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Eighth grade mathematics outline People's Education Edition Volume I
Compared with primary school, junior high school mathematics has a wider and more comprehensive knowledge; It is required to increase the application ability of observation, reading, memory, thinking, imagination, operation and expression. The following is the first volume of the eighth grade mathematics outline of PEP, which I compiled for you. I hope it helps you. Welcome to read!

Eighth grade mathematics outline People's Education Edition Volume I

Fractional knowledge point

The basic properties of 1. Fraction: both the numerator and denominator of the fraction are multiplied (or divided) by the same algebraic expression that is not equal to zero, and the value of the fraction remains unchanged.

2. General Fraction: Using the basic properties of fractions, the numerator and denominator are multiplied by an appropriate algebraic expression, and several fractions with different denominators are converted into fractions with the same denominator without changing the value of fractions. This kind of fractional deformation is called the general fraction of a fraction.

The key to general division is to determine the simplest common denominator of several fractions. The general method to determine the simplest common denominator is: (1) If all denominators are monomials, then the simplest common denominator is the least common multiple of all coefficients, the power of the same letter, and the product of all different letters and exponents.

(2) If each denominator has a polynomial, then the denominator should first be the factorization factor of the polynomial, and then the simplest common denominator can be determined from three aspects: coefficient, same factor and different factor.

3. Simplification: According to the basic properties of the fraction, the common factor of the numerator and denominator of the fraction is removed without changing the value of the fraction. This fractional distortion is called fractional reduction.

Note: (1) If both the numerator and denominator are monomials, the common factor of the numerator and denominator can be directly eliminated, that is, the common factor of the numerator and denominator coefficients and the lowest power of the same letter can be eliminated; (2) If there is at least one polynomial in the numerator and denominator, first decompose the factors, then find their common factors, and then reduce them; (3) The divisor must be finished.

Real number knowledge point

1, classification of real numbers: rational numbers and irrational numbers.

2. Number axis: A straight line with origin, positive direction and unit length is called number axis. Real numbers correspond to points on the number axis one by one.

3. Ancient numbers: Two numbers with different symbols are called reciprocal numbers. The reciprocal of a is -a, and the reciprocal of 0 is 0. (If A and B are opposites, then a+b=0)

4. Absolute value: the distance from the point representing the number A to the origin on the number axis is called the absolute value of the number A, which is marked as ∣a∣, and the absolute value of a positive number is itself; The absolute value of a negative number is its reciprocal; The absolute value of 0 is 0.

5. Reciprocal: Two numbers whose product is 1.

6. Power: the operation of seeking common ground factor product is called power, and the result of power operation is called power (square and cube).

7. Square root: Generally speaking, if the square of a number X is equal to A, that is, x2=a, then this number X is called the square root of A (also called quadratic square root). Positive numbers have two square roots, and the two square roots are in opposite directions; 0 has only one square root, which is 0 itself; Negative numbers have no square root. (Arithmetic square root: Generally speaking, if the square of a positive number X is equal to A, that is, x2=a, then this positive number X is called the arithmetic square root of A, and the arithmetic square root of 0 is 0. )

Real number is a general term for rational number and irrational number. Mathematically, real numbers are defined as the number of corresponding points on the number axis. Real numbers can be intuitively regarded as finite decimals and infinite decimals, and can "fill" the number axis. But the whole of real numbers can't be described only by enumeration. Real and imaginary numbers * * * make up a complex number.

Real numbers can be used to measure continuous quantities. Theoretically, any real number can be expressed as an infinite decimal, and to the right of the decimal point is an infinite series (cyclic or acyclic). In practice, real numbers are often approximate to a finite decimal (n digits are reserved after the decimal point, and n is a positive integer, including integers). In the computer field, because computers can only store a limited number of decimal places, real numbers are often represented by floating-point numbers.

1) inverse number (there are only two numbers with different signs, and their sum is zero. We say that one of them is the inverse number of the other, which is called reciprocal inverse number). The reciprocal of the real number a is -a, and the distance between a and -a on the number axis is equal to the origin 0.

2) Absolute value (the distance between a number A and the origin 0 on the number axis) The absolute value of the real number A is |a|

(1) When a is a positive number, |a|=a (constant), and a is itself;

② When a is 0, |a|=0, and A is itself;

③ When A is negative, | a | =-a(a (the absolute value of A), and -a is the inverse of A. ..

The absolute value of any number is greater than or equal to 0, because there is no negative number in the distance. )

3) Reciprocal (the product of two real numbers is 1, so these two numbers are reciprocal) The reciprocal of real number A is: 1/a(a≠0).

4) Counting axes

Definition: The straight line defining the origin, positive direction and unit length is called the number axis.

Three elements of (1) axis: origin, positive direction and unit length.

(2) There is a one-to-one correspondence between points on the number axis and real numbers.

How to improve junior high school math scores

To improve junior high school math scores, we need to study hard and finish the homework assigned by the teacher in each class in order to keep up with the learning progress.

You must listen carefully in class, and it is best to preview what these math classes will talk about one class in advance, so that you can understand the relevant content more quickly.

When class is over, we can also discuss topics that we can't do together or give each other math problems.

If you really can't catch up with the trip, you can also hire a special teacher for one-on-one tutoring. Generally speaking, junior high school mathematics is still in the formulation stage, which is not particularly difficult. You can learn as long as you study hard.

Of course, you need to improve your grades. The best way is to study hard and be diligent, and don't always think about relying on others, and don't think about falling pie in the sky. This is unrealistic. Work hard.

Math answering skills

Quickly find out the "topic"

When you get the test paper for the first time, you will feel nervous. Don't rush to answer in this state of tension. First, we should browse the whole volume from beginning to end, from front to back, and get as much information as possible from the surface of the volume. The principles of finding out the "topic situation" are: easily answer simple multiple-choice questions or fill-in-the-blank questions that can be seen at a glance; Questions that cannot be answered immediately can be divided into two categories: familiar and unfamiliar. Mastering this information will ensure that there will be no embarrassing situation that "the difficult problems in front will not be done, and the easy problems behind will not have time to do".

The principle of doing the problem is "one is fast and one is slow"

The so-called "one fast and one slow" here means that the questions are slowly examined and the questions are quickly done.

The topic itself is actually all the information sources of this topic, so when examining the topic, we must read it word by word, and strive to truly see the meaning of the topic from grammatical structure, logical relationship, mathematical significance and other aspects. Some conditions don't seem to be given. In fact, after careful investigation, you will find that you can collect more known information and seek protection for the correct rate of doing the questions.

When thinking about the methods and ideas of solving problems, the answers must be concise, fast and standardized. This will not only win time for the following questions, but also simplify the problem-solving steps as much as possible on the basis of ensuring that you step on the scoring point, so that the marking teacher can see your problem-solving steps more clearly.

Master the skill of "grading by sections"

For the math problems in the senior high school entrance examination, it doesn't mean that only students with excellent grades score, and other students don't score. In fact, the strategy of "grading by sections" is adopted in the big math questions of the senior high school entrance examination. Simply put, if you do the right step, you will be given a step. This ensures that you don't lose points on the topics you can do and strive for more points on some topics you understand.

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