First, rational numbers.

rational number

1, classification of rational numbers:

Classification by definition of rational number: classification by sign of rational number: positive integer, positive integer, integer zero and positive rational number.

Rational Number Negative Integer Positive Fraction Positive Fraction Rational Number 0

Fractional negative integer negative integer negative rational number

Negative score

2. Positive numbers and negative numbers are used to represent numbers with opposite meanings.

(2) Number axis

1, definition: the straight line defining the origin, positive direction and unit length is called the number axis. 2. The three elements of the number axis are: origin, positive direction and unit length.

(3) reciprocal

1. Definition: Only two numbers with different symbols are opposite to each other.

2. Geometric definition: The number represented by two points on both sides of the origin with the same distance from the origin on the number axis is called reciprocal.

3. Algebraic definition: Only two numbers with different signs are called reciprocal, and the reciprocal of 0 is 0.

(4) Absolute value

1, definition: the distance from the point representing the number A on the number axis to the origin is called the absolute value of the number A.

2. Geometric definition: the absolute value of a number A is the distance between the point representing the number A on the number axis and the origin.

3. Algebraic definition: the absolute value of a positive number is itself, the absolute value of a negative number is its reciprocal, and the absolute value is 0.

It's 0.

A (a > 0), that is, for any rational number A, there exists the law of | A | = 0(A = 0)-A(A < 0)4. Calculation of absolute value:

(1) The absolute values of two opposite numbers are equal. (2) If | a | = | b |, then a = b or a =-b. (3) If | a |+| b | = 0, then | a | = 0 and | b | = 0.

Related conclusions:

The inverse of (1)0 is itself.

(2) The absolute value of non-negative number is itself.

(3) The absolute value of a non-positive number is its reciprocal.

(4) The number with the smallest absolute value is 0.

(5) The absolute values of two opposite numbers are equal.

(6) The absolute value of any number is its positive number or 0, that is |a|≥0.

Teaching plan exercises of the whole class courseware in grade one summarize the historical geography of mathematical English in China.

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(5) Countdown

1. Definition: Two numbers whose product is "1" are reciprocal. 2. Solution: Reverse the numerator and denominator of this number. 3. The reciprocal of a (a ≠ 0) is 1.

a

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Rational number operation

First, the addition rule of rational numbers:

1, two numbers with the same sign are added, the same sign is taken, and the absolute value is added;

2. Add two numbers with different absolute values, take the sign of the addend with larger absolute value, and subtract the number with smaller absolute value from the number with larger absolute value.

3, a number with zero, or get this number; 4. Two opposite numbers add up to get 0.

Second, the subtraction rule of rational numbers:

Subtracting a number is equal to adding the reciprocal of this number.

Third, the multiplication rule of rational numbers:

1, two numbers are multiplied, the same sign is positive, the different sign is negative, and the absolute value is multiplied; 2. Multiply any number by 0 to get 0; 3. Two numbers whose product is 1 are reciprocal.

Fourth, the division rule of rational numbers:

1, divided by a number not equal to 0, is equal to multiplying the reciprocal of this number;

2. Divide two rational numbers, the same sign is positive and the different sign is negative, and divide by the absolute value. Divide 0 by any number that is not equal to 0 to get 0.

Fifth, the multiplier

1. Definition: The operation of finding the product of n identical factors is called power. 2, the symbolic law of power:

The power of any positive number is positive; The odd power of a negative number is a negative number; Even the power of negative numbers is positive;

Any sub-positive integer power of 0 is 0.

Six, the reasonable number of mixed operation order:

1. Multiply first, then multiply and divide, and finally add and subtract; 2. Operation at the same level, from left to right;

3. If there are brackets, do the operation in brackets first, and then follow the brackets, brackets and braces in turn.

Seven, scientific counting method, effective number and divisor.

1, a scientific counting method

(1) Definition:

A number whose absolute value is greater than 10 is expressed as a? 0? 6 10n (where a is an integer with only one bit)

Number, that is, 1 ≤| a | < 10, n is a positive integer), this counting method is called scientific counting method.

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(2)N-bit integers are expressed by scientific counting method, where the exponent of 10 is the integer digits of this number minus 1.

2, the definition of significant figures:

The rounded approximation, from the first digit on the left that is not 0 to the most accurate digit, is called the number of significant digits.

3. Definition of divisor:

A number that is close to the exact number (slightly more or less than the exact number) is called a divisor.

The concepts of addition and subtraction, monomial, polynomial and algebraic expressions of algebraic expressions.

Monomial: An algebraic expression consisting of the product of numbers and letters is called a monomial. A single number or letter is also a monomial. Polynomial: The sum of several monomials is called polynomial. Algebraic expression: monomials and polynomials are collectively called algebraic expressions.

Second, the coefficient and number of monomials

The coefficient of a single item refers to the numerical factor in a single item, and the number of times of a single item refers to all the letters in a single item.

Sum of indices.

Third, the term, constant term and degree of polynomial

In polynomials, each monomial is called a polynomial term, and the term without letters is called a constant term. In polynomials,

The degree of the term with the highest degree is the degree of this polynomial.

Fourth, the concept of similar items:

Items with the same letters and indexes are called similar items, and all constant items are similar items.

V. Rules for merging similar projects:

The coefficients of similar items are added together, and the results are taken as coefficients, and the indexes of letters and letters remain unchanged.

6. Similar item merging steps: (1) Find out the similar items accurately.

(2) Reverse the distribution law, add the coefficients of similar items together (enclosed in brackets), and keep the letters and their indices unchanged. (3) Write the merged result.

VII. Ascending Power Arrangement and Descending Power Arrangement

In order to facilitate the operation of polynomials, we can use the commutative law of addition to rearrange the positions of polynomial terms in the order of exponential size of letters.

If the index of a letter is arranged in descending order, it is said that this polynomial is arranged in descending order of this letter.

If the index of a letter is arranged in descending order, it is said that this polynomial is arranged in ascending order of this letter.

Eight, bracket rules.

Parentheses are preceded by a "+"sign. Remove the brackets and the preceding "+"sign, and all items in brackets have the same symbol;

There is a "-"before the brackets. Remove the brackets and the "-"in front, and change the symbols of everything in brackets.

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Nine, the general steps of algebraic expression addition and subtraction are:

(1) If you encounter brackets, first delete the brackets according to the rules for deleting brackets:

There is a "ten" before the brackets. Delete the brackets and the "+"before them. The symbols in brackets indicate that everything remains the same; There is a "one" before the brackets. Remove the brackets and the preceding "one". Everything in parentheses changes sign.

(2) Merging similar items: add the coefficients of similar items, and the result is taken as the coefficient. Letters and letter indexes remain unchanged.

One-dimensional linear equation concept of one-dimensional linear equation

Definition: The equation contains only one unknown (element), the exponent of the unknown is 1 (degree), and the formulas of the unknown are all

Algebraic expressions, such equations are called linear equations.

Properties of equation 1: Add (or subtract) the same number (or formula) on both sides of the equation, and the results are still equal.

If a = b, then a c = b c

Property 2 of the equation: Multiply both sides of the equation by the same number, or divide by the same number that is not 0, and the result is still equal.

If a = b, then ac = bc；; If a = b(c≠0), then AC = B.

c

Shift term: a term in the equation moves from left (right) to right (left) after the sign changes. such

Deformation is called transfer.

General steps for solving linear equations with one variable;

1. Denominator: both sides of the equation are multiplied by the least common multiple of each denominator;

2. Remove the brackets: first remove the brackets, then remove the brackets, and finally remove the braces;

3. Move the term: move all terms containing unknowns to one side of the equation, and all other terms to the other side of the equation; 4. Merge similar terms: transform the equation into ax=b(a≠0);

5. Coefficient division 1: divide the unknown coefficient a on both sides of the equation to get the solution of equation x = b.

a

A preliminary understanding of graphics 1. Common three-dimensional figures: cylinder, cone and sphere.

1, there is a cylinder in the cylinder: the bottom circle is curved; (2) Prism: the bottom is polygonal and the side is rectangular; 2. There is a cone in the cone: the bottom is round and the side is curved; (2) Pyramid: the bottom is polygonal and the side is triangular;

Second, geometric figures are all composed of points, lines, surfaces and bodies.

Around the body is a face, where the face intersects with the face is a line, and where the line intersects with the line is a point. Points move into lines, lines move into planes, planes move into volumes, and volumes, planes, lines and points are all geometric figures.

Iii. Straight line, ray, line segment 1, straight line

(1) concept: a straight line extending infinitely in two directions.

For example, the number axis in algebra is a straight line (it only specifies the origin, direction and length unit).

(2) Basic properties: there is a straight line passing through two points, and there is only one straight line; You can simply say "two-point confirmation"

A straight line. "

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(3) Features: ① A straight line has no length and extends infinitely in two directions; ② The straight line has no thickness; ③ Two points determine a straight line; ④ When two straight lines intersect, there is only one intersection point.

Step 2 light

(1) concept: a point on a straight line and the part next to it are called rays. (2) Features: There is only one endpoint, which extends to one side indefinitely and cannot be measured.

3. Line segment

(1) Concept: Two points on a straight line and the part between them are called line segments. A line segment has two endpoints and a length. (2) Basic property: The line segment between two points is the shortest.

(3) Features: There are two endpoints, which cannot extend to both sides, can be measured, and can be relatively short.

4. The midpoint of a line segment: the point that divides a line segment into two equal line segments.

Fourth, the angle

1, the concept of angle: a graph composed of two rays with a common endpoint is called an angle, and this common endpoint is the vertex of the angle. These two

A ray is two sides of an angle. 3. Angle system and conversion

(1) The concept of angular system: The measurement system of angles in degrees, minutes and seconds is called angular system.

(2) Angle system transformation:

1= 60'1'= 60 "1fillet = 3601flat angle = 180 1 right angle = 90.

(3) conversion method:

The propulsion rate of converting high-level units into low-level units; The conversion of low-level units into high-level units should be divided by the forward speed; The transformation must be gradual, and the "leapfrog" transformation is prone to mistakes.

4. Comparison of angles:

(1) superposition method, so that the vertices and one side of two angles coincide, and the other side is compared on the same side of the overlapping side; (2) Measurement method.

5. Angle bisector:

Starting from the vertex of an angle, the ray that divides the angle into two equal angles is called the bisector of the angle.

6. Complementary angle and complementary angle:

(1) complementary angle: If the sum of two angles is equal to 90 (right angle), then these two angles are complementary angles, and one of them is the other.

The complementary angle of an angle;

(2) Complementary angle: If the sum of two angles is equal to 180 (flat angle), then these two angles are complementary angles, and one of them is

The complementary angle of the other angle; (3) The nature of complementary angles: the complementary angles of equal angles are equal;

The quality of equiangle: the complementary angles of the same angle are equal.