I. Multiple choice questions
1. Given 5m = 6, 5n = 3, the value of 5m+n is ().
A. 18 D. -3
2. If a-b = 2, the value of a2-2ab+b2 is ().
A.8b 2c 4d。
3. Given that x+y =-5 and xy = 6, the value of x2+y2 is ().
A. 1 b . 13 c . 17d . 25
4. if a > 0 and ax = 2 and ay = 3, the value of ax-y is ().
A.- 1 B
*5. If x+y = is known, the value of x2+x+y=+y2 is ().
A. BC 1 year.
Step 2 fill in the blanks
1. Given x =, y =- 1, then (x+y) 2-(x+y) (x-y) = _ _ _ _ _.
2. Given that Xn = 5, Yn = 3, the value of (xy)2n is _ _ _ _ _ _ _.
3. If (a-b) 2 = 4 and AB =, then (a+b) 2 = _ _ _ _ _.
4. If ︱ A-2 ︱+(B+) 2 = 0, then a10b10 = _ _ _ _ _.
5. Given X+Y = 4, X-Y = 10, 2xy = _ _ _ _ _ _ _
6. When s = t+, the value of algebraic expression S2-2st+t2 is _ _ _ _ _ _ _.
**7. Given that y = x- 1, the value of x2-2xy+3y2-2 is _ _ _ _ _ _ _.
Three. solve problems
1. Simplify before evaluating: (x+3) 2+(x+2) (x-2)-2x2, where x =-.
2. Given that A+B = 5 and AB = 3, find the value of A2+B2.
*3. Given x2-4 = 0, find the value of the algebraic expression x (x+ 1) 2-x (x2+x)-x-7.
**4. Given ︱ x+y-3 ︱+(x-y- 1) 2 = 0, find the value of algebraic expression [(-x2y) 2] 3.
Test answer
I. Multiple choice questions
1.C 2。 C 3。 B 4。 C 5。 B
Step 2 fill in the blanks
1. 1 2.225 3.6 4. 1 5.-42 6.7. 1
Three. solve problems
1. Solution: Original formula = 6x+5 = 3.
2. Solution: A2+B2 = (a+b) 2-2ab = 52-2× 3 =19.
3. Solution: From the known x2 = 4,
x(x+ 1)2-x(x2+x)-x-7
= x(x+ 1)[(x+ 1)-x]-x-7
=x2-7
Original formula = 4-7 =-3.
4. Tip: First get the values of x and y from "If the sum of two non-negative numbers is 0, then each non-negative number is 0", and then simplify the evaluation.
Solution: I know from the meaning of the problem, so.
So [(-x2y) 2] 3 = x12y6 =× 212×16 = 211.
Algebra problems often test knowledge points.
Zhao Hechun and Jiang Shuling
Algebraic evaluation is a necessary knowledge for senior high school entrance examination. In recent years, the proposition of senior high school entrance examination requires reducing the difficulty of calculation, avoiding complicated calculation and paying attention to examination methods and observation ability, so there are several noteworthy trends in the proposition. Taking the mid-term examination questions in 2004 as an example, this paper talks about the characteristics and solving methods of this kind of questions.
First, use formulas, holistic substitution or alternative evaluation methods.
Example 1. If x > y is known, the value of is equal to _ _ _ _ _ _ _.
Solution: from, available
Substitutes, you can get
therefore
From, you can know.
Note: This evaluation question adopts the most commonly used collocation method and overall replacement method. The focus of the exam is not calculation, but method.
Example 2. If the value of the algebra is 7, then the value of the algebra is equal to ().
A.2 B. 3 C. D. 4
Solution: from, available
that is
therefore
You should choose a.
Note: the essence of this question is substitution method, that is, it will be evaluated as S $.
For the above two problems, we can use the equation to find the value of the letter and then substitute it. Of course, you can also find the value of algebra, but it is more troublesome and requires a lot of calculation.
Second, the use of basic concepts to transform the evaluation of conditions
Example 3. If is, the value of is ()
A. 13
Solution: It can be obtained by conditional expression.
So you should choose a.
Note: The key to this problem is to transform the conditional expression by "the sum of two non-negative numbers is 0, then both numbers are 0", and the whole substitution is an important step to simplify the calculation.
Example 4. If and are opposites, then _ _ _ _ _ _ _.
Solution: The values of the two formulas are not negative, so we can see that:
By solving the system of equations consisting of two equations, we can get:
therefore
Explanation: The basic concept used in this question is that if two non-negative numbers are in opposite directions, then both numbers are 0.
The above two questions are traditional questions, but the knowledge and methods used to solve them are important test points for the proposition of the senior high school entrance examination over the years.
Third, the score simplifies the evaluation.
Example 5. Simplify first, then evaluate:, where
Solution: Original formula
Example 6. Known, evaluated.
Solution: Original formula
Note: the simplified evaluation of scores is an important test center for the senior high school entrance examination. Generally, this kind of problems should comprehensively use the knowledge of total score, polynomial multiplication and division, factorization, quadratic radical calculation, denominator rationalization and so on. To solve this kind of problem, we should observe carefully, try to find a simple method, concentrate on calculation, be careful and don't jump too many steps.
practise
1. If known, the value of is _ _ _ _ _ _ _.
2. If the real number is known, the value of xy is ().
A. the fourth century BC.
3. Known, find the value of the algebraic expression.
4. Simplify before evaluation:, in which.
answer
1.2.B 3。 4.
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