The concept of (1) number axis: A straight line with origin, positive direction and unit length is called number axis.
Three elements of the number axis: origin, unit length and positive direction.
(2) Points on the number axis: All rational numbers can be represented by points on the number axis, but not all points on the number axis represent rational numbers. (Generally, the right direction is the positive direction, and the points on the number axis correspond to any real number, including irrational numbers. )
(3) Compare the size with the number axis: Generally speaking, when the number axis is to the right, the number on the right is always greater than the number on the left.
Second, the opposite number.
(1) The concept of antipodal: Only two numbers with different symbols are called antipodal.
(2) The meaning of opposites: Grasp that opposites appear in pairs and cannot exist alone. From the number axis, except 0, they are two mutually opposite numbers, both on both sides of the origin, and the distance from the origin is equal.
(3) Simplification of multiple symbols: No matter the number of "+",the odd number of "﹣" is negative and the even number of "﹣" is positive.
(4) Summary of conventional methods: The way to find the reciprocal of a number is to add "﹣" in front of this number. For example, the reciprocal of A is ﹣a, and the reciprocal of m+n is ﹣(m+n). At this time, m+n is a whole. When you put a minus sign before an integer, use parentheses.
Third, absolute value.
1. Concept: The distance between a number and the origin on the number axis is called the absolute value of this number.
(1) The absolute values of two opposite numbers are equal;
② There are two numbers whose absolute values are equal to positive numbers, one number whose absolute values are equal to 0, and no number whose absolute values are equal to negative numbers.
③ The absolute values of rational numbers are all non-negative.
2. If the letter A is used to represent rational numbers, then the absolute value of the number A should be determined by the value of the letter A itself:
(1) When a is a positive rational number, the absolute value of a is itself a;
(2) When A is a negative rational number, the absolute value of A is its inverse-A;
③ When a is zero, the absolute value of a is zero.
That is | a | = {a(a >；; 0)0(a=0)﹣a(a<； 0)
A comparison of rational numbers: a compulsory knowledge point in junior one mathematics.
Comparison of 1. rational numbers
The number axis can be used to compare the sizes of rational numbers, and their order is from left to right, that is, from big to small (the number on the right of two rational numbers represented on the number axis is always greater than the number on the left); You can also use the nature of numbers to compare the sizes of two numbers with different symbols and 0, and use absolute values to compare the sizes of two negative numbers.
2. The rational number size comparison law:
① Positive numbers are all greater than 0;
② Negative numbers are all less than 0;
③ Positive numbers are greater than all negative numbers;
(4) Two negative numbers, the greater the absolute value, the smaller it is.
Regularization of rational numbers and three comparison methods;
(1) Rule comparison: all positive numbers are greater than 0, all negative numbers are less than 0, and all positive numbers are greater than all negative numbers. Two negative numbers are bigger, but the absolute value is bigger.
(2) Number axis comparison: the number represented by the right point on the number axis is greater than that represented by the left point.
(3) Compare the differences:
If a-b > 0, then a & gtb；;
If a-b
If a-b = 0, then a-b = 0 b.
A compulsory knowledge point of junior one mathematics: reciprocal
(1) The concept of antipodal: Only two numbers with different symbols are called antipodal.
(2) The meaning of opposites: Grasp that opposites appear in pairs and cannot exist alone. From the number axis, except 0, they are two mutually opposite numbers, both on both sides of the origin, and the distance from the origin is equal.
(3) Simplification of multiple symbols: No matter the number of "+",the odd number of "﹣" is negative and the even number of "﹣" is positive.
(4) Summary of conventional methods: The way to find the reciprocal of a number is to add "﹣" in front of this number. For example, the reciprocal of A is ﹣a, and the reciprocal of m+n is ﹣(m+n). At this time, m+n is a whole. When you put a minus sign before an integer, use parentheses.
Knowledge points that must be tested in the first grade of mathematics 2 Chapter 1 Rational Numbers
1. Positive and negative numbers
2. Rational number
3. Addition and subtraction of rational numbers
4. Multiplication and division of rational numbers
5. Power of rational number
Key points: number axis, reciprocal, absolute value, rational number calculation, scientific counting method, effective number.
Difficulty: absolute value
Error-prone point: calculation of absolute value and rational number
Compulsory examination for senior high school entrance examination: scientific counting method and relative number (multiple choice)
Chapter II Addition and subtraction of algebraic expressions
1. algebraic expression
2. Addition and subtraction of algebraic expressions
Emphasis: the concepts of monomial and polynomial, the determination of coefficients and degrees, similar terms, addition and subtraction of algebraic expressions.
Difficulties: determination of coefficients and degrees of monomials and polynomials, and merging of similar terms.
Error-prone points: merging similar items, calculation errors, and determination of integer multiples.
Must be tested in the senior high school entrance examination: similar items, determination of multiples of integer coefficients, addition and subtraction of algebraic expressions.
Chapter III One-variable Linear Equation
1. From formula to equation
2. Solve a linear equation with one variable-merge similar terms and shift terms.
3. Solve the unary linear equation-remove the brackets and denominator.
4. Practical problems and one-dimensional linear equations
Emphasis: linear equation of one variable (definition, solution and application)
Difficulty: Solving the linear equation of one variable (steps)
Error-prone point: when naming, items without denominator are easily multiplied, and when solving application problems, I don't know how to find equivalence.
Chapter IV Practical Steps of Graphic Understanding
1. color graphics
2. Lines, rays and line segments
3. Angle
4. Project Practice-Design and manufacture rectangular packaging cartons.
Emphasis: the understanding of straight line, ray, line segment and angle, the calculation of midpoint and bisector of angle, complementary angle and complementary angle, azimuth angle, etc.
Difficulties: calculation of midpoint and bisector, application of complementary angle and complementary angle.
Error-prone point: I can't convert the equivalence relation, so I can't examine it clearly.