# 【University】EJU and its countermeasure ③（ The subjects you need the skill of logical thinking）and how to prevent careless mistakes

Math belongs to the academic field that requires you to have “the ability to think.” To be able to solve math’s questions, first you must understand the theory of each question and math’s “logic,” and secondly practice many questions to completely understand its “logic”, then go to the next step. If you go through these steps, then you will deeply understand the math’s theory, and you can solve any questions perfectly.

**Understand the logic of each math question! **

The questions of EJU math are from **the things we learned in high school**, and above all they are the **basic level**.

For example, let’s say “**quadratic function**” as an example! This is one of **the most frequently-asked questions** of EJU, for both Liberal Arts-majors and Science-majors.

Today, we will use a quadratic function’s easiest question to explain about how to study EJU math efficiently.

But please wait! The most basic equation for a function is y=ax+c (Junior High School level), isn’t it? After you make sure you have the basic knowledge of equation, then, please practice high school level’s basic questions [quadratic function： y=ax²+bx+C]→ intermediate level → advanced level (if you are a Science-major), go step by step just like this.

**This is an actual question!**

**「二次関数のグラフ、最大値と最小値を求めましょう」**

**[The graph of quadratic function, find the **

**“maximum point” and “minimum point”]**

**方程式：y=3(x+2)²+5**

**The equation： y=3(x+2)²+5**

**①方程式を解いて、二次関数の頂点を求めなさい。**

**① Solve the equation y=3(x+2)²+5,**

** and find the vertex of the graph.**

**②グラフを描きなさい。**

**② Draw the graph.**

**③-2≦x≦0の時の最大値、最小値を求めなさい。**

**③When it is -2≦x≦0, find the maximum point **

**and minimum point. **

**Answer**

Do you know how the graph of junior high level math, y=3 x²,

how does it look like? Yes, it is a graph of parabola.

When you draw the graph of ** y=3(x+2)²+5**, you have to move

a graph parallel to -2 on the x-axis, and to 5 on the y-axis.

Then, you will figure out the vertex will be **(-2, 5)**.

The solution of equation is this：

y=3(x+2)²+5

=3(x²＋4x＋4-4)＋17

**=3 x²＋12x＋17**

**The intersection with the Y axis is（ when x=0）**, **17**

If you have these information, you will be able to draw the graph just like the one right above.

Also, when you draw the graph, you can automatically understand when it is **-2≦x≦0**, y=5（x=2）、y=17（x=0) .

**The advice regarding how to study**

❶ The logic of this question (**“Answer”** written above) is the most important thing, and you have to fully understand when you study mathematics. Please use **the textbook printed in your mother tongue**, in order to understand the “logic” of this question. If you do so, you could understand this logic more exactly and more quickly. After you completely understand this, please solve the similar basic questions.

❷ After you thoroughly understand the logic, then start to learn

**the vocabulary of Japanese questions **and **terminology**.

… for example, what does 「方程式を解く」 and 「グラフを描く」 mean?

❸ After you completely master this kind of beginner level of quadratic function, then go to the intermediate level, and to the advanced level.

**It is the most important to understand the basis of math’s logics.**

**How to avoid making careless mistakes?**

A careless mistake refers to the simple miscalculation, and thus you failed to reach the correct answer in the end although your understanding for this question was completely correct.

Especially after the exam, “Whoops! I made a careless mistake again! What a waste!” this kind of things often happen to us. However, making a careless mistakes could be avoid if you take the preventive measures.

**Do not take careless mistakes too easily！**

**Making mistakes always has the causes.** Misread the question sentences, or miscalculation,** you must find out the cause of the mistakes, and take the preventive measures, otherwise you may make the same mistakes again**. “I was just careless. This was because of my body condition. I was absent-minded.” You cannot leave the problem alone like this…

**Without taking the preventive measures, then you will make the same mistakes repeatedly.**

Things as far as a human does, it is impossible to avoid mistakes completely. However, there are some points that we may easily make the mistakes, and there are ways to avoid them as well. It all depends on the analysis and the investigation about the cause.

**Is it a careless mistake or a lack of understanding?**

It is painful, but please face to the problem, and think why you had made this mistakes. Could it be that…because of a lack of understanding?

**When you analyze whether this mistake was caused by simply carelessness or a lack of understanding, the best method to check is to solve the very same question another day!**

**To begin with, what is a careless mistake？**

For example…such as 2＋4=8. “**How come did I miscalculate like this?**” I want to ask myself,,, this is a typical example of a careless mistake.

If this is the real careless mistake, then you definitely will not do the same thing next time. You do not need to look for the answer or the reference on the textbook, at the next time you can make the correct answer without any trouble.

**The difference between a careless mistake and a lack of understanding **

Even though you tried to solve the same question but failed again,,, this could be due to **a lack of understanding**. You may have some misunderstandings while you study math’s logics, or your understanding is still vague, and you might just feel like you had understand that.** At the next challenge if you could not make 100% correct answer, then it must be due to a lack of understanding.** For the lack of understanding, please read the textbook carefully, and review it again.

**The cause of a careless mistake**

OK then, how should we do in order to avoid making careless mistake?

The causes which have led the careless mistake frequently are：

・The mistakes happened while you calculated it in your head…simple calculation mistake

・The mistakes while you copy the number or sign in the equation…the mistake in writing

**①The countermeasure for avoiding the miscalculation in your head**

Basically a calculation mistake often occurs when you are too hurry to pursue an answer and calculate some of them in your head, or skip writing a part of equation on the paper, then these things eventually led to be the errors. You cut off some workload and do it in your head, then this could be the cause of mistakes.

**・Do not count on your mental arithmetic too much.** **Always write each process of calculation on a paper.**

**・Write each equation, everything on a paper**. Do not abbreviate it. **→And in this case, when you recalculate the answer, you will find out where was wrong.**

**②The countermeasure for avoiding miswriting **

This refers to the situation “there is no way I was doing this kind of thing”. For example, forgetting to write minus sign (－), very surprisingly this happens frequently. Especially, writing each equation longer and more times, the more mistakes you will make.

**・When you write the calculation process, write the number or sign largely. **

**・Use the big space for your calculation. **

**③And finally at the test, recalculate it from the beginning to the end. **

**If you make the mistakes, then it is your true ability! **

The most important thing for reducing the careless mistakes is **do not leave this problems alone**. Could it be your lack of understanding or a simple careless mistake, you must figure out. Then, **consider the cause of the mistakes and take the preventive measures**, without doing this it will be the same. **Your true ability, and the things you can do or the things you cannot do**, to understand these are indispensable while you are learning and improve your performance. The fact that you made this mistakes, and this is your true ability. Be strict to yourself, and this could be the points toward the success and to reduce the careless mistakes and get the high score on the test.