Name ______Period ______
Pre-AlgebraFinal ReviewPart 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 infinitelyin 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.
29. Name two different rays from the diagram: __________and __________.
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:
a) XB and BC ___intersecting______d) RA and AR ____coincidental______
c) XY and DE ___skew______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.
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.
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
a) a purple:.12 12%
b) a green: .2929%
c) a red or a yellow:.5959%
d) a yellow then a green: .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?
P(red) = .15ORP(red) =
x = .15(200) 100x = 3000
x = 30 x = 30
Pre-Algebra Final Study Guide continuedName: ______KEY______
1)Solve and check the following equations algebraically.
Example:
- x + 4x + 6 = 31b. 5r + 3r – 6 = 10c. 1 – 3y + y = 5
5x + 6 = 315r + 3r + (-6) = 101 + (-3y) + y = 5
-6 -6 8r + (-6) = 10 1 + (-2y) = 5
5x = 25 +6 +6 -1 -1
5 5 8r = 16 -2y = 4
x = 5 8 8 -2 -2
r = 2 y = -2
Check:
2) Use the percent proportion or the percent equation to solve each problem.
Example: What is 5% of 224?
- What is 16% of 36.2?b. 60 is 28% of what number?c. What percent of 48 is 0.6?
x = .16 (36.2) 60 = .28 (x) p (48) = 0.6
x = 5.792 .28 .28 48 48
214.29 = x p = 0.0125
= 1.25%
OR
3) A dress originally priced at $75 is on sale for 30% off. What is the discount? What is the sales price?
4a) Graph y = -2x + 1 by firstcompleting the table below and then graph on the coordinate plane.
x / Work / y / (x, y)-2 / y = -2(-2) + 1 = 4 + 1 = / 5 / (-2, 5)
-1 / y = -2(-1) + 1 = 2 + 1 = / 3 / (-1, 3)
0 / y = -2(0) + 1 = 0 + 1 = / 1 / (0, 1)
1 / y = -2(1) + 1 = -2 + 1 = / -1 / (1, -1)
2 / y = -2(2) + 1 = -4 + 1 = / -3 / (2, -3)
b) Is the graph increasing or decreasing?(1 pt)___decreasing______
c) Is the graph proportional? Explain why or why not. (2 pts)
__No, the graph is not proportion because it does not pass through the origin.______
5) Use the table to find the rate of change. Explain the meaning of the rate of change.
Example
Time(Hours) / Amount earned
($)
4 / $25
6 / $40
8 / $55
a)Rate of change = = $7.50 per hour
b)Explain the meaning of the rate of change.
For each additional hour, you earn $7.50 more.
Use the table to find the rate of change. Explain the meaning of the rate of change.
Time(min) / Energy burned
(Calories)
15 / 60
30 / 120
45 / 180
a)Rate of change = = 4 calories per min
b)Explain the meaning of the rate of change.
For each additional minute, on average 4 more calories are burned.
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 3as 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 / FREQUENCY1 / | | | | / 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.
___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. ______
______