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The final examination paper of the second volume of mathematics in the first day of junior high school of Jiangsu Education Edition?
Ten years' cold window has now been broken, which has opened a bright future. Wave a cloud and put pen to paper, and the horse will succeed! Purple gas comes from the east, and it is auspicious and wishful, and the dream is tireless today. I wish the seventh grade math final exam success! The following is what I carefully arranged for you, for reference only.

The final examination questions of the second volume of mathematics in the first day of junior high school of Jiangsu Education Press.

First, the multiple-choice question * * * This big question * * has six small questions, each with 3 points, *** 18 points * * *

A solution to the inequality 1. is * * ▲ * * *

A. 1

2. The following calculation is correct: * * ▲ * * *

A.B. C. D。

3. In the transformation from left to right of the following equation, factorization belongs to * * * ▲ * * *

a . x2-6x+9 = * * * x-3 * * * 2 b . * * * x+3 * * * * * * x- 1 * * * = x2+2x-3

c . x2-9+6x = * * * x+3 * * * * * * x-3 * * *+6x d . 6ab = 2a? 3b

Xiao Ming accidentally smashed a triangular glass into four * * * as shown in the figure, that is, the four * * marked with 1, 2, 3 and 4 in the figure. Which one do you think will match a triangular glass of the same size as the original one? You should bring * * *.

A. 1 B area 2 C area 3 D area 4 area

5. If the solution of binary linear equations is also the solution of binary linear equations 3x-4y=6, then the value of k is * * * ▲ * *.

A.-6 B. 6 C. 4 D. 8

6. The following proposition: * * 1 * * * Two acute angles are complementary; * * * 2 * * The square of any integer, and the last digit is not 2; * * * 3 * * Two triangles with equal areas are congruent triangles; ***4*** Internal angles are equal. Among them, the number of true propositions is * * ▲ * * *

A.0 B. 1 C.2 D.3

Second, fill in the blanks * * * This big question * * has 10 small questions, each with 3 points * * * 30 points.

7. Expressed by inequality: A is a negative number.

8. If expressed in scientific notation, the value of n is ▲.

9. Write the proposition "the vertex angles are equal" as "If ……, then …": ▲.

10. The sum of the inner angles of a polygon is equal to three times the sum of its outer angles. This polygon is a polygon.

1 1. Given △ ABC△ def, ∠ A = 40, ∠ B = 50, ∠ F = ▲.

12. If the inequality group has no solution, the value range of is ▲.

13. As shown in the figure, it is known that a condition needs to be added in order to make. This condition can be: ▲. * * * Only fill in one * * *

14. Read the following text: We know that a mathematical equation can be obtained when the area of a graph is calculated by different methods. For example, this picture can be obtained from the left picture. Please write the mathematical equation shown on the right.

15. Team A and Team B played a football match. According to the rules of the game, each team scored 3 points in one game, 1 draw, and lost one game. The two teams 10 game, team a remained unbeaten. If the score exceeds 22 points, Team A will win at least.

16. As shown in figure ∠ C = ∠ CAM = 90, AC = 8°, BC = 4°, P and Q move on line segment AC and ray AM respectively, and PQ=AB. When AP= ▲, δδABC and δδPQA are equal.

Iii. Answer * * * This big question * * has 10 small questions, *** 102 points. Write the necessary steps when you answer * * *

17.* * The full mark of this question is 12 * * *

*** 1*** Calculation: * * * * * *-72014 * * * * * 2012;

***2*** Simplify first and then evaluate: * * 2A+B * * * 2-4 * * * A+B * * * * A-B * * * * 3A+5B * *, where a=- 1.

18.*** The full mark of this question is 8 * * * Factorization:

*** 1*** ; ***2*** .

19.*** This question has a perfect score of 8 * * * to solve the inequality group, indicating the solution set on the number axis and writing all integer solutions of the inequality group.

20.*** The full mark of this question is 8 * * *

* * *1* * As shown in the figure, points A, B, C and D are in a straight line, and fill in the following spaces:

∫EC∨FD * * Known * * *,

∴∠F=∠ ▲ *** ▲ ***。

∫∠F =∠E *** Known * * *,

∴∠ ▲ =∠E*** ▲ ***,

∴ ▲ ∥ ▲ *** ▲ ***.

***2*** Tell me what two contradictory true propositions are used in the reasoning of * * * 1 * *?

2 1.*** The full mark of this question is 10 * * *

* * *1* * Let a+b=2, a2+b2= 10, and find the value of * * * A-B * * 2;

* * * 2 * * Observe the following kinds: 32- 12=4×2, 42-22=4×3, 52-32=4×4, …, explore the law of the above formula, try to write the nth equation, and use the learned mathematical knowledge to explain the correctness of the formula.

22.*** The full mark of this question is10 * * A school organized students to go camping in nature reserves by car, first leveling the road at a speed of 60km/h, then climbing the mountain at a speed of 30km/h, and when it took 6.5h hours to return, the car went downhill at a speed of 40km/h and leveled the road at a speed of 50km/h, which took * * * 6.

According to the above information, please put forward a problem solved by binary linear equations and write out the solution process.

23.* * The full score of this question is 10 * * * The known equations about X and Y.

*** 1*** Find the solution of the equations * * * Use an algebraic expression containing m to express * * *;

***2*** If the solution of the equation satisfies the condition X.

24.*** The full mark of this question is 10 * * *

* * * 1 * * Known: As shown in the figure, in △ABC, ∠ ACB = 90, AE is the angular bisector, CD is high, and AE and CD intersect at point F. Verification: ∠ CFE = ∠ CEF;

* * * 2 * * Exchange the conditions and conclusions in * * *1* *, and get an inverse proposition of *** 1***:

It is known that in △ABC, ∠ ACB = 90, CD is high, E is a point on BC, AE and CD intersect at point F, and if ∠CFE=∠CEF, ∠CAE=∠BAE. Do you think this question is true or false? If it is a true proposition, please give proof; If it is a false proposition, please give a counterexample.

25.*** The full mark of this question is 12 * * * A fruit dealer bought a total of 10 boxes of fruits A and B, and distributed them to his two retail stores * * * * * * * * * * * * * * * * *.

A kind of fruit/box

Jiadian 1 1 yuan 17 yuan.

Yi branch 9 yuan 13 yuan

* * * 1 * * If the goods are delivered according to the plan of "Store A and Store B each deliver 10 boxes, including 5 boxes of fruit of type A and 5 boxes of fruit of type B", please calculate how much profit the dealer can get?

* * * 2 * * If the goods are distributed according to the plan of "the profit distribution of Store A and Store B is the same", please write down the distribution plan: A kind of fruit, Store A ▲ box, Store B ▲ box; B zhong fruit Jia branch

▲ box, store B▲ box, according to the plan you fill in, how much profit can the dealer make?

* * * 3 * * Store A and Store B each distribute 10 boxes, and under the condition that the profit of Store B is not lower than 1 15 yuan, please design a distribution plan that can maximize the profit of the fruit distributor and find out what the maximum profit is.

26.* * The full mark of this question is 14 * * As shown in the figure, among the known △ABD and△ △AEC, AD=AB, AE=AC, ∠DAB=∠EAC=

60, CD and BE intersect at point p.

*** 1***△ABE can coincide with △ △ADC through what motion;

* * * 2 * * Proved by congruent triangles's judgment method: BE = DC;;

* * * 3 * * Find the degree of ∠BPC;

***4*** On the basis of ***3***, Xiao Zhi found that ray AP divided ∠BPC equally. Please judge whether Xiao Zhi's findings are correct and explain the reasons.

Reference answer

First, the multiple-choice question * * * This big question * * has six small questions, each with 3 points, *** 18 points * * *

1.d; 2.c; 3.a; 4.b; 5.d; 6.B。

Second, fill in the blanks * * * This big question * * has 10 small questions, each with 3 points * * * 30 points.

7.a & lt0; 8.-4; 9. If two angles are antipodal angles, then the two angles are equal; 10.8; 1 1.90; 12.a≤2; 13.AB=AE or ∠C=∠D or ∠ b = ∠ e; 14.2 a2+5 ab+2 B2 = * * * 2a+b * * * * * * a+2b * * *; 15.7; 16. Four or eight.

Three. Answer the question * * * *10, score 102. The following answers are for reference only. If there are other answers or solutions, score according to the standard. * * *

17.* * Full mark of this question 12 * * (1) Original formula =+1+49-49*** 4 * * = 1 * * 6 * *;

* * * 2 * * Original formula = 4a2+4ab+B2-4 * * * A2-B2 * * * 3 points * * * = 4a2+4ab+B2-4a2+4b2-3ab-5b2 * * 4 points * * = AB.

18.*** This question is full of 8 points * * *1* * * Original formula = ***4 points * * *;

***2*** Original formula =-AB * * * 4a2-4ab+B2 * * * 2 points * * * =-AB * * * 2A-B * * * 2 * * 4 points * * *.

19.*** The full mark of this question is 8 ** * by * *1* *, x < 3*** 1 minute * * *, by * * * 2 * *, x ≥-/kloc-0.

20.*** The full mark of this question is 8 * * * * 1 * *1,* * * Two straight lines are parallel, and the internal angle is equal to * *,1,equivalent substitution, ***AE, BF***, * *. ***2*** 8 points * * slightly. * * * You can also use ∠F=∠2***

2 1.*** The full mark of this question is10 * * *1* * Because a+b=2 and a2+b2= 10, it is * * * A+B * * 2 = A2+.

***2*** Rule: * * n+2 * * 2-N2 = 4 * * * n+1* * * * n is a positive integer, with 8 points. If you don't write "n is a positive integer", you won't lose points. Verification: * * n+2.

22.*** Full score of this question 10 * * * Full score of this question10 * * The answer to this question is not unique. The following solutions are for reference.

Solution 1 Question: How many kilometers is the distance from the flat road to the hillside? ***3 points * * Solution: Let the distance of the flat road be km and the distance of the hillside be km. According to the meaning of the question, get ***6 points * * * solution * * 9 points * * *. Answer: The flat road distance is 150km, and the hillside distance is 120km * *.

Solution 2 Question: How many hours did the car drive uphill and downhill? ***3 points * * * Solution: Assuming that the uphill of the car is H and the downhill is H, you will get ***6 points according to the meaning of the question. * * * Solution will get ***9 points * * *. Answer: the car goes uphill for 4 hours and downhill for 3 hours * * 10 * *.

23.*** The full mark of this question is 10 * * * 1 * * * 5, x and y each have 2 points, and the solution of the equations is1min * * *;

***2*** According to the meaning of the question, get ***7 points * * *, m.

24.*** The full mark of this question is 10 * * *

* * *1* * ∠ ACB = 90, CD height ∴∠ ACD+∠ CAB = 90, ∠ B+∠ CAB = 90,

∴∠ACD=∠B***2 points * * *; ∫AE is the angular bisector, ∴∠CAE=∠BAE***3 points * * *; ∫∠CFE =

∠CAE+∠ACD, ∠CEF=∠BAE+∠B, ∴∠ CFE = ∠ CEF * * 5 points * * *;

***2*** Zhenti ***6 points * *. Proof: ∫∠ACB = 90, CD height ∴∠ ACD+∠ CAB = 90.

∠ b+∠b+∠cab = 90°, ∴∠ACD=∠B***8 points * * *; ∠∠CFE =∠CAE+∠ACD,∠CEF=

∠BAE+∠B, ∠CFE=∠CEF, ∴∠CAE=∠BAE, that is, AE is the angular bisector * *10 point * *.

25.*** The full mark of this question is 12 * * *

* * * 1 * * If the goods are distributed according to the first scheme, the profit of the dealer is 5 *11+5 * 9+5 *17+5 *13 = 250 * * * * *.

* * * 2 * * * * Only one case is needed * * * The first case: 2, 8, 6, 4; The second clock case: 5, 5, 4, 6; The third case: 8,2,2,8 * * * 4 points * *. According to the first case: * * 2×11+17× 6 * * * * 2 = 248 * * * *; According to the second case: * * 5×11+4×17 * * * * 2 = 246 * * * yuan * *; According to the third calculation: * * 8×11+2×17 * * * * 2 = 244 * * * yuan * * * 6 points * * *.

* * * 3 * * If Store A is equipped with X boxes of type A fruits, Store A is equipped with X boxes of type B fruits *** 10-x***, and Store B is equipped with X boxes of type A fruits *** 10-x***. Store B is equipped with 10-* * 10-x * * = X boxes. Then 9 * * *10-x * *+13x ≥115, and the solution is X. 10 * * 10 minute * *. According to the calculation, when x=7, the profit is the largest. At this time, the plan is as follows: Store A is equipped with 7 boxes of type A fruits, 3 boxes of type B fruits, and Store B is equipped with 3 boxes of type A fruits and 7 boxes of type B fruits, with a maximum profit of 246 * * * * * * 66.

26.*** The full mark of this question is14 * * * *1* * * △ Abe rotates 60 clockwise around point A, which coincides with △ADC ***3 points * * *

* * * 2 * * Proof ∠BAE=∠DAC***5 points * * *, Proof △ Abe △ ADC * * * omitted, 7 points * * *; * * * 3 * * * by△ Abe

△ ADC ∠ Abe = ∠ ADC * * 8 points * *, while ∠ BPD = ∠ DAB = 60 *** 9 points * * *,

Get ∠ BPC = 120 * * 10 * *; ***4*** are AM⊥CD and AN⊥BE, and the vertical feet are M and N respectively.

Get AM=AN*** from △ ADM △ ABN or AM=AN*** from △ Abe △ ADC and prove it again.

The score of Rt△APM≌Rt△APN and PA is equal to ∠DPE, which proves that AP is equal to ∠ BPC * * 14 * * *.