Download Study Guide Part II due Monday

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 _______________ is part of a line between 2 endpoints.
b) A flat surface made up of points, extended infinitely in 2 directions is a ________________.
c) A _______________ is made up of points extended infinitely.
d) The intersection of two rays at a common endpoint is an ________________________.
e) A _______________ is a location without shape or size.
f) Points that are ___________________ are on the same line.
g) Points that are on the same plane are called _____________________.
h) In order for two rays to be the same, they must share the same ________________ and extend
infinitely in the ____________ direction.
Use the diagram to answer questions 26-30. Use the vocabulary words above to help you.
26. FH names a ______________.
27. < EFH names a _____________.
28. Name a ray that is the same as GF:
___________
H
E
F
G
29. Name two different rays from the diagram: ____________ and _____________.
30. Are EF and FG the same ray? ____________ Why or why not? _____________________________
Line Relationships:
Fill in the blank.
a) ______________________ lines share no points and are in the same plane.
b) ______________________ lines share no points and are NOT parallel.
c) ______________________ lines share ONE point ONLY.
e) ______________________ 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 ___________________________
c) XY and DE ___________________________
d) RA and AR ________________________
e) XY and BE ________________________
ANGLE CLASSIFICATION:
a) _____________________ angles are formed by intersecting lines.
b) _____________________ angles are next to each other, share a common vertex, common ray and
do not overlap.
c) _____________________ angles are angles whose measures add up to 90 degrees.
d) _____________________ 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.
Use the diagram to the right to answer questions 33-36.
33. Name two vertical angles:
_____________ and _____________
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 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 ___________________ triangle has 2 equal sides and 2 equal angles.
d) A ____________________ triangle has all different sides and angles.
e) An ____________________ triangle has all equal sides and angles.
f) An ___________________ triangle has 3 angles less than 90 degrees.
g) A ___________________ has one angle that measures 90 degrees.
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be
________________ 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.
42. Could the following measures be the sides of a triangle? Why or Why not? 2 , 2, 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: ________________________ and ______________________
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.
a) a purple:
b) a green:
c) a red:
d) a yellow:
44. In Mrs. Ellwood’s closet, she has 6 pairs of shoes, 4 skirts and 9 shirts. How many possible outfits
are possible?
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?
Pre-Algebra Final Study Guide continued
Name: _______________________________
1) Solve and check the following equations algebraically.
Example: 5a  9  a  21
5a  9 ( a)  21 Change subtraction to adding the opposite
4a  9  21
9  9
4a  12
44
a 1
Combine like terms
Undo addition by subtracting 9 on each side
Simplify
Undo multiplication by dividing by 4 on each side
Simplify
b. 5r + 3r – 6 = 10
a. x + 4x + 6 = 31
c. 1-3y + y = 5
2) Use the percent proportion or the percent equation to solve each problem.
Example: What is 5% of 224?
Percent Proportion
is
%

of 100
Percent Equation
x
5
part  (% as decimal)( whole)

224 100
x  (.05)(224)
100 x  1120
x  11.2
x  11.2
a. What is 16% of 36.2?
b. 60 is 28% of what number?
c. What percent of 48 is 0.6?
3) A dress originally priced at $75 is on sale for 30% off. What is the discount? What is the sales
price?
4a) Graph y = -2x + 1 by first completing the table below and then graph on the coordinate plane.
x
Work
y
(x, y)
b) Is the graph increasing or decreasing? (1 pt) ______________________
c) Is the graph proportional? Explain why or why not. (2 pts)
_____________________________________________________________________________________
_____________________________________________________________________________________
5) Use the table to find the rate of change. Explain the meaning of the rate of change.
Example
Time
(Hours)
4
Amount earned
($)
$25
6
$40
b) Explain the meaning of the rate of change.
8
$55
For each additional hour, you earn $7.50 more.
Δ𝑦
a) Rate of change = Δ𝑥 =
15
= $7.50 per hour
2
Use the table to find the rate of change. Explain the meaning of the rate of change.
Δ𝑦
Time
(min)
15
Energy burned
(Calories)
60
30
120
_________________________________________________
45
180
_________________________________________________
a) Rate of change = Δ𝑥 =
= _________________
b) Explain the meaning of the rate of change.
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. _______________________________________________________
__________________________________________________________________________________
b) You select 20 names of students from a hat._______________________________________________
__________________________________________________________________________________
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?
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?
c) Name the probability you found in question 7b.
__________________________________________________
d) How does the probability in question 7a compare to the probability in question 7b?
_____________________________________________________________________________________
_____________________________________________________________________________________