(2) the concept of absolute value of reciprocal, reciprocal and number;
(3) When the sum of non-negative numbers a2, |a| and a (a≥0) is zero, solve related problems.
(4) Investigate the real number operation (operation type of rational number, various operation rules, operation rules, operation sequence, scientific counting method, divisor and significant number, calculator function key and its application. )
2. Algebraic expressions and fractions.
Knowledge points of algebra: algebra, algebraic values, algebraic expressions, similar terms, merging similar terms, bracket removal and bracket removal rules, power operation, algebraic addition, subtraction, multiplication, division and power operation, multiplication formula and factorization.
The key points of algebraic expression examination: (1) Examining the ability of column algebra; (2) Investigate the operation of integer exponential power and zero exponent.
(3) Mastering and flexibly using common factor method and formula method (directly using the formula no more than twice) for factorization.
Score:
Key points of score examination: (1) Examine the operation of integer exponential power, zero operation; (2) Investigate the simplified evaluation of scores.
3. Quadratic radical. Formula (a≥0) is called quadratic radical.
Focus of investigation: (1) Understanding the concepts of quadratic root, simplest quadratic root and similar quadratic root can distinguish the simplest quadratic root from similar quadratic root. If you master the properties of quadratic roots, you will simplify the simple quadratic roots and simplify the quadratic roots according to the scope of the specified letters;
(2) Mastering the algorithm of quadratic root, being able to perform four operations of addition, subtraction, multiplication and division of quadratic root, and rationalizing simple denominator.
New exercise:
New question 1: between real numbers-,0, -3. 14,-0. 1 00 1 … (between every two1,there is/kloc in turn.
1。
Analysis: the classification of real numbers should be judged by the final result, not just by the superficial form. Firstly, the concept of irrational number is defined, that is, "infinite acyclic decimal is called irrational number" Generally speaking, a number represented by a radical sign is not necessarily an irrational number, for example, =2 is a rational number, and the key lies in whether the final result of this form of a radical number is an infinite acyclic decimal. Similarly, the number represented by the triangle symbol is not necessarily irrational. Such as sin30, tan45, etc. , and -0. 10 100 1 ... although they are regular, they are infinite acyclic decimals, irrational numbers, not fractions. Of the real numbers given above, only,, -0.
Answer: c
Question 2: It is known that X and Y are real numbers and +(y2-6y+9) = 0. If AXY-3x = Y, the value of real number A is ().
A.b .-c . d-
Analysis: If the sum of several non-negative numbers is equal to zero, then each non-negative number is equal to zero. This is an important property of nonnegative numbers. In this problem, ∵ and (y-3) 2 are both non-negative, and their sum is zero, only 3x+4=0, y-3 = 0, from which the values of x and y can be obtained and substituted into AXY-3x =.
Answer: +(y-3) 2 = 0 ∴ 3x+4 = 0, y-3 = 0 ∴ x =-, y = 3.
∵ AXY-3x = Y, ∴-× 3a-3x (-) = 3 ∴ A = ∴ Choose A.
Question 3: If A, B and C are the lengths of three sides of a triangle, then the value of the algebraic formula A2+B2-C2-2AB ().
A. greater than zero B. less than zero C. greater than or equal to zero D. less than or equal to zero
Analysis: This question is a comprehensive question to determine the value range of algebraic and factorial decomposition. Factorizing some factors of a given polynomial, combined with "A, B and C are three sides of a triangle", is a common method to solve this kind of problem.
Answer: (1) ∵ A2+B2-C2-2ab = (A2-2ab+B2)-C2 = (a-b) 2-C2.
=(a-b+c)(a-b-c)，
A, b and c are the lengths of three sides of a triangle.
∴a+c>； B, a-b-C & lt；B+c, that is, A-B+C > 0, a-b-c <; 0
∴(a-b+c)(a-b-c)<； 0
That is, a2+B2-C2-2ab < 0, so choose B.
New question 4: Simplify first, and then please take any suitable number as the value of x for evaluation.
Analysis: This topic examines the factorization of algebraic expressions and the mixed operations of addition, subtraction, multiplication and division of fractions, paying attention to the operation order. Multiply first, then divide, then add and subtract. If there are brackets, count them first or remove them according to the distribution law of multiplication.
When choosing the value, we should consider the meaning of the score, that is, x ≠ 2.
Answer: Original formula =
(X can be used as long as it doesn't need 2)
Take x=6 to get the original formula = 1.
On Two Equations (Groups) and Inequalities (Groups)
Kaoban hotpot
1. One-dimensional linear equation.
Knowledge points: equation and its basic properties, equation, solution of equation, solution equation, linear equation.
Key points: master the general steps of solving a linear equation, and skillfully solve a linear equation.
2. Binary linear equations (groups).
Understand binary linear equations and their solutions, and flexibly use method of substitution and addition and subtraction to solve binary linear equations.
Emphasis: master the idea of elimination, skillfully solve binary linear equations, and solve some simple practical problems with binary linear equations.
Difficulties: the idea of combining numbers and shapes to solve binary linear equations by mirror method.
3. One-variable quadratic equation.
Knowledge points: quadratic equation of one variable, solving quadratic equation of one variable and its application, discriminant of roots of quadratic equation of one variable, and the relationship between discriminant and the number of roots.
Key points: (1) Understanding the concept of quadratic equation with one variable will turn quadratic equation with one variable into a general form;
(2) Solving the quadratic equation with one variable by collocation method, formula method and factorization method;
(3) The mathematical model of quadratic equation with one variable can be used to solve practical problems.
4. Fractional equation.
Key points: (1) can solve fractional equation, and the basic idea is to transform fractional equation into integral equation;
(2) Fractional equation and its practical application.
5. Unary linear inequality (group).
Knowledge points: concept of inequality, basic properties of inequality, solution set of inequality, solution set of inequality, solution set of inequality group, solution set of inequality group, unary linear inequality, unary linear inequality group and application of unary linear inequality group.
Focus of examination: examine the ability to solve linear inequalities (groups).
New exercise:
Question 1: If the solution of the equation about x is known, then the value of m is _ _ _ _ _ _ _.
Analysis: This question examines the significance of the solution of a linear equation with one variable. Because it is the solution of this equation, the process of substitution is still valid, that is, to solve this equation about m, m = 2.
Answer: m=2
Question 2: If the solution of binary linear equations about X and Y is also the solution of binary linear equations, then the value of k is
A.B. C. D。
Analysis: By substituting equation 2x = 14k, y =-2k, 14k-6k = 6, the solution is k =.
Answer: b
New question 3: Solving equations:
Analysis: according to the characteristics of the equation, choose flexible methods to solve the equation. Observe the characteristics of this problem and solve it with collocation method.
Answer:
Question 4: Solve the equation:.
Analysis: From the concept of fractional equation, we can know that this equation is a fractional equation, so we should choose the denominator removal method according to its characteristics, and we must check the root when solving this equation. The specific method to solve fractional equation by denominator removal method is: after decomposing the denominator of the equation into factors, find out the simplest common denominator of the denominator; Then multiply both sides of the equation by the simplest common denominator and turn the fractional equation into an integral equation. Finally, we must attach importance to the root test and master the root test method in solving fractional order equations.
Answer: Solution: (x-2) 2-(x2-4) = 3.
-4x=-5。 x=。
X = is the solution of the original equation.
I wish you good grades and relax!