Math, Exam Arithmetic Strategies

. A summary of the efficiency of learning in each area and the areas where students are likely to be in trouble.


Junior High School Math Field-Specific Strategies

Junior High School 1st Grade

Positive and negative numbers

Many first-year middle school students are not used to dealing with calculations that involve a negative number twice.
Many students are stuck with fractional divisors.
Also, many students are unable to convert divisors to multiples.
Many students in the first year of middle school are not used to handling two-fold calculations.

Literal expressions

Often cannot understand the concept of x,y variables.
Unable to apply letters to expressions.

Equations

Equations are quite difficult to solve. Often cannot transfer from the left side to the right side.

Functions

Cubic formulas are difficult; it is advantageous to have the instructor explain the xy coordinate plane and slope.


Plane figures

Difficult to cover because of the myriad of patterns.
If you go and write down the lengths and angles of the figures, you can notice the similarities.



Spatial figures

Although there are surprisingly few patterns compared to plane figures,
A certain number of students have difficulty in drawing three-dimensional figures.
Many middle school students do not memorize multiplying cones by 1/3.


Organizing the material

. Basically, you only need to pay attention to memorizing statistical terms.
It is easy to forget class values (a and b averages over a and less than b),
frequencies, and relative frequencies (total is 1.0).

Second year of junior high school

Calculating expressions

. Many students do not organize terms of higher degree to the left (in descending order).

Sequential equations

A series of sign errors occur in addition and subtraction.
In addition, it is often impossible to eliminate one of the character expressions.


First order functions

. Many students do not get the habit of equating y=ax+b.
The concept of the xy coordinate plane and slope is difficult to understand.
Without understanding the basic concepts, they have trouble with quadratic functions in high school, but
You can memorize the procedure and get through it until the high school entrance exam.

Triangles and Quadrilaterals, Parallel and Congruent

Memorizing the congruence conditions of triangles is essential.
The conditions of rhombuses and parallelograms are also frequently
used in high school entrance exams and should be memorized if possible.
Proofs of congruence can be done by writing the conditions on the shapes, but
In many cases, the solution is not known because the similarity
and isosceles triangles are not noticed in many cases.


Probability

Many questions can be answered if the tree diagram can be drawn out, but
If you use fractions, as in high school probability, you can greatly reduce the time required to answer the question.


Data analysis

Although it is complicated to memorize the quartile range, etc.
There are not many application patterns, so you just need to be careful about calculation errors and miscounting.

3rd year of junior high school

Expansion and factorization of expressions

The difficulty level of learning the procedures is about standard, but
It is tough if you have difficulty with accuracy and speed, as it often comes up quite often in fusion problems.

Square roots

Hard to get in and out of root and rationalization habits, but an easy area to understand.

Square Root

The procedure for prime factorization to square numbers in and out of the root should be mastered if possible.

Quadratic equations

The equation of the sentence problem is often quite tricky.
Calculations are also redundant and prone to errors.
Easily trapped in the equation of points of fan-shaped and white figures, calendars, and moving figures.

Functions

The introduction of functions is somewhat difficult to understand and it is easy to make mistakes,
such as incorrectly assigning a numerical value to the slope a.
Standard questions can be answered in a pattern.
Problems involving figures and moving points are difficult to solve,
If there is a hole in the area of factorization, the calculation cannot be completed.

Similarity

Surprisingly, many junior high school students do not remember that outer terms = inner terms,
The theory does not have to be understood at the junior high school level.
It is acceptable to use related theorems, such as high school content (the square theorem).

Circles

There are few theorems such as area formula, circumference angle central angle, etc. Many students remember most of them, but
Many students cannot apply them or cannot give a quick formula.

Three Square Theorem

. The formula is easy to remember, and the proof is somewhat difficult but not necessary to understand.
The application of the formula to three-dimensional figures is a little troublesome,
but basically you just apply the formula to one pattern.

High school mathematics field-specific strategies

Expressions and Proofs (math 1)

The procedure of factorizing two letters twice is a bit tedious.
Also, it is difficult to read if you combine the pattern of lumping out
by common factors and the pattern of putting together by quadratic expressions.

Inequalities (math 1)

Basically a plain field.
It is difficult when absolute values are involved, but you can proceed mechanically without understanding.
|x|< 3 → "the distance from the origin is less than 3" is a good interpretation.

Quadratic function (Math 1)

If you know the concept of the xy coordinate plane in junior high school, it is an easy field to learn and apply.
Quadratic functions are easy to learn and apply if you know the concept of the xy coordinate plane.
I hope to get a good score.
This should be a source of points. However,
many students in the lower grades fail to understand the equations of junior high school.

Data Analysis (Math 1)

There are very few patterns, but it is difficult to get an image of the terminology.
Variance: the mean of the square of the difference between the mean and data X.
It represents the variation in the amount of work done by data X.
Covariance: whether there is a proportional relationship between X and Y
[e.g., the amount of work done by X and Y]
Correlation coefficient:
a simple generalization of whether there is a proportional relationship
between X and Y in the range [-1<=correlation coefficient<=1].
[X and Y are proportional if the correlation coefficient is 1,
not proportional if 0, and inversely proportional if -1])
Examples of correlation coefficients:
Correlation coefficient between suicide rate and divorce rate for Japanese women is 0.03 (almost no relationship)
. Correlation coefficient between suicide rate and divorce rate for Japanese men: 0.91 (strong correlation)
Correlation coefficient between suicide and divorce rates for Italian men -0.80 (inverse correlation)
. The correlation coefficient for foreign men is nearly zero,
with Italian men committing fewer suicides upon divorce,
while shows that Japanese men commit suicide upon divorce.

Logic (Math A)

It is not very difficult to master the basics.
Many students cannot use de Morgan's law.
It is not a problem to apply the contraposition and the back-rithm
in a pattern manner without understanding the logic.
(may be in the scope of graduate entrance exams for science and engineering)

Number of cases and probability (Math A)

The basic skills are limited to distinguishing permutations P and combinations C, and duplicate combinations,
which are moderately difficult to master.

Case Numbers and Probability (Math A)

The basic skills are only moderately difficult in distinguishing permutations P and combinations C,
but the aptitude for applied problems varies considerably among students.
If a problem doesn't spark in the real test, you can throw it away without hesitation.

Integer (Math A)

An area where self-study of the basic concepts is difficult there,
the transformation of mod (remainder) and the proof that the remainder of dividing an integer is a loop is difficult, but

Integer (Math A)

The standard problems are manageable
if you can derive the formulas by transforming them with the binomial theorem or memorize all of them.
Applied problems are also quite varied and difficult;
if you don't have the aptitude, you can discard the applied problems.

Trigonometric ratio (Math A)

Learning the basic concepts is reasonably difficult, and the instructor's ability to explain the concepts makes a difference.
Difficulty in applying sinθ and cosθ to the unit circle using the unit circle.
It is preferable to recall theorems by writing the unit circle.
The application problem is a shallow area that only requires forceful application of the sine and cosine theorems if it is about the common test.

Equations, Expressions and Proofs (math 2)

The patterns of the problems are maniacal and varied,
and it is difficult to determine which pattern is which in a short time.
This is an area of high difficulty.
It also requires a lot of calculation. However,
unlike integers and probability,
it is an area that is easy to score points if the amount of study is increased.

Exponents and logarithms (math 2)

If you don't study, you won't be able to answer at all on the regular exam.
At first glance, many students have a sense of difficulty,
but once they learn the basic concepts and typical transformations, it is easy.
It is good to just memorize the concepts without understanding them,
but students with a Kawai deviation score of 40
or so cannot memorize the deformations without doing them many times.
The application problems are not too difficult,
but at a glance, they are difficult to understand.
There are many students who cannot solve the problems in regular exams
because they don't like to eat,
but it is an easy field for the middle class.
The logarithmic function is difficult to understand the graph,
but once you get used to it,
the problem itself is not much different from quadratic functions.

Figures and Equations (Number 2)

There are many minor theorems, such as the formula
for the inner and outer divisors and the center of gravity,
and it is troublesome to maintain knowledge without missing anything.
Proofs of theorems are also difficult and hard to memorize.
There are also a wide variety of application problems and a lot of calculations.
This is an area in which students suffer considerably in regular examinations.
(However, using vectors in Math B, it is often possible to answer the questions
with a few solutions and a lot of calculations.)
The field of circles and trajectories is a little troublesome to introduce
unless you understand the concept of coordinate planes used in junior high school.

Differential and integral calculus (math 2)

There are few areas that are difficult to understand in terms of basic concepts,
memorize the integration procedure, and

Differential Integral (math 2)

Shallow area of just subtracting the lower function from the upper function.
Calculations are difficult.
If you have good computational skills,
you can usually answer the applied questions.

Trigonometric functions (math 2)

FFormulas such as the additive theorem are redundant and quite difficult to remember.
Students with a Kawai deviation score of 40 or so have difficulty in composing trigonometric functions
due to a hazy memory of the additive theorem.
It is a tough field for students in the lower and middle ranks.
It is better to memorize the additive theorem and sum product formulas by word recognition,
as they are complicated to derive and memorize.
The sum-of-products formula is easy and may be derived. In this field, applied problems tend to be complicated.
Although many students drop out of this field,
it is an important field that is related to complex functions and curves in Math 3.

Vectors (Math B)

A super easy field that basically just uses the fact
that the inner product of a right-angled vector is zero.
Understanding the concept of sliding vectors is a bit tricky, but
The application problems after that are a bonus stage.
The figures and equations area (Math 2) can also be answered with vectors in quite a few cases.
(which may be in the scope of the entrance exam for graduate schools of science and engineering)

Number Sequence (Math B)

An area that is somewhat difficult to both learn and apply,
requiring a certain amount of formula memorization and speed of recall.
Logic, such as characteristic equations of an asymptotic formula,
should be answered mechanically rather than with a deep understanding of the reasons.
There are more than 10 patterns of asymptotic equations,
and it is quite tough when figures are involved in applied problems.
There is a lot of calculation and frequent calculation errors.
If the subject is not frequently asked at private universities,
it may be a good strategy to discard it.
However, if you can't do at least characteristic equations,
you can't do all the patterns, which will be a problem in regular exams.

Probability Distribution (Math B)

The concepts are difficult, but you can understand them
by watching some videos that explain and answer the concepts.
There are few patterns in the questions and it is easier to complete
in less time than choosing the number series
and vectors in the common test.
Difficult to be asked in the second test,
and sometimes out of the scope of the questions.
The key is to approximate the binomial distribution to the normal distribution.

Complex Number Plane (math 3)

Students become familiar with the complex number plane early on. Standard difficulty.
Trigonometric functions, vectors, and figures and equations (number 2) are required in many situations.
(often in the scope of entrance examinations for graduate schools of science and engineering)

Curves (math 3)

Concepts of new figures such as parabolas, ellipses,
and hyperbolas are difficult to understand and formulas are difficult to memorize.
The amount of memorization required is also a little high.
If you understand the concepts of the figures and memorize the formulas,
you will be able to solve the problems.
The application problems are not that rich in patterns.

Extreme Limit (math 3)

The limit theorem itself is not very complicated, but
You have to learn the unique deformation patterns to a certain extent.
There is a problem that cannot be solved
unless you can find the general term of an asymptotic expression in a number sequence (number B).

Calculus (math 3)

Concepts such as Napier numbers, inverse functions and composite functions are introduced,
but you can proceed without understanding them deeply.
It is not always possible to show the figure of an equation,
but it is acceptable to answer in a pattern by using two derivatives and so on.
The application problems are not difficult, but the amount of calculation is extraordinary.
(Often falls within the scope of graduate entrance examinations in science and engineering.)

Short Notes

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