I. Fill in the blanks (2 points × 15 points = 30 points)

In 1 and polynomial -abx2+x3-ab+3, the coefficient of the first term is and the degree is.

2. Calculation: ①100×103×104 =; ②-2a3b4÷ 12a3b2 =。

3 、( 8xy2-6x2y)÷(-2x)=。

4 、(-3x-4y) ( ) = 9x2- 16y2。

It is known that the side length of a square is a, if its side length increases by 4, its area will increase.

6. If x+y = 6 and xy = 7, then x2+y2 =.

7. According to the data, the forest called "the lung of the earth" is disappearing from the earth at the rate of 65,438+0,500,000 hectares per year, and the area of forest disappearing every year is expressed as _ _ _ _ _ _ _ hectares by scientific notation.

8. The radius of the sun is 6.96× 104km, accurate to _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

9. Xiao Ming marks six numbers (1, 2, 3, 4, 5, 6) on the six faces of a small cube, and throws the small cube at random, so p (the thrown number is less than 7) = _ _ _ _ _.

10 and figure (1), when the cut ∠AOB increases 15, ∠COD increases.

1 1, as shown in figure (2), ∠1=10, then ∠ 2 = 0 (the top and bottom of the can are parallel to each other).

Figure (1) Figure (2) Figure (3)

12. There is a spotlight at the top of the parallel building. When the beams intersect, as shown in Figure (3), ∠1+∠ 2+∠ 3 = _ _ _ _ _

Second, multiple-choice questions (3 points ×6 points = 18 points) (carefully review the questions, beware of traps! )

13, if x 2+ax+9 = (x+3) 2, the value of a is ().

(A) 3 (B) 3 (C) 6 (D) 6

14, as shown in the figure, the length of the rectangle is a, the width is b, and the horizontally shaded part is a rectangle.

The other shaded part is a parallelogram, and their width is C, so the face of the blank part

The product is ()

(A) ab-bc+ac-c 2

(C) ab- ac -bc (D) ab-ac-bc-c 2

15, the following calculation ① (-1) 0 =-1②-x2.x3 = x532× 2-2 = ④ (m3) 3 = M6.

(5) (-A2) m = (-AM) 2 The correct one is ............................. ().

1 (B) 2 (C) 3 (D) 4。

Figure a figure b

16 As shown in the figure, the error in the following judgment is ().

(A)A+∠ADC = 180—→AB‖CD

(B)AB‖CD—→∞ABC+∞C = 180

(C) 1 =∠2—→ BC

(d) BC-3 = 4

17, as shown in figure b, the times of A ‖ B and ∠ 1 are half of ∠2, so ∠3 is equal to ().

(A)60(B) 100(C) 120(D) 130

18, the winning rate of a game is 1%, and Xiaohua bought a lottery ticket of 100. The following statement is correct ().

(a) I will definitely win the prize; (b) I will definitely not win the prize; (c) I have a high probability of winning the prize; My chances of winning the prize are slim.

Third, solve the problem: (write the necessary calculus process and reasoning process)

(1) calculation: (5 points× 3 =15 points)

19、 123? -124× 122 (calculated by algebraic expression multiplication formula)

20、9(x+2)(x-2)-(3x-2)2 2 1、0. 125 100×8 100

22. A liquid contains 10 12 harmful bacteria per liter, and 1 drop of insecticide can kill 109 such harmful bacteria. Now, how many drops of this pesticide should be used to kill the harmful bacteria in this 2 liters of liquid? If 10 drop of this pesticide is one liter, ask: How many liters of pesticide should be used? (6 points)

24. The complementary angle of an angle is 18 degrees, which is more than twice its complementary angle. What's the angle? (5 points)

Mid-term examination paper of seventh grade mathematics in 2007

(The full mark of this volume is 100, and the completion time is 90 minutes)

Name: Achievements:

1. Fill in the blanks (this big question * *, a total of 15 questions, 2 points for each question, out of 30 points).

1, as shown in the figure: the number whose distance from point A on the number axis is equal to 5 is.

2. It is correct to round 3. 14 15926 to one thousandth. If 302400 is expressed by scientific notation, it should be recorded as about 3.0× accurate to one decimal place.

3. It is known that the circumference of a circle is 50, and the radius of the circle is expressed by an algebraic expression containing π, which should be.

4. Each pencil 300 yuan. Xiaoming bought n pencils with 10 yuan, and there was still RMB left.

5. When a =-2, the value of algebraic expression is equal to.

6. The algebraic expression 2x3Y2+3x2Y- 1 is a second-order term.

7. If 4amb2 and abn are similar terms, then m+n=.

8. Polynomials 3x3y- xy3+x2y2+y4+Y4 are arranged in ascending order of the letter X. 。

9. If it is ∣x-2∣= 1, then it is ∣x- 1∣=.

10, calculation: (A- 1)-(3A2-2A+ 1) =.

1 1. Calculate with a calculator (keep 3 significant figures): =.

12, Blackjack Game: Use the following numbers to score 24 points (each number can only be used once).

2, 6, 7, 8. Formula.

13, calculation: (-2a)3 =.

14, calculation: (x2+x- 1)? (-2x)=。

15. Observe the rule and calculate: (2+1) (22+1) (24+1) (28+1) =. Calculator is not allowed, and the result is in the form of power.

Second, the choice (this big topic * * * a total of 4 questions, each question 2 points, out of 8 points)

16, the following statement is correct .................................................. ()

(A)2 is not algebraic; (b) it is a single item.

The linear coefficient of (c) is 1 (D) 1 is a monomial.

17. The following merged similar projects are correct ....................................................................... ()

(A)2a+3a = 5(B)2a-3a =-A(C)2a+3b = 5ab(D)3a-2b = ab

18, the following set of numbers arranged according to the law: 1, 2, 4, 8, 16, ..., No.2002 should be ().

A, b,-1 C, d, the above answers are incorrect.

19. If we know that A and B are reciprocal, and X and Y are reciprocal, then algebraic expression.

The value of |a+b|-2xy is ().

A.0b-2 c.-1d. cannot be determined.

Iii. Answer: (This big question is * * *, with a total of 4 questions, with 6 points for each question, out of 24 points).

20. Calculation: x+ +5

2 1, evaluation: (x+2) (x-2) (x2+4)-(x2-2) 2, where x =-

22. It is known that a is the smallest positive integer. Try to find the value of the following algebraic expression: (4 points for each small question, *** 12 points)

( 1)

(2) ;

(3) By (1), (2) What did you find or think of?

23. Given that a = 2x2-x+ 1, a-2b = x- 1, find b.

Four, the application problem (this big problem * * * has five questions, 24, 25 each question 7 points, 26, 27, 28 each question 8 points, out of 38 points)

24. It is known (as shown in the figure) that the side length of square ABCD is B, and the side length of square DEFG is A.

Find the area of (1) trapezoidal ADGF.

(2) the area of triangle AEF

(3) Area of triangular AFC

25. Known (as shown in the figure): use four right-angled triangles with base B, height A and hypotenuse C.

Make a square and find the area of the small square in the center of the figure. You can find it easily.

The area of the solution (1) small square =

Solution (2) Area of small square =

By solving (1) and (2), we can get the relationship between a, b and c as follows:

26. It is known that the taxi charging standards in our city are as follows: all taxis with a mileage of less than five kilometers will be charged to 5 yuan; If the mileage exceeds 5 kilometers, the excess part will be charged at 1.2 yuan per kilometer except 5 yuan.

(1) If someone travels by taxi for x kilometers (x >: 5), how much should he pay? (Column Algebra) (4 points)

(2) A tourist takes a taxi from Xinghua to Shagou and pays 4 1 yuan. Try to estimate how many kilometers it is from Xinghua to Shagou. (4 points)

27, the members of the first team and the second team get together. There are m people in the first team, and the second team has two more people than the first team. If every member of two teams gave a gift to everyone on the other team.

Q: (1) The total number of gifts given by all players. (represented by the algebraic expression of m)

(2) When m= 10, how many gifts are given?

28. The price of a commodity at 1998 is 5% higher than that at 1997, while the price at 1999 is 5% higher than that at 1998. In 2000, the price ratio was lower than 1999 12%. What is the percentage of price increase or decrease?

In 2006, the first semester, the first grade, the mid-term exam.

Mathematics test paper answer

I. 1, 2, 10-Mn 3, -54,-1, 25, 5, 3, 6, 3

7、3x3y+x2y2- xy3 +y4 8、0、2 9 、-3a2+3a-2 10 、-a6

1 1 、-x8 12 、-8a3 13 、-2x3-x2+2x 14、4b2-a2 15、2 16- 1

2. 16, D 17, B 18, B 19, d.

Three. 20. Original formula = x+ +5 (1')

= x+ +5 ( 1 ')

= x+ +5 ( 1 ')

= x+4x-3y+5 ( 1 ')

= 5x-3y+5 (2 ')

2 1, the original formula = (x2-4) (x2+4)-(x4-4x2+4) (1')

= x4- 16-x4+4x2-4 ( 1 ')

= 4x2-20 ( 1 ')

When x =, the value of the original formula = 4× () 2-20 (1').

= 4× -20 ( 1')

=- 19 ( 1')

22. Original formula = x2-2x+1+x2-9+x2-4x+3 (1')

=3x2-6x-5 ( 1 ')

= 3 (x2-2x)-5 (2') (or 3x2-6x = 6 from x2-2x = 2).

=3×2-5 ( 1')

= 1 ( 1')

23、A-2B = x- 1

2B = A-(x- 1) ( 1 ')

2B = 2 x2-x+ 1-(x- 1)( 1 ')

2B = 2 x2-x+ 1-x+ 1( 1 ')

2B = 2x2-2x+2 ( 1 ')

B = x2-x+ 1 (2 ')

24、( 1) (2')

(2) (2')

(3) + - - = (3')

25 、( 1)C2 = C 2-2ab (3 ')

(2) (b-a) 2 or b 2-2ab+a 2 (3')

(3)C 2= a 2+b 2 ( 1 ')

26 、( 25)2 = a2 ( 1 ')

a = 32 ( 1 ')

2 10 = 22b ( 1 ')

b = 5 ( 1 ')

Original formula = (a) 2-(b = (a) 2-(b) 2-(A2+AB+B2) (1'+0').

= a2- b2- a2- ab- b2 ( 1 ')

=- ab- b2 ( 1 ')

When a = 32 and b = 5, the value of the original formula =-× 32× 5 -× 52 =-18 (1').

If directly substituted: (8+1) (8-1)-(8+1) 2 =-18.

27. Solution (1): The first team gave the second team ***(m+2)? M pieces (2 feet)

Team two gave team one ***m? (m+2) pieces (2')

Two teams * * * give 2m? (m+2) pieces (2')

(2): When m = 2× 102+4× 10=240 pieces (2')

28. Suppose the commodity price of 1997 is X yuan (1').

The commodity price of 1998 is (1+5%)x yuan (1').

The commodity price in 1999 is (1+5%) (1+kloc-0/0%) x yuan (1').

In 2000, the commodity price was (1+5%) (1+10%) x yuan =1.0160%.

=0.0 164= 1.64% (2')

Answer: The price increase in 2000 was 1.64% compared with 1.997. (65,438+0')

The first grade math contest. Multiple choice questions (5 points for each question, ***50 points) Only one of the following four conclusions is correct. Please put the English letters indicating the correct answers in brackets after each question. Any positive and odd power of the number 1 A equals the inverse of a, then () A.B.C.D does not exist. Then the integer closest to the number represented by point C is () A. B. 0 C. 1 D. 2 (adapted from the topic provided by Wang Yuanzheng of Shekou Middle School in Nanshan District, Shenzhen). 3. Zu Chongzhi, a great mathematician in ancient China, calculated the pi as 3. 14 15926 and quite accurately. 5927, and take it as the density rate and reduction rate, then () A.B.C.D.4 Given that X and Y satisfy, then the value of the algebraic expression is () A.4B.3C.2D. 1.5. The sum of two positive integers is 60, and their least common multiple is 273. Then their product is () a.273b.819c.1911d.3549 6. Enclose an equilateral triangle with a line one meter long, and measure the area of this equilateral triangle as b square meters. Now choose any point p in this equilateral triangle. Then the sum of the distances from point P to the three sides of an equilateral triangle is () m A.B.C.D.7 If we assume that be is the largest prime number not greater than a, then the result of the expression is () a.1333b.1999c.2001d.223. Results results; 8. The ancients recorded the order of heavenly stems and earthly branches, including 10 heavenly stems: A, B, C, D, E, G, N, N, and also 12 earthly branches: Zi Chou and Tatsumi, who failed to submit their letters at noon, 10 in heavenly stems and/0 in earthly branches. N, n, n, n, n, n, n, n, n The serial number of this column is () a.31b.61c.91d.1219. Satisfied rational numbers A and B are () A.B.C.D. 19. For any two monomials, first look at the power of X, and stipulate that the monomials with high power of X are in front of the monomials with low power of X; Look at the power of y again, and stipulate that the power of y is higher than y; Looking at the power of z again, the specified power of z is higher than that of z. If the monomials are sorted according to the above rules, they should be ranked in () A. B. C. D. D. B. Fill in the blanks (6 points for each small question, ***60 points) 1 1. Then the degree of this acute angle is _ _ _ _ _ _ _. 12. If, then the result is _ _ _ _ _. 13. Known: as shown in figure 1, where d, e, f and g are all points on the side of BC. Then the sum of the areas of all triangles in the diagram is _ _ _ _. 14. The value of the integer A that makes the equation about X have both a positive root and a negative root is _ _ _ _.15. When Xiaoming's brother celebrated his birthday, his mother gave him a gift: he could withdraw an educational savings of 3,000 yuan after three years. Xiao Ming knows this saving. Then Xiaoming's mother must deposit at least _ _ _ _ _ _ yuan in the bank for this birthday present. (The bank will store it as an integer) 16. M is a positive integer, and it is known that binary linear equations have integer solutions, that is, both X and Y are integers, then _ _ _ _ _ _.17. Known:. Then the shaded area is equal to _ _ _ _ square meters. 18. An image can be regarded as a big rectangle consisting of m rows and n columns of small squares, in which each small square is called a point, and the color of each point is one of several colors. Given m, n and the color of each point, an image is determined. Now, one byte can store two colors. So when m and n are odd numbers, at least _ _ _ bytes are needed to store the colors of all points in this image. 19. In a positive integer, the largest odd number that cannot be written as the sum of three unequal composite numbers is _ _ _ _ _ _ _ _ _ _ _ _. 20. In cryptography, what can be seen directly is called plain code, and plain code gets the password after some processing. For a password with four letters, the numbers corresponding to the four letters are known: integer, and the remainder divided by 26 is 9 16, 23, 12 respectively, so the password is _ _ _ _ _ _ _ _ _. Three. Solve the problem (2 1, 26). ***40 points) Requirements: Write the calculation process. 2 1. There are three numbers in sequence: 3, 9 and 8. For any two adjacent numbers, subtract the number on the left from the number on the right, and write the difference between the two numbers to generate a new number string: 3, 6, 9, 8, which is called the first operation; After doing the same operation for the second time, a new number string can be generated: 3, 3, 6, 3, 9, 9, 8. Continue to operate in turn. Q: What is the sum of all the digits of the new digit string generated after the hundredth operation on the logarithmic strings 3, 9 and 8? 22. As shown in Figure 3, the certificate: 23. A toy factory uses 450 working hours and 400 units of raw materials for production. It takes 15 working hours and 20 units of raw materials to produce a bear, and the price is 80 yuan; It takes 10 working hours and 5 units of raw materials to produce a kitten, and the price is 45 yuan. Reasonable arrangement of the number of bears and kittens under the limitation of labor and raw materials can make the total selling price of bears and kittens as high as possible. Please analyze it with your mathematical knowledge. Is it possible to reach 2200 yuan? [Answer] 1. Multiple choice questions:1.a2.c3.c4.d5.b6.c7.b8.b9.a10.d2. Fill in the blanks (this big question ***60 points. For each small question, answer one question correctly and get 6 points; Answer wrong or not, do not score)11.12.13.714.015.274616.417. 3. Problem solving: 2 1. An N-number string is formed by arranging N numbers in sequence, and the new number can be obtained by setting the operation method according to the problem. Therefore, the sum of the new numbers is: the original number string is 3 numbers: 3, 9, 8, 1 The number string obtained after the operation is: 3, 6, 9, 8 according to (*), and the sum of the two new items is: according to this rule. (Two straight lines are parallel and the internal angles are equal) and because, (two straight lines are parallel and the internal angles are equal), so (definition of fillet), so (equivalent replacement) Prove 2: Because, so (two straight lines are parallel and the internal angles are complementary), because (as shown in Figure 2), so (two straight lines parallel to the same straight line are parallel) because, there is, (there is). (Two straight lines are parallel and the internal angles on the same side are complementary) So (equivalent substitution) 23. Let the number of bears and kittens be X and Y, respectively, and the total selling price be Z, then (*) according to the limitation of labor and raw materials, X and Y should be simplified, and when the total selling price is reached, it can be obtained by (*), that is, the combination of (a) and (b). There are constraints on working hours and raw materials, and at this time there is a total selling price (RMB). A: As long as we arrange to produce 14 bears and 24 kittens, the total selling price can reach 2200 RMB. ，2， 12x3 = 36，2，α+β ≥ 123456789，0。