1, algebraic expression:

Algebraic expressions that only contain "×" and "∫" operations are called monomials.

Algebraic expression with "x", "24

2. Addition and subtraction of algebraic expressions:

(1) When deleting brackets, if there is a "+"in front of the brackets, the brackets will be deleted directly.

(2) When the brackets are deleted, when there is a "-"sign in front of the brackets, the symbols in the brackets should be changed.

(3) The essence of algebraic addition and subtraction is to merge similar items.

3. Multiplication of powers with the same base:

Multiplied by the power of the base, the base remains the same, and the exponents add up.

4. Power supply and products:

Power of (1), constant radix, exponential multiplication.

(2) The power of the product is equal to the power of each radix.

5. Division of power on the same basis:

(1) divided by the power of the same base, the base is unchanged, and the exponent is subtracted.

(2) Zero exponent and negative integer exponent: a0= 1 (a≠0)

A-p = 1/AP (a ≠ 0, p is a positive integer)

6. Multiplication of algebraic expressions:

(1) When the monomial is multiplied by the monomial, their coefficients are multiplied by the power of the same letter respectively, and the remaining letters, together with their exponents, remain the same as the factors of the product.

(2) Multiplication of monomial and polynomial: m(a+b)=ma+mb.

(3) Multiplication of polynomials: (m+n)(a+b)=ma+na+mb+nb.

7. Variance formula:

(1) square difference formula: (a+b)(a-b)=a2-b2.

(2) The product of the sum of two numbers and the difference between the two numbers is equal to their square difference.

8. Complete square formula

(1) complete square formula: (A B) 2 = A2 2AB+B2.

(2) The relationship between two complete square formulas:

(a+b)2-(a-b)2=4ab

9. Division of algebraic expressions:

(1) monomial division is the factor of quotient divided by coefficient and the same base power respectively. For letters contained only in the division formula, it is a factor of quotient and its exponent.

(2) Polynomial divided by monomial, first divide each term of this polynomial by monomial, and then add the obtained quotients.

Chapter II Parallel Lines and Intersecting Lines

1, complementary angle and complementary angle:

(1) If the sum of two angles is a right angle, then these two angles are called complementary angles.

(2) If the sum of two angles is a right angle, then these two angles are called complementary angles.

(3) The complementary angles of the same angle or equal angle are equal, and the complementary angles of the same angle or equal angle are equal.

(4) The equivalent angles are equal.

2, explore the conditions of parallel lines:

(1) At the same angle, two straight lines are parallel.

(2) The internal dislocation angles are equal and the two straight lines are parallel.

(3) The internal angles on the same side are complementary and the two straight lines are parallel.

3, the characteristics of parallel lines:

(1) Two straight lines are parallel with the same included angle.

(2) The two straight lines are parallel and the internal dislocation angles are equal.

(3) Two straight lines are parallel and complementary.

4. Measure the line segment and angle with a ruler:

(1) Drawing with a ruler and compasses out of proportion is called ruler drawing.

(2) When drawing with a ruler, the functions of the ruler are: ① straight line, ② line segment and ③ ray; The function of compasses is ① to draw and ② to draw an arc.

five

Chapter III Life Information

1, one in a million knows:

1 m = 106 micron, 1 m = 109 nm.

One millionth of a meter is 1 micron = 10-6 meters, 1 nanometer = 10-9.

2. Approximate values and significant figures:

The measurement results of (1) are all approximate.

(2) When taking the divisor of a number by rounding method, it means that the divisor is rounded to the nearest place.

(3) For a divisor, from the first number on the left that is not 0 to the most accurate number, all numbers are called the significant digits of this number.

3, the world newborn map:

(1) The statistical charts we know are: bar chart, fan chart and line chart.

(2) The essence of "pictographic statistical chart" is graphic statistical chart.

Chapter IV Probability

1. Is the game fair?

(1) Game fairness means that both sides have the same possibility of winning. The game is fair only when both sides have the same possibility of winning, otherwise the game is unfair.

(2) Use the part between 0 and 1 on the number axis to indicate the size of the possibility.

The probability of inevitable occurrence is represented by 1, the probability of impossible event is represented by 0, and the probability of uncertain event is between 0 and 1.

2. The probability of touching the red ball:

(1) usually use P= the number of possible results of touching a red ball/all possible results of touching a ball.

To indicate the possibility of touching the red ball, also known as the probability of touching the red ball.

(2) The probability of the inevitable event is 1, and it is recorded as p (inevitable event) =1; The probability of an impossible event is 0, and it is recorded as p (impossible event) = 0; If a is an uncertain event, then 0

3. Probability of staying in black brick:

Significance of geometric probability: the probability of a geometric event is equal to the area of all possible figures of the event divided by the area of all possible results.

P uncertain events = area of uncertain events/total area of time.

The fifth chapter triangle

1, know the triangle:

(1) A figure composed of three line segments that are not on the same line end to end is called a triangle.

(2) Among the connecting lines between two points, the straight line is the shortest.

(3) The sum of any two sides of a triangle is greater than the third side.

The difference between any two sides of a triangle is less than the third side.

(4) The sum of the interior angles of the triangle is 180. ; The two acute angles of a right triangle are complementary.

(5) In a triangle, the bisector of the inner angle intersects its opposite side, and the line segment between the vertex and the intersection of this angle is called the bisector.

(6) In a triangle, the line segment connecting the vertex and the midpoint of its opposite side is called the center line of the triangle.

(7) Draw a vertical line from the vertex of the triangle to the line where the opposite side is located, and the line segment between the vertex and the opposite side is called the high line of the triangle.

2, graphic congruence:

Two figures that can completely overlap are called congruent figures, and the shapes and sizes of congruent figures are the same.

3. congruent triangles:

Congruent triangles's corresponding edges are equal, and the corresponding relationship is called equality.

4. Explore the conditions of triangle congruence:

(1) Three sides correspond to the congruence of two equal triangles, abbreviated as side or SSS.

(2) Two corners of two triangles and their edges correspond to the same congruence, abbreviated as corner or ASA.

(3) The opposite side of two angles and one of them corresponds to the congruence of two triangles, which is referred to as angular edge or AAS for short.

(4) Two triangles with equal included angles on both sides are congruent, or SAS for short.

5. Make a triangle:

. . . . . . . . . . . . . . . .

6. Measure with triangle congruence distance

There are three ways to judge whether a triangle is congruent: corner edge, corner edge, corner edge and side edge.

7. Explore the condition of congruence of right triangle;

(1) The hypotenuse and right-angled side correspond to the coincidence of two right-angled triangles, abbreviated as "hypotenuse, right-angled side" or "HL"

(2) There are HL, SAS, ASA, SSS and AAS to judge the coincidence of two right-angled triangles. * * * Five kinds.

Chapter VI Relationship between Variables

1, car downtime:

In a certain change, the ever-changing quantity is called a variable. If one quantity changes with another quantity, then this quantity is called independent variable and the other quantity is called dependent variable.

2. The changing triangle:

Relationship is another way for us to express the relationship between variables. With the relationship, we can find the value of the corresponding dependent variable according to the value of any independent variable.

3. Temperature change:

Image is a way to express the relationship between variables, and its characteristic is very intuitive. When the relationship between variables is represented by images, the independent variables are usually represented by points on the horizontal axis (horizontal axis) and the dependent variables by points on the vertical axis (vertical axis).

4, the change of speed:

In the image of speed changing with time, generally "horizontal line" means that the car is driving at a constant speed, "ascending line" means that the car speed is increasing, and "descending line" means that the car is decelerating.

Chapter VII Axisymmetric Graphics

1, axisymmetric phenomenon:

(1) If a graph is folded along a straight line and the parts on both sides of the straight line can overlap each other, then the graph is called an axisymmetric graph, and this straight line is called an axis of symmetry.

(2) For two graphs, if they can overlap each other after being folded in half along a straight line, then the two graphs are said to form an axial symmetry.

2, simple axisymmetric graphics:

3. The angle (1) is an axisymmetric figure with an axis of symmetry. The straight line where the angular bisector is located is its axis of symmetry, and the distance between points on the angular bisector is equal to both sides of the angle.

4.(2) The line segment is an axisymmetric figure, and its axis of symmetry is perpendicular to this line segment and bisects this line segment. Such a straight line is called the midline of this line segment, and the distance from the point on the midline of the line segment to the two endpoints of this line segment is equal.

5.(3) The isosceles triangle is an axisymmetric figure. The height of the bisector of the top angle and the bottom of the isosceles triangle coincide, and the straight line where they are located is the symmetry axis of the isosceles triangle.

6.(4) An equilateral triangle has three axes of symmetry, and the bisector of three inner angles, the midline of three sides or the straight line where the heights of three sides are located are all its axes of symmetry.

7.(5) The two base angles of an isosceles triangle are equal. If the two internal angles of a triangle are equal, then their opposite sides are equal, and the three internal angles of an equilateral triangle are equal and all equal to 60 degrees.

8. 3. Explore the essence of axial symmetry.

The corresponding angles of (1) are equal, so are the corresponding line segments.

(2) The line segments connected by corresponding points are vertically bisected by the symmetry axis.

4. Application of axisymmetric design pattern:

(1) When drawing with axisymmetric properties, it is only necessary to make the symmetrical points of several key points in the graph and connect them in sequence.

(2) Axisymmetric graphics can be designed in the form of perforation, inking, folding, paper cutting, drawing or equivalent calculation.

5. What has the mirror changed?

(1) Mirror symmetry is axial symmetry, and the axis of symmetry varies according to the relative position of the mirror and the object.

(2) The mirror does not change the top and bottom of the object, but changes the relationship between the top and bottom of the object.

6, trimming and paper-cutting:

Edge grinding and paper-cutting are both applications of axisymmetric knowledge.

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