Basic knowledge of mathematics algebra in senior one must be tested.
1. Algebraic expression: Use operation symbols? + - ? The formula of the number of connections and the letters representing the number is called algebraic expression. Note: There are certain restrictions on using letters to represent numbers. First, the number obtained by letters should ensure that its formula is meaningful, and second, the number obtained by letters should also make real life or production meaningful; A single number or letter is also algebraic.
2. Some points for attention in column algebra:
(1) Are commonly used numbers multiplied by letters or letters multiplied by letters? Multiply, or omit not to write;
(2) Do you still want to use the number multiplier? Take it, don't you Multiplication, multiplication sign cannot be omitted;
(3) When a number is multiplied by a letter, the number is usually written in front of the letter in the result, such as A? 5 should be written as 5a;
(4) When multiplying the band fraction with letters, change the band fraction to a false fraction, such as A? It should be written as a;
(5) When there is a division operation in the algebraic expression, a fractional line is generally used to connect the divided expression with the divided expression, such as 3? Written form;
(6) The difference between A and B should be written in alphabetical order; If we only talk about the difference between two numbers, when we set two numbers as A and B respectively, we should classify them and write them as a-b and B-A. 。
3. Several important algebraic expressions: (m and n represent integers)
(1) The square difference between A and B is: A2-B2; The square of the difference between a and b is: (a-b) 2;
(2) If a, b and c are positive integers, the two-digit integer is 10a+b and the three-digit integer is10a+10b+c;
(3) If both m and n are integers, the quotient m is divided by 5, and the remainder n is 5m+n; Even number is 2n, and odd number is 2n+1; Three consecutive integers are: n- 1, n, n+1;
(4) If b>0, positive number is: a2+b, negative number is: -a2-b, non-negative number is: a2, and non-positive number is: -a2.
The knowledge points of rational number in junior one mathematics must be tested.
1. rational number:
(1) Any number that can be written in form is a rational number. Positive integers, 0 and negative integers are collectively referred to as integers. Positive and negative scores are collectively called scores; Integers and fractions are collectively called rational numbers. Note: 0 is neither positive nor negative; -a is not necessarily negative, and +a is not necessarily positive; Not a rational number;
(2) Classification of rational numbers: ① ②
(3) Note: among rational numbers, 1, 0 and-1 are three special numbers with their own characteristics; These three numbers divide the numbers on the number axis into four areas, and the numbers in these four areas also have their own characteristics;
(4) Natural number 0 and positive integer; A>0 a is a positive number; A<0 a is a negative number;
Answer? 0 a is positive or 0 a is non-negative; Answer? 0 a is negative or 0 a is not positive.
2. Number axis: The number axis is a straight line that defines the origin, positive direction and unit length.
3. The opposite number:
(1) There are only two numbers with different signs, and we say that one of them is opposite to the other; The antonym of 0 is still 0;
(2) Note: The inverse of a-b+c is-A+B-C; The inverse of a-b is b-a; The inverse of a+b is-a -a-b；;
(3) The sum of opposites is 0 a+b=0 a, and b is the reciprocal.
4. Absolute value:
(1) The absolute value of a positive number is itself, the absolute value of 0 is 0, and the absolute value of a negative number is its inverse; Note: the absolute value means the distance between the point representing a number on the number axis and the origin;
(2) The absolute value can be expressed as: or; The problem of absolute value is often discussed in categories;
(3) ; ;
(4) |a| is an important non-negative number, that is |a|? 0; Note: |a|? |b|=|a？ b|，。
5. Rational number ratio: (1) The greater the absolute value of a positive number, the greater the number; (2) Positive numbers are always greater than 0 and negative numbers are always less than 0; (3) Positive numbers are greater than all negative numbers; (4) The absolute values of two negative numbers are larger than the size, but smaller; (5) Of the two numbers on the number axis, the number on the right is always greater than the number on the left; (6) large number-decimal number >; 0, decimal-large number < 0.
6. Reciprocal: Two numbers whose product is 1 are reciprocal; Note: 0 has no reciprocal; If a? 0, the reciprocal is; Is the reciprocal its own number? 1; If ab= 1 a and b are reciprocal; If ab=- 1 a and b are negative reciprocal.
7. The rational number addition rule:
(1) Add two numbers with the same symbol, take the same symbol, and add the absolute values;
(2) Add two numbers with different symbols, take the symbol with larger absolute value, and subtract the one with smaller absolute value from the one with larger absolute value;
(3) Adding a number to 0 still gets this number.
8. Arithmetic of rational number addition:
The commutative law of (1) addition: a+b = b+a; (2) The associative law of addition: (a+b)+c=a+(b+c).
9. Rational number subtraction rule: subtracting a number is equal to adding the reciprocal of this number; That is, a-b=a+(-b).
10 rational number multiplication rule:
(1) Multiply two numbers, the same sign is positive, the different sign is negative, and the absolute value is multiplied;
(2) Multiply any number by zero to get zero;
(3) When several numbers are multiplied, one factor is zero and the product is zero; Each factor is not zero, and the sign of the product is determined by the number of negative factors.
1 1 rational number multiplication algorithm;
(1) The commutative law of multiplication: ab = ba(2) The associative law of multiplication: (AB) C = A (BC);
(3) Distribution law of multiplication: a(b+c)=ab+ac.
12. rational number division rule: dividing by a number is equal to multiplying the reciprocal of this number; Note: Zero cannot be divisible.
13. Power Law of Rational Numbers:
(1) Any power of a positive number is a positive number;
(2) The odd power of a negative number is a negative number; Even the power of negative numbers is positive; Note: When n is positive odd number: (-a)n=-an or (a -b)n=-(b-a)n, when n is positive even number: (-a)n =an or (a-b) n = (b-a) n. 。
14. Definition of power:
(1) The operation of seeking common ground factor product is called power;
(2) In power, the same factor is called base, the number of the same factor is called exponent, and the result of power is called power;
(3)a2 is an important non-negative number, that is, a2? 0; If a2+|b|=0 a=0, b = 0；;
(4) According to the law, the decimal point of the cardinal number moves by one place and the decimal point of the square number moves by two places.
15. scientific notation: write a number greater than 10 as a? 10n, where a is an integer with only one bit. This notation is called scientific notation.
16. Approximation precision: a divisor rounded to that bit, that is, the divisor is accurate to that bit.
17. Significant digits: All digits from the first non-zero digit on the left to the exact digit are called significant digits of this approximation.
18. Mixed algorithm: multiply first, multiply then divide, and finally add and subtract; Note: How to calculate simply and accurately is the most important principle of mathematical calculation.
19. special value method: it is a method of substituting numbers that meet the requirements of the topic into speculation to verify the establishment of the topic, but it cannot be used for proof.
Knowledge points of addition and subtraction of algebraic expressions in junior high school mathematics must be tested.
1. monomial: in algebraic expressions, if only multiplication (including power) operations are involved. Or algebraic expressions that contain division but do not contain letters in division are called monomials.
2. The coefficient and times of single item: the non-zero numerical factor in single item is called the numerical coefficient of single item, which is simply referred to as the coefficient of single item; When the coefficient is not zero, the sum of all the letter indexes in a single item is called the degree of the item.
3. Polynomial: The sum of several monomials is called polynomial.
4. Number and degree of polynomials: the number of monomials contained in a polynomial is the number of polynomial terms, and each monomial is called a polynomial term; In polynomials, the degree of the term with the highest degree is called the degree of polynomials; Note: (If A, B, C, P and Q are constants) ax2+bx+c and x2+px+q are two common quadratic trinomials.
5. Algebraic expression: Any algebraic expression that does not contain division operation or contains division operation but does not contain letters in the division formula is called algebraic expression.
Algebraic expressions are classified as:
6. Similar items: monomials with the same letters and the same index are similar items.
7. Rules for merging similar items: When the coefficients are added, the letter index remains unchanged.
8. Rules for deleting (adding) brackets: When deleting (adding) brackets, if there is? +? No, the items in brackets remain unchanged; What if it's in front of parentheses? -? No, all items in brackets should be changed.
9. Algebraic addition and subtraction: Algebraic addition and subtraction is actually to combine similar terms of polynomials on the basis of removing brackets.
10. Ascending power and descending power arrangement of polynomials: arrange the items of a polynomial from small to large (or from large to small) according to the exponent of a letter, which is called ascending power arrangement (or descending power arrangement). Note: The final result of polynomial calculation should generally be ascending power (or descending power arrangement).
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