1
,
Copyright © 2023 Paul McConville
All rights reserved. No part of this book may be reproduced, stored, or
transmitted by any means—whether auditory, graphic, mechanical, or
electronic—without written permission of both publisher and author,
except in the case of brief excerpts used in critical articles and reviews.
Unauthorized reproduction of any part of this work is illegal and is
punishable by law.
2
, Table of Contents
Table of Contents 3
SECTION 1: Simple Algebra and Number Properties 10
Intro: Algebra Basics 10
1. Solving for a Variable 10
2. Operations with Fractions 10
a. Adding / Subtracting 10
b. Multiplying / Dividing 11
c. Improper Fractions 11
3. PEMDAS 11
4. Common Uses of Different Operations 12
Unit 1: Multiples and Factors 13
1. Least Common Multiple / Denominator 13
a. Straight-forward Presentation 13
b. Prime Factors 14
c. Word Problems 14
2. Factors / Greatest Common Factor 14
3. Rational Expressions / Equations 14
4. Remainders 15
Unit 2: Ratios 16
1. Simple Ratios 16
2. Frequency Tables 17
3. Unit Conversion 17
4. Colon Type 17
5. Ratios in Context 18
6. Sample Proportions 18
7. Two Variables / Fraction Expression 18
Unit 3: Exponents and Radicals 20
1. Properties 20
2. Base Change 21
3. Scientific Notation 21
4. Operations with Radicals 21
a. Simplifying 21
b. Adding / Subtracting 22
c. Multiplying / Dividing 22
d. Rationalizing 22
Unit 4: Logs 24
1. Evaluating 25
2. Converting to Exponential 25
a. Exponentials to Logs 25
b. Logs to Exponentials 25
3
, 3. Properties 26
4. Algebra Problems in Context 26
Unit 5: Percents 28
1. Percent Of / Percent More Than / Percent Less Than 28
2. Percent Increase / Decrease 29
3. ‘Percent of’ Given Two Numbers 29
4. Concentration 29
5. Fractions (Percents) of a Whole 29
Unit 6: Sequences 32
1. Arithmetic 32
2. Geometric 32
3. Sequences Defined by Notation 33
4. Arithmetic Series 33
Unit 7: Number Theory 35
1. Evaluate by Plugging-in 35
2. Maximize / Minimize Expressions 36
3. Positivity / Negativity of Exponent Expressions 36
4. Vocabulary You Should Know 36
a. Integers 36
b. Rational vs. Irrational 36
c. Prime Numbers 37
d. Imaginary Numbers 37
e. Perfect Squares / Cubes 37
Unit 8: Direct vs. Inverse Relationships 40
1. Direct 41
2. Inverse 41
Unit 9: Pattern Questions 42
1. Repeating Decimals 42
2. Non-decimal Patterns 42
3. Patterns with Exponents 43
Unit 10: ‘Fake Operations’ 44
Unit 11: Venn Diagrams 44
Unit 12: Matrices 46
1. Adding / Subtracting 46
2. ‘Scalar’ Multiplication 46
3. Multiplying two Matrices 46
a. When Can We Multiply? 46
b. Actually Multiplying 47
4. Matrices in Context 47
5. Determinants 48
Section 1 Appendix: Miscellaneous Topics 50
Topic 1: Ordering Numbers 50
Topic 2: Evaluating Complex Fractions 51
Topic 3: Cross-Multiplication with Two Variables 51
4
,
Copyright © 2023 Paul McConville
All rights reserved. No part of this book may be reproduced, stored, or
transmitted by any means—whether auditory, graphic, mechanical, or
electronic—without written permission of both publisher and author,
except in the case of brief excerpts used in critical articles and reviews.
Unauthorized reproduction of any part of this work is illegal and is
punishable by law.
2
, Table of Contents
Table of Contents 3
SECTION 1: Simple Algebra and Number Properties 10
Intro: Algebra Basics 10
1. Solving for a Variable 10
2. Operations with Fractions 10
a. Adding / Subtracting 10
b. Multiplying / Dividing 11
c. Improper Fractions 11
3. PEMDAS 11
4. Common Uses of Different Operations 12
Unit 1: Multiples and Factors 13
1. Least Common Multiple / Denominator 13
a. Straight-forward Presentation 13
b. Prime Factors 14
c. Word Problems 14
2. Factors / Greatest Common Factor 14
3. Rational Expressions / Equations 14
4. Remainders 15
Unit 2: Ratios 16
1. Simple Ratios 16
2. Frequency Tables 17
3. Unit Conversion 17
4. Colon Type 17
5. Ratios in Context 18
6. Sample Proportions 18
7. Two Variables / Fraction Expression 18
Unit 3: Exponents and Radicals 20
1. Properties 20
2. Base Change 21
3. Scientific Notation 21
4. Operations with Radicals 21
a. Simplifying 21
b. Adding / Subtracting 22
c. Multiplying / Dividing 22
d. Rationalizing 22
Unit 4: Logs 24
1. Evaluating 25
2. Converting to Exponential 25
a. Exponentials to Logs 25
b. Logs to Exponentials 25
3
, 3. Properties 26
4. Algebra Problems in Context 26
Unit 5: Percents 28
1. Percent Of / Percent More Than / Percent Less Than 28
2. Percent Increase / Decrease 29
3. ‘Percent of’ Given Two Numbers 29
4. Concentration 29
5. Fractions (Percents) of a Whole 29
Unit 6: Sequences 32
1. Arithmetic 32
2. Geometric 32
3. Sequences Defined by Notation 33
4. Arithmetic Series 33
Unit 7: Number Theory 35
1. Evaluate by Plugging-in 35
2. Maximize / Minimize Expressions 36
3. Positivity / Negativity of Exponent Expressions 36
4. Vocabulary You Should Know 36
a. Integers 36
b. Rational vs. Irrational 36
c. Prime Numbers 37
d. Imaginary Numbers 37
e. Perfect Squares / Cubes 37
Unit 8: Direct vs. Inverse Relationships 40
1. Direct 41
2. Inverse 41
Unit 9: Pattern Questions 42
1. Repeating Decimals 42
2. Non-decimal Patterns 42
3. Patterns with Exponents 43
Unit 10: ‘Fake Operations’ 44
Unit 11: Venn Diagrams 44
Unit 12: Matrices 46
1. Adding / Subtracting 46
2. ‘Scalar’ Multiplication 46
3. Multiplying two Matrices 46
a. When Can We Multiply? 46
b. Actually Multiplying 47
4. Matrices in Context 47
5. Determinants 48
Section 1 Appendix: Miscellaneous Topics 50
Topic 1: Ordering Numbers 50
Topic 2: Evaluating Complex Fractions 51
Topic 3: Cross-Multiplication with Two Variables 51
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