1. The number represented by a point 3 unit lengths away from the origin on the number axis is

A.3B.-3C.3 or -3D. 1 or-1

If you subtract a larger number from a smaller number, the difference must be.

A. positive number B. negative number C.0D. Can't determine the positive or negative.

3. The reciprocal of-3 is

The third century BC to the third century BC

4. In the following group, the values are equal.

A.32 and 23B. -23 and (-2)3

C.-32 and (-3)2D. (-1×2)2 and (-1)×22.

5. If a=b and b=2c, then a+b+2c=

a . 0b . 3c . 3 ad-3a

6. If the solution of equation 2x+k-4=0 about x is x=-3, then the value of k is

A. 10B。 - 10C.2D.-2

7. The algebraic formula (x+1) (x-2) (x-4) has a value of 0 when x takes the numbers1,2, 3, 4 and 5 respectively.

1。

8. In the numbers 4,-1, -3 and 6, add any three different numbers, of which the smallest sum is

a . 0b . 2c-3d . 9

9. (-2)10+(-2)11

A.2B。 -22C。 -2 10D。 (-2)2 1

The nth number in the column 10. -3, -7,-1 1,-15 ... is.

A.n，-4B。 -(2n+ 1)c . 4n- 1d . 1-4n

Fill in the blanks (3 points for each small question, 30 points for * * *)

1 1. The number 5 less than -3 is _ _ _ _.

12. The sum of all integers whose absolute value is greater than 3 and less than 3.

13.90340000 This number is expressed as _ _ _ _ by scientific notation.

14. Use letters to indicate the area of the shaded part in the drawing: _ _ _ _ _ _ _ _ _ _ _.

15. If x2+x- 1=0, 3x2+3x-6 = _ _ _ _.

16. Write a quartic monomial about letters A and B with a coefficient of-1_ _ _ _.

17. The original price of the computer is one yuan, and the price is reduced by 20% after subtracting M yuan. The current price is _ _ _ _ _ _ _.

18. Use 16m long fence to enclose a circular biological park as large as possible to raise rabbits, so the area of the biological park is _ _ _ _ _ m2. (The result is still π).

19. If x+y=3 and xy=-4, then (3x+2)-(4xy-3y) = _ _ _ _ _.

20. In order to encourage residents to save water, a city stipulates that when the monthly water consumption of a family of three does not exceed 25 cubic meters, 3 yuan will be charged per cubic meter; If the water exceeds the standard, the excess will be charged per cubic meter. 4 Yuan Liming's family used 1000 cubic meters of water (a & gt25) in July this year, and his family has to pay _ _ _ _ _ yuan for water this month.

Iii. Answering questions (***70 points)

2 1. calculation (3 points for each small question, *** 12 points)

( 1)- 12×4-(-6)×5(2)4-(-2)3-32÷(- 1)3

(3)(4)

22. Simplify the complex (3 points for each small question, *** 12 points)

( 1)a2 b-3a B2+2ba 2-b2a(2)2a-3 b+(4a-(3 b+ 2a)]

(3)-3+2(-x2+4x)-4(- 1+3 x2)(4)2x-3(3x-(2y-x)]+2y

23. Simplify before evaluating. (4 points for each small question, * * * 8 points)

(1) (2x2+x-1)-3 (-x2-x+1), where x=-3.

(2) 3xy-(4xy-9x2y2)+2 (3xy-4xx2y2), where x= and y=-

24. (3 points for each small question, ***6 points)

Known: A=4a2-3a. B=-a2+a- 1。

Q:

( 1)2A+3B

⑵A-4B

25. Solve the following equation (4 points for each small question, 8 points for * * *).

( 1)x-3=4-x

26. (This question is 2 points +6 points, ***8 points)

(1) Use "

(2) The postman starts from the post office by bike, rides 3km east to village A, continues to ride 2km east to village B, then rides 10km west to village C, and finally returns to the post office.

① Take the post office as the origin and the east direction as the positive direction, use lcm to represent 1km, draw a number axis, and indicate the positions of Village A, Village B and Village C on this number axis.

② How far is Village C from Village A?

How many kilometers did the postman ride?

27. (5 points for this question)

Given the polynomial M=x2+5ax-x- 1, N=-2x2+ax- 1, and the value of 2M+N has nothing to do with x, find the value of constant a. 。

28. (5 points for this question)

Please follow the following formula:

① 1×3-22=3-4=- 1

②2×4-32=8-9=- 1

③3×5-42= 15- 16=- 1

④_____________________;

…………

(1) Please write the fourth formula according to the above rules;

(2) Use a formula containing letters to express this rule.

29. (3 points for each small question, ***6 points)

(1) Try to write an algebraic expression with x, so that when x= 1 and x=2, the value of the algebraic expression is 5.

(2) Try to write an algebraic expression with A, so that the value of this algebraic expression is not greater than 1, no matter what value A takes.

Extended reading-summary of mathematics knowledge in the second volume of Grade One in senior high school.

Summary of knowledge points and concepts

1. Inequality: Formulas that express the relationship between size with symbols ",","≤" and "≥" are called inequalities.

2. Classification of inequalities: Inequalities are divided into strict inequalities and non-strict inequalities.

Generally speaking, inequalities connected by pure greater than signs and less than signs are called strict inequalities, while inequalities connected by not less than signs (greater than or equal to signs), not greater than signs (less than or equal to signs), ≥ and ≤ are called non-strict inequalities or generalized inequalities.

3. Solution of inequality: the value of the unknown quantity that makes inequality valid is called the solution of inequality.

4. Solution set of inequality: All solutions of an unknown inequality constitute the solution set of this inequality.

5. Representation method of inequality solution set;

(1) is expressed by inequality: generally, an inequality with unknowns has countless solutions, and its solution set is a range, which can be expressed by the simplest inequality. For example, the solution set of x- 1≤2 is x≤3.

(2) Expressed on the number axis: The solution set of inequality can be intuitively expressed on the number axis, which vividly shows that inequality has infinite solutions. Two points should be paid attention to when expressing the solution set of inequality with the number axis: first, the boundary line should be fixed; The second is to set the direction.

6. Some of the same problem-solving principles that can be followed when solving inequalities.

(1) inequality F(x) G(x) and inequality G(x)F(x) have the same solution.

(2) If the definition domain of inequality F(x) G(x) is included in the definition domain of analytic formula H(x), then inequality F(x) G(x) and inequality H(x)+F(x).

(3) If the definition domain of inequality F(x) G(x) is contained by the definition domain of analytic expressions H(x) and H(x)0, then inequality F(x) G(x) and inequality H(x) 0, then inequality F(x) G(x) and inequality h (x).

7. The nature of inequality:

(1) If xy, then YY; (symmetry)

(2) if xy, y then x (transitivity)

(3) If xy and z are arbitrary real numbers or algebraic expressions, then x+z (addition rule).

(4) If xy, z0, then xz If xy, z0, then xz

(5) If xy, z0, then x \u z If xy, z0, then x \ u z.

(6) if xy, mn, then x+my+n (necessary and sufficient condition)

(7) If x0, m0, xmyn

(8) If x0, then the n power of x is the n power of y (n is a positive number).

8. One-dimensional linear inequality: the left and right sides of the inequality are algebraic expressions, and there is only one unknown, and the highest order of the unknown is 1. Inequalities like this are called one-dimensional linear inequalities.

9. The general order of solving one-dimensional linear inequality:

(1) denominator (using inequality properties 2 and 3)

(2) Dismantle the bracket

(3) Shift term (using inequality property 1)

(4) merging similar projects

(5) Transform the unknown coefficient into 1 (using inequality properties 2 and 3).

(6) Sometimes it is necessary to express the solution set of inequality on the number axis.

10. Comprehensive application of linear inequality and linear function;

Generally, the function expression is obtained first, and then the inequality is simplified.

1 1. One-dimensional linear inequality group: Generally speaking, it is a combination of several one-dimensional linear inequalities about the same unknown quantity.

A set of one-dimensional linear inequalities is established.

12. Steps to solve a set of linear inequalities:

(1) Find the solution set of each inequality;

(2) Find the common part of each inequality solution set; (Generally, several axes are used)

(3) The public part is expressed in algebraic symbolic language. (it can also be said that it is a conclusion)

13. tips for solving inequality

(1) is greater than the maximum (much larger);

For example: X- 1, X2, and the solution set of inequality group is X2.

(2) less than the minimum (small and small);

For example: X-4, X-6, the solution set of inequality group is X-6.

(3) Crossing the middle is greater than or less than;

(4) There is no solution to the part that is not disclosed;

14. Formulas for solving inequality groups

(1) Maximize the same size.

For example, x2, X3, the solution set of inequality group is x3.

(2) Take the small as the big.

For example, X2, x3, the solution set of the inequality group is x2.

(3) Find the middle between big and small.

For example, x2, x 1, and the solution set of inequality group is 1.

(4) Keep the change, more or less.

For example, x2, x3, the inequality group has no solution.

15. Steps to solve practical problems by applying inequality groups

(1) Check the meaning of the problem

(2) Set unknowns, and list inequality groups according to the set unknowns.

(3) Solving inequality groups

(4) The solutions of practical problems are established by the solutions of inequality groups.

(5) Answer

16. Solving practical problems with inequality groups: its general solution is not necessarily the solution of practical problems, but should be combined with concrete analysis of real life to finally determine the result.