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Mathematical concepts in the seventh classroom of Beijing Normal University
Review outline of seventh grade mathematics

The first chapter is a rich graphic world.

1. Common geometric bodies in life: cylinder, cube, cuboid and sphere.

2. Classification of common geometric bodies: sphere, cylinder (cylinder, prism, cube and cuboid) and cone (cone and 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 total diffusion on the surface is two and one; The total expansion diagram of the cone is one and one; The unfolding diagram of the cube surface is one and two small squares; The expansion diagram of a rectangle is a big two.

5, special three-dimensional graphics section graphics:

(1) The cross sections of cuboids and squares are: triangle, quadrilateral (rectangle, square, trapezoid, parallelogram), pentagon,.

(2) The cross section of a cylinder is circular.

(3) The cross section of the cone is triangular.

(4) The cross section of the ball is:

6. We often refer to the figure seen from the front view, the figure seen from the left view and the figure seen from the top view as.

7. Top view of common three-dimensional graphics

Geometric cuboid cube cone cylindrical ball

Front view square rectangle

Rectangular circle in top view

Left view rectangular square

8, point in, line in, face in.

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 integer, 0, negative integer, positive fraction, negative fraction.

Integer and fraction are collectively referred to. 0 is neither a number nor a number.

(2) Numbers are usually represented by points on a straight line, which is called the number axis.

Three elements of number axis: origin and unit length.

Take any point on a straight line to represent the number 0. This point is called.

(3) Numbers with only two different signs are called reciprocal.

Example: the reciprocal of 2 is; The reciprocal of -2 is; The reciprocal of 0 is

(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, and add the absolute values.

② Add two numbers with different symbols whose absolute values are not equal, take the symbol, and subtract the smaller 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. For example, the reciprocal of-is; The absolute value is; The opposite number is.

(3) Rational number division rule 1: dividing by a number that is not equal to 0 is equal to multiplying the reciprocal of this number.

Rule 2 of rational number division: divide two numbers, those with the same sign and those with different signs. Divide 0 by any number that is not equal to 0 to get 0.

(4) 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 the base and n is the exponent.

The odd power of a negative number is negative, and the even power of a negative number is. Any power of a positive number is a positive number, and any power of 0 is 0. The odd power of-1 is; The even power of-1 is.

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; The same letters are 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, add the coefficients of similar items and keep them unchanged.

6. Rules for removing brackets:

(1) is preceded by a "+". After removing the brackets and the preceding "+"sign, the original brackets

(2) brackets before "-",remove the brackets and the "-"before it, the original brackets.

Chapter IV Plane Figure and Position Relationship

1, straight line, shoot