1. The following calculation is correct ()
A.a2+b3=2a5B.a4÷a=a4C.a2a3=a6D。 (﹣a2)3=﹣a6
2. The calculation result of (x-a) (x2+ax+a2) is ().
a.x3+2ax+a3b.x3﹣a3c.x3+2a2x+a3d.x2+2ax2+a3
3. The following excerpt is from a classmate's calculation in an exam:
①3x3(﹣2x2)=﹣6x5 ②4a3b÷(﹣2a2b)=﹣2a ③(a3)2=a5④(﹣a)3÷(﹣a)=﹣a2
The correct number is ()
1。
4. If x2 is the square of a positive integer, then the square of the integer after it should be ().
a.x2+ 1b.x+ 1c.x2+2x+ 1d.x2﹣2x+ 1
5. The following decomposition factor is correct ()
a.x3﹣x=x(x2﹣ 1)b.m2+m﹣6=(m+3)(m﹣2)c.(a+4)(a﹣4)=a2﹣ 16d.x2+y2=(x+y)(x﹣y)
6. As shown in the figure, in the rectangular garden ABCD, AB=a, AD=b, there is a rectangular road LMPQ and a parallelogram road RSTK. In the garden. If LM=RS=c, the area of the green part in the garden is ().
a.bc﹣ab+ac+b2b.a2+ab+bc﹣acc.ab﹣bc﹣ac+c2d.b2﹣bc+a2﹣ab
Answer:
1, test site: division in the same base power; Merge similar projects; Multiplication with the same base; Power and products. 1923992
Analysis: according to the division of the same base number, subtract the index of the same base number; Same base powers multiplication, exponential addition of base constant; Multiply the power by the exponent of the same base number, and each option is calculated and solved by exclusion method.
Solution: Solution: A, a2 and b3 are not similar items and cannot be merged, so this option is wrong;
B, it should be a4÷a=a3, so this option is wrong;
C, should be a3a2=a5, so this option is wrong;
D, (-A2) 3 =-A6, correct.
So choose D.
Comments: This topic examines the properties of merging similar terms, division of same base powers, multiplication of same base powers and idempotency of power. Mastering the essence of operation is the key to solving the problem.
2.
Test center: polynomial multiplication polynomial. 1923992
Analysis: According to the rule of polynomial multiplication, multiply each term of one polynomial with each term of another polynomial, and then add the products to calculate.
Solution: solution: (x-a) (x2+ax+a2),
=x3+ax2+a2x﹣ax2﹣a2x﹣a3，
=x3﹣a3.
So choose B.
Comments: This question examines the law of polynomial multiplication. When merging similar items, pay attention to whether the indexes and letters in the items are the same.
3.
Test center: single item multiplied by single item; The power of power and the power of products; The division of power with the same base; Division of algebraic expressions. 1923992
Analysis: According to the law of single item multiplication, the law of single item division, the nature of power and the division of same base powers, the options are calculated and solved by exclusion method.
Solution: Solution: ①3x3(﹣2x2)=﹣6x5, correct;
② 4a3b ÷ (-2a2b) =-2a, correct;
③ It should be (a3)2=a6, so this option is wrong;
④ It should be (﹣ a) 3 ﹣ (﹣ a) = (﹣ a) 2 = A2, so this option is wrong.
So ① ② Two items are correct.
So choose B.
Comments: This topic examines the single item multiplication, single item division, power of power, and division of same base powers. Pay attention to master all the algorithms.
four
Test center: complete square formula. 1923992
Special topic: calculation problems.
Analysis: first find the following integer x+ 1, and then solve it according to the complete square formula.
Solution: x2 is the square of a positive integer, followed by x+ 1.
The square of an integer after it is: (x+ 1) 2 = x2+2x+ 1.
So choose C.
Comments: This question mainly examines the complete square formula, and memorizing the formula structure is the key to solving the problem. Complete square formula: (ab) 2 = A2AB+B2.
5,
Test sites: factorization-cross multiplication, etc. The significance of factorization. 1923992
Analysis: According to the definition of factorization, a polynomial is transformed into the product of several algebraic expressions. The deformation of this formula is called factorization of this single item, and the result of factorization should be correct.
Solution: A, x3-x = x (x2-1) = x (x+1) (x-1), and the decomposition is incomplete, so this option is wrong;
B, decompose m2+m﹣6=(m+3)(m﹣2) by cross multiplication, which is correct;
C, algebraic multiplication, not factorization, so this option is wrong;
D, there is no square sum formula, x2+y2 can't decompose the factor, so this option is wrong.
So choose B.
Comments: This question examines the definitions of factorization and cross factorization. Note: (1) factorization is a polynomial, and the result of factorization is a product. (2) Factorization must be thorough until it can no longer be decomposed.
6.
Test center: column algebra. 1923992
Special topic: application problem.
Analysis: the area of the green part =S rectangle ABCD-s rectangle LMPQ-s? The overlapping part of RSTK+.
Solution: ∫ The area of rectangle is ab, the area of rectangular road LMPQ is bc, the area of parallelogram road RSTK is ac, and the overlapping area of rectangle and parallelogram is C2.
The area of the green part is AB-BC-AC+C2.
So choose C.
Comments: It should be noted that the overlapping part of the pavement is a parallelogram with an area of c2.
When using letters to represent numbers, pay attention to writing:
① Multiplication symbols in algebraic expressions are usually abbreviated as ""or omitted, and numbers are usually multiplied by numbers with "×";
(2) When there is a division operation in the algebraic expression, it is generally written in fractional form;
③ Numbers are generally written in front of letters;
Those with scores should be written as fake scores.