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PRE - ALGEBRA
2nd Edition
Austin Community
College A.E. Dept.
1 | P a g e
2 | P a g e
Table of Contents Pre-requisite Review 5 Probability – Introduction 10 Probability – Expressing Probability as a Number 11 Probability – Prediction 12 Probability – Listing Predictable Outcomes 13 Probability – Using a Tree Diagram 14 Probability – Basing Probability on Data 15 Probability – Two Events 16 Probability – Review 17
Exponents – Introduction 18 Exponents – Addition and Subtraction 19 Exponents – Multiplication and Division 20 Exponents – Simplifying 21 Exponents – Negative 22 Exponents - Order of Operation 23 Exponents – Scientific Notation 24 Exponents – Review 25
Squared Roots – Introduction 26 Squared Roots – Approximating 27
Squared Roots - Review 28 Integers – Introduction 29 Integers – Addition 31 Integers – Subtraction 32 Integers – Multiplication 33 Integers – Division 34 Integers – Order of Operation 35 Integers – Review 36
Algebraic Thinking – Introduction 37 Algebraic Thinking – Writing Expressions 38 Algebraic Thinking – Simplifying an Expression 39 Algebraic Thinking – Evaluating Expressions 40 Algebraic Thinking – Evaluating Formulas 41 Algebraic Thinking – Review 42
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Algebraic Equations – Introduction 43 Algebraic Equations- One Step Addition 44 Algebraic Equations- Two Step Addition 45 Algebraic Equations – One Step Subtraction 46 Algebraic Equations – Two Step Subtraction 47 Algebraic Equations – One Step Multiplication 48 Algebraic Equations – Two Step Multiplication 49 Algebraic Equations – One Step Division 50 Algebraic Equations – Two Step Division 51 Algebraic Equations – One Step Fraction Coefficient 52 Algebraic Equations – Distributive Property 53 Algebraic Equations – Review 54
Special Equations – Introduction 55 Special Equations – Ratios 56 Special Equations – Ratio Equations 57 Special Equations – Proportion 58 Special Equations – Proportion Equations 59 Special Equations – Rate 60 Special Equations – Review 61
Graphing – Introduction 62 Graphing – Coordinate Grid 63 Graphing – Plotting Points on a Coordinate Grid 64 Graphing – Graphing a Line on a Coordinate Grid 65 Graphing – Finding the Slope of a Line 66 Graphing – Graphing a Linear Equation 67 Graphing – Review 68
Inequalities – Introduction 69 Inequalities – Graphing 70 Inequalities – Solving 71 Inequalities – Picturing a Range 72 Inequalities – Word Problems 73 Inequalities – Review 74
Geometric Angles – Introduction 75 Geometric Angles – Measuring 76 Geometric Angles – Types and Labeling 77 Geometric Angles – Pairs of Angles 78 Geometric Angles – Intersecting Lines 79 Geometric Angles – Review 80
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Geometric Triangles – Introduction 81 Geometric Triangles – Sum of Angles in a Triangle 82 Geometric Triangles – Similar Triangles 83 Geometric Triangles – Right Triangles and the Pythagorean Theorem 84 Geometric Triangles – Review 85
Geometric Planes – Introduction 86 Geometric Planes – Recognizing Common Polygons 87 Geometric Planes – Perimeter 88 Geometric Planes – Area 89 Geometric Planes – Working with Circles 90 Geometric Planes – Solving Two-Step Problems 91 Geometric Planes – Review 92
Geometric Solid Figures – Introduction 93 Geometric Solid Figures – Common Figures 94 Geometric Solid Figures – Volume Cubes 95 Geometric Solid Figures – Volume Rectangular Solids 96 Geometric Solid Figures – Volume Cylinders 97 Geometric Solid Figures – Volume Cones 98 Geometric Solid Figures – Solving Two-Step Problems 99 Geometric Solid Figures – Review 100 Math Topics – Mean, Mode, Median & Range 102 Conversions – Introduction 103 Conversions – Using Conversions 104 Conversions – Addition 105 Conversions – Subtraction 106 Conversions – Multiplication 107 Conversions – Division 108
Graphic Data Graphic Data – Bar Chart 109 Graphic Data – Pie Chart 111 Graphic Data – Line Graph 113
Glossary 118
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Prerequisite Review
21
5+ 6
3
10= 7 - 4
7
9=
Usually, Nathan drives 3
5mile to pick up Jane. They then drive another
4
5mile to
class at ACC. Today Jane is sick, so Nathan drives 1 mile directly to class. How
much shorter is the direct route?
Carrie worked at ACC yesterday for 72
3hours yesterday and 6
3
5hours today.
How many hours did she work in the two days?
Charles has an annual salary of $39,000. If he receives a bonus of 1
20of his
annual salary, about what is his bonus?
34
7 x
2
5= 0.12 x 1.5 =
6 | P a g e
Marisa works at a plant store in Austin. Most of the plants grow at a rate of
51
2inches per week. At these rates, how many inches will most of the plants
grow in 21
2 weeks?
In his woodworking class at ACC, Joe is replacing 8 warped shelves in a
bookshelf. Each piece of wood is 151
2inches long. How much wood will he
need to replace all 8 shelves?
2.3004(.022)= .055/.5 =
A flight from Austin to El Paso took 24
5hours total. Because of delays, the
return flight took 31
8hours. How much longer did the return flight take?
Kim gets 10 vacation days a year. If she has already used, 41
4of a day, how
many more vacation days does she have left?
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Write 33 ⅓ % as a fraction. = Find 4% of 450. =
Kathy has a stack of 50 books in her office. If each book is 13
4inches thick,
what is the height of the stack?
One cubic foot of water weighs 621
2 pounds. How much does 1
1
4cubic feet of
water weigh?
Rosalinda collected 21
9 pounds of newspaper for Austin’s recycling drive. Alec
collected42
4times as much newspaper as Rosalinda. How many pounds of
newspaper did Alec collect?
Write 3
25as a percent. = Write 55% as a fraction. =
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Carlos has a board that is 12 feet long. He needs to cut it into pieces that
measure 3
4foot. How many pieces can he cut from the board?
Which of the following is the same as 16 ⅔% of 90? =
a. 90 ÷4
b. 90 ÷6
c. 90 ÷8
d. 90 ÷12
Jason uses 1
4 pound of chicken making the lunch special for ACC’s culinary arts
program. How many lunch specials can he make from 12 pounds of chicken?
Jim works for ACC fixing computers. On average, he can make a repair in 3
4of
an hour. How many repairs can he make in a 71
2hour workday?
Find 12.5% of 240. =
Jana needs 21
2yards of material to make a dress for her daughter’s birthday
party at Amy’s Ice Cream. How many dresses can she make from 101
2yards of
material?
9 | P a g e
Round 3.895 to the nearest hundredth. =
Find 2.48÷4 to the nearest tenth. =
Write 0.245 as a percent. =
Write 32% as a decimal. =
Conrad knows that the average lifespan of a dog is about 12 years. If his dog is
3 years old. What percent of its life has it lived? What fraction of time does the
dog have left to live?
April works at a supermarket where she gets 10% off anything in the store. If
she buys a $38 shirt and pays with a $50 dollar bill, what will her change be?
Belinda has saved $54. This is 20% of what she needs to buy the cheapest
robotic vacuum cleaner she can find. How much is the robotic vacuum
cleaner?
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– Introduction Video
What is the probability of landing on 6 in one spin?
What is the probability of landing on an even number?
What is the probability of landing on an even number?
What is the probability of landing on a shaded color?
What is the ratio of shaded to unshaded?
What is the ratio of even to odd numbers?
11 | P a g e
Probability - Expressing Probability as a Number Video
If there are 5 favorable and 10 unfavorable, what is the fraction of favorable to unfavorable?
What is the percent?
If there are 2 favorable and 12 unfavorable, what is the fraction of favorable to
unfavorable?
What is the percent?
If there are8 favorable and 24 unfavorable, what is the fraction of favorable to unfavorable?
What is the percent?
Suppose you roll a 6 sided die
a. What is the probability of rolling a 5?
b. What is the probability of rolling an even number? c. What is the probability of rolling a number divisible by 3?
12 | P a g e
Probability – Prediction Video 1 Video 2
Suppose you roll a die 10 times,
a. How many times will you likely roll a 5?
b. How many times will you likely roll an odd number? c. How many times will you likely roll a number divisible by 3?
Suppose you flip a two sided coin 80 times,
a. How many times will you likely get heads?
Suppose you flip a two, two sided coins 50 times,
a. How many times will you likely get one head and one tail?
b. How many times will you likely get one head and one head?
There are 48 marbles that are red green and brown in this jar.
a. If 40% are green and 1
5 are green, how many are brown?
b. List a ratio for each color. c. List a percent for each color.
13 | P a g e
Probability - Listing Predictable Outcomes Video
Using the table above, what are all the possible combinations of the numbers
4, 7, and 9?
a. What is the probability that a 7 would be in the first position?
b. What percent is the proportion above? c. What is the probability that a 9 would be in the middle position?
d. What percent is the proportion above?
14 | P a g e
Probability - Using a Tree Diagram Video
In the lunch room, you can buy the complete lunch package. You get a choice of egg, ham, or cheese sandwich. Vegetables or chips, as a side dish, and your
choice of soda, water, or coffee as a drink. Create a tree diagram to illustrate
all possible outcomes.
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Probability - Basing Probability on Data Video
Kyle plays baseball. He has gotten a hit 20 times out of 140 times at bat. He is
playing today and this is his first time up to bat. What is the probability
that he will get a hit the first time up to bat?
a. What are his chances of getting hits both on his first and second time
at bat?
b. If Kyle gets to bat 5 times in today’s game, how many times is he
likely to get a hit?
Based on the pie graph, what is the probability that Mario will get a sale on the
next customer he talks to?
a. Who has the better shot of getting their next customer?
36%
28%
16%
20%
SALES
Sara Mario Steven Jenny
16 | P a g e
Probability - Two Events Video
If you randomly take 2 of the above cards, what is the probability that you will
get a king and the jack?
a. What is probability that if you continue to choose, you will get the
ace?
Start over with the cards. This time you randomly take one card return it and
chose again. What is likelihood that you will choose a queen both times?
17 | P a g e
Probability - Review
If you have a ratio of 4;10, What is the percentage?
Can ratios be simplified?
Which is a better likelihood, 3
8 or 18;32 ?
Suppose you have a die and you roll it 50 times, how many times are you
likely to roll a 5?
a. What is it likelihood you will roll a 3 twice in a row?
A spinner has three colors green, yellow, and orange. There are a total of 15
slots on the spinner. The ratio of green to yellow is 5:8. What is the ratio of orange to the total?
a. What is the ratio of green to orange? b. What is the ratio of yellow to orange?
c. If you hit the spinner one time, what color is it likely to land on?
d. What is probability of hitting three greens in a row? e. If I spin the spinner 200 times, what is the likelihood of hitting
yellow?
18 | P a g e
– Introduction Video
Power Root Exponential
Squared Cubed
22 means = _______________ 25 means = _______________
26 means = _______________ 53 means = _______________
12 = 22 = 32 = 42 =
152 = 262 = 372 = 482 =
10 = 21 = 30 = 41 =
1002 = 204 = 3002 = 4003 =
19 | P a g e
Exponents - Addition and Subtraction
22 + 22 = 32 + 42 = 62 + 62 =
23 + 92 = 43 + 10 = 212 + 33 =
101 + 1002 = 34 + 25 = 53 + 33 =
52 − 22 = 34 − 23 = 73 − 31 =
104 − 53 = 10002 − 92 = 40 − 18 =
93 − 92 = 85 − 83 = 32 − 22 =
20 | P a g e
Exponents - Multiplication and Division
22(22) = (22)(22) = (22)22 =
22(22) = (22)(22) = (22)22 =
22(22) = (22)(22) = (22)20 =
42
21=
52
32=
25
33=
53
43 = 52
16 = 1002
25 =
92
32 = 252
53 = 5002
53 =
21 | P a g e
Exponents – Simplifying Video
(5)(5)(5)(5)= (3)3(3)= (9)(9)(9)
(9) (9)=
(2)(2)(2)(2)
(2)(2)(2)=
23 + 25 = (2)3(2)5 = (5)6(5)3 = (6)12(6)10 =
47
43=
68
62=
812
87=
998
996=
(𝑥2)2 = (𝑥3)2 = (𝑥5)4 = (𝑥8)5 =
(2
3)2 = (
4
5)2 = (
6
7)2 = (
1
8)2 =
22 | P a g e
Exponents – Negative Video
2−2 = 3−4 = 5−5 =
2−2 + 2−3 = 3−2 + 1−4 = 5−2 + 5−3 =
2−2 − 2−3 = 3−4 − 1−5 = 5−2 − 5−3 =
2−2(2−3) = (3−3)1−5 = (4−2)(7−3) =
2−3
2−2 = 3−2
2−2 = 6−2
1−2 =
23 | P a g e
Exponents - Order of Operation Video Arithmetic expression strategy
(3 + 4)2 = (3 + 4)3+(4 − 3)4 – 1 =
3+(10 + 2 − 3)2 − 1 = 33+4+22-(3-1) =
3+(4 + 2)3−(3 − 1)2= (3+42+2)-3-14=
3 (4)
(2)3 + 43=
44+33−22
22 =
3(4)
(2)(3)+6= 2(3) + 42+2 = =
24 | P a g e
Exponents - Scientific Notation Video
5.1 𝑥 102 = 6.23 𝑥 104 = 8.335 𝑥 106 =
5.1 𝑥 10−2 = 6.23 𝑥 10−4 = 8.335 𝑥 10−6 =
Change the following numbers to scientific notation.
5000 = 134000= 53333 =
.0004 = .1221 = .0002323 =
25 | P a g e
Exponents - Review
34+23−22
22 = 9.999 𝑥 104 =
(4 + 5)3 = 5−3
3−2 =
31+23−20
21 = 1012
1011 =
The distance of Earth to the Sun is approximately 93,000,000 miles. Express
this distance using scientific notation.
Which expression is worth more 1.5 𝑥 104 𝑜𝑟 (10 + 50)3
26 | P a g e
– Introduction Video
Squared Square Root Cubed
Radical Sign Perfect Square Cube Root
√16 = √49 = √144 = √225 =
√25 = √64 = √169 = √9 =
√10 + 6 = √50 − 1 = √20 + 5 =
√100 + 69 = √300 − 25 = √104 + 40 =
√(50)(2) = √12
3= √
32
2=
27 | P a g e
Squared Roots- Approximating Video Approximate Estimate Consecutive
√5 ≈ √12 ≈ √23 ≈
√30 ≈ √41 ≈ √111 ≈
√52 + 11 ≈ √121 − 11 ≈ √232 − 200 ≈
√5(4) ≈ √80
2 ≈ √23(5) ≈
28 | P a g e
Squared Root – Review
√16 + √25 = √36 − √25 = (√16)( √25) =
√16+ √25
3=
500
√100+ √25= (5)( √144) =
5 + √25
4=
9
√100 − √25= (5)( √100)(2) =
29 | P a g e
– Introduction
Using the above thermometer, if you start at +4 and gain 6, where are you?
If you start at -4 and lose 6, where are you?
If you start at +100 and lose 110, where are you?
If you start at -20 and gain 50, where are you?
If you start at -10 and lose 10, where are you?
If you start at +70 and lose 55 then gain back 10, where are you?
30 | P a g e
If you start at -2 and lose 3, where are you?
If you start at -5 and gain 10, where are you?
If you start at -2 and lose 2 then gain 5, where are you?
If you start at -10 and gain 15 and lose 1, where are you?
If you have +6 and subtract 8 where are you?
If you have -6 and add +8 where are you?
What is the absolute value of |−5| ?
What is the absolute value of |8| ?
What is the absolute value of |−5 𝑎𝑑𝑑 3| ?
31 | P a g e
Integers – Addition Video Absolute value Infinite Integer
Opposite Addends
-13 + -42= 18 + 28= -43 + 18=
-11 + 46= 3 + -48 = 35 + 6 =
43 + 29= 21 + -32 = 14 + 49=
18 + 5 = -14 + 32 = -11 + -5=
7 + -34= -46 + -20= 21 + 22 =
31 + -22 = 22 + 20= -40 + 19 =
32 | P a g e
Integers – Subtraction Video
3 - 25= -44 - 11= -43 - 5 =
19 – (-21)= 3 - 6 = -32 - 9=
27 – (-38) = 46 - 24= 10 - 18 =
-10 – (-42)= 16 – (-22)= -43 – (-2) =
-41 – (-38)= 31 – (-5) = 26 – (-38)=
-11 - 16= 32 - 22 = 45 - 39 =
33 | P a g e
Integers – Multiplication Video
-12 x -8= -13 x 13= 12 x -7=
-3 x -1= 12 x 13 = -5 x -4 =
-10 (14) = 11 (4) = -13 (6) =
(1) 5 = (-9) 7 = -5(13) =
6 (-3) = 0 (7) = (9) -9 =
3 (-4) = - (-3) -7= (5)8 =
34 | P a g e
Integers – Division Video
28 ÷ -7 = 108 ÷ -12 = -124 ÷ -4 =
12
3=
−60
12=
121
−11=
-96 ÷ 8 = -28 ÷ -2 = 99 ÷ 11 =
-48 ÷ 12 = 24 ÷ 8 = 77 ÷ 11 =
120 ÷ 2 = -34 ÷ 1 = 26 ÷ -13 =
-96 ÷ -4 = -55 ÷ -11= 32 ÷ -4=
35 | P a g e
Integers – Order of Operation Video
(−7 + 0)2 (-5 + 14)= 6 + 32=
-12 – (-9) + 33 = -14 + (-7) + 4 =
(3)(2)3 ÷ 9 = -7 (-9)( 01) =
-15(-3)(22) + -14 = (10)14 + −23=
(−15 + 52) ÷ -10 = (-3)22(-10 + 15) =
36 | P a g e
Integers – Review
Kelly is working with a chemical reaction in the lab. She is recording temperatures for the experiment. She starts at -45. The temperature change in
an hour is now +247. How much did the temperature change?
Tina is recording transactions for her business. She started with a balance of
$5,467. These are the transactions; +$567, -$225, -$850, +$330. What is her ending balance after the transactions are recorded?
-56 – (-33)= 56 + (-33)= -500 – (-125)=
(-90)(-2) = (70)(-4) = (-100)(-40) =
−4
−2 =
500
−2 =
−1200
40 =
37 | P a g e
– IntroductionVideo
Variables Algebraic Expression
38 | P a g e
Algebraic Thinking – Writing Expressions Video
10 times the sum of four plus x. ____________________________________________
The product of 8 and 5 divided by y. _______________________________________
X times the quotient of 12 divided by 4.____________________________________
The sum of five and three divided by c._____________________________________
30 less four divided by x times 3.____________________________________________
The difference of 8 and 3 times y plus four._________________________________
The quotient of y divided by x plus 7 all divided by g._____________________
39 | P a g e
Algebraic Thinking – Simplifying an ExpressionVideo
12x+ -3x + -11x -b + 5b + -3b 9a- (-11a) - (-3a)
4x+3+6x 12c-5+8c-7-c -6v+5v+16+8v-4
-9+18a-14a d - 9 -7d -8+ 12d 7g-4g+9-8g-5
9y + 4(y -3) 6- 7(w + 5) + w -4(2d-8) -5d
12b-(9-4)b 3+ 4(p-7) +10 5a+ 2(a-6)
-3(5-8c) + 9(2+c) 2(7-x) - 3(-3+x) 5(-9+3n) - 4(2-n)
40 | P a g e
Algebraic Thinking – Evaluating Expressions Video Evaluate
2b-2 for b=7 5u+9 for u=3 3w for w=5
6f+15 for f=4 7q-29 for q=8 𝑑
7+ 24 for d=42
d÷6 + 24 for d=12 9n-7 for h=7 7x-1 for x=3
z/2 + z for z=1 2b+7 for b=5 24÷n-2 for n=4
(n+4 x 1) for n =74 7 + 34 + n for n=11 96÷f x 15 for f=8
n x (48÷6) for n=9 98+1 + m for m=43 48÷8 x a for a =1
41 | P a g e
Algebraic Thinking – Evaluating Formulas Video
A+ B(r) = y – 4 + t =
𝑓
𝑡 + g = 𝑒2 +
𝑤
𝑠 =
1
2 𝑇 + 5 = 6h +
1
4 𝑘 =
4+ 𝑟2
𝑔 =
𝑓−𝑦 𝑒
𝑓
=
42 | P a g e
Algebraic Thinking – Review
If r = 2 and g = 4 If f = 12 , t = 4 and g = 12
4+ 𝑟2+45
𝑔 =
𝑓−6
𝑡+2 + g(2) =
Simplify the following four expressions
-6v+5v+16+8v-4 d - 9 -7d -8+ 12d
2(7-2x) - 3(-3+(-2x)) 5(-10+5n) - 5(2-n)
43 | P a g e
– Introduction
44 | P a g e
Algebraic Equations – One Step Addition Video
1
4 + y =
6
7 12+ y =23 11.34+ y =34.09
W + 22=67 W + 23% =77% W + .09 = 11.77
1
4 + y =
3
5 12% + y =89% -3+ y = -14
W + 7
10 =
13
15 W + (-3) = 12 W + 22% = 80%
1
4 + y =
2
3 -
3
8 + y =
2
3 - 3.09+ y =-5.008
45 | P a g e
Algebraic Equations – Two Step Addition Video
1
4 + y +
1
4 =
6
7 12+ y =23 + 5 11.34 + y + .06 =34.09
99 + W + 22=67 18% + W + 23% =77% W + .09 = 11.77 + .44
1
4 + y =
3
5 +
1
4 12% + y =89% + 125% -3+ y + (-2) = -14
1
5 + W +
7
10 =
13
15 -4 + W + (-3) = 12 18% + W + 22% = 80%
1
4 + y =
2
3 +
1
4 -
3
8 + y +
1
4 =
2
3 - 3.09+ y =-5.008 + (-.05)
46 | P a g e
Algebraic Equations – One Step Subtraction
1
4 - y =
3
5 12% - y =89% -3- y = -14
W - 7
10 =
13
15 W - (-3) = 12 W - 22% = 80%
1
4 - y =
2
3 -
3
8 - y =
2
3 - 3.09- y =-5.008
1
4 - y =
6
7 12- y =23 11.34- y =34.09
W - 22=67 W - 23% =77% W - .09 = 11.77
47 | P a g e
Algebraic Equations – Two Step Subtraction
1
4 - y =
3
5 -
1
4 12% - y – 10% = 89% -3- y + (-3) = -14
1
4 - W -
7
10 =
13
15 -2 - W - (-3) = 12 W - 22% = 80%- 13%
1
4 - y =
2
3 -
1
4
1
4 -
3
8 - y =
2
3 - 3.09- y =-5.008 - .5
1
4 - y =
6
7 -
1
8 12- y - 16 =23 11.34 - .009 - y =34.09
18 - W - 22=67 W - 23% =77% - 12% W - .09 = 11.77 - .88
48 | P a g e
Algebraic Equations – One Step Multiplication
1
4 (y) =
6
7 12( y) = 23 (11.34)y =34.08
(W)22 = 67 W(23%) = 49% W ( .09) = 11.77
1
4 (y) =
3
5 (12%) y = 89% (-3)y = -14
(W) 7
10 =
13
15 W(-3) = 12 W(22%) = 80%
(1
4 )y =
2
3 -
3
8( y) =
2
3 (- 3.09)y =-5.008
49 | P a g e
Algebraic Equations – Two Step Multiplication
1
4 (y) =
6
7(
1
4) 12( y) = 23(2) (11.34)y =34.08(.02)
(3)(W)22 = 67 W(23%) = 49%(3%) (.3)W ( .09) = 11.77
1
4 (y)(
1
4) =
3
5 (12%) y = 89%(2%) (-3)y = -14(-2)
(1
5) (W)
7
10 =
13
15 (-2)W(-3) = 12 (2%)W(22%) = 80%
(1
4 )y =
2
3(
2
4) -
3
8( y) =
2
3(-
1
4) (- 3.09)y =-5.008(-.2)
50 | P a g e
Algebraic Equations – One Step Division
Y ÷ 1
4 =
3
5 12%÷ y =89% -3 ÷ y = -14
W÷ 7
10 =
13
15 W÷ (-3) = 12 W ÷ 22% = 80%
Y ÷ 1
5 =
2
3 h ÷ -
3
8 =
2
3 - 3.09÷ y =-5.008
1
4 ÷ y =
6
7 12÷ y =23 11.34÷ y =34.09
51 | P a g e
Algebraic Equations – Two Step Division
1
4 ÷ y =
3
5 ÷
1
3 12%÷ y =89% ÷ 3% -3÷ y = -14 ÷ -2
2 ÷ W÷ 7
10 =
13
15 W÷ (-3) = 12 ÷ -3 11% ÷ W ÷ 22% = 80%
8 ÷ 1
4 ÷ y =
2
3 -
3
8 ÷ y =
2
3 ÷ −3 - 3.09÷ y =-5.008 ÷ −2
1
4 ÷ y =
6
7 ÷ 7 12÷ y =20 ÷ 2 11.34÷ y =34.09 ÷ .3
52 | P a g e
Algebraic Equations – One Step Faction Coefficient Inverse Reciprocal Coefficient
1
4 (y) =
6
7
2
3 (y) =
8
9
6
7 (y) =
8
15
5
6 (y) =
9
10
2
5 (y) =
14
15
7
9 (y) =
2
7
8
9 (y) =
2
3
3
4 (y) =
5
7
12
17 (y) =
6
17
4
5 (y) =
3
5
9
10 (y) =
3
4
2
7 (y) =
9
13
53 | P a g e
Algebraic Equations – Distributive Property Distribute
x(3+1) 3(y-9) 4(x+3-2) 2x(3+1) 3x(7-9) 4y(x+3-2) 2x(3x+1x) 3x(x-9x) 4y(x+3y-2y)
2x(3𝑥2+1x) 3x((x-(3𝑥2)) 4y(x+3y-(3𝑦2)
54 | P a g e
Algebraic Equations – Review
Solve for the missing variable.
5
9 (y) =
2
5
3
8 (y) =
5
12 (W)
7
10 =
13
15
W(23%) = 49%(3%) 11% ÷ W ÷ 22% = 80%
-3- y + (-3) = -14 12%÷ y =89%
11.34 + y + .06 =34.09 y ÷1
4 =
6
7 ÷ 7
2(3x+1x) =20 4(x+3-2) = 90
55 | P a g e
– Introduction
Proportion Rate Ratio
Per
56 | P a g e
Special Equations – Ratios Video
What is 6in of a foot?
What are 10 of a dozen?
What is the ratio of women in this class?
What is the ratio of men in this class?
What is the ratio of the weekend to the week?
What is the ratio of daughters you have?
What is the ratio of sons you have?
What is the ratio of people wearing white shirts today?
What is the ratio of people wearing a color other than white?
What is the ratio of hours you work this week compared to 40?
57 | P a g e
Special Equations – Ratio Equations
A baseball team has 21 wins, 14 losses, 2 forfeitures, and 1 rain-out.
a. What is the ratio of wins to rain-outs?
b. What is the ratio of losses to wins?
c. What is the ratio of rain-outs to forfeitures?
d. What is the ratio of wins to all games?
e. What is the ratio of losses to all games?
James has 18 women and 16 men in his college calculus class.
a. What is the ratio of men to women?
b. What is the ratio of women in the class?
c. What is the ratio of women to men?
58 | P a g e
Special Equations – Proportions Video
Are these proportions equal?
3
4=
5
20
4
5=
8
10
1
5=
2
9
7
8=
10
16
9
21=
3
7
3
4=
8
9
Solve.
𝑛
9=
26
30
𝑦
3=
8
2
𝑘
4=
48
64
3
7=
ℎ
6
𝑏
5=
8
20
𝑤
4=
12
9
4
7=
𝑤
21
6
9=
3
𝑓
6
7=
𝑟
5
59 | P a g e
Special Equations – Proportion Equations Video
There are 31 instructors in the Austin Community College AE department. Of these, 7 are male and 24 are female. If Houston College has the same rate for
their 68 instructors, how many women do they employ?
In a survey of 500 students, 3 out of 5 said that they plan on completing their
GED this year. What is the number of students that plan on graduating?
While working at Dell, Sarah found 8 defects in 330 microchips. Given this
rate, how many defects will she find in 1200 microchips?
60 | P a g e
Special Equations – Rate Video Rate Per
Given 300 miles on 4 gallons of gas, what is miles per gallon?
Given 550 words in 8 minutes, what is words per minute?
Given 400 tablets for $3.50, what is tablets per dollar?
Given 5 pounds of chicken for $4.25, what is pounds per dollar?
Given 25 miles in 2 hours, what is the hours per mile?
61 | P a g e
Special Equations – Review
Mila found 87 pennies out of 158 coins. Given this rate, how many pennies will she likely find in 500 coins?
James has 3 cats and 4 dogs, what is his ratio of dog per cat?
3
9=
ℎ
6
𝑏
55=
5
100
𝑤
12=
4
9
James has 8 women and 15 men in his college psychology class.
a. What is the ratio of men to women?
b. What is the ratio of women in the class?
c. What is the ratio of women to men?
62 | P a g e
– Introduction Video
Coordinate plane x-axis y-axis
Origin
63 | P a g e
Graphing – Coordinate Grid Quadrants
64 | P a g e
Graphing – Plotting Points on a Coordinate Video x-coordinate y-coordinate Ordered pairs
Plot (4,5) , (-2,-3) , (3,-6) Plot A(2,-7) B(-4,-8)
Move the shape (-5,-8) At point (0,1), turn the shape
180°clckwise. Where is A now?
A
65 | P a g e
Graphing – Graphing a Line on a Coordinate Grid
Plot (-4,-5) and (-3,6) Plot A(2,-7) and B(-4,-8)
x = y +2 y = x - 1
66 | P a g e
Graphing – Finding the Slope of a Line Video Slope Rise Run
x-intercept y-intercept
67 | P a g e
Graphing – Graphing a Linear Equation Video
Graph y = 2x + 1 Graph y = 2x - 1
Graph y = -2x + 1 Graph y = -2x - 1
68 | P a g e
Graphing – Review
If given the points (2,0) and (4,3), what is the equation of this line?
Plot the shape at A=(3,2), B=(5,2) C=(3,5) and D= (5,5). Now, move this
figure (-5, -5). What is the new position of
A=______
B=______
C=______
D=______
69 | P a g e
– Introduction Video
Use < , > , ≤, ≥, = for the following problems.
4 ____ 6 143_____ 99 1
2 ______
3
4
5
10 ______
1
3 3+4 _____9-2 6(7)______(9)(8)
3
4 ____1 99%____99.5% .5_____
2
4
70 | P a g e
Inequalities – Graphing Video
Graph 4 < 𝑥
Graph 7 ≤ 𝑥
Graph 9 ≥ 𝑥
71 | P a g e
Inequalities – SolvingVideo
𝑟 − 7 > 10 𝑡 − 10 > -5 𝑦 + 2 < 5
𝑟
3> -10
𝑤
3> 5 𝑦(3) < 15
𝑟
3+ 4 > -10 𝑦(3) − 3 < 15
𝑤
5+ 2 > 22
𝑟
3+ 4 > -10 𝑦(3) − 3 < 15
𝑤
5+ 2 > 22
72 | P a g e
Inequalities – Picturing a Range Video
Graph the following inequality. −2 ≤ 𝑥 < 4
Graph the following inequality. −10 ≤ 𝑥 ≤ 6
Graph the following inequality. 5 < 𝑥 < 11
Graph the following inequality. −4 < 𝑥 ≤ 11
73 | P a g e
Inequalities – Word Problems
Nina used in the inequality 4𝑠 + 35 ≥ 180 to find the least amount that she
will have to pay to learn how to use a database. What is the least she will have
to pay per session (s)?
A print shop manager estimated that it would cost no more than $70 to print
150 flyers, plus $15 for paper. Write the inequality that can be used to find the greatest cost per flyer.
74 | P a g e
Inequalities – Review
Graph the following inequality. 5 ≤ 𝑥 ≤ 4
Which is greater?
1
2 ______
3
4 3+4 _____9-2 4(7)______(9)(3)
Solve.
𝑟
3+ 3 > -17 𝑦(6) < 48
𝑟
4> -48
Salvio used in the inequality 3𝑠 + 6 ≥ 1933 to find the least amount that he would need to spend on tile for his countertop. What is the least number of
tiles he can purchase?
75 | P a g e
– Introduction
Line Ray Parallel
Perpendicular Vertical Horizontal
Line Segment Angle Vertex
Degree Protractor
76 | P a g e
Geometric Angles – Measuring Video Video 2 Protractor
77 | P a g e
Geometric Angles – Types and Labeling Video 1 Video 2 Acute Angle Right Angle Obtuse Angle
Straight Angle Reflex Angle
Labeling Styles.
78 | P a g e
Geometric Angles – Pairs of Angles Video
Complementary Angles = 90° Supplementary Angles = 180°
Instructor provided example. Instructor provided example.
Instructor provided example. Instructor provided example.
79 | P a g e
Geometric Angles – Intersecting Lines Video Transversal
Given D= 47°, find all angles. Instructor will provide info.
Given 1= 75°, find all angles. Instructor will provide info.
80 | P a g e
Geometric Angles – Review
Given 1 = 120°, what is 2? Given 2 = 49°, what is 1?
Given H = 137°, find all angles. Given N = 83°, find all angles.
81 | P a g e
– Introduction
Isosceles Equilateral Right
82 | P a g e
Geometric Triangles – Sum of Angles in a Triangle Video
60° 89°
35° 40°
37°
49°
35°
44°
83 | P a g e
3
3 3
Geometric Triangles – Similar Triangles
6° 42°
35°
? °
18
10 ?
84 | P a g e
Geometric Triangles – Right Triangles and the
Pythagorean Theorem Video
If a = 10 and b = 5, what does c =?
If a = 15 and c = 25, what does b =?
85 | P a g e
Geometric Triangles – Review
Given a = 37° and d = 125°, what are c and b?
Given c = 15 and b = 6, what is a ?
Given Michael is 6 feet tall, he is 8 feet from the mirror and the tree is 18 feet
from the mirror, how tall is the tree?
86 | P a g e
– Introduction
87 | P a g e
Geometric Planes – Recognizing Common Polygons Square Rectangle Triangle Parallelogram
Trapezoid
88 | P a g e
Geometric Planes – Perimeter Perimeter
P = P=
If BC = 7, what does P =? Given this is equilateral, what does P=?
Given AD=5, what does P =?
4
18 7
5
89 | P a g e
Geometric Planes – Area
90 | P a g e
Geometric Planes – Working with Circles Diameter Radius Circumference
Pi
Given d = 4.5 what is C = ?
Given r = 2.7, what is A = ?
91 | P a g e
Geometric Planes – Solving Two Step Problems
Sally has a square bathroom. She would like to replace the tile. Given one side
of the room is 5 feet and the new tile will cost $1.50 per foot, how much will
her new tile cost in total?
Bill broke a window in his house. It has the shape as above, He wants to
replace it. If the height is 3.5 ft. and the base is 4.75 ft. and the new window
will cost $1.75 per sq. ft., how much will the new window cost?
Given the above information, what is the total area? If we are going to cover the space with microchips that are 1 x 1 cm sq. , how many do we buy?
92 | P a g e
Geometric Planes – Review
Given a triangle with b= 4 and h = 7
a. What is the area?
b. What is the perimeter?
Given a parallelogram with l = 7 and w = 3
a. What is the perimeter?
b. What is the area?
Given a circle with d = 5.5
a. What is the area?
b. What is the circumference?
Given a trapezoid with a = 10, h = 4, c= 6
a. What is the area?
b. What is the perimeter?
93 | P a g e
– Introduction
Volume Rectangular Solid Rectangular Prism
Depth
94 | P a g e
Geometric Solid Figures – Common Figures Area Perimeter Volume
95 | P a g e
Geometric Solid Figures – Volume Cubes
Given s = 5 sq.ft. , what is the volume?
Given the volume of 100 cft., what is s ?
96 | P a g e
Geometric Solid Figures – Volume Rectangular Solids
Given l = 8, w = 4 and h = 10, what is the volume?
Given the v = 100, l = 5 and w = 7, what is h?
97 | P a g e
Geometric Solid Figures – Volume Cylinders
Given h = 10 and r = 5.5, what is the volume?
Given the volume of 150 cft., and r = 5, what is h?
98 | P a g e
Geometric Solid Figures – Volume Cones
Given r = 3.25 and h = 4, what is the volume?
Given the volume is 150 cm cubed, radius 5 and height 10, what is s?
99 | P a g e
Geometric Solid Figures – Solving Two Step Problems
Fred needs to replace is oxygen tank. The height is 5ft. and the diameter is
6in. Oxygen cost $6 per cft. How much will it cost to refill this tank?
Given the above info, what is the volume? If we are going to fill the above shape with radon gas that cost $45 per cm cubed, what will the cost be?
100 | P a g e
Geometric Solid Figures – Review
Given the shape above, if the diameter is 4 feet and the length is 7 feet, what is the total volume?
Given the shape above, what is the total volume?
101 | P a g e
This cone is partially filled now. How fluid can be added to fill the shape?
Given the above information, how much of the cones volume is not be taken up by the inserted cylinder?
102 | P a g e
– Mean, Mode, Median & Range
Name Grade
Jill 35
Hane 187
Kim 55
Lisa 21
Nancy 336
Tom 197
Leo 222
Time Temp
1:10 105°
1:20 174°
1:30 253°
1:40 376°
1:50 376°
2:00 103°
2:10 48°
Given the above information, Mean ______ Median_______
Mode_______ Range________
103 | P a g e
- Introduction
1 Ton = ______lb 1 lb = ______ounces
1 year = ______weeks 1 week = ______days
1 day = ______hours 1 hour = ______minutes
1 mile = ______feet 1 foot = ______inches
1 kilometer= ______meters 1 meter = ______centimeters
1 miles = ______yards 1 yard = ______feet
104 | P a g e
Conversions - Using Conversions
2 T=____lb 4 lb=____oz
3 yr=____wks 6 wks____days
12 days=_____hr 11 hrs_____min
2 miles=______ft 5 ft=_____in
3 km=_______m 5 m=_____cm
5 mi=_____yds 4 yds=______ft
105 | P a g e
Conversions – Addition
4 days 20 hr 10 hr 56 min
+ 3 days 14 hr + 1 hr 37 min
3 ft 16 in 3 yds 2 ft
+ 2 ft 13 in + 1 yd 4 ft
1 T 1999 lb 15 oz 1 yr 18 hr
+ 14 oz + 364 days 5 hr
300 days 18 hr 8 km 165 m 76 cm
+ 400 days 30 hr + 3 km 775 m 97 cm
106 | P a g e
Conversions – Subtraction
8 days 13 hr 10 hr 22 min
- 3 days 14 hr - 1 hr 37 min
1 km 1345 m 4 m
- 2234 m - 2 m 99 cm
1 T 1999 lb 10 oz 1 yr 1 hr
- 14 oz - 364 days 5 hr
300 days 18 hr 8 km 165 m 67 cm
- 100 days 30 hr - 3 km 775 m 97 cm
107 | P a g e
Conversions – Multiplication
4 days 20 hr 10 hr 56 min
X 3 x 5
3 ft 16 in 3 yds 2 ft
X 4 x 6
1 T 1999 lb 15 oz 1 yr 18 hr
X 7 x 9
300 days 18 hr 8 km 165 m 76 cm
X 8 x 6
108 | P a g e
Conversions – Division
13 𝑑𝑎𝑦𝑠 12 ℎ𝑟𝑠
4
4 𝑦𝑑𝑠 2 𝑓𝑡
5
4 𝑘𝑚 1500 𝑚
2
5 𝑦𝑟 234 𝑑𝑎𝑦𝑠 10 ℎ𝑟 52 𝑚𝑖𝑛
6
4 𝑘𝑚 1356 𝑚 65 𝑐𝑚
3
1 𝑐𝑒𝑛𝑡𝑢𝑟𝑦 4 𝑑𝑒𝑐𝑎𝑑𝑒𝑠 54 𝑦𝑟𝑠
2
8 𝑘𝑙 5 𝑙
4
7 𝑦𝑟 5 𝑚𝑜 50 𝑤𝑘 6 𝑑 10 ℎ𝑟 33 min 10 𝑠𝑒𝑐
6
109 | P a g e
– Bar Chart
Use the data above to answer the following questions.
1. What is the lowest year of enrollment?
2. What is the difference between the highest and lowest enrolments?
3. What is the percentage of increase?
4. What is the estimated average enrollment for the four years listed?
5. Based on the data, what do you think the enrollment will be for 2015
0 500 1000 1500 2000 2500
Number of Students
2014 2013 2012 2011
110 | P a g e
Use the data above to answer the following questions.
1. Based on the data, what is the average number of graduates?
2. True or false, the highest numbers of graduates are in 2011 and 2012.
3. Is the trend ascending or descending?
4. Why do you think the number of graduates is increasing?
5. What is your estimate for 2015?
0 100 200 300 400 500 600 700
Number of GED Graduates
2014 2013 2012 2011
111 | P a g e
Graphic Data – Pie Chart
Use the data above to answer the following questions.
1. What is the largest piece of the budget? Estimate the percentage.
2. What is the smallest piece of the budget? Estimate the percentage.
3. True or false, food and rent take the largest portion of the total budget?
4. True or false, rent and gas have the same portion as food?
5. If the total budget is $1000, place a dollar amount on each piece of the
pie based on the size of the portion.
Budget
Rent
Food
Gas
Bills
Entertainment
112 | P a g e
My budget
Use the empty pie chart to show the portions of your bills compared to your
total budget. Use this space to do your calculations before you fill in the pie
chart.
113 | P a g e
Graphic Data – Line Graph
Use the data above to answer the following questions.
1. Based on the data, what are the average sales per month for each sales
person?
2. True or false, Hector has had the highest sales each month.
3. Who totaled the most sales for the five months? What is the difference
between the highest and lowest person for the five months together?
4. Based on the trends, who should have the highest amount of sales for
June? Why?
0
50
100
150
200
250
300
350
400
450
500
January Febuary March April May
Linda
Sammy
Hector
114 | P a g e
Now create your own line chart with the data provided by the instructor.
115 | P a g e
A Abbreviate
To use a short form of a word, often followed by a period, in order to save space.
Abbreviation
A shortened form of a word or phrase.
Absolute Value
The distance between a number and zero: it is always a positive number.
Acute Angle
An angle with a measure greater than 0 and less than 9.
additive identity
The number zero is called the additive identity because the sum of zero and any number is that
number.
additive inverse
The additive inverse of any number x is the number that gives zero when added to x. The additive
inverse of 5 is -5.
adjacent angles
Two angles that share both a side and a vertex.
angle
The union of two rays with a common endpoint, called the vertex.
arc
A portion of the circumference of a circle.
area
The number of square units that covers a shape or figure.
associative property of addition
(a + b) + c = a + (b + c)
associative property of multiplication
(a x b) x c = a x (b x c)
average
A number that represents the characteristics of a data set.
axis of symmetry
A line that passes through a figure in such a way that the part of the figure on one side of the line is
a mirror reflection of the part on the other side of the line.
B base
The bottom of a plane figure or three-dimensional figure.
Bisect
To divide into two congruent parts.
116 | P a g e
Box and whisker plot
A type of data plot that displays the quartiles and range of a data set.
C Cartesian coordinates
A system in which points on a plane are identified by an ordered pair of numbers, representing the
distances to two or three perpendicular axes.
central angle
An angle that has its vertex at the center of a circle.
chord
A line segment that connects two points on a curve.
circle
The set of points in a plane that are a fixed distance from a given point, called the center.
circumference
The distance around a circle.
coefficient
A constant that multiplies a variable.
collinear
Points are collinear if they lie on the same line.
combination
A selection in which order is not important.
common factor
A factor of two or more numbers.
common multiple
A multiple of two or more numbers.
commutative property of addition
a + b = b + a.
commutative property of multiplication
a*b = b*a.
complementary angles
Two angles whose sum is 90 degrees.
composite number
A natural number that is not prime.
cone
A three-dimensional figure with one vertex and a circular base.
congruent
Figures or angles that have the same size and shape.
constant
A value that does not change.
117 | P a g e
coordinate plane
The plane determined by a horizontal number line, called the x-axis, and a vertical number line,
called the y-axis, intersecting at a point called the origin. Each point in the coordinate plane can be
specified by an ordered pair of numbers.
coplanar
Points that lie within the same plane.
counting numbers
The natural numbers, or the numbers used to count.
counting principle
If a first event has n outcomes and a second event has m outcomes, then the first event followed by
the second event has n times m outcomes.
cross product
A product found by multiplying the numerator of one fraction by the denominator of another
fraction and the denominator of the first fraction by the numerator of the second.
cube
A solid figure with six square faces.
cylinder
A three-dimensional figure having two parallel bases that are congruent circles.
D data
Information that is gathered.
decimal number
The numbers in the base 10 number system, having one or more places to the right of a decimal
point.
degree
A unit of measure of an angle.
denominator
The bottom part of a fraction.
dependent events
Two events in which the outcome of the second is influenced by the outcome of the first.
diagonal
The line segment connecting two nonadjacent vertices in a polygon.
diameter
The line segment joining two points on a circle and passing through the center of the circle.
difference
The result of subtracting two numbers.
digit
The ten symbols, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The number 215 has three digits: 2, 1, and 5.
distributive property
a(b + c) = ab + ac
dividend
In a / b = c, a is the dividend.
118 | P a g e
divisor
In a / b = c, b is the divisor.
E ellipse
The set of all points in a plane such that the sum of the distances to two fixed points is a constant.
equation
A mathematical statement that says that two expressions have the same value; any number
sentence with an =.
equilateral triangle
A triangle that has three equal sides.
equivalent equations
Two equations whose solutions are the same.
equivalent fractions
Fractions that reduce to the same number.
error of measurement
The difference between an approximate measurement and the actual measure taken.
evaluate
To substitute number values into an expression.
even number
A natural number that is divisible by 2.
event
In probability, a set of outcomes.
exponent
A number that indicates the operation of repeated multiplication.
equivalent fractions
Fractions that reduce to the same number.
F
factor
One of two or more expressions that are multiplied together to get a product.
factoring
To break a number into its factors.
face
A flat surface of a three-dimensional figure.
formula
A equation that states a rule or a fact.
fraction
A number used to name a part of a group or a whole. The number below the bar is the denominator,
and the number above the bar is the numerator.
119 | P a g e
frequency
The number of times a particular item appears in a data set.
frequency table
A data listing which also lists the frequencies of the data.
G
graph
A type of drawing used to represent data.
greatest common factor (GCF)
The largest number that divides two or more numbers evenly.
H
horizontal
A line with zero slope.
hypotenuse
The side opposite the right angle in a right triangle.
I
identity property of addition
The sum of any number and 0 is that number.
identity property of multiplication
The product of 1 and any number is that number.
improper fraction
A fraction with a numerator that is greater than the denominator.
independent events
Two events in which the outcome of the second is not affected by the outcome of the first.
inequality
A mathematical expression which shows that two quantities are not equal.
infinity
A limitless quantity.
inscribed angle
An angle placed inside a circle with its vertex on the circle and whose sides contain chords of the
circle.
inscribed polygon
A polygon placed inside a circle so that each vertex of the polygon touches the circle.
integers
The set of numbers containing zero, the natural numbers, and all the negatives of the natural
numbers.
120 | P a g e
intercept
The x-intercept of a line or curve is the point where it crosses the x-axis, and the y- intercept of a
line or curve is the point where it crosses the y-axis.
intercepted arc
The arc of a circle within an inscribed angle.
interpolation
A method for estimating values that lie between two known values.
intersecting lines
Lines that have one and only one point in common.
inverse
Opposite. -5 is the additive inverse of 5, because their sum is zero. 1/3 is the multiplicative inverse
of 3, because their product is 1.
inverse operations
Two operations that have the opposite effect, such as addition and subtraction.
irrational number
A number that cannot be expressed as the ratio of two integers.
isosceles triangle
A triangle with at least two equal sides.
L
least common denominator
The smallest multiple of the denominators of two or more fractions.
least common multiple
The smallest nonzero number that is a multiple of two or more numbers.
like fractions
Fractions that have the same denominator.
line
A straight set of points that extends into infinity in both directions.
line of symmetry
Line that divides a geometric figure into two congruent portions.
line segment
Two points on a line, and all the points between those two points.
locus
A path of points.
logic
The study of sound reasoning.
lowest terms
Simplest form; when the GCF of the numerator and the denominator of a fraction is 1.
121 | P a g e
M
mean
In a data set, the sum of all the data points, divided by the number of data points; average.
median
The middle number in a data set when the data are put in order; a type of average.
midpoint
A point on a line segment that divides the segment into two congruent segments.
mixed number
A number written as a whole number and a fraction.
mode
A type of average; the number (or numbers) that occurs most frequently in a set of data.
multiple
A multiple of a number is the product of that number and any other whole number. Zero is a
multiple of every number.
multiplicative identity
The number 1 is the multiplicative identity because multiplying 1 times any number gives that
number.
multiplicative inverse
The reciprocal of a number.
mutually exclusive events
Two or more events that cannot occur at the same time.
N
mutually exclusive events
Two or more events that cannot occur at the same time.
normal
Perpendicular.
number line
A line on which every point represents a real number.
numerator
The top part of a fraction.
O
obtuse angle
An angle whose measure is greater than 90 degrees.
obtuse triangle
A triangle with an obtuse angle.
octagon
A polygon with 8 sides.
122 | P a g e
odd number
A whole number that is not divisible by 2.
operation
Addition, subtraction, multiplication, and division are the basic arithmetic operations.
opposites
Two numbers that lie the same distance from 0 on the number line but in opposite directions.
ordered pair
Set of two numbers in which the order has an agreed-upon meaning, such as the Cartesian
coordinates (x, y), where the first coordinate represents the horizontal position, and the second
coordinate represents the vertical position.
origin
The point (0, 0) on a coordinate plane, where the x-axis and the y-axis intersect.
outcome
In probability, a possible result of an experiment.
P
parallel
Two lines are parallel if they are in the same plane and never intersect.
parallelogram
A quadrilateral with opposite sides parallel.
pentagon
A five-sided polygon.
percent
A fraction, or ratio, in which the denominator is assumed to be 100. The symbol % is used for
percent.
perimeter
The sum of the lengths of the sides of a polygon.
permutation
A way to arrange things in which order is important.
perpendicular
Two lines are perpendicular if the angle between them is 90 degrees.
pi
The ratio of the circumference of a circle to its diameter.
plane
A flat surface that stretches into infinity.
point
A location in a plane or in space, having no dimensions.
polygon
A closed plane figure made up of several line segments that are joined together.
polyhedron
A three-dimensional solid that is bounded by plane polygons.
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positive number
A real number greater than zero.
power
A number that indicates the operation of repeated multiplication.
prime number
A number whose only factors are itself and 1.
probability
For an experiment, the total number of successful events divided by the total number of possible
events.
product
The result of two numbers being multiplied together.
proper fraction
A fraction whose numerator is less than its denominator.
proportion
An equation of fractions in the form:
a/b = c/d
protractor
A device for measuring angles.
pyramid
A three-dimensional figure that has a polygon for its base and whose faces are triangles having a
common vertex.
Pythagorean Theorem The theorem that relates the three sides of a right triangle:
Q
quadrant
One of the quarters of the plane of the Cartesian coordinate system
quadrilateral
A polygon with 4 sides.
quotient
The answer to a division problem.
R
radius
The distance from the center to a point on a circle; the line segment from the center to a point on a
circle.
range
In statistics, the difference between the largest and the smallest numbers in a data set.
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rate
A ratio that compares different kinds of units.
ratio
A pair of numbers that compares different types of units.
rational number
A number that can be expressed as the ratio of two integers.
ray
part of a line, with one endpoint, and extending to infinity in one direction.
real numbers
The combined set of rational numbers and irrational numbers.
reciprocal
The number which, when multiplied times a particular fraction, gives a result of 1.
rectangle
A quadrilateral with four 90-degree angles.
reflection
A transformation resulting from a flip.
regular polygon
A polygon in which all the angles are equal and all of the sides are equal.
repeating decimal
A decimal in which the digits endlessly repeat a pattern.
rhombus
A parallelogram with four equal sides.
right angle
An angle whose measure is 90 degrees.
right triangle
A triangle that contains a right angle.
root
The root of an equation is the same as the solution to the equation.
rotation
A transformation in which a figure is rotated through a given angle, about a point.
S
sample space
For an experiment, the sample space includes all the possible outcomes.
Scale drawing
A drawing that is a reduction or enlargement of the original.
scalene triangle
A triangle with three unequal sides.
scattergram
A graph with points plotted on a coordinate plane.
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scientific notation
A method for writing extremely large or small numbers compactly in which the number is shown as
the product of two factors.
set
A well-defined group of objects.
similar
Two polygons are similar if their corresponding sides are proportional.
simplifying
Reducing to lowest terms.
skew lines
Lines that are not in the same plane and that do not intersect.
slope
The steepness of a line expressed as a ratio, using any two points on the line.
solution
The value of a variable that makes an equation true.
sphere
A three-dimensional figure with all points in space a fixed distance from a given point, called the
center.
square
A quadrilateral with four equal sides and four 90 degree angles.
square root
The square root of x is the number that, when multiplied by itself, gives the number, x.
statistics
The science of collecting, organizing, and analyzing data.
stem and leaf plot
A technique for organizing data for comparison.
straight angle
An angle that measures 180 degrees.
supplementary angles
Two angles are supplementary if their sum is 180 degrees.
surface area
For a three-dimensional figure, the sum of the areas of all the faces.
T
terminating decimal
A fraction whose decimal representation contains a finite number of digits.
translation
A transformation, or change in position, resulting from a slide with no turn.
transformation
A change in the position, shape, or size of a geometric figure.
transversal
A line that intersects two other lines.
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trapezoid
A quadrilateral that has exactly two sides parallel.
tree diagram
A diagram that shows outcomes of an experiment.
triangle
A three-sided polygon.
U
unit price
Price per unit of measure.
V
variable
A letter used to represent a number value in an expression or an equation.
vertex
The point on an angle where the two sides intersect.
vertical angles
A pair of opposite angles that is formed by intersecting lines.
volume
A measurement of space, or capacity.
W
whole numbers
The set of numbers that includes zero and all of the natural numbers.
X
x-axis
The horizontal axis in a Cartesian coordinate plane.
x-intercept
The value of x at the point where a line or curve crosses the x-axis.
Y
y-axis
The vertical axis in a Cartesian coordinate system.
y-intercept
The value of y at the point where a curve crosses the y-axis.
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Z
zero
The additive identity; the number that, when added to another number n, gives n.
zero property of multiplication
The product of zero and any number is zero.
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