Equipment overview:

Through the process of expressing quantitative relations with letters, we can further understand the meaning of letters expressing numbers in real situations, develop the sense of symbols, explore the algorithmic process of algebraic expressions, understand the arithmeticity of algebraic expressions, further develop the ability of observation, induction, analogy and generalization, develop the ability of orderly thinking and language expression, and understand the meaning of integer exponential power and the operational nature of positive integer exponential power. Understand the background and concept of algebra, and can do simple algebra addition, subtraction, multiplication and Divison. I can deduce the multiplication formula, understand the geometric background of the formula and make simple calculations.

1. 1 algebraic expression

I. Target navigation

1. Further understand the meaning of using letters to represent numbers in real situations and cultivate a sense of symbols.

2. Knowing the background and concept of algebraic expression, we can find the degree of algebraic expression, the coefficient of single term, the coefficient and degree of polynomial.

3. Cultivate students' ability to observe, analyze and summarize, so that students can initially understand the dialectical relationship between the special and the general.

2. Basic clearance

1. Fill in the following algebraic numbers in the brackets of the corresponding set: a.3-xy, b.3-x2+; c； d； EF.x3g . x3-a2 x2+x； h . x+y+z； Me.

(1). The monomial set {} (2). Polynomial set {}

(3). Quadratic itemset {0 }(4). Cubic polynomial set {}

(5). Non-algebraic expression set {}

The radius of a circle is r, which is five times the radius of another circle. What is the sum of the perimeters of these two circles? ___________.

3. If you dig a small cube with a side length of A inside a sphere with a radius of R, what is the remaining geometry? The volume of is _ _ _ _ _ _ _.

4.4a2+2a3- ab2c+25 is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

5. If (3m-2)x2 is a quintic monomial with a coefficient of 1 about x and y, then m = _ _ _ _ _, n? =______.

6. If the letter factor of a single item is a3b2c, and A = 1, B = 2, and C = 3, then the value of this single item is 4,? Then this monomial is _ _ _ _ _ _ _.

7. With regard to the cubic trinomial formula of X, the cubic term coefficient is 3, the quadratic term coefficient is -2, and the linear term coefficient is-1. Then this cubic trinomial is _ _ _ _ _ _ _.

8. A computer, the purchase price is 1000 yuan/set, and it will be sold after the price is increased by 10%. This computer is _ _ _ thousand yuan/set. Later, the price was reduced by 5%, and the price after the price reduction was _ _ _ _ _ _ _ thousand yuan/set.

9. The following statement is true ()

A.x3yz2 has no coefficient; B. it is not an algebraic expression;

C.42 is a monomial; D.8x-5 is a linear binomial.

10. Algebraic expressions 4a2b+3ab2-2b2+a3 are arranged in ascending order of a ().

A.-2 B2+3ab 2+4a2b+a3 b . a3+4a2b+3ab 2-2 B2

c . 4a2b+3ab 2-2 B2+a3 d . 4a2b+3ab 2+a3-2 B2

1 1. The algebraic expression (x2+y2) is ().

A. single item; B. polynomials; C. it is neither a monomial nor a polynomial. D. it is impossible to judge.

12. If a polynomial is a quintic polynomial, then ()

A. This polynomial has at most 6 terms. B. This polynomial can only have one term of degree 5.

C. This polynomial must be a quintic six-term formula D. Does this polynomial have at least two terms and one term? The number of times is five

13. It is known that -│m│ab3 is a monomial about A and B, and │m│=2. What is the coefficient of this monomial? ( )

A.B. 1 C.- 1 D. 1

Three. Capacity improvement

14. The distance of a person going up and down the mountain is s. If the speed of going up the mountain is V 1, the speed of going down the mountain is V2? What is the average speed of this person going up and down the mountain?

15. When a is what value, simplify the formula (2-7a)x3-3ax2-x+7 to get the quadratic trinomial about x?

16. The known polynomial is a quartic polynomial, and the degree of the monomial is the same as that of this polynomial. What? The value of n.

4. Collect sand and make a tower

If the polynomial x2+2kxy-3y2+x- 12 contains no xy term, find the value of k3- 1.

Addition and subtraction of algebraic expression 1.2

I. Target navigation

1. Experience and letters represent the process of quantitative relationship and develop a sense of symbol. Mao (surname)

2. Can add and subtract algebraic expressions, and can explain arithmetic, and cultivate the ability of organizational thinking and language expression.

2. Basic clearance

1. The sum of the monomials 2xy, 6xy2, -3xy and -4xy2 is _ _ _ _ _ _. Mao.

2. Subtract the monomial from -3x2, and the difference between -5x2 and 2x2y is _ _ _ _ _ _ _.

3. If sum is similar, then m+n = _ _ _ _ _ _.

4. The result of calculating (3a2+2a+ 1)-(2a2+3a-5) is _ _ _ _ _ _ _.

5. The single digit number is A, the tenth digit number is B, and the hundredth digit number is C? The difference between the single digit and the last three digits of the hundred digit position is _ _ _ _ _ _.

6. Given a = 3x2y-4y3 and b =-x2y2+2y3, then 2a-3b = _ _ _ _ _ _ _ _

7.=_________.

8. The difference between polynomials and is _ _ _ _ _.

9. If one side of a rectangle is 2a+3b and the other side is a-b larger than it, then the circumference of this rectangle is equal to ().

a . 3a+2b b . 6a+4b c . 4a+6b d . 10a+ 10b

10. The sum of polynomial x4-3x3+9x+2 and polynomial 3x3-x4+8-4x must be ().

A. even B. odd C.2 and multiples of 5 D are not correct.

1 1. In the following operations, the correct result is ().

a . 4+5ab = 9ab b . 6xy-x = 6y c . 6a 3+4 a3 = 10a 6d . 8a2b-8ba 2 = 0

12. Let x represent two digits and y represent four digits. For example, put X to the left of Y to form a six-digit number, which is expressed by algebra as ().

a . xy b . 10000 x+y c . x+y d . 1000 x+y

13. For rational numbers A and B, define a⊙b=3a+2b, then [(x+y) ⊙(x-y)]⊙3x is simplified to get ().

A.0 B.5x C.2 1x+3y D.9x+6y

14. If is, the value of is ().

A.4b.-4 c.-2a+2b+6 d. Not sure.

15. If both m and n are quartic polynomials, the degree of polynomial M+N is ().

A. it must be 4 B, not more than 4 C, not less than 4 d, and it must be 8.

16. If the value of algebraic expression 2a2+3a+ 1 is 6, then the value of algebraic expression 6a2+9a+5 is ().

A.18 b.16 c.15 d 20

17. A wire can just enclose a rectangular frame with a length of 2a+3b and a width of A+B, and cut it off to enclose a wire with a length of a and a width of b (excluding seams). The remaining wire length is ().

A.a+2b B.b+2a C.4a+6b D.6a+4b

Three. Capacity improvement

18. Simplified evaluation, (where a =-2 and x = 3. )

19. Given that m, x, y, satisfy: ①, ② and are similar terms, find the value of algebraic expression.

20. There were (3a-b) people on the bus, but they got off halfway, and several others got on the bus. At this time, there are * * * passengers (8a-5b) on the bus. How many passengers are there? When A = 10 and B = 8, how many passengers are there in the car?

2 1. Known evaluation value.

22.( 1) As shown in the figure, how many cubes does the first one have? How many cubes are there in a second? What about the third one?

(2) According to the chart, how many cubes does the fifth one have? How many cubes are there in 10 power? What about the n th one?

4. Collect sand and make a tower

There is a package that needs to be packed in three different ways, as shown in the figure below. Which method uses the shortest rope? Which method uses the longest rope?

( 1)

a

b

c

(2)

(3)

1.3 Multiplication of the same radix power

I. Target navigation

1. Understand the meaning of the power with the same base, master the operational nature (or law) of the power, and perform basic operations;

2. In the process of deducing "nature", cultivate students' ability of observation, generalization and abstraction.

2. Basic clearance

1.= _ _ _ _, = _ _ _ _. Mao (surname)

2.=________, =_________________.

3.=___________.

4. If, then X = _ _ _ _ _ _

5. If yes, then M = _ _ _ _ _ If yes, then a = _ _ _ _ _ _ _ _

If yes, then y = _ _ _ _ If yes, then x = _ _ _ _ _

6. If yes, then = _ _ _ _ _.

7. The following calculation is correct ()

A.B. C. D。

8.8 1×27 can be written as ()

A.B. C. D。

9. If, the following polynomial is incorrect ()

A.b；

C.D.

10. The calculation is equal to ()

A.b-2c . d。

1 1. The following statement is true ().

A. the sum must be reciprocal. When n is odd, the sum is equal.

C. when n is an even number, the sum is equal. D. the sum cannot be equal.

Three. Capacity improvement

12. Calculate the following questions:

( 1) (2)

(3) (4)

13. On the known land, the energy obtained from the sun in one year is equivalent to the energy generated by burning coal. So how many kilograms of energy is gained from the sun in a year, which is equivalent to burning coal on the land of China? (Keep two significant figures)

14.( 1) Calculate and write the result as a base power: ①; ② .

(2) Find the following x: ①; ② .

15. Calculation.

16. If, find the value of x 。

4. Collect sand and make a tower

Known: Try to write 105 as a power of 10.

The power of the product of the power sum of 1.4

I. Target navigation

1. Go through the process of exploring the essence of product power operation, further understand the meaning of power, and develop reasoning ability and orderly expression ability. baby

2. Understand the operating characteristics of product power supply and solve some practical problems.

2. Basic clearance

1.= _ _ _ _, = _ _ _ _. Mao (surname)

2.=_________, .

3.。

4.=__________.

5.=__________.

6.=_________, =_____.

7. If yes, then = _ _ _ _ _, = _ _ _ _.

8. If, then n = _ _ _ _ _ _ _

9. If a is a rational number, the value of is ().

A. rational number B. positive number C. zero or negative number D. positive number or zero

10. If, then the relationship between A and B is ().

A. different numbers B. the same number C. none of them is zero D. the relationship is uncertain

1 1. The result of calculation is ()

A.- BC-BC.

12.= ( )

A.B. C. D。

13. Among the following propositions, the correct one is ().

When ① and ② m are positive odd numbers, there must be an equation.

③ The equation, no matter what the value of m is, does not hold.

④ Three equations: none of them hold water.

1。

14. If │x│= 1, │y│=, the value of is equal to ().

A. or b or c.d.

15. If known, the relationship between a, b and c is ().

A.b & gtc & gta B.a & gtb & gtc C.c & gta & gtb D.a & ltb & ltc

16. Calculation equals ()

A.- BC 1

Three. Capacity improvement

17. Calculation

( 1) ;

(2) ;

(3) (m is a positive integer).

18. Known,

Find the value of: (1); The value of (2)

19. Compare the sizes of sums.

20. Known, evaluated.

2 1. If A =-3 and B = 25, what is the last digit of?

4. Collect sand and make a tower

Given an = 5 and BN = 4, find the value of (ab) 2 n.

1.5 Division of the same radix power

I. Target navigation

1. Experience the process of exploring the operational nature of power division with the same radix, further understand the meaning of power, and develop reasoning ability and organizational expression ability.

2. Understand the operability of power division with the same base and solve some practical problems.

2. Basic clearance

1. Calculation = _ _ _ _, = _ _ _ _. general

2. The mass of water is 0.000204kg, which is expressed as _ _ _ _ _ _ by scientific notation.

3. If it makes sense, then X _ _ _ _ _ _ _ _ _

4.=________.

5.=_________.

6. If 5x-3y-2=0, then = _ _ _ _ _.

7. If, then = _ _ _ _ _.

8. If, then m = _ _ _ _ _ _ _

9. If the integers X, Y and Z are satisfied, then X = _ _ _ _ _ _, Y = _ _ _ _ _, and Z = _ _ _ _ _ _.

10., (5a-b), then the relationship between m and n (m, n is a natural number) is _ _ _ _ _.

1 1. The following operation result is correct ()

①2x 3-x2 = x②x3(X5)2 = x 13③(-x)6÷(-x)3 = x3④(0. 1)-2× 10-〉 1 = 10

A.①② B.②④ C.②③ D.②③④

12. if a=-0.32, b=-3-2, c=, d=, then ()

A.a & ltb & ltc & ltd B.b & lta & ltd & ltc C.a & ltd & ltc & ltb D.c & lta & ltd & ltb

13. If is, it is equal to ().

A. BC-or BC.

14. Known, then the size relationship between P and Q is ()

A.P & gtQ B.P=Q C.P<。 Q D. can't be sure

15. Given a≠0, the following equation is incorrect ().

A.(-7a)0 = 1 b .(a2+)0 = 1 c .(│a │- 1)0 = 1d。

16. If is, it is equal to ().

A.2 1 D.20

Three. Capacity improvement

17. Calculation:

( 1) ; (2) ;

(3) .

(4) (n is a positive integer)

18. If (3x+2y- 10)0 is meaningless, 2x+y=5, find the values of x and y. 。

19. Simplify:

20. As we all know,

Q: (1) (2).

2 1. Known evaluation value.

4. Collect sand and make a tower

Known, find the integer X.

Multiplication of 1.6 algebraic expression

I. Target navigation

1. Make students understand and master the multiplication rule of single item, and be able to perform the multiplication calculation of single item skillfully;

2. Pay attention to cultivating students' ability of induction, generalization and calculation.

2. Basic clearance

1.(-3xy)(-x2z)6x2z = _ _ _ _ _ _ _。 general

2.2(a+b)2 5(a+b)3 3(a+b)5 = _ _ _ _ _ _ _ _ _ _ _ _。

3.(2x2-3xy+4y2) (-xy)=_________。

4.3a(a2-2a+ 1)-2 a2(a-3)= _ _ _ _ _ _ _ _。

5. Given that rational numbers A, B and C satisfy │a- 1│+│a+b│+│a+b+c-2│=0, then the algebraic expression (-3? Ab)。 The value of (-a2c).6ab2 is _ _ _ _ _.

6.(a+2)(a-2)(a2+4)=________。

7. If (3x+1) (x-1)-(x+3) (5x-6) = x2-10x+m, then m = _ _ _ _

8. It is known that the product of ax2+bx+ 1 and 2x2-3x+ 1 contains neither the term of x3 nor the term of X, so a = _ _ _ _ _ _ ，b=_____。

9 . a(an- 1+a n-2 b+a n-3 B2+…ab n-2+b n- 1)-b(an- 1+a n-2 b+a n-3 B2+…+ab n-2+b n- 1)= _ _ _ _ _ _ _ _ _ _ _。

10. If, the values of m and a can be ().

A.M=8，a=8 B.M=2，a=9 C.M=8，a= 10 D.M=5，a= 10

1 1. Three consecutive odd numbers. If the middle is n, their product is ().

A.6n2-6n B.4n3-n C.n3-4n D.n3-n

12. The number of errors in the following calculation is ()

①(2a-b)(4a 2+4a b+B2)= 8 a3-B3②(-a-b)2 = a2-2ab+B2

③(a+b)(b-a)= a2-B2④(2a+b)2 = 4a 2+2ab+B2

A. 1

13. Let polynomial A be trinomial and b be quartic, then the number of terms of the polynomial of the result of A×B is certain? Yes ()

A. More than 7 items B. No more than 7 items C. No more than 12 items D. No more than 12 items.

14. When n is even, the relationship with is ().

A. Equality B. Opposing each other

C. when m is even, the two are opposite, and when m is odd, the two are equal.

D and m are equal when they are even numbers, and reciprocal when m is odd numbers.

15. If, then the following equation is correct ()

A.abcde & gt0 B.abcde & lt0c . BD & gt； 0d . BD & lt； 0

16. Known

A. odd B. even C. positive integer D. integer

17.m = (a+b) (a-2b), n =-b (a+3b) (where a≠0), then the relationship between m and n is ().

Morning & gtN B. M = N C. M< can't be determined.

Three. Capacity improvement

18.( 1) Solve Equation 4 (x-2) (x+5)-(2x-3) (2x+1) = 5.

(2) Simplified evaluation: x(x2-4)-(x+3)(x2-3x+2)-2x(x-2), where x= 1.5.

19. Known, and m is twice that of n, find m, n.

20. Given the value of x+3y=0,.

2 1. In the polynomial, when x=3, the value of the polynomial is 5. When x=-3, what about polynomials? The value.

22. Verification: the value of polynomial (a-2) (a2+2a+4)-[3a (a+1) 2-2a (a-1) 2-(3a+1)]+(/kloc-0)

23. Verification: N= divisible by 13.

4. Collect sand and make a tower

Inquiry: N= is a positive integer of several digits.

1.7 square difference formula (1)

I. Target navigation:

1. The square difference formula can be derived and can be used for simple calculation;

2. Understand the geometric background of the square difference formula.

2. Basic clearance

1.(x+6) (6-x) = _ _ _ _ _ _ _，= _ _ _ _ _ _。 general

2.( )= .

3.(x- 1)(+ 1)()=- 1。

4.(a+b+c)(a-b-c)=[a+( )][a-( )]。

5.(a-b-c-d)(a+b-c+d)=[()+()][()-()]

6.=_________,403×397=_________.

7. The following formula can be calculated by the square difference formula ().

①(x- y)(x+ y)，②(3a-bc)(-bc-3a)，③(3-x+y)(3+x+y)，④( 100+ 1)？ ( 100- 1)

1。

8. In the following formula, the correct operation is ().

① , ② , ③ ,

④ .

A.①② B.②③ C.②④ D.③④

9. The letters A and B in the multiplication equation stand for ().

A. it can only be a number B. it can only be a monomial C. it can only be a polynomial D. monomial, polynomial? Both types are fine.

Three. Capacity improvement

10. Calculate (a+1) (a-1) (+1).