The second volume of eighth grade mathematics knowledge points (1) quadratic root.
1. Quadratic root: Generally speaking, the formula, (a? 0) is called quadratic radical. Note: (1) If a? If this condition does not hold, then A is not a quadratic radical; (2) is an important non-negative number, that is; Answer? 0.
2. Important formula: (1)((a? 0)? a； Pay attention to using a? (a)2(a？ 0).
a)2？ a(a？ 0)，(2)a2？ aa(a？ 0)
? Answer? b(a？ 0，b？ 0), the arithmetic square root of the product is equal to the product of the arithmetic square root of each factor in the product; Note: Formulas in this chapter generally require a range of letters.
4. the multiplication rule of quadratic root: a? b？ ab(a？ 0，b？ 0).
5. Quadratic root comparison method:
(1) Compare sizes with approximate values;
(2) Move the coefficient of the quadratic root into the quadratic root number, and then compare the sizes;
(3) Square separately and then compare the sizes.
Divide by the arithmetic square root of the formula. a(a？ 0，b？ 0), the arithmetic square root of quotient is equal to the arithmetic square root of divisor divided by b.
7. Division rule of quadratic roots: (1)? a(a？ 0，b？ 0); (2) a? b？ Answer? b(a？ 0，b？ 0); b
(3) The denominator is rational: removing the radical sign in the denominator is called denominator rationalization; The specific method is: multiply the numerator and denominator of the fraction.
The denominator has physical and chemical factors, which makes it an algebraic expression. 8. Commonly used denominators are physical and chemical factors:
They are also called mutual rational factors. Also, a? B and a? B, mom? Nb and ma? nb，
Eighth grade Zhejiang Education Edition (II) Volume II Mathematical knowledge points One-variable quadratic equation
1, know a quadratic equation:
Concept: contains only one unknown, which can be converted into ax2? bx？ c？ 0 (a, b, c are constants, a? 0) is called quadratic equation.
Three important conditions for forming a quadratic equation with one variable;
(1), the equation must be an integral equation (the denominator does not contain the unknown equation).
22 For example: x23? 0 is a fractional equation, so x23? 0 is not a quadratic equation. Eighth grade, the second book of mathematical knowledge points, Zhejiang Education Edition.
(2), contains only one unknown.
③ The maximum number of unknowns is 2.
2, the general form of quadratic equation:
General form: ax2? bx？ c？ 0 (a？ 0), among the coefficients A, B and C, A must not be 0, while B and C can be 0.
Therefore, the following situations are all quadratic equations with one variable:
1. If b? 0，c？ 0, you get ax2? c？ 0, for example: 3x2? 2? 0;
2. if b? 0，c？ 0, you get ax2? bx？ 0, for example: 3x2? 4x？ 0;
3. if b? 0，c？ 0, you get ax2? 0, for example: 3x2? 0;
4. if b? 0，c？ 0, you get ax2? bx？ c？ 0, for example: 3x2? 4x？ 2? 0。
Among them, ax2 is called quadratic term, and A is called quadratic term coefficient; Bx is called a linear term, and b is called a linear term coefficient; C is called a constant term. Ordering of any unary quadratic equation (removing brackets, shifting terms, merging similar terms? ) can be simplified to a general form.
A preliminary study on the data analysis of mathematics knowledge points in the second volume of the eighth grade (Zhejiang Education Edition) (3)
1, average
The average value is the characteristic number to measure the sample (find a set of data) and the average level of the population. The average value of the sample is usually used to estimate the average level of the population.
Average: the quotient obtained by dividing the sum of a set of data by the number of the set of data. The average reflects the average level of a set of data, and the average is divided into arithmetic average and weighted average.
1(x 1？ x2？ x3？ Xn) generally has n numbers: x 1, x2, x3? , xn, we call n the arithmetic flat of this n number.
The average value is abbreviated as the average value and recorded as x (pronounced as? X pull? )
(Definition method)
When there are duplicate data in a given set of data, the weighted average formula is usually used.
And f 1+f2++fk=n (weighting method), where f 1, f2, f3? Fk represents the number of the same data, which is called weight. Right? The greater the influence on the average, the denominator of the weighted average is only the sum of weights.
When a given set of data fluctuates around a constant a, a simplified average formula is generally adopted.
Where a is compared with the average value of this set of data. The whole? Number of; ? ,
2. Mode and median
Mean, mode and median are all quantities used to describe the trend of data sets. The size of the average is related to every data, and the fluctuation of any number will cause the fluctuation of the average.
When one data in a set of data is too high or too low, it is not appropriate to describe the overall trend with the average value, but it is more appropriate to use the median or the mode. The median is related to the arrangement of data, and the fluctuation of individual data has no effect on the median;
When a group of data has a lot of repeated data, it can be described by patterns.
Mode: the number with the highest frequency (sometimes more than one) in a set of data is called the median of the mode of this set of data: arrange a set of data in order of size, and call the middle number (or the average of two numbers) as the median of this set of data.
Example 1. Find the average, median and mode of the following set of data.