________
5) Use the table to find the rate of change. Explain the meaning of the rate of change.
Example
Time
(Hours)
4
Amount earned
($)
$25
6
$40
b) Explain the meaning of the rate of change.
8
$55
For each additional hour, you earn $7.50 more.
Δ
a) Rate of change = Δ =
15
= $7.50 per hour
2
Use the table to find the rate of change. Explain the meaning of the rate of change.
Time
(min)
15
Energy burned
(Calories)
60
30
120
b) Explain the meaning of the rate of change.
45
180
For each additional minute, on average 4 more calories are
burned.
Δ
a) Rate of change = Δ =
60
= 4 calories per min
15
6) You are planning to sell school supplies at the school store for NJHS and you want to know what to
sell. To answer your question, you survey the following groups below. Determine whether the following
samples are random samples or biased samples and explain why.
a) The students at your lunch table. Biased Sample; Each student does not have an equal chance of being
chosen. Students at your lunch table are favored over others.________________________________
b) You select 20 names of students from a hat. Random sample; Each student has an equal chance of
being chosen.______________________________________________________________________
7) You roll a six sided die once.
a) What is the theoretical probability that you roll a number less than 3 as a simplified fraction, decimal
to the nearest tenth, and as a percent?
P(less than 3) 
2 1
  0.33  33%
6 3
Rodejha rolls the die 25 times and records her results in the frequency table shown below.
Number
TALLY
FREQUENCY
1
||||
4
2
|||| |
6
3
|||| |
6
4
||||
4
5
||
2
6
|||
3
b) What is the probability that Rodejha rolled a number less
than 3 as a simplified fraction, decimal to the nearest
hundredth, and a percent?
P(less than 3) 
10 2
  0.40  40%
25 5
c) Name the probability you found in question 7b.
___Experimental Probability_____________________
c) How does the probability in question 7a compare to the probability in question 7b?
The theoretical probability is less than the experimental probability. _________________________
________________________________________________________________________________