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 * * *.