Ⅰ.
polynomial

01 Polynomial Operations⑴
(1) Various terms related to polynomials (2) Polynomial theorem
(3) Addition and subtraction of polynomials

02 Polynomial Operations⑵
(1) Multiplication of polynomials (2) Multiplication formula
(3) Modification of the multiplication formula

03 Polynomial Operations⑶
(1) Division of polynomials (2) Synthetic division
Practice Problems (Level A / Level B)

04 Identity and Remainder Theorem⑴
(1) Identity (2) Properties of identity
(3) Undetermined coefficient method

05 Identity and Remainder Theorem⑵
(1) Remainder theorem (2) Factor theorem
Practice Problems (Level A / Level B)

06 Factorization⑴
(1) Meaning and formula of factorization

07 Factorization⑵
(1) Factorization of complex expressions (2) Factorization of expressions containing multiple characters
(3) Factorization using the factoring theorem
Practice Problems (Level A / Level B)

Ⅱ.
Equations and Inequalities

08 Complex number⑴
(1) Complex number (2) Conditions for complex numbers to be equal
(3) Conjugate complex number

09 Complex number⑵
(1) Arithmetic operations on complex numbers (2) Properties of conjugate complex numbers
(3) Power of imaginary unit i

10 Complex Numbers⑶
(1) Square root of a negative number (2) Properties of square roots of negative numbers
Practice Problems (Level A / Level B)

11 Quadratic Equation ⑴
(1) Solution to equation ax=b (2) Equation including absolute value sign

12 Quadratic Equation ⑵
(1) Solution of quadratic equation (2) Discriminant of quadratic equation

13 Quadratic Equation ⑶
(1) Relationship between roots and coefficients of quadratic equations (2) Factorization of quadratic equations
(3) Writing a quadratic equation

14 Quadratic Equation ⑷
(1) Conjugate roots of quadratic equations
Practice Problems (Level A / Level B)

15 Quadratic Equations and Quadratic Functions⑴
(1) Graph of quadratic function (2) Relationship between quadratic equation and quadratic function
(3) Positional relationship between the graph of a quadratic function and a straight line

16 Quadratic Equations and Quadratic Functions⑵
(1) Maximum and minimum of quadratic function (2) Maximum and minimum of quadratic function in a limited range
Practice Problems (Level A / Level B)

17 Cubic and quartic equations⑴
(1) Solving higher-order equations (2) Solving higher-order equations using the factoring theorem
(3) Solving higher-order equations using substitution (4) Solving quadratic equations
(5) Solution of the quartic reciprocal equation

18 Cubic and quartic equations⑵
(1) Relationship between roots and coefficients of cubic equations (2) Writing cubic equations
(3) Conjugate roots of cubic equations (4) Properties of imaginary roots of cubic equations x³=±1
Practice Problems (Level A / Level B)

19 Simultaneous equations⑴
(1) Solution of simultaneous linear equations (2) Solution of simultaneous quadratic equations
(3) Symmetric simultaneous equations for x and y

20 Simultaneous equations⑵
(1) Common root (2) Indefinite equation
Practice Problems (Level A / Level B)

21st linear inequality
(1) Properties of inequalities (2) Arithmetic operations of inequalities
(3) Solution to inequality ax〉b (4) Solution to simultaneous linear inequalities
(5) System of linear inequalities with special solutions (6) Inequalities including absolute value symbols
Practice Problems (Level A / Level B)

22 Quadratic Inequality⑴
(1) Quadratic inequality (2) Solution to quadratic inequality
(3) Writing quadratic inequalities (4) Conditions for quadratic inequalities to always hold true

23 Quadratic inequality⑵
(1) Solution of simultaneous quadratic inequalities (2) Sign of real roots of quadratic equations
(3) Location of roots of quadratic equations
Practice Problems (Level A / Level B)

Ⅲ.
Number of cases

24 cases
(1) Number of cases (2) Law of agreement
(3) Law of multiplication (4) Application of the law of sum and the law of multiplication
Practice Problems (Level A / Level B)

25 Permutations⑴
(1) Permutation (2) Number of permutations
(3) Factorial of n

26 Permutations⑵
(1) The number of permutations listed adjacently (2) The number of permutations including the condition 'at least'
Practice Problems (Level A / Level B)

27 Combination ⑴
(1) Combination (2) Number of combinations
(3) The nature of the number of combinations

28 combinations⑵
(1) Number of cases that include a specific thing (2) Number of combinations that include the condition 'at least'
(3) Utilization of the number of combinations
Practice Problems (Level A / Level B)

Ⅳ.
procession

29 Matrices and their operations⑴
(1) Meaning of matrix (2) (i, j) component of matrix
(3) Same matrices (4) Addition and subtraction of matrices
(5) Properties of matrix addition (6) Zero matrix
(7) Real multiple of the matrix

30 Matrices and Their Operations⑵
(1) Multiplication of matrices (2) Exponentiation of matrices
(3) Properties of matrix multiplication (4) Identity matrix
Practice Problems (Level A / Level B)

Secret Subnote SUB NOTE

〈 Structure and Use of This Book 〉

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.