■ Preface ㆍ 4
■ User Manual ㆍ 14

Common Mathematics 1

Ⅰ Polynomial

Do I have to sort it in descending or ascending order?
Why do we multiply numbers vertically, but multiply strings horizontally?
How far should I calculate the quotient of a division?
Why does ｘ disappear?
How do I find the remainder without division?
Can't I just memorize the formula for factoring?

Ⅱ Equations and Inequalities

Is there a number that becomes negative when squared?
If you calculate 5i-3i, isn't only 2 left?
When ａ〈0, is (√ａ)²=-ａ correct?
How do you know if a root is real or imaginary without finding the root?
How do you find the sum or product of two roots without finding the roots themselves?
Can all quadratics be factored?
If D〉0, isn't the graph on the x-axis?
How can we tell if the graph of a quadratic function intersects a straight line using the discriminant?
Can you find the maximum height the water rocket can reach?
How do you find the roots of the cubic equation ｘ³ + ｘ² - 2ｘ= 2?
How do I find the number to substitute when using the factoring theorem?
Can you also solve simultaneous quadratic equations using the elimination method?
Why do we find the common part of a system of inequalities?
Is it okay to just remove the minus sign to find the absolute value?
What do quadratic equations and quadratic inequalities have in common?
How many quadratic inequalities are there in a system of quadratic inequalities?

Ⅲ Number of cases

Why multiply when they don't happen simultaneously?
Do I have to list them in order?
1! is 1, so how is 0! also 1?
Are there already combinations in the permutations?

Ⅵ matrix

Are only rectangular arrays considered matrices?
How do I add two matrices (12 34) and (123 456)?
Matrix multiplication can take different forms, right? How so?

Common Mathematics 2

Ⅰ Equation of a figure

Is the distance between two points the absolute value of the difference between the coordinates?
How do you do an external division when there is no outside of a line segment?
Are internal and external divisions on the coordinate plane the same as internal and external divisions on the vertical line?
Isn't the slope m?
Can you find the equation of a line with just two points, not just the slope and y-intercept?
Do equations have graphs?
How can you tell if a line is parallel or perpendicular just by looking at its equation?
How do you measure the distance between a point and a line?
Does a circle have an equation?
How can you tell if a circle and a line intersect just by looking at the equation without drawing a picture?
Are all lines that intersect a circle at a point tangent lines?
Is diagonal translation possible?
When we say movement, doesn't it mean moving in the direction of the x-axis or y-axis?
Can't the symmetry of a shape be explained by a parallel translation?

Ⅱ Sets and Propositions

How many tall students are there in our class?
It's the same, but how does it become a part?
If you add sets, does the number of elements increase by that amount?
Why does the intersection suddenly appear when subtracting sets?
If I change the order, will the result of the intersection be the same?
Why do the operations inside the set change when finding the complement?
Do I have to count the number of elements in the union myself?
If it's false, why is it a proposition?
Is the negation of 'and' 'or'?
Don't all flowers bloom in spring?
Aren't both 'Yejun is human' and 'Humans are Yejun' correct?
If you're a boy, don't you go to a boys' high school?
What is necessary and what is sufficient?
Why are parallelograms so complicated?
Is the converse of a proposition true or false?
Are there any inequalities that always hold true, like the identity of an equation?

Ⅲ Function

Isn't a function when one variable changes and the other variables change accordingly?
The graph of a quadratic function is a parabola, so why are only a few points plotted?
Does a one-to-one function depend on its domain?
How do you calculate the composite function g 。f?
Does every function have an inverse function?
Why are the graphs of functions and inverse functions symmetrical y = x?
Are polynomials also rational?
Why is the graph of the rational function y = ¹/x drawn as two curves that are symmetrical about the origin?
Why is √ｘ¹ - 2ｘ + 1 not an irrational equation?
Why is an irrational function the inverse of a quadratic function?

■ Middle and High School Math Concept Connection Guide ㆍ 308
■ High School 1st Grade Math Concept Connection Guide ㆍ 309
■ Search ㆍ 310

Time required to connect concepts

High school first-year math serves as a bridge between middle school math and second and third-year high school math.
When you become a second or third year high school student, you will study various elective subjects such as calculus, probability and statistics.
The foundation for these elective subjects is first-year high school mathematics.
High school first-year math is a very important stage because it expands and completes the concepts of middle school math and serves as a foundation for studying various elective subjects learned in the second and third years of high school.
If you have a clear understanding of the concepts up to the first year of high school mathematics, you will be sufficiently prepared to study elective subjects later on.

Which students would benefit from reading this?

This book is essential for both students who are good at math and those who find math difficult and are about to give up.
Students who are good at math need to repeatedly check the connection between concepts.
Even students who are good at math have weak links.
You can easily find weaknesses and immediately supplement the necessary areas.
Students who are tempted to give up on math because it is too difficult should slowly and steadily learn the concepts and increase their experience solving problems using the power of those concepts.
Even if it's just one or two problems a day, you can continue studying math only when you have the experience of solving problems on your own based on a conceptual understanding, rather than memorizing problem-solving formulas.
And, when solving difficult problems on the CSAT, the 『Concept Connection Advanced Mathematics Dictionary』 will be of great help.
Difficult problems often involve a mix of concepts.
To solve this problem, even if it takes a long time, the secret to getting a perfect score is to find and organize the various concepts in the problem one by one and find the connections. The "Concept Connection Advanced Mathematics Dictionary" will help you with this training.


All high school math concepts covered in 69 questions

The mathematical concepts covered in this book begin with questions.
This question is a compilation of the author's major questions and thoughts on students' misconceptions, which he discovered through extensive teaching experience and research, as well as through mathematics clinics and consulting.
This is arranged based on the new curriculum and textbook progress, and contains all concepts and content of first-year high school mathematics.
Furthermore, in "Ah! I see," we examine why students ask these questions and the causes of misconceptions.
Misconceptions arise from a lack of sufficient understanding in the process of learning a concept.
To overcome the wall of misconceptions, you must know exactly where the conceptual deficit occurs.

The concept will come naturally to you.

After confirming misconceptions, the '30-second summary' introduces concepts and properties from the textbook and provides correct answers to misconceptions.
You can use it when you don't have time or need to organize something quickly.
Reading '30-Second Summary' and then reading 'Discovering Concepts' will help you correct misconceptions about the concept and learn things you didn't know before.
If you have sufficient understanding with the '30-second summary', you can skip the 'concept discovery' that comes next.
In 'Discovery of Concepts', concepts are explained from the basics.
It is explained in connection with previously learned math concepts, so it helps to reinforce the basics and review concepts that students may have missed.
We hope you'll learn the core concepts with '30-second summary' and use 'concept discovery', which provides a more user-friendly explanation, to help you internalize the concepts.

Experience the connection of concepts

In 'Discovering Connections', we go one step further than 'Discovering Concepts' and examine the connections between concepts.
Helps build deeper understanding by seeing how the fundamental concepts learned in elementary and middle school develop.
The 'tail-chasing-tail concept' shows at a glance how the unit I am studying now connects from middle school to high school.
'Ask Me Anything' provides answers to some difficult but essential questions.
Some of the questions include somewhat difficult content, so if you do not understand them well, please repeat them several times to familiarize yourself with them.

Find your location using the concept connection map.

Once you have a 'blister', your confidence drops and it is difficult to recover.
Even if you want to start again, you don't know where to start, so you just waste time and end up giving up.
Whether you're a student trying to escape the "water bubble" and regain your math self-esteem, a student who feels they lack a solid foundation, or a student curious about future math concepts, we've included a concept connection map that you can easily use to identify your weaknesses.
You can see at a glance the concepts that are connected after middle school.
We also included a map that expands only the concepts of high school 1st grade math.
It will provide you with a clue to fill in your shortcomings and study ahead in areas where you are confident.