Ⅰ.
Equation of a shape

01 Plane Coordinates⑴
(1) Distance between two points on a vertical line (2) Distance between two points on a coordinate plane

02 Plane Coordinates⑵
(1) Internal division of a line segment (2) Internal division point of a line segment on a perpendicular line
(3) Internal division point of a line segment on a coordinate plane (4) Center of gravity of a triangle
Practice Problems (Level A / Level B)

03 Equation of a straight line⑴
(1) Overview of the equation of a straight line
(2) Equation of a straight line given a slope and a point
(3) Equation of a straight line passing through two points (4) Equation of a straight line parallel to the coordinate axis
(5) General form of the equation of a straight line

04 Equation of a straight line⑵
(1) Positional relationship between two lines (2) Equation of the line passing through the vertices
(3) Equation of the straight line passing through the intersection of two straight lines

05 Equation of a straight line⑶
(1) Distance between a point and a line
Practice Problems (Level A / Level B)

06 Equation of a circle⑴
(1) Equation of a circle (2) Equation of a circle tangent to the coordinate axes

07 Equation of a circle⑵
(1) Positional relationship between circles and lines (2) Equation of the shape passing through the intersection of two circles
(3) Equation of the tangent to a circle
Practice Problems (Level A / Level B)

08 Moving shapes⑴
(1) Parallel translation of points (2) Parallel translation of shapes

09 Movement of shapes⑵
(1) Symmetric movement of points (2) Symmetric movement of shapes
Practice Problems (Level A / Level B)

Ⅱ.
Sets and Propositions

10 Meanings and Expressions of Sets⑴
(1) Sets and elements (2) Relationship between sets and elements
(3) How to represent a set

11 Meaning and expression of set ⑵
(1) Classification of sets (2) Subsets
(3) Same sets (4) Proper subsets

12 Meaning and expression of sets⑶
(1) Number of subsets
(2) The number of subsets that include or do not include a specific thing
Practice Problems (Level A / Level B)

13 Set Operations⑴
(1) Union and intersection (2) Complement and difference
(3) De Morgan's law

14 Set Operations⑵
(1) Set operation rules (2) Number of elements in a finite set
Practice Problems (Level A / Level B)

Proposition 15
(1) Propositions and conditions (2) Negation of propositions and conditions
(3) Set of truths

Proposition 16⑵
(1) Proposition p → q (2) Truth, falsity, and truth set of proposition p → q
(3) Propositions with 'all' or 'any' (4) Converse and contrapositive of propositions

Proposition 17⑶
(1) Sufficient and necessary conditions (2) Necessary and sufficient conditions
(3) Syllogism
Practice Problems (Level A / Level B)

Proof of Proposition 18⑴
(1) Definition, proof, and theorem (2) Proof using antithesis
(3) Law of reductio ad absurdum

Proof of Proposition 19⑵
(1) Absolute inequality (2) Arithmetic mean and geometric mean
(3) Cauchy-Schwarz inequality
Practice Problems (Level A / Level B)

Ⅲ.
function

20 Function ⑴
(1) Meaning of function (2) Domain, codomain, and range of a function
(3) Same functions (4) Graphs of functions

21 Function⑵
(1) One-to-one function (2) One-to-one correspondence
(3) Identity function (4) Constant function
Practice Problems (Level A / Level B)

22 Composite functions and inverse functions⑴
(1) Meaning of composite function (2) Properties of composite function

23 Composite functions and inverse functions⑵
(1) Meaning of inverse function (2) Finding the inverse function
(3) Properties of inverse functions (4) Properties of graphs of inverse functions
Practice Problems (Level A / Level B)

24 Rational Function ⑴
(1) Meaning of rational expression (2) Calculation of various rational expressions
(3) Properties of proportions

25 Rational Function⑵
(1) Meaning of rational function (2) Graph of rational function y=k/x (k≠0)
(3) Graph of the rational function y=k/(xp) + q (k≠0)
(4) Graph of the rational function y=(ax+b)/(cx+d) (c≠0, ad-bc≠0)
(5) Inverse function of rational function y=(ax+b)/(cx+d) (c≠0, ad-bc≠0)
Practice Problems (Level A / Level B)

26 Irrational Function ⑴
(1) Meaning of irrational expression (2) Properties of square roots
(3) Rationalization of denominators (4) Conditions for irrational numbers to be equal

27 Irrational function⑵
(1) Meaning of irrational function (2) Graph of irrational function √ax (a≠0)
(3) Graph of the irrational function √a(xp) + q (a≠0)
(4) Graph of the irrational function √ax+b + c (a≠0)
(5) Inverse function of the rational function
Practice Problems (Level A / Level B)

Secret Subnote SUB NOTE

There is no miracle method for learning math!!

1.
There are no shortcuts to learning math.
Concept learning must be thoroughly mastered one by one.
2.
Learn step by step, starting with concept organization, basic problems, and then development problems.
3.
The more I ponder a difficult problem, the more it becomes mine.
4.
Be sure to write your problem solutions in columns in your solution notebook.
5.
Your skills will grow as your notebook of wrong answers accumulates.

〈 Structure and Use of This Book 〉

01 This is the optimal self-directed learning book for perfect concept learning.

The foundation of learning mathematics is a thorough understanding of the concepts.
We have divided the units into sub-units that form the basis of the concepts, and explained them so that the basic concepts can be clearly understood.
Along with the “Formula Summary,” we have explained “The Principles of Formula Creation,” “Tips from Authors” who are senior learners, and “Common Errors” when solving problems, to help you establish a solid concept.

Additionally, learning concepts in mathematics is about mastering the essence of mathematics.
In each unit, questions about the core fundamental principles are presented as Qs.
By reading these questions and the easy-to-understand answers in A, you can make mathematics completely your own.
By following Summa Cum Laude's innovative learning method, you will gain confidence in mathematical reasoning and discover yourself capable of explaining concepts.

02.
This book is designed to help you achieve the best learning outcomes with optimal problems.

1. EXAMPLE & CONCEPT TEST

To help you immediately apply the concepts you learned in the subtopics, the most basic EXAMPLES are presented below the concept explanations.
You can gain a solid understanding of the concepts and move on through various approaches or additional explanations.
For each part of the intermediate unit bundle, we have presented concepts from various subtopics and problems that apply or apply the concepts learned in EXAMPLE in the form of a short test so that you can organize and move on to the concepts once more.

2.
Basic and Advanced Examples
After studying the concepts, you can learn representative problems by type.
We divided the essential types of mathematics into “Basic Examples” and “Advanced Examples” and provided solution guides and solutions, allowing you to perfectly practice the types with the same type of problem.
Additionally, through 〈Summa's Advice〉, we have added important points and precautions to help you thoroughly prepare for the corresponding type.

3.
Practice Problems (Level A / Level B)
It is designed to test the concepts and types learned in each unit.
The questions are divided into A/B according to difficulty level, and representative questions from previous education office exams are also included to help you prepare for various mock exams.
Additionally, unique and high-quality problems that can only be found in Summa Cum Laude are marked with an S (challenge) to allow you to adapt to any math problem.

03.
Self-study is possible with easy and detailed explanations.

Detailed explanations are essential to a clear understanding of the problem.
We have provided the most appropriate explanation for each problem, and even for problems that you were unfamiliar with, we have provided a clear solution method so that you can easily understand it through self-study.
If you just want to check the answer in a short period of time, you can use “Quick Answer,” and it is a self-directed learning textbook that can help you conquer math on your own by providing “Other Solutions,” “References,” “Summa Special Lectures,” and even “Solution Strategies” for previous exam questions from the Office of Education.