A few; △& lt； 0, the equation has no real root.

4. Vieta Theorem:+=

? =?

.

5. Fractional equation that can be transformed into quadratic equation. (The roots of fractional equations should be tested) II. Key points and difficulties:

Key point: the method of solving equations.

Difficulties: Establish equation model to solve practical problems.

Chapter iii frequency and its distribution. Knowledge points:

1. Frequency: The frequency is the number of times the respondents appear. The sum of frequencies is equal to the total. 2. Frequency: The ratio of frequency to total number is called frequency. The sum of frequencies is equal to 1.

3. Histogram of frequency distribution: the horizontal semi-axis represents the group, the vertical semi-axis represents the frequency, and the rectangle with equal width represents different frequency distributions. This graph is called frequency distribution histogram.

When drawing the histogram of frequency distribution, if the number of the left end points is far from 0, the horizontal semi-axis should be drawn as a dotted line near the origin.

4. Group median: the average of the numbers represented by the left and right endpoints in each group is the group median. When calculating the average, use the values in the group.

5. Group distance: in each group, the number represented by the left end point is subtracted from the number represented by the right end point, and the difference is the group distance. In the same frequency distribution histogram, the interval between groups must be equal. The main contents of this chapter are frequency and frequency, frequency allocation and frequency application. Two. Key points and difficulties:

Key point: the concept of frequency.

Difficulties: Draw and analyze the histogram of frequency distribution.

Chapter iv proposition and proof 1. Knowledge points:

1. Definition: The correct judgment of what a concept is is called definition.

Yulong education: edited by teacher Zhong Daiqin 2065438+Friday, March 2, 2002

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2. Proposition: A statement expressing conditions and conclusions in the form of "if …… then ……" is a proposition. A correct proposition is called a true proposition; A false proposition is called a false proposition. 3. Theorem: The correct proposition that has been proved is called theorem.

4. Give a counterexample: Give an example that is completely opposite to the proposition to prove that the proposition is a false proposition. 5. Reduction to absurdity: first assume that the conclusion is wrong, and then deduce a result that is contrary to the condition of the topic or contradicts a theorem, indicating that the original proposition is true.

The main contents of this chapter: definition and proposition, proof, counterexample and proof, reduction to absurdity. Two. Key points and difficulties:

Emphasis: Understand the necessity of geometric proof and master the general steps and formats of proof. Difficulties: How can we make the proof process clear and orderly?

Chapter v parallelogram 1. Knowledge points:

1. Polygons and quadrilaterals

Attribute: 1) sum of inner angles, sum of outer angles and diagonal number of an n polygon. 2) The sum of the inner angles, the sum of the outer angles and the number of diagonals of a quadrilateral.

2. Regular polygon: A polygon with equal sides and internal angles is called a regular polygon. The condition that a regular polygon can be embedded in a plane: 1) A single regular polygon.

2) Various regular polygons

Condition: The sum of angles of vertices is equal to 360. 3. The center is symmetrical.

1) The definitions of centrosymmetric graphs and ordinary centrosymmetric graphs.

Definition: If a graph rotates180 around a certain point and can coincide with the original graph, then the graph is called a centrosymmetric graph. Common centrosymmetric figures are parallelogram, English capital letters S and Z.

2) The straight line passing through the center of symmetry must bisect the area of the central symmetric figure, and the line segment connecting the symmetrical points must pass through and be bisected by the center of symmetry.

Yulong Education: Edited by Teacher Zhong Daiqin 2065 438+02 March 2nd Friday 5

4. The midline of triangle and its theorem.

Note: The proof method and application of triangle midline theorem are the key points.

Theorem: In a right triangle, the right side of 30 is equal to half of the hypotenuse. 5 Definition of parallelogram: Two groups of parallelograms with parallel opposite sides are called parallelograms. 6. The nature and judgment of parallelogram

Property: 1) Two groups of opposite sides of a parallelogram are parallel and equal respectively. 2) The diagonals of parallelograms are equal and the adjacent angles are complementary. 3) The diagonal of the parallelogram is bisected. 4) The parallelogram is a central symmetrical figure.

Judgment method: 1) Definition: Two groups of parallelograms with parallel opposite sides are parallelograms. 2) A set of parallelograms with parallel opposite sides is a parallelogram. 3) Two groups of parallelograms with equal opposite sides are parallelograms. 4) A quadrilateral with a diagonal bisector is a parallelogram.

Note: There are other methods to determine parallelogram, but none of them can be used as theorems. For example, "two groups of quadrangles with equal diagonals are parallelograms" is obviously a true proposition, but it cannot be used as a theorem.

7. Inverse propositions and theorems;

Inverse proposition: the proposition obtained by exchanging the conditions and conclusions of the original proposition is called the inverse proposition of the original proposition. Inverse theorem: the theorem obtained by exchanging the conditions and conclusions of the theorem is called the inverse theorem in the original scheme.

The main contents of this chapter are: the nature of polygons, parallelograms, parallelograms, central symmetry, the judgment of parallelograms, the midline of triangles, inverse propositions and inverse theorems. Two. Key points and difficulties:

Emphasis: the nature and judgment of parallelogram. Difficulties: Relevant proofs.

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Chapter VI Special parallelogram. Knowledge points:

1. Definition: Parallelogram and trapezoid are collectively called special quadrilaterals.

Special parallelogram includes rectangle, diamond and square; Special trapezoid includes isosceles trapezoid and right-angled trapezoid.

2. The nature and judgment of rectangle

Attribute: 1) A rectangle has all the attributes of a parallelogram. 2) All four corners of a rectangle are right angles. 3) The diagonals of the rectangles are equal.

Determination method: 1) Definition: A parallelogram with a right angle is a rectangle. 2) A parallelogram with three right angles is a rectangle. 3) Parallelograms with equal diagonals are rectangles.

Note: There are other methods to determine the rectangle, but none of them can be used as theorems. 3. The nature and identification of diamonds.

Attribute: 1) A diamond has all the attributes of a parallelogram. 2) All four sides of the diamond are equal.

3) Diagonal lines of the diamond are perpendicular to each other, and each diagonal line bisects a set of diagonal lines. 4) The area of the diamond is equal to half of the diagonal product. If the diagonals of a quadrilateral are perpendicular to each other, then the area of this quadrilateral is equal to half of the diagonal product. ) Judgment method: 1) Definition: A set of parallelograms with equal adjacent sides is a diamond. 2) A quadrilateral with four equilateral sides is a diamond.

Note: There are other ways to determine the diamond, but none of them can be used as theorems.

4. The nature and judgment of the square

Property: 1) A square has all the properties of parallelogram, rectangle and diamond. Judgment method; 1) Definition: A parallelogram with a right angle and a set of equal adjacent sides is a square.

2) rectangle+a set of adjacent sides are equal 3) diamond+an angle is a right angle.

Note: There are other ways to determine a square, but none of them can be used as theorems. 5. Trapezoid: A group of quadrangles with parallel opposite sides and another group with non-parallel opposite sides are trapeziums. The nature of isosceles trapezoid: the two base angles on the same base of isosceles trapezoid are equal; The diagonal lines of the isosceles trapezoid are equal.

Determination of isosceles trapezoid: 1) Definition: isosceles trapezoid is called isosceles trapezoid. 2) A trapezoid with two equal base angles on the same base is an isosceles trapezoid. 3) A trapezoid with equal diagonal lines is an isosceles trapezoid. (The proof method must be mastered. )

Note: the drawing methods of several common auxiliary lines in trapezoid.

Supplement: Trapezoidal midline theorem, especially its proof method.

Content of this chapter: the center of gravity of rectangle, diamond, square, trapezoid and simple plane figure. Two. Key points and difficulties:

Emphasis: the properties and judgments of various special quadrangles. Difficulties: Relevant proofs.