分數:fractions
分子:numerator
分母:denominator
分數的加減乘除:addition,subtraction,multiplication and division of fractions
繁分數和假分數:mixed number and improper fraction
繁分數是指壹個數由壹個整數和壹個分數構成。
假分數是指分子大於分母的分數。例如:7/3
小數:decimals
科學計數法:scientific notation
Sometimes decimals are expressed as the product of a number with only one digit to the left of the decimal point and a power of 10. This is called scientific notation. For example, 231 can be written as 2.31×102 and 0.0231 can be written as 2.31×10-2. When a number is expressed in scientific notation, the exponent of the 10 indicates the number of places that the decimal point is to be moved in the number that is to be multiplied by a power of 10 in order to obtain the product. The decimal point is moved to the right if the exponent is positive and to the left if the exponent is negative. For example, 20.13×103 is equal to 20,130 and 1.91×10-4 is equal to 0.000191.
數學的基本概念附英文翻譯 21、mode(眾數)
壹堆數中出現頻率最高的壹個或幾個數,例如:mode of 1,1,1,2,3,0,0,0,5 is 1 and 0.
2、range(值域)
壹堆數中最大和最小數之差,例如:range of 1,1,2,3,5 is 5-1=4
3、mean(平均數)
arithmatic mean(算術平均數),geometric mean (幾何平均數:n個數之積的n次方根)
4、median(中數)
將壹堆數排序之後,正中間的壹個數(奇數個數字),或者中間兩個數的平均數(偶數個數字),例如:“median of 1,7,4,9,2,2,2,2,2,5,8 is 2”,“median of 1,7,4,9,2,5 is (5+7)/2=6”。
5、standard error(標準偏差)
壹堆數中,每個數與平均數的差的絕對值之和,除以這堆數的個數(n)。例如:
standard error of 0,2,5,7,6 is:
(|0-4|+|2-4|+|5-4|+|7-4|+|6-4|)/5=2.4
6、standard variation
壹堆數中,每個數與平均數之差的平方之和,再除以n,例如:standard variation of 0,2,5,7,6 is6.8
7、standard deviation
就是standard variation的平方根,標準方差的公式:d^2=[(a1-a)^2+(a2-a)^2+....+(an-a)^2 ]/n,d 為標準方差。
8. 三角形余玄定理
C^2=A^2+B^2-2ABCOSt,其中t為AB兩條線間的夾角。
9. Y=k1X+B1,Y=k2X+B2,兩線垂直的條件為K1K2=-1
10. 三的倍數的特點
所有位數之和可被3整除。