I. Arithmetic

Attribute is 1 integer, integer):

(6) x, y are integers, and x is not equal to 0. If y=xn(n is an integer), x is a divisor/factor of y, and y is a multiple of X. 。

(7) y = xq+rq-quotant quotient, r- remainder; R=0, y is divisible by x; When 5 is divided by 7, the quotient is 0 and the remainder is 5.

(8) Even-even, odd-odd

(9) Prime number-prime number: There are only two factors, 1 is not a prime number, and any integer is either a prime number or a product of several prime numbers.

(10) continuous integer: n, n+ 1, n+2. ...

Continuous even numbers: 2n, 2n+2, 2n+4 ...

Continuous odd numbers: 2n+ 1, 2n+3 ...

(22) 0 is neither positive nor negative. 0 cannot be partitioned.

2 score

(3) n/d, n numerator, d denominator: denominator (denominator cannot be 0), common denominator.

(4) If two scores represent the same number, it can be said that the two scores are equivalent.

(5) greatest common divisor: greatest common divisor, least common multiple: least common multiple (the least common multiple of A and B is C, which means that both A and B are factors of C).

(6) reciprocity.

(7) Mixed number: composed of integer and fraction * * *.

(8) Multiplication of fractions: numerator multiplied by numerator, denominator multiplied by denominator.

3 decimal places (decimal)

(1) 7654.32 1 thousand, hundred, ten, one or one bit. One tenth, one percent, one thousandth

(2) Scientific notation: notation based on 10: 231= 2.31*102, 0.0231= 2.31*/kloc-.

(3) Decimal number-decimal point-decimal point

4 Real number (real number)

(1) Real numbers correspond to points on the number axis.

(2) Except 0, all real numbers are either positive or negative.

(3) n is between 1 and 4—1

(4) Absolute value: absolute value, the absolute value of any non-zero number is positive, | x+y |

5 ratio/proportion

(1) The ratio of two to three: two to three, two to three, two to three.

(2) Proportion is a statement that two proportions are equal, for example, 2/3=8/ 12 is a proportion.

Power sum root of 6 numbers

(1) kn-n power of k

(2) Square-Square

(3) square root square root: the square root of a negative number is not a real number; Every positive number has two square roots, one positive and one negative; √n stands for positive square root, √ x2 = | x |; radical

(4) Cube roots: each real number has only 1 cube roots.

7 statistical data

(1) average: average (arithmetic average)-arithmetic average; Geometric mean-geometric mean-(the n-th root of the product of n numbers)

(2) Median median: a group of numbers are arranged from small to large, and if the number of numbers is odd, it is the middle number; If the number of numbers is even, it is the average of the middle two numbers; The median can be greater than, less than or equal to the average; For a group of very large numbers, it is possible that half of them are greater than the median and half are less than the median, but this is often not the case, for example: 3, 5, 7, 7, 7, 8, 9, 9, 10, 10.

The median is 7, but only 2/ 15 is less than the median.

(13) mode: The number with the highest frequency in a group may be more than one.

(14) indicates the degree of dispersion of a set of numbers:

Range: maximum minus minimum.

B standard deviation: the sum of the absolute values of the differences between each number in a group and the average value, and then divided by the number n of this group. For example, the standard error of 0,2,5,7,6 is: (| 0-4 |+2-4 |+| 5-4 |+| 7-4 |+| 6-4 |)/5 = 2.4.

C standard deviation variation: the sum of squares of the differences between each number in a group and the average value, and then divided by the number of the group. N examples: 0, 2, 5, 7, 6 is | (0-4) 2+(2-4) 2+(5-4) 2+(7-4) 2+(6-6).

D standard deviation standard deviation: the square root of standard deviation.

E arrays A and B, it is known that the arithmetic mean of A is greater than B, and the median of A is greater than B, so the standard deviation of A and B cannot be compared.

8 arrays:

The numbers in the (1) array are called elements.

(2) If s is an array, the number of elements in the array is represented by |S|.

(3) If all elements in the S array are elements in the T array, then S is called a subset of T..

(4) the union of two arrays A, B, A and B-the union of A and B; The intersection of a and b-the intersection of a and b; If two arrays have no common elements, they are called disjoint or mutually exclusive.

(5) venn diagram is often used to represent arrays.

(6)| S U T | = | S |+| T |-| ST |； If s and t do not intersect | s ut | = | s |+t |, because |ST|=0.

(7)| au buc | = | A |+| B |+| C |-| AB |-| BC |-| AC |+| ABC |

Nine number algorithm

(1) factorial: n! = n(n- 1)(n-2)(n-3)…… 1； 0! = 1! = 1

(2) permutation of permutation: the permutation number of any m different elements among n different elements AMN = n (n-1) (n-2) ... (n-m+1) = n! /(n-m)！ ; Amm=m！ ; An- 1n= Ann

(3) combination: cmn (n m) = n! /m！ (n-m)！ = Amn/Amm； (n k)=(n n-k)； Cmn+ Cm+ 1n= Cmn+ 1

10, discrete probability

Probability of (1) P(E) E event; 0 & lt= P(E)& lt； = 1

(2) Equal possibility

(3) E does not occur, P (not E) =1-P (E); P(E or F)=P(E)+P(F)-P(E and f)

(4) The two events A and B are independent. Assuming that B occurs, the probability of A is |AB|/|B|, that is, the occurrence of any one event will not affect the other event, then P(A and B)=P(A)P(B).

(5) A and B are two mutually exclusive events mutexes P (A or B) = P (A)+P (B).

1 1 series

(1) arithmetic progression: tolerance an = a1+(n-1) d; sn =(a 1+An)* n/2 = a 1 * n+n(n- 1)d/2

(2) Geometric series: common ratio an = a1* qn-1; Sn = (a 1-an * q)/(1-q) = a1(1-qn)/(1-q) (q is not equal to1).