Summary of Mathematics Knowledge Points in Book 2 of Grade 2
Random surprise inspection
(1) The survey sample is randomly selected, and the probability of each unit being selected in the population is equal. Therefore, it can ensure the uniform distribution of the selected units in the whole population, and there will be no bias error, which is very representative.
(2) Take all sample units as a "delegation" and use the whole "delegation" to represent the whole. Instead of using randomly selected individual units to represent the whole.
(3) The number of selected survey samples is determined by scientific calculation according to the requirements of survey error, and there is a reliable guarantee on the number of survey samples.
(4) The error of sampling survey can be calculated according to the overall difference between the number of samples and the units before the survey, and controlled within the allowable range, so the accuracy of the survey results is high.
homework
1. the sampling score is a (a)
A. structural relative number B. proportional relative number C. comparative relative number D. intensity relative number
2. The relationship between percentage and variance of percentage is (c)
A. The closer the score is to 0, the greater the variance of the score. B. The closer the score is to 1, the greater the variance of the score.
C. The closer the score is to 0.5, the greater the variance of the score. D. The closer the score is to 0.25, the greater the variance of the score.
3. Cluster sampling is a comprehensive survey of the sampled group, so cluster sampling is (b)
A. Comprehensive investigation B. Incomplete investigation C. One-time investigation D. Recurrent investigation
4. Select 19% of 400 college students for non-repeated sampling survey, in which the proportion of top students is 20% and the probability guarantee degree is 95.45%, then the limit sampling error of the proportion of top students is (a).
4. 13% c 9. 18% d 8.26%
5. According to the sampling data of 5%, the qualified rate of product A is 60%, and that of product B is 80%. When the number of sampled products is equal, the sampling error of qualified rate is (b).
A.a product is big, B. B product is big, C. equals D. It is impossible to judge.
Induction of knowledge points in the first volume of junior two mathematics
1 There is only one straight line at two points.
The line segment between two points is the shortest.
The complementary angles of the same angle or equal angle are equal.
The complementary angles of the same angle or the same angle are equal.
One and only one straight line is perpendicular to the known straight line.
Of all the line segments connecting a point outside the straight line with points on the straight line, the vertical line segment is the shortest.
7 Parallel axiom passes through a point outside a straight line, and there is only one straight line parallel to this straight line.
If both lines are parallel to the third line, the two lines are also parallel to each other.
The same angle is equal and two straight lines are parallel.
The internal dislocation angles of 10 are equal, and the two straight lines are parallel.
1 1 are complementary and two straight lines are parallel.
12 Two straight lines are parallel and have the same angle.
13 two straight lines are parallel, and the internal dislocation angles are equal.
14 Two straight lines are parallel and complementary.
Theorem 15 The sum of two sides of a triangle is greater than the third side.
16 infers that the difference between two sides of a triangle is smaller than the third side.
The sum of the internal angles of 17 triangle is equal to 180.
18 infers that the two acute angles of 1 right triangle are complementary.
19 Inference 2 An outer angle of a triangle is equal to the sum of two non-adjacent inner angles.
Inference 3 The outer angle of a triangle is greater than any inner angle that is not adjacent to it.
2 1 congruent triangles has equal sides and angles.
Axiom of Angular (SAS) has two triangles with equal angles.
The Axiom of 23 Angles (ASA) has the congruence of two triangles, which have two angles and their sides correspond to each other.
The inference (AAS) has two angles, and the opposite side of one angle corresponds to the congruence of two triangles.
The axiom of 25 sides (SSS) has two triangles with equal sides.
Axiom of hypotenuse and right angle (HL) Two right angle triangles with hypotenuse and right angle are congruent.
Theorem 1 The distance between a point on the bisector of an angle and both sides of the angle is equal.
Theorem 2 is a point with equal distance on both sides of an angle, which is on the bisector of this angle.
The bisector of an angle 29 is the set of all points with equal distance to both sides of the angle.
Knowledge points of trigonometric proof in eighth grade mathematics
Chapter 1 Proof of Triangle
1, isosceles triangle
Properties and Judgement of (1) Triangular Congruence
The corresponding sides of congruent triangles are equal and the corresponding angles are equal: SSS, SAS, ASA, AAS,
(2) Determination, nature and inference of isosceles triangle.
Properties: The two base angles of an isosceles triangle are equal (equilateral and equiangular).
Judgment: A triangle with two equal angles is an isosceles triangle.
Inference: The bisector of the top angle of an isosceles triangle, the median line on the bottom edge and the height on the bottom edge coincide (that is, "the three lines are one")
(3) The properties and judging theorem of equilateral triangle.
Property theorem: all three angles of an equilateral triangle are equal, and each angle is equal to 60 degrees; All three sides of an equilateral triangle meet the property of "three lines in one"; An equilateral triangle is an axisymmetric figure with three axes of symmetry.
Decision Theorem: An isosceles triangle with an angle of 60 degrees is an equilateral triangle. Or a triangle with three equal angles is an equilateral triangle.
(4) The properties of each side of a 30-degree right triangle.
Theorem: In a right triangle, if an acute angle is equal to 30 degrees, then the right side it faces is equal to half of the hypotenuse.
2. Right triangle
(1) Pythagorean Theorem and Its Inverse Theorem
Theorem: The sum of squares of two right angles of a right triangle is equal to the square of the hypotenuse.
Inverse theorem: If the sum of squares of two sides of a triangle is equal to the square of the third side, then the triangle is a right triangle.
(2) The relationship between the two acute angles of a right triangle.
Theorem: The two acute angles of a right triangle are complementary.
Inverse theorem: Two triangles with complementary acute angles are right triangles.
(3) The side length theorem of 30-degree right triangle.
Theorem: In a right triangle, if an acute angle is equal to 30 degrees, then the right side it faces is equal to half of the hypotenuse.
Inverse theorem: In a right triangle, a right-angled side is half of the hypotenuse, so the acute angle of this right-angled side is 30 degrees.
(4) Proposition and Inverse Proposition
Proposition includes two parts: known and conclusion; Inverse proposition is to exchange known and conclusion; The correct inverse proposition is the inverse theorem.
(5) Theorem for judging congruence of right triangle.
Theorem: The hypotenuse and a right-angled side correspond to the congruence (HL) of two equal right-angled triangles.
3. perpendicular bisector of the line segment
The Nature and Judgment of the Vertical Line in (1) Line Segment
Property: The distance between the point on the vertical line of a line segment and the two endpoints of this line segment is equal.
Judgment: The points with the same distance to the two ends of a line segment are on the middle vertical line of this line segment.
The eighth grade mathematics second volume knowledge point arranges the related article;
★ The arrangement of mathematics knowledge points in the second volume of the eighth grade
★ Knowledge point induction and mathematics learning methods in the second volume of junior two mathematics.
★ Arrangement of knowledge points in the second volume of eighth grade mathematics
★ Summarize the mathematics knowledge points in the second volume of the eighth grade.
★ Summarize the mathematics knowledge points in the second volume of the eighth grade.
★ Combing the knowledge points of mathematics in the second volume of the eighth grade
★ People's Education Edition Grade 8 Volume II Mathematics Review Outline
★ General review of mathematics knowledge points in the second volume of the eighth grade
★ Summary of knowledge points in the second volume of Mathematics in the second day of junior high school.
★ Summary of Mathematical Knowledge Points in the Second Volume of Grade 8