Induction of important test sites of mathematics in the next semester of Grade Two in Senior High School.
1, the median line on the hypotenuse of a right triangle is equal to half of the hypotenuse.
2. The sum of the external angles of the quadrilateral is equal to 360.
3. The property theorem of isosceles trapezoid: the two angles of isosceles trapezoid on the same base are equal.
4. The complementary angles of the same angle or equal angle are equal.
5. There is one and only one straight line perpendicular to the known straight line.
6. Parallelism axiom: After passing a point outside a straight line, there is one and only one straight line parallel to this straight line.
7. If two straight lines are parallel to the third straight line, the two straight lines are also parallel to each other.
8. The same angle is equal, and two straight lines are parallel.
9. The internal angles on the same side are complementary and the two straight lines are parallel.
10, two straight lines are parallel and have the same angle.
Quadratic radical knowledge point
(1) Generally speaking, an algebraic expression in the form of √a is called a quadratic radical, where a is called a radical sign. When a≥0, √a represents the arithmetic square root of a; When a is less than 0, the value of √a is pure imaginary.
(2) Addition and subtraction of quadratic roots
1. Homogeneous quadratic roots: Generally speaking, after several quadratic roots are transformed into the simplest quadratic roots, if their roots are the same, they are called homogeneous quadratic roots.
2. Merging similar secondary roots: Merging several similar secondary roots into one secondary root is called merging similar secondary roots.
3. When adding and subtracting secondary roots, you can first convert the secondary roots into the simplest secondary roots, and then merge the roots with the same number.
(3) Multiplication and division of quadratic root
Quadratic root multiplication and division, multiplication and division of square number, keep the root index unchanged, and then turn the result into the simplest quadratic root.
Knowledge point of linear function
(1) Generally speaking, a function in the form of y=kx+b(k, b is a constant, k≠0) is called a linear function, where x is an independent variable. When b=0, the linear function y=kx, also known as the proportional function.
(2) Images and properties of linear functions
Any point P(x, y) on 1. linear function satisfies the equation: y = kx+b.
2. The coordinate of the intersection of the linear function and the Y axis is always (0, b), and the coordinate of the intersection of the linear function and the X axis is always (-b/k, 0).
3. The image of the proportional function always passes through the origin.
4. The relationship between k, b and the quadrant where the function image is located:
When k>0, y increases with the increase of x; When k < 0, y decreases with the increase of x.
When k>0, b>0, the straight line passes through the first, second and third quadrants;
When k>0, b<0, the straight line passes through the first, third and fourth quadrants;
When k < 0, b>0, a straight line passes through the first, second and fourth quadrants;
When k < 0, b<0, a straight line passes through the second, third and fourth quadrants;
When b=0, the straight line passing through the origin o (0 0,0) represents the image of the proportional function.
At this time, when k>0, the straight line only passes through the first and third quadrants; When k < 0, the straight line only passes through the second and fourth quadrants.
Induction of important test sites of mathematics in the next semester of Grade Two in Senior High School.
1, variables and constants
In a certain change process, the quantity that can take different values is called a variable, and the quantity whose value remains unchanged is called a constant.
Generally speaking, there are two variables, X and Y, in a certain change process. If for each value of X, Y has a unique and definite value corresponding to it, then X is an independent variable and Y is a function of X. ..
2. Resolution function
The mathematical formula used to express functional relationship is called resolution function or functional relationship.
The whole set of values of independent variables that make a function meaningful is called the range of independent variables.
3. Three representations of functions and their advantages and disadvantages.
(1) analysis method
The functional relationship between two variables can sometimes be expressed by an equation containing these two variables and the symbols of digital operations. This representation is called analytical method.
(2) List method
A series of values of the independent variable x and the corresponding values of the function y are listed in a table to represent the functional relationship. This representation is called list method.
(3) Image method
The method of expressing functional relations with images is called image method.
4. General steps of drawing images with resolution function.
(1) List: List gives some corresponding values of independent variables and functions.
(2) Point tracking: Take each pair of corresponding values in the table as coordinates, and track the corresponding points on the coordinate plane.
(3) Connection: according to the order of independent variables from small to large, connect the tracked points with smooth curves.
Induction of important test sites of mathematics in the next semester of Grade Two in Senior High School.
Chapter 16 Scores
I. Knowledge framework
Two. The concept of knowledge
1. Fraction: A/B, where a and b are algebraic expressions, and algebraic expressions in which b contains unknowns and b is not equal to 0 are called fractions. Where a is called the numerator of the fraction and b is called the denominator of the fraction.
2. The meaningful condition of the score: the denominator is not equal to 0.
3. Simplification: The common factor of the numerator and denominator of a fraction (not the number of 1) is simplified, and this deformation is called simplification.
4. Total score: Scores with different denominators can be converted into scores with the same mother, which is called total score.
The basic property of the fraction: the numerator and denominator of the fraction are multiplied (or divided) by the same algebraic expression that is not zero at the same time, and the value of the fraction remains unchanged. The formula is: A/B=A_C/B_C A/B=A÷C/B÷C(A, b, c are algebraic expressions, C≠0).
5. simplest fraction: When the numerator and denominator of a fraction have no common factor, the fraction is called simplest fraction. When it is simplified, a fraction is generally simplified to the simplest fraction.
6. Four operations of fractions: 1. Addition and subtraction of the same denominator fraction: addition and subtraction of the same denominator fraction and addition and subtraction of the same denominator numerator. Expressed in letters: A/CB/C = AB/C.
2. Addition and subtraction of fractions with different denominators: add and subtract fractions with different denominators, first divide them into fractions with the same denominator, and then calculate them according to the addition and subtraction rules of fractions with the same denominator. Expressed in letters: A/B C/D = AD CB/BD.
3. Multiplication rule of fractions: two fractions are multiplied, the product of numerator multiplication is the numerator of product, and the product of denominator multiplication is the denominator of product. Expressed in letters: a/b _ c/d=ac/bd.
4. Division rule of fractions: (1). Divide two fractions, and then multiply the numerator and denominator of the divisor by the divisor. a/b÷c/d=ad/bc。
(2) dividing by a fraction is equal to multiplying the reciprocal of this fraction: a/b ÷ c/d = a/b _ d/c.
7. Meaning of fractional equation: The equation with unknown number in denominator is called fractional equation.
8. Solution of fractional equation: ① denominator (both sides of the equation are multiplied by the simplest common denominator at the same time, and the fractional equation is transformed into an integral equation); ② Find the unknown value according to the steps of solving the whole equation; ③ Root test (root test is needed after finding the value of the unknown quantity, because in the process of transforming the fractional equation into the whole equation, the range of the unknown quantity is expanded, which may lead to the increase of roots).
There are many similarities between scores and scores. When teaching this chapter, teachers can compare the characteristics and nature of scores, so that students can learn independently. The emphasis is on the practical application of fractional equation solutions.
Chapter 17 Inverse proportional function
I. Knowledge framework
Two. The concept of knowledge
1. inverse proportional function: a function with the shape y= (k is a constant, k≠0) is called an inverse proportional function. Other forms xy=k
2. Image: The image of inverse proportional function belongs to hyperbola. The image of inverse proportional function is both axisymmetric and centrally symmetric. There are two axes of symmetry: straight lines y=x and y =-X, and the center of the axis of symmetry is the origin.
3. Naturally: when k> is 0, the two branches of hyperbola are located in the first and third quadrants respectively, and the y value of each quadrant decreases with the increase of x value;
When k < 0, the two branches of hyperbola are located in the second and fourth quadrants respectively, and the y value of each quadrant increases with the increase of x value. ..
4.| k |: represents the area of a rectangle surrounded by a point on the inverse proportional function image and a vertical line segment formed by two coordinate axes and two coordinate axes.
When learning inverse proportional function, teachers can let students compare a previously learned function and inspire students to learn by comparison. When doing problems, cultivate and develop the idea of combining numbers and shapes.
Chapter 18 Pythagorean Theorem
I. Knowledge framework
Second, the concept of knowledge
1. Pythagorean Theorem: If the lengths of two right angles of a right triangle are A and B and the length of the hypotenuse is C, then a2+b2=c2.
Inverse Pythagorean Theorem: If the three sides of triangle A, B and C satisfy a2+b2=c2. Then this triangle is a right triangle.
2. Theorem: A proposition that is proved to be correct is called a theorem.
3. We call two propositions with opposite topics and conclusions reciprocal propositions. If one of them is called the original proposition, then the other is called its inverse proposition. (Example: Pythagorean Theorem and Pythagorean Theorem Inverse Theorem)
Pythagorean theorem is an important property of right triangle. This chapter requires students to understand Pythagorean theorem and learn to use it to solve practical problems. You can gain mathematical knowledge through the development experience of autonomous learning.
Chapter 19 Quadrilateral
I. Knowledge framework
Two. The concept of knowledge
1. Definition of parallelogram: A parallelogram with two groups of opposite sides parallel to each other is called a parallelogram.
2. The nature of parallelogram: the opposite sides of parallelogram are equal; Diagonal angles of parallelogram are equal. Diagonal bisection of parallelogram.
3. Determination of parallelogram 1. Two sets of quadrilaterals with equal opposite sides are parallelograms.
2. The quadrilateral whose diagonal lines bisect each other is a parallelogram;
3. Two groups of quadrangles with equal diagonal are parallelograms;
4. A set of quadrilaterals with parallel and equal opposite sides is a parallelogram.
4. The midline of the triangle is parallel to the third side of the triangle, which is equal to half of the third side.
5. The midline of the hypotenuse of a right triangle is equal to half of the hypotenuse.
6. Definition of rectangle: a parallelogram with a right angle.
7. The nature of the rectangle: all four corners of the rectangle are right angles; The diagonals of a rectangle are equally divided. AC=BD
8. Rectangular judgment theorem: 1. A parallelogram with a right angle is called a rectangle.
2. Parallelograms with equal diagonals are rectangles.
A quadrilateral with three right angles is a rectangle.
9. Definition of diamond: parallelogram with equal adjacent sides.
10. The nature of the diamond: all four sides of the diamond are equal; The two diagonals of the diamond are perpendicular to each other, and each diagonal bisects a set of diagonals.
The judgement theorem of 1 1. diamond: 1. A set of parallelograms with equal adjacent sides is a diamond.
2. Parallelograms with diagonal lines perpendicular to each other are diamonds.
A quadrilateral with four equilateral sides is a diamond.
12.s diamond =1/2× ab (A and B are two diagonal lines).
13. Definition of a square: a rhombus with right angles or a rectangle with equal adjacent sides.
14. The essence of a square: all four sides are equal and all four corners are right angles. A square is both a rectangle and a diamond.
15. Square judgement theorem: 1. A rectangle with equal adjacent sides is a square. Diamonds with right angles are squares.
16. Definition of trapezoid: A set of quadrangles with parallel opposite sides and another set of non-parallel opposite sides is called trapezoid.
17. Definition of right-angled trapezoid: a trapezoid with a right angle.
18. Definition of isosceles trapezoid: isosceles trapezoid.
19. Properties of isosceles trapezoid: two angles on the same base of isosceles trapezoid are equal; The two diagonals of an isosceles trapezoid are equal.
20. Judgment theorem of isosceles trapezoid: A trapezoid with two equal angles on the same bottom is an isosceles trapezoid.
The content of this chapter is the study of the classification and nature of quadrangles on the plane, which requires students to use their hands and brains more in the learning process and bring their own discoveries and knowledge into problem solving. Therefore, teachers can encourage students to summarize the characteristics of quadrangles themselves in teaching, which is conducive to students' mastery of knowledge.
Chapter 20 Data Analysis
I. Knowledge framework
Two. The concept of knowledge
1. weighted average: the calculation formula of weighted average. Understanding of weight: It reflects the importance of a certain data in the whole data.
2. Median: arrange a set of data in order from small to large (or from large to small). If the number of data is odd, the middle number is the median of this set of data; If the number of data is even, the average of the middle two data is the median of this set of data.
3. Pattern: The data with the highest frequency in a group of data is the pattern of this group of data.
4. Range: the difference between the maximum data and the minimum data in this group of data is called the range of this group of data.
5. The greater the variance, the greater the data fluctuation; The smaller the variance, the smaller the data fluctuation and the more stable it is.
Expanding reading: how to improve the poor math performance in junior two?
First, learn to listen. Students should listen carefully in class, not just express themselves by rushing to answer questions.
Secondly, learn to take notes. You can't just listen carefully, but learn to take some notes effectively while listening, so that you can effectively grasp the knowledge points that are easy to make mistakes in after-class review.
Third, start with basic concepts and formulas, understand the essence of concepts, and never change from their ancestors. Infiltrate them one by one and solve problems with basic concepts.
Fourth, establish the wrong book. Put the wrong questions in homework and test paper into the wrong book in time, not only write out the questions and answers, but also write out the problem-solving process, and mark the reasons, test sites and error-prone points of your own mistakes.
Fifth, when doing problems, we should develop the habit of active thinking. Doing the problem lies not in the result, but in thinking and analyzing, studying the idea of solving the problem, analyzing the process of solving the problem and summarizing the method of solving the problem.
Sixth, calculation is the most important. Practice once a day, such as the calculation of rational numbers, real numbers and equations. Every problem can not be separated from calculation, so it is just around the corner to improve the calculation accuracy and shorten the calculation time.