Review outline of seventh grade mathematics
The first chapter is a rich graphic world.
1. Understand the common geometric features in life: cylinder, cone, cube, cuboid, prism and sphere.
2. Know the classification of common geometry. One can be divided into three categories: sphere, cylinder (cylinder, prism, cube, cuboid) and cone (cone, pyramid).
3. When a plane figure is folded into a solid figure, it should be noted that the number of sides is equal to the number of sides of the base map.
4. The side of the cylinder is unfolded into a rectangle; The development diagram is two circles and a rectangle;
The development diagram of the cone is fan-shaped and circular;
Cubic expansion diagram is a figure composed of six small squares;
The expansion diagram of a cuboid is similar to that of a cube. (easily available)
5, special three-dimensional graphics section graphics:
(1) The cross sections of cuboids and squares are: triangle, quadrilateral (rectangle, square, trapezoid, parallelogram), pentagon and hexagon.
(2) The cross section of the cylinder is rectangular, circular and elliptical.
(3) The cross section of the cone is triangle, circle and ellipse.
(4) The cross section of the ball is circular.
6. We often refer to the figure seen from the front as the front view, the figure seen from the left as the left view, and the figure seen from above as the top view.
7. Points move into lines, lines move into faces, and faces move into adults.
Chapter II Rational Numbers
1, positive and negative numbers
A number preceded by a minus sign "-"is called a negative number.
It has the opposite meaning to negative number, that is, I learned that numbers other than 0 are called positive numbers (sometimes "+"is added before positive numbers as needed).
2. Rational number
(1) Positive integers, 0 and negative integers are collectively called integers, and positive and negative fractions are collectively called fractions.
Integers and fractions are collectively called rational numbers. 0 is neither positive nor negative.
(2) Numbers are usually represented by points on a straight line, which is called the number axis.
Three elements of number axis: origin, directional arrow and unit length.
Take any point on a straight line to represent the number 0, and this point is called the origin.
(3) Numbers with only two different signs are called reciprocal.
Special: The antonym of 0 is 0.
(4) The distance between the point representing the number A on the number axis and the origin is called the absolute value of the number A, which is denoted as |a|.
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;
Two negative numbers, the larger one has the smaller absolute value.
3. Addition and subtraction of rational numbers
(1) rational number addition rule:
① Add two numbers with the same symbol, take the same symbol, and add the absolute values.
(2) Add two numbers with different absolute values, take the sign of the number with larger absolute value, and subtract the number with smaller absolute value from the number with larger absolute value. The sum of two opposite numbers is 0.
③ A number with 0 still gets this number.
(2) Rational number subtraction rule: subtracting a number is equal to adding the reciprocal of this number.
4. Multiplication and division of rational numbers
(1) rational number multiplication rule: two numbers are multiplied, the same sign is positive, the different sign is negative, and the absolute value is multiplied. Any number multiplied by 0 is 0.
(2) Two numbers whose product is 1 are reciprocal.
(3) Rational number division rule: dividing by a number that is not equal to 0 is equal to multiplying the reciprocal of this number.
(4) The operation of finding the product of n identical factors is called the power, and the result of the power is called the power. In the n power of a, a is called the base and n is called the exponent.
The odd power of a negative number is negative and the even power of a negative number is positive. Any power of a positive number is a positive number, and any power of 0 is 0.
Chapter three, letters representing numbers
1, and the letters formed by connecting numbers and letters representing numbers with operation symbols are called algebraic expressions.
2. Pay attention to the algebraic value: the value of letters must ensure that the algebraic value is meaningful; The value of a letter should ensure that the number it represents is meaningful.
3, algebraic coefficient should include the symbol before this item; If an algebraic term contains only one letter factor, its coefficient is 1 or-1, not 0.
4. Similar items contain the same letters; The index of the same letter is the same.
Note: Similar items have nothing to do with coefficient and alphabetical order; Several constant terms are similar.
5. Rules for merging similar items: When merging similar items, the coefficients of similar items are added, and the letters and their indexes remain unchanged.
Chapter IV Plane Figure and Position Relationship
1, line, ray, line segment
(1) The difference between straight lines, rays and line segments: straight lines have no end points; The endpoint of the ray; A line segment has two endpoints.
(2) Axiom of line segment: between two points, the line segment is the shortest.
(3) Line segment comparison method: superposition method and measurement method.
2. Angle measurement and representation
Three representations of angles: three capital letters or one capital letter (for example, < < ABC, < a); Expressed in Greek letters (e.g.