I. Conceptual knowledge

1, monomial: The product of numbers and letters is called monomial.

2. Polynomial: The sum of several monomials is called polynomial.

3. Algebraic expressions: monomials and polynomials are collectively referred to as algebraic expressions.

4. The number of monomials: The sum of the indices of all the letters in the monomials is called the number of monomials.

5. Degree of Polynomial: The degree of the term with the highest degree in the polynomial is the degree of the polynomial.

6. Complementary angle: The sum of two angles is 90 degrees, and these two angles are called complementary angles.

7. Complementary angle: The sum of two angles is 180 degrees, and these two angles are called complementary angles.

8. Relative vertex angles: two corners have a common vertex, and two sides of one corner are opposite to the extension lines of two sides of the other corner. These two angles are antipodal angles.

9. Common angle: In the "three-line octagon", the angles at the same position are common angles.

10, internal angle: in the "three-line octagon", the angle sandwiched between two straight lines is the internal angle.

1 1, ipsilateral inner angle: in "trilinear octagon", the angle on the same side of trilinear is ipsilateral inner angle.

12, significant number: an approximation, starting with the first number on the left that is not 0 and ending with the exact 1, all numbers are significant numbers.

13, probability: the probability of an event is the probability of this event.

14, triangle: A figure composed of three line segments that are not on the same line is called a triangle.

15, Angle bisector of triangle: In a triangle, the angle bisector of an inner angle intersects its opposite side, and the line segment between the intersection of the vertex and this angle is called the angle bisector of triangle.

16, triangle midline: the line segment connecting the vertex and the midpoint of the opposite side of the triangle is called the midline of the triangle.

17. Height line of triangle: Draw a vertical line from one vertex of triangle to the line where its opposite side is located, and the line segment between vertex and vertical foot is called height line of triangle.

18, congruent graphics: two graphics that can overlap are called congruent graphics.

19, variable: the number of changes is called variable.

20. Independent variable: If there is an active change in the amount of change, it is called an independent variable.

2 1, dependent variable: the quantity that changes passively with the change of independent variables is called dependent variable.

22. Axisymmetric figure: If a figure is folded along a straight line and the parts on both sides of the straight line can overlap each other, then this figure is called an axisymmetric figure.

23. Symmetry axis: A straight line folded in half in an axisymmetric figure is called symmetry axis.

24. perpendicular bisector: The line segment is an axisymmetric figure, and its symmetry axis is perpendicular to this line segment and divides it into two parts. Such a straight line is called the midline of this line segment. (refers to the middle vertical line)

Second, computing power.

(a) Calculation of algebraic expressions.

1, addition and subtraction of algebraic expressions

Remove brackets and merge similar items!

2. Power operation (seven formulas)

① Power with the same base: the base is constant, and the exponents are added. (2) Power of power: the base number is unchanged, multiplied by the index.

③ Power of product: equal to the product of the power of each element. (4) Multiply with exponential power: the exponent is constant and the base is multiplied.

⑤ same base powers division: the base number is unchanged, and the exponent is subtracted. ⑥ Zero exponent: the zero power of any non-zero number is equal to 1.

⑦ Negative exponent: The negative exponent of any non-zero number is equal to the reciprocal of its positive exponent.

3. Multiplication formula

① Square difference formula: square difference, square difference; Multiply the sum of two numbers by the difference of two numbers.

② Complete square formula: the first side and the last side; The head and tail are in the middle twice.

Attachment: (1) The complete square of the sum of three numbers;

(2) Cubic sum:

(3) Cubic difference:

4. Multiplication of algebraic expressions

(1) Monomial Multiplication by Monomial: coefficient multiplication, same letter multiplication, written in different letters.

(2) Polynomial Multiplying Single Item: Multiply each item of polynomial by single item, and then add the results.

③ Polynomial Multiplication Polynomial: Multiply each term of the second polynomial with each term of the first polynomial, and then add the results. (handshake principle)

5. Division of algebraic expressions

① monomial divided by monomial: the coefficient is divided by the coefficient, and the same letters are divided, only the letters appearing in the division formula are written.

② Polynomial divided by single term: divide each term of polynomial by single term, and then add the results.

(b) calculation of angle.

1, using the interior angle theorem and exterior angle theorem of triangle to calculate.

The sum of the three internal angles of a triangle is 180 degrees. The outer angle is equal to the sum of two non-adjacent inner angles.

2. Use the relationship angle of parallel lines to calculate.

3. Use the bisector and height line of the triangle for calculation.

Calculation of area

1, rectangular area = length× height or the sum of the areas of four small triangles (the areas of four small triangles are equal)

2. Area of a square = side length × side length or half of diagonal product. Or the sum of the areas of four isosceles right triangles.

3. Triangle area = base × height ÷2

4. The area of a right triangle = half the product of two right angles or half the product of the hypotenuse and the height on the hypotenuse.

(d) Calculation of triangular line segments

(1) is calculated with special positions (centerline, midpoint, vertical line).

② Calculated by isosceles triangle and congruent triangles.

(3) using the relationship between the sides of the triangle to calculate.

Calculation of probability

1, general algorithm: 2, area algorithm:

Third, graphics and operations.

1, the height line, angle bisector and center line of a triangle. (For basic drawings, see 143~ 146)

2. Make an axisymmetric figure. Find out the key points and find out the corresponding points by the method of middle vertical line. )

3. Make a triangle.

① Basic drawing: (1) Name three sides, (2) Name the included angle between two sides, and (3) Name the side between two angles (see 169~ 17 1 page of the book).

② Comprehensive drawing: (1) Tell the center lines of the two sides and the third side, tell the high lines of the two sides and the third side, and tell the bisector and included angle of the two sides.

Methods: The congruent triangles was formed by connecting lines with twice the length.

4. Draw the shortest distance in life.

(1) Make a point on the third straight line with equal distance between two points. A milk station was built on the highway, and the distance to the two houses was equal. Make the middle vertical line intersect with the highway. )

(2) Make the point with the shortest sum of two points on the third straight line. Building a milk station on the expressway is the shortest distance to the two houses. Make a symmetrical corresponding point about the highway, the intersection of the corresponding point and another connecting line with the highway. )

5. Parallel interpretation (proof)

Based on "three-line octagon"

Judgment: Equal equilibrium angle Property: Equal equilibrium angle

Internal angles are equal, two straight lines are parallel, and internal angles are equal.

Complementarity between ipsilateral internal angle and ipsilateral internal angle

6, congruence description (proof)

Judgment: Trilateral Correspondence Equation (SSS) Attribute:

Two angles correspond to equal sides (SAS) corresponding to equal sides.

One side of two corner clips corresponds to two congruent triangles (ASA).

The opposite sides of two angles and one angle are equal (AAS), and the corresponding angles are equal.

The right angle and hypotenuse are equal (HL)

Four. Data and statistics

1, scientific notation: count 0, left 0, negative exponent; There is a positive exponent of 0 on the right. A few zeros on the left, the index is negative; For the zero on the right, the exponent should be written as a positive number first, then A should be written as a number between 0 and 10, and then the exponent should be modified.

1mm = 10-3m 1 μm = 10-6m 1nm = 10-9m 1 mm2 = 10-6mm 2 1 mm3 =

2. Three representations of variables:

(1) tabular method: independent variables are at the top and dependent variables are at the bottom.

② Relationship method: independent variable comes first and dependent variable comes last.

③ Mirror image method: the independent variable is the horizontal axis and the dependent variable is the vertical axis.

3. Understanding of the image: mainly analyze whether the variable is increasing or decreasing.

The application of verb (verb's abbreviation) in mathematics

1, light reflection

The incident angle is equal to the reflection angle. The complementary angles of the incident angle and the reflection angle are also equal. As shown in the figure:

∠ 1 and ∠2 are the angle of incidence and reflection, so ∠ 1=∠2.

∠3 and∠ 4 are complementary angles of∠1and∠ 2, and∠ 3 =∠ 4.

2. Measure the distance with congruent triangles.

Construct congruent triangles, and change the line segments that cannot be directly measured into measurable ones! Such as measuring lakes, mountains, bottles, etc.

3, the secret of the mirror:

(1) The image in the mirror is symmetrical to the things outside the mirror, and the symmetry axis is mirror surface, sometimes vertical and sometimes horizontal.

(2) Time in the mirror+actual time = 12.

Six, the typical problem set

1, the sum of several non-negative numbers is 0, and these numbers are all 0. Known: a2+b2-2a+6b+ 10=0, a2008+ 1/b=?

2. Bottom: (x-y) 2n (y-x) n (y-x) =? Given 3x-4y+5 = 0, then 8x÷ 16y=?

3. Change the index: compare the sizes of 266 and 355. 0. 1252006×82007=

4. Flexible application of complete square: (1) Find one or more complete square methods. Known: a+b= 12, ab=30, which can be found.

(2) hide a condition: known, find (3) hide two conditions. Known: x2-5x+ 1=0.

(4) Find the sum of other high powers.

5, the use of square difference. Calculation: (a-b+c)(a+b-c)

6. Given that the lengths of two sides of a triangle are A and B, find the length of the midline of the third side. Given that two sides of a triangle are 4 and 10 respectively, find the range of the median line on the third side.

A

4 ? 10 Find the range of BC first: 6~ 14. Then BD is between 3 and 7. (The range of AD in the left triangle ABD is between 1 and 1 1).

B D C reanalysis D C is also between 3 and 7. (The range of AD in right triangle ACD is between 7~ 17) The comprehensive AD on both sides should be between 7~ 1 1.

7. Several algorithms of telephone charges. (Variables and Relationships)

There are two ways to calculate the telephone number: (1) the landline is in 25 yuan every month, and the telephone number is 0. 1 yuan per minute. (b) There is no fixed telephone fee. Telephone charges per minute 0.2 yuan.

A, write the relationship between the total cost y (yuan) and time x (minutes) of the two payment methods. B, Xiaoming's family will make a phone call for 300 minutes this month. Which way is better? Explain why. C, how many minutes do you play? The amount of these two payment methods is the same.

8. Exact range of approximation. The accurate range of the approximate value of 2.46 is the precision plus or minus 0.5, the left is greater than or equal to, and the right is less than.

9, explore the law: (1) pendulum graphics.

Pay attention to classification! Parts with the same characteristics are divided into one category for calculation. For example, the head and tail of the adhesive paper are one kind, the middle is one kind, and the adhesive part is one kind.

(2) Paste the paper