Eight-grade mathematics knowledge points
Collection, collation and description of data
I. Knowledge framework
Two. The concept of knowledge
1. Comprehensive survey: The survey method for all the subjects is called comprehensive survey.
2. Sampling survey: The survey method of investigating some data and estimating the whole according to some data is called sampling survey.
3. Population: All the investigated objects are called population.
4. Individuals: Each survey object that constitutes the population is called an individual.
5. Sample: All the extracted individuals constitute a sample.
6. Sample size: The number of individuals in a sample is called sample size.
7. Frequency: Generally speaking, the number of times the data falls into different groups is called the frequency of that group.
8. Frequency: The ratio of frequency to total data is frequency.
9. Number of groups and distance between groups: When counting data, the data is divided into several groups according to a certain range, and the number of groups is called the number of groups, and the difference between the two ends of each group is called the distance between groups.
Sorting out the knowledge points of eighth grade mathematics
A preliminary understanding of statistics
1, broken-line statistical chart: you can get the information of data changes and make simple predictions.
2. The method of broken-line statistical chart: on the grid paper, mark the points according to the given data, and then connect the points with lines in order.
3. Be able to see the information provided by the dotted statistical chart and answer related questions.
Supplementary content:
1. The difference between a bar chart and a line chart: a bar chart indicates the quantity with a straight line, and a line chart indicates the change of quantity with a broken line.
2. Have a preliminary understanding of the statistical chart of compound broken lines, from which we can get the corresponding information and answer the questions raised.
homework
1. The basic meaning of statistics is (d).
A. Statistical information
B. Statistics
C. Statistical activities
D is the science of data processing methods and techniques, or statistics is the science of studying "data". The task is how to effectively collect, sort out and analyze these data, explore the inherent quantitative regularity of the data, and make inferences or predictions about the observed phenomena until it provides a basis for decision-making.
2. Understand the production and operation of state-owned industrial enterprises in a certain area, and the overall statistics are (b).
A. Every state-owned industrial enterprise
B. All state-owned industrial enterprises in the region
C. Production and operation of all state-owned industrial enterprises in this region
D. Every enterprise
3. To understand the learning situation of 20 students, the overall unit is (C).
A.20 students
B. Learning situation of 20 students
C. Every student
D. Learning situation of each student
4. Among the following items, (b) is a quantitative symbol.
A. Gender
B. Age
C. Professional title
D. Health status
5. The whole and the whole unit are not fixed, but change because of the research purpose (a).
A. the whole unit can be transformed into the whole unit, and the whole unit can also be transformed into the whole unit.
B the whole can only be transformed into a whole unit, and the whole unit cannot be transformed into a whole.
C the whole unit cannot be converted into the whole unit, nor can the whole unit be converted into the whole unit.
D any pair of population and population units can be converted to each other.
6. Take laid-off workers as a whole and observe the gender composition of laid-off workers. At this time, the symbol is (c).
A. Number of male employees
B. Number of female employees
C. Gender of laid-off workers
D. Gender composition
Mathematics review materials in the second volume of the eighth grade
Zero exponential power and negative integer exponential power
Important point: The nature of power (exponents are all integers) will be used in calculation and scientific notation to represent some numbers with smaller absolute values.
Difficulties: Understanding and applying the properties of integer exponential power.
First, review the exercises:
1、; =; =,=,=。
2. Calculation without calculator: ⊙(-2)2-2- 1+
Second, the scope of the index has been extended to all integers.
1, explore
Now, we have introduced zero exponential power and negative integer power, and the range of exponent has been extended to all integers. Then, is the essence of power learned in the operation of power still valid? Discuss with your classmates and judge whether the following formula is true.
( 1); (2)(a？ b)-3 = a-3 B- 3； (3)(a-3)2=a(-3)×2
2. Summary: After the range of exponent is extended to all integers, the arithmetic of power is still valid.
3. Example 1 calculates (2mn2)-3(mn-2)-5, and converts the result into a form containing only positive integer exponential powers.
Solution: The original formula = 2-3m-3n-6× m-5n10 = m-8n4 =
Exercise: Calculate the following categories and convert the results into a form that only contains positive integer exponential powers:
( 1)(a-3)2(ab2)-3； (2)(2mn2)-2(m-2n- 1)-3。
Third, scientific notation.
1. Memories: In previous studies, we used scientific notation to represent some numbers with large absolute values, that is, using the positive integer power of 10, we expressed the numbers with absolute values greater than 10 as a× 10n, where n is a positive integer,1≤ For example, 864000 can be written as 8.64× 105.
2. Similarly, we can use the negative integer power of 10 to express some numbers with smaller absolute values by scientific notation, that is, in the form of a× 10-n, where n is a positive integer,1≤∣∣∣∣.
3. Explore:
10- 1=0. 1
10-2=
10-3=
10-4=
10-5=
Induction: 10-n=
For example, 0.00002 1 in the above example 2(2) can be expressed as 2. 1× 10-5.
4. Example 2. The diameter of nanoparticles is 35 nanometers. How many meters is it equal to? Please use scientific symbols.
The analysis shows that:1nm = m. From = 10-9, we can know that1nm =10-9 m.
So 35 nm =35× 10-9 meters.
And 35×10-9 = (3.5×10 )×10-9.
=35× 10 1+(-9)=3.5× 10-8,
So the diameter of this nanoparticle is 3.5× 10-8 meters.
Step 5 practice
(1) expressed in scientific notation:
( 1)0.00003; (2)-0.0000064; (3)0.00003 14; (4)20 13000.
② Fill in the blanks with scientific symbols:
(1) 1 sec is 1 microsecond 100000 times, then 1 microsecond = _ _ _ _ _ _ _ sec;
(2) 1mg = _ _ _ _ _ _ _ kg；
(3) 1 micron = _ _ _ _ _ _ meters; (4) 1 nanometer = _ _ _ _ _ _ micron;
(5) 1 cm2 = _ _ _ _ _ m2; (6) 1 ml = _ _ _ _ _ cubic meters.
Summarize and sort out the relevant articles about the knowledge points of mathematics in senior two;
★ Summary of mathematics knowledge points in senior two.
★ Sort out and summarize the knowledge points of Grade 2 mathematics.
★ Sort out and summarize the knowledge points of eighth grade mathematics.
★ The arrangement of mathematics knowledge points in the second volume of the eighth grade
★ Review and arrangement of mathematics knowledge points in Grade Two.
★ Summary of knowledge points in the first volume of Mathematics in the second day of junior high school
★ The first volume of mathematics knowledge points induction of the second grade teaching edition.
★ Summarize the knowledge points of senior two mathematics.
★ Summarize and sort out the key knowledge of senior two mathematics.
★ Knowledge point induction and mathematics learning methods in the second volume of junior two mathematics.