People's Education Edition, the first day of mathematics, the second book, knowledge points, Chapter 5, Intersecting lines and parallel lines
5. 1 intersection line
The vertex angles 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 and a point on the straight line, the vertical line segment is the shortest (in short, the vertical line segment is the shortest. This knowledge point can be tested in the upcoming fill-in-the-blank questions.
5.2 Parallel lines (requires key knowledge)
1, after a point outside the straight line, there is one and only one straight line parallel to it.
2. If two straight lines are parallel to the third straight line, then the two straight lines are also parallel to each other.
3. Conditions of parallel lines:
4. Two straight lines are cut by the third straight line. If congruent angles are equal, two straight lines are parallel and cut by a third straight line. If the offset angles are equal, two straight lines are parallel (offset angles are equal, two straight lines are parallel).
5. Two straight lines are cut by the third straight line. If they are complementary to the inside corner, then two straight lines are parallel (complementary to the inside corner, two straight lines are parallel).
5.3 Nature of parallel lines (requires key knowledge)
1, two parallel lines are cut by the third straight line, and the apposition angles are equal (the two straight lines are parallel and the apposition angles are equal).
2. Two parallel lines are cut by the third line, and the internal dislocation angles are equal (the two lines are parallel and the internal dislocation angles are equal).
3. The two parallel lines are cut by the third straight line, which are complementary to the lateral inner angle (the two straight lines are parallel and complementary to the lateral inner angle). The sentence that judges a thing is called a proposition (this test site may appear in the rewriting of the proposition in the fill-in-the-blank question and in the multiple-choice question to judge whether the proposition is true or false).
Analysis of test sites of knowledge points in this chapter:
1, the nature of parallel lines and the content of judgment.
2, the authenticity of the proposition, rewrite the proposition.
3. Proof questions (cloze, independent proof)
4. Test sites of relevant knowledge in multiple-choice questions and fill-in-the-blank questions (the nature of intersecting lines and parallel lines; The shortest vertical line segment has one and only one straight line parallel to the known straight line at a point outside the straight line)
People's education printing plate, the first day of mathematics, the second book, knowledge points, chapter 6, real numbers
6. 1 square root
If the square of a number is equal to a, then this number is called the square root of a; (that is, if x2=a, then x is called the square root of a, where a is nonnegative, that is, a? 0. The expression is x2=a? x=？ A, where x A is called the arithmetic square root of a), (this knowledge test site focuses on the application of fill-in-the-blank questions, multiple-choice questions and calculation questions).
6.2 cube root
If a number is the cube of a, then it is called the cube root of a (that is, if x3=a, then x is called the cube root of a, expression: x3=a? x？ There is only one cube root), (this knowledge test center focuses on the application of fill-in-the-blank questions, multiple-choice questions and calculation questions).
6.3 real numbers
Infinitely cyclic decimals are also called irrational numbers.
Rational numbers and irrational numbers are collectively called real numbers.
Test center analysis:
1, rational numbers and irrational numbers may appear in fill-in-the-blank questions and multiple-choice questions.
2. The difference between the square root of a number and the square root of an algebraic expression (be careful)
3. A positive number has two square roots, which are opposite (that is, their sum is equal to 0).
4. Uniqueness: the square root is only equal to its own number 0; There are three numbers in which the cube root equals itself: 1,-1 and 0 * * *; There are two numbers whose arithmetic square root equals itself: 1 and 0.
People's education printing plate, the first day of mathematics, the second book, knowledge points, chapter 7, plane rectangular coordinate system
7. 1 plane rectangular coordinate system
A word containing two numbers indicates a definite position, where the two numbers each mean different things. We call this number pair composed of two numbers, A and B, in sequence an ordered number pair.
The knowledge test sites in this chapter may appear in:
1, judge which quadrant a point is in or which quadrant a point is in, and then find the value corresponding to the unknown quantity;
2. After the figure is translated once or twice in the plane rectangular coordinate system, the coordinates of the corresponding points before and after translation are obtained.
People's Education Press Grade One Mathematics Book 2 Knowledge Points Chapter 8 Binary Linear Equations
8. 1 binary linear equations
1, the equation contains unknowns (such as x and y), and the exponent of the unknowns (or the number of unknowns) is 1. Equations like this are called binary linear equations (this knowledge test site will appear in fill-in-the-blank questions and multiple-choice questions, with the number of concerns being 1 and the coefficient not being 0).
2. Two binary linear equations with the same unknowns are combined into one binary linear equation group.
3. The values of two unknowns that make the values on both sides of the binary linear equation equal are called the solutions of the binary linear equation (the solutions of the binary linear equation may appear in the root test of multiple-choice questions).
4. The common * * * solution of two equations of binary linear equations is called the solution of binary linear equations (the solution of binary linear equations may appear in the root test problem in multiple-choice questions).
8.2 elimination
5. The idea of changing the number of unknowns from multiple to one (finally solving the equation of one yuan once, and then solving binary and ternary in turn, one by one) is called elimination thought.
6. Knowledge test sites in this chapter
First, the calculation problem
Choose and fill in the blanks.
C, application questions
People's Education Press Grade One Mathematics Book 2 Knowledge Points Chapter 9 Inequality and Inequality Group
9. 1 inequality
1, the formula that indicates the relationship between size with less than sign or greater than sign is called inequality.
2. The value of the unknown quantity that makes the inequality valid is called the solution of the inequality.
3. The range of value of x that can make inequality hold is called the solution set of inequality, or simply the solution set.
4. An inequality with an unknown degree of 1 is called one-dimensional linear inequality.
5, the essence of inequality:
Add (or subtract) the same number (or formula) on both sides of the inequality, and the direction of the inequality remains unchanged.
Both sides of inequality multiply (or divide) the same positive number, and the direction of inequality remains unchanged.
When both sides of the inequality are multiplied (or divided) by the same negative number, the direction of the inequality changes.
The difference between any two sides in a triangle is less than the third side.
The sum of any two sides in a triangle is greater than the third side.
9.3 One-dimensional linear inequality system
6. When two linear inequalities are combined, a group of linear inequalities is formed.
7. Knowledge test sites in this chapter
First, multiple choice questions
B, calculation questions)
C. Simple application of one-dimensional linear inequality
Data collection, arrangement and knowledge point description in Chapter 10, Volume 2, Mathematics, Grade 1, People's Education Press
First, the main points of knowledge
1, comprehensive survey: the survey of all objects is called comprehensive survey (advantages: the survey results are more accurate; Disadvantages: time-consuming and laborious).
2. Sampling survey: only a part of the objects are selected for investigation, and then all the objects are inferred according to the survey data. This survey method is called sampling survey (advantages: less investment, convenient operation, and sometimes only sampling can be used for investigation; Disadvantages: there may be some errors between the survey results and the overall results)
3. Population: All the investigated objects are called population.
4. Individuals: Each survey object that constitutes the population is called an individual.
5. Sample: individuals extracted from the sample.
6. Sample size: The number of individuals in a sample is called sample size.
7. Simple random sampling survey: In the sampling process, every individual in the group has an equal opportunity to be drawn. Sampling methods like this are simple random sampling.
Second, the classification of statistical charts:
1. Bar charts are suitable for displaying quantitative characteristics between different objects. According to the height of the rectangle (bar), the size and quantity of the counted objects can be seen intuitively.
2. Broken-line statistical charts are suitable for displaying different quantities of features of the same thing. According to the change of broken line, we can directly see the trend of things (such as rising or falling, growth rate, etc.) ).
3. The pie chart represents the whole with a circle, which can intuitively show the percentage of each part (different statistical objects) and is suitable for showing the quantitative proportional relationship between different objects.
Note: Find the degree of central angle = percentage? 3600
4. The histogram of frequency distribution can be used to collect data. Plan? The method is sorted into a frequency distribution table and the histogram of frequency distribution is drawn. Can display the distribution of data, it is easy to display the frequency difference between groups. The steps of making frequency distribution histogram are as follows: ① Find out the maximum and minimum values of all data and calculate their values.
Range range or group distance? Difference (range = maximum-minimum). ② Determine the distance and number of groups (number of groups =). ③ List the number distribution table of frequency group distance. ④ Draw the histogram of frequency distribution.
5. Analysis of knowledge test sites in this chapter:
1, group, sample, individual and sample size will appear in multiple-choice questions.
2. The emphasis is on the completion of histogram, fan chart and histogram, and the completion frequency of four kinds of statistical charts in the test center.