Catalogue of seventh-grade mathematics textbooks of People's Education Publishing House
Chapter V Intersecting Lines and Parallel Lines
5. 1 intersection line
Observe and guess the illusion when looking at pictures.
5.2 Parallel lines and their determination
5.3 Properties of parallel lines
Using information technology to explore the positional relationship between two straight lines
5.4 Translation
Mathematical activities
summary
Review question 5
Chapter VI Real Numbers
6. 1 square root
6.2 cube root
6.3 real numbers
Reading and thinking. Why? 2 is not a rational number.
Digital activity
summary
Review question 6
Chapter VII Plane Cartesian Coordinate System
7. 1 plane rectangular coordinate system
Reading and thinking indicate geographical location with latitude and longitude.
7.2 Simple application of coordinate method
Mathematical activities
summary
Review question 7
Chapter VIII Binary Linear Equations
8. 1 binary linear equations
8.2 Eliminating and Solving Binary Linear Equations
8.3 Practical Problems and Binary Linear Equations
8.4 Solutions of ternary linear equations
Reading and thinking about the ancient and modern expressions and solutions of linear equations
Mathematical activities
summary
Review question 8
Chapter 9 Inequality and Unequal Groups
9. 1 inequality
Reading and thinking compare sizes with the difference method.
9.2 One-dimensional linear inequality
9.3 One-dimensional linear inequality system
Mathematical activities
summary
Review question 9
Chapter 10 Data Collection, Arrangement and Description
10. 1 statistical survey
Experiment and explore how many beans are in the bottle.
10.2 histogram
The application of information technology uses computers to draw statistical charts.
10.3 project learning talking about water saving from data
Mathematical activities
summary
Review questions 10
Index of some Chinese and English words
Key points of algebraic operation knowledge in the second volume of seventh grade mathematics published by People's Education Press.
I. Algebraic expressions
1, monomial: an algebraic expression representing the product of numbers and letters. In addition, it is stipulated that a single number or letter is also a monomial.
The numerical factor in a single item is called the coefficient of the item. Note that the coefficient includes the preceding symbol, which is usually omitted when the coefficient is 1. It is a coefficient, and its coefficient is.
The degree of monomial refers to the sum of the indices of all letters.
2. Polynomial: The sum of several monomials is called polynomial. (several terms)
Each monomial is called a polynomial term. Note that this term includes the preceding symbols.
Degree of polynomial: the degree of the term with the highest degree in polynomial. The number of items is called several items, and items without letters are called constant items.
3. Algebraic expression; Monomial and polynomial are collectively called algebraic expressions. (The most obvious feature: the denominator has no letters)
2. Addition and subtraction of algebraic expressions: ① Remove brackets first; (Note the number factor before parentheses)
② Reorganize similar projects. (When adding a coefficient, letters and letter indexes remain unchanged.)
Third, the operability of power.
1, power with the same base: the base is constant, and the exponents are added.
2. Power of power: the base is constant and the index is multiplied.
3. Power of product: multiply each factor in the product separately, and then multiply the obtained power.
4. Zero exponential power: the power of 0 of any number that is not equal to 0 is equal to 1. () Note that 00 is meaningless.
5. Negative integer exponential power: (positive integer,)
6. same base powers division: the base is unchanged, and the exponent is subtracted. ( )
Note: The positive and negative application of the above formula.
Common errors:,,,
Fourth, the monomial is multiplied by the monomial: the coefficients are multiplied and the same letters are multiplied. Letters that only appear in one factor are used as the factors of the product together with their indices.
5. Polynomial multiplied by monomial: this monomial is multiplied by each term of polynomial multiplied by the distribution rate of multiplication.
6. Polynomial Multiplication Polynomial: Multiply each term of one polynomial with each term of another polynomial and the sign of each term.
Seven, square difference formula
The sum of two numbers multiplied by the difference of two numbers is equal to the square of the difference of two numbers.
That is, one sign is the same and the other sign is opposite, which is equal to the square of the same sign MINUS the square of the opposite sign.
Eight, the complete square formula
The square of the sum (or difference) of two numbers is equal to the sum of the squares of the two numbers plus (or minus) twice the product of the two numbers.
Common errors:
Nine, single item divided by single item: divided by the coefficient of single item, divided by the same letter, only the letter appearing in the divided formula and its index are used as the factor of quotient.
X. Polynomial divided by single item: all terms of the polynomial are divided by single item together with the symbols of the terms.
Key points of real number knowledge in the second volume of seventh grade mathematics published by People's Education Press
Knowledge point classification-real number
1. Classification by definition: 2. Classification by natural symbols:
Note: 0 is neither positive nor negative.
Knowledge point 2 Related concepts of real numbers
1. Inverse
Algebraic meaning of (1): There are only two numbers with different signs, and we say that one of them is opposite to the other. The antonym of 0 is 0.
(2) Geometric meaning: On both sides of the origin on the number axis, two points with the same distance from the origin represent two opposite numbers, or on the number axis, the points corresponding to two opposite numbers are symmetrical about the origin.
(3) The sum of two opposites is equal to 0.a and B are opposites a+b=0.
2. Absolute value |a|? 0.
3. The reciprocal (1)0 has no reciprocal. (2) Two numbers whose product is 1 are reciprocal. A and b are reciprocal.
4. Square root
(1) If the square of a number is equal to a, it is called the square root of a, a positive number has two square roots, and the two square roots are in opposite directions. 0 has a square root, and the square root itself is 0; Negative numbers have no square root. a(a？ The square root of 0) is recorded as.
(2) the positive square root of a positive number is called the arithmetic square root of a(a? The arithmetic square root of 0) is recorded as.
5. Cubic root
If x3=a, then x is called the cube root of a, and positive numbers have positive cube roots; Negative numbers have negative cubic roots; The cube root of zero is zero.
Knowledge point 3 Real number and axis
Definition of number axis: the straight line defining the origin, positive direction and unit length is called number axis, and the three elements of number axis are indispensable.
Comparison of real numbers of knowledge point four
1. For any two points on the number axis, the point on the right represents a larger number.
2. Positive numbers are all greater than 0, negative numbers are all less than 0, and two positive numbers, the greater the absolute value, the greater the positive number; Two negative numbers; The absolute value is large but small.
3. The relative size of irrational numbers:
The operation of knowledge point five real numbers
1. Add
Add two numbers with the same sign, take the same sign, and add the absolute values; Add different symbols with different absolute values of two numbers, take the symbol with the larger absolute value, and subtract the symbol with the smaller absolute value from the larger absolute value; Two opposite numbers add up to 0; When a number is added to 0, it still gets the number.
2. subtraction: subtracting a number is equal to adding the reciprocal of this number.
multiply
Multiply several non-zero real numbers, and the sign of the product is determined by the number of negative factors. When there are even negative factors, the product is positive. When there are odd negative factors, the product is negative. Multiply several numbers, one factor is 0 and the product is 0.
break up
Dividing by a number is equal to multiplying the reciprocal of this number. Divide two numbers, the same sign is positive, 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.
5. Multipliers and prescriptions
The meaning of (1)an is the product a of n, any power of positive number is positive, even power of negative number is positive, and odd power of negative number is negative.
(2) Positive numbers and 0 can be squared, but negative numbers cannot be squared; Positive numbers, negative numbers and 0 can all be turned on.
(3) Zero exponent and negative exponent
Six significant figures of knowledge points and scientific notation
1. Valid numbers:
A divisor, from the first non-zero number on the left to the exact number, is called the significant digits of this divisor.
2. Scientific symbols: