Chapter 1: Operation of Rational Numbers
This chapter mainly introduces the conceptual knowledge, and distinguishes the relationship between scores with graphs or symbols. Defined as follows:
1, the concept of rational number: positive integer, 0, negative integer, positive fraction and negative fraction are collectively called rational numbers; Number axis and origin: Numbers are represented by points on a straight line, which is called number axis. Any point on this line represents 0, which is called the origin. The distance from this point to the left or below the origin is represented by a negative number, and the distance from this point to the right or above the origin is represented by a positive number. The two numbers represented by two points with opposite and equal distances from the origin on the number axis are opposite numbers, and the distance from point A to the origin on the number axis is called the absolute value of this number.
2. Addition and subtraction of rational numbers: two numbers with the same sign are added, the sign is unchanged, and the absolute value is added; Add two numbers with different signs and different absolute values, take the sign of the addend with larger absolute value, subtract the absolute value of the smaller number from the absolute value of the larger number, and add two numbers with opposite numbers to get 0; One rational number MINUS another rational number is equivalent to adding the reciprocal of this number;
3. Multiplication and division of rational numbers: two numbers with the same sign are multiplied, the same sign is positive, and the different sign is negative. The product of multiplication is the product of their absolute values, division is the dividend multiplied by the reciprocal of the divisor, and the divisor cannot be 0; Two numbers whose product is 1 are reciprocal, and 0 has no reciprocal; Multiplication turnover rate and combination rate of integers are also applicable to rational numbers; The operation of finding the product of n identical factors is called power, and the result of power is called power. In the n power of a, a is called the base and n is called the exponent. Write a ∧ n;
4. Mixed operation of rational numbers: multiply first, then multiply and divide, and finally add and subtract; Operation at the same level, from left to right; If there are brackets, do the operation in brackets first, and then follow the brackets, brackets and braces in turn;
5. Scientific notation: A number greater than 10 is expressed as a× 10∧n, where a is greater than or equal to 1 less than 10, and n is a positive integer, which is called scientific notation.
Chapter 2: Addition and subtraction of algebraic expressions.
Addition and subtraction of algebraic expressions is the calculation of merging similar terms; In a formula, items with the same letters and the same letter index are called similar items, and several constant items are also similar items; Merging similar terms in polynomials into one term is called merging similar terms. After merging similar items, the coefficients of the obtained items are the sum of the coefficients of similar items before merging, and the letters and their indexes remain unchanged. Generally, several integers are added together. If there are brackets, remove them first, and then merge similar items. If the factor outside the brackets is positive, the symbols of the items in the original brackets are the same as those after the brackets are removed. If the factor outside the brackets is negative, the symbols of the items in the original brackets are opposite to those after the brackets are removed.
Chapter 3: One-dimensional linear equations
An equation contains only one unknown, the degree of the unknown is 1, and both sides of the equal sign are integers. Such an equation is called one-dimensional linear equation; The addition or subtraction of the same numbers or formulas on both sides of the equation is still equal, and the multiplication or division of the same numbers on both sides of the equation is still equal.
Chapter 4: Three-dimensional graphics and geometric graphics
This chapter mainly introduces the understanding of three-dimensional graphics and geometric graphics; Understanding of the relationship between point, line, surface and body; Understanding of straight lines, rays and line segments; Comparison of concepts and sizes from different angles.
1, plane graphics and three-dimensional graphics: geometric graphics with all parts in the same plane are called plane graphics; Some parts of geometric figures are not on the same plane, which are called three-dimensional figures, such as cuboids, cylinders and cones. Some three-dimensional graphics are surrounded by some plane graphics and expanded into plane graphics, and the expanded plane graphics are called the expanded drawings of this three-dimensional graphics;
2. Understanding of points, lines, surfaces and bodies: the geometric body is called the body, the enclosing body is called the surface, the place where the surface intersects with the surface is called the line, and the place where the line intersects with the line is called the point, and the line is composed of countless points;
3. Understanding of straight lines, rays and line segments: Only one straight line passes through two points, and two points determine a straight line. The shortest connecting line between two points is called a line segment, the length of the line segment is called the distance between these two points, and it extends infinitely from the line segment to one end, which is called a ray;
4. Angle: If the sum of two angles is equal to 90, then the two angles are complementary; If the sum of two angles is equal to 180, then the two angles are complementary; Starting from the vertex of an angle. The ray that divides this angle into two equal angles is called the bisector of this angle, and the two rays of these three equal angles are called the bisector of this angle.
Chapter 5: Algebraic expressions.
(1) algebraic expression
1. Algebraic expression: monomials and polynomials are collectively called algebraic expressions.
2. Monomial: The formula consisting of the product of numbers and letters is called monomial. A single number or letter is also a monomial.
3. coefficient; In the monomial, the numerical factor is called the coefficient of the monomial.
4. Times: The sum of the indices of all the letters in the monomial is called the times of this monomial.
5. Polynomial: The sum of several monomials is called polynomial.
6. Term: Each monomial that constitutes a polynomial is called a polynomial term.
7. Constant term: the term without letters is called constant term.
8. Degree of Polynomial: In a polynomial, the degree of the term with the highest degree is called the degree of this polynomial.
9. Similar terms: In polynomials, terms with the same letters and the same index of the same letters are called similar terms.
10. Merging similar items: Merging similar items in polynomials into one item is called merging similar items.
(2) Algebraic expression addition and subtraction Algebraic expression addition and subtraction operation, if you encounter brackets, remove the brackets first, and then merge similar items.
1. bracket removal: Generally speaking, several algebraic expressions are added and subtracted. If there are brackets, remove them first, and then merge similar items. If the factor outside the brackets is positive, the symbols of the items in the original brackets are the same as the original symbols after the brackets are removed. If the factor outside the brackets is negative, the symbols of the items in the original brackets are opposite to those after the brackets are removed.
2. Merging similar items: Merging similar items in polynomials into one item is called merging similar items. After merging similar items, the coefficient of the obtained item is the sum of the coefficients of similar items before merging, and the letter part remains unchanged.