Mid-term examination questions of mathematics in the second volume of the seventh grade.
Each multiple-choice question is 3 points smaller and ***30 points.
1. As shown in the figure, line b.c is cut by line A, then ∠ 1 and ∠2 are.
A. internal dislocation angle B. equilibrium angle C. internal angle D. antipodal angle
2. Among the following equations, the one that belongs to binary linear equation is
A.B. C. D。
As shown in the figure, the rungs of the ladder are parallel to each other. If ∠ 1=80o, the number of times ∠2 is
a . 80o b . 120 o c . 1 10o d . 100 o
4. The following calculation is correct
A.B.
C.D.
5. Given the solution of the equation mx+3y=5, the value of m is
BC 1 year
6. As shown in the figure, if point E is on the extension line of BC, it cannot be determined that AB∑CD is there.
A.∠ 1=∠2.B. ∠3=∠4。
C.∠B=∠DCE。 D.∠D+∠ 1+∠3= 180。
7. If it is the solution of one of the following binary linear equations, then this equation group is
A.B. C. D。
8. The result of the calculation is
A.B. C. D。
9. The following algebraic expression multiplication operation, the correct is
A.B.
C.D.
10. If the side length of the square decreases and the area decreases by 39, then the side length of the original square is
A5 B6 C7 D8
Fill-in-the-blank question: There are 6 sub-questions in this question, with 4 points for each sub-question and 24 points for * * *.
1 1. Calculation: =.
12. As shown in the figure, the straight line AB∨CD is known. If ∠1=10? Then ∠2=
13. It is known that if y is represented by an algebraic expression about x, then y=.
14. Please write a system of binary linear equations:, so that its solution is.
15. As shown in figure △ABC, △DEF is obtained. If AE= 1 1 and DB=5,
Then the translation distance is _ _ _ _ _.
16. There is a large square card with a side length of A and three small square cards with a side length of B as shown in figure 1. Take out two small square cards and put them into the "big square card" to form the pattern as shown in Figure 2, and then put three small square cards into the "big square card" to form the pattern as shown in Figure 3. It is known that the shaded area in fig. 3 is 2 ab larger than that in fig. 2.
Three. Answer ***46 points
17. Calculation: 3 points for each small question, * * 6 points.
1 2
18. Solving the equation: 6 points.
1 2
19.6 Simplify before evaluating:, where.
20. Fill in the blanks with 5 points in this question.
As shown in the figure, point E is on the straight line DC and point B is on the straight line AF. If ∠ 1=∠2, ∠3=∠4,
Then ∠A=∠D, please explain the reason.
Solution: ∫≈ 1 =∠2 known.
∠2=∠DME
∴∠ 1=∠DME
∴BC∥EF
∴∠3+∠B= 180？
It is also known that ≈3 =≈4
∴∠4+∠B= 180？
∴∥∥∥∥∥∥∥∥∥∥∥∥∥∥∥∥∥∥∥∥∥∥∥∥∥∥∥∥874
∴∠A=∠D
2 1. The perfect score for this question is 6. As shown in the figure, a quadrilateral piece of paper is folded as shown in the figure, so that the point that falls on the edge is a crease.
1 Try to judge the positional relationship of sum;
If, find the degree.
22.5 Operation Exploration: Figure 1 is a rectangle with a length of. The width is. Cut it into four small rectangles with scissors along the dotted line in the figure, and then put it together into a square according to the shape of Figure 2.
1 The shaded part in Figure 2 is also a square with a side length of
Please find the shaded area in Figure 2 in two different ways.
Method 1:
Method 2:
Look at Figure 2 and write the equivalent relationship between these three algebraic expressions.
Algebraic formula: x#k#b# 1
4 according to the equivalence relation in the three questions, solve the problem: if, evaluate.
Number of people 0
Charge standard yuan/person 90 80 70
23.6 Yueqing Yandang Travel Agency plans to launch a "Yandang Day Tour" to students during the summer vacation, and the fees are as follows:
Two schools, A and B, plan to organize students to participate in this activity voluntarily. It is known that the number of students enrolled in A school is more than 100, while the number of students enrolled in B school is less than 100. According to the accounting, the two universities need 1.73 million yuan for a separate group, and only need 1.47 million yuan for a joint group.
1 How many students have signed up for the tour in the two schools?
How many students have signed up for the tour in these two schools?
24. The six points of this problem are shown in Figure ①. Known BC∨OA, ∠ B = ∠ A = 100. Try to answer the following questions:
(1) test description: ob ∨ AC;
(2) As shown in Figure ②, if the point E.F is on BC and ∠FOC=∠AOC, then OE shares ∠BOF equally. Try to find the degree of ∠EOC;
(3) Under the condition of (2) small problem, if AC moves in parallel from left to right, as shown in Figure (3), will the ratio change accordingly? If yes, try to explain the reasons; If it is unchanged, find this ratio;
(4) When ∠OEB=∠OCA, the number of times to find ∠OCA.
The second volume of the seventh grade, the mid-term exam of mathematics, the reference answer of People's Education Edition.
1. Choose the answer 3 points ***30 points for each question.
The title is 1 23455 6789 10.
Answer B C D C B B A D A D
2. Fill in the blanks with 4 points each ***24 points.
The title is11213141516.
Answer -2x2y+6xy 700 2-2x Not Unique 3 5
Three. Answer ***46 points
17. Calculation: 3 points for each small question, * * 6 points.
1 1 2
=...2 points =...2 points
=... 1 = ... 1
18. Solving the equation: 3 points for each small question, 6 points.
1 2
Y =- 1... 1 point, X = 3... 1 minute.
The solution is x = 0... 1, and the solution is y =... 1.
Write the solution of the equation ... 1 ... 1.
19.6 Simplify before evaluating:, where.
Get ... two points.
Get ... two points.
When, the original formula =-1... 2 points.
20. This problem is scored 5 points, with each step 1 point.
Solution: ∫≈ 1 =∠2 known.
∠2=∠DME vertex angles are equal.
∴∠ 1=∠DME
∴BC∥FE has the same angle and two straight lines are parallel.
∴∠3+∠B= 180？ These two lines are parallel and complementary.
It is also known that ≈3 =≈4
∴∠4+∠B= 180？
∴ De∑ AB is complementary to the inner corner of the side, and the two straight lines are parallel.
∴∠a =∞∠d Two straight lines are parallel and the internal dislocation angles are equal.
2 1. The topic is 6 points.
1 reasoning process ... 2 points.
∥ ... 1 point
2 reasoning process ... 2 points
..... 1 point
22. Question 5
1 side length of shadow square ... 1 min.
Please find it in two different ways.
Method 1:... 1.
Method 2: ... 1.
3... 1 point
4 If, the value of.
Solution:
..... 1 point
23. Question 2+4=6 points
Solution:1:If there are no more than 200 people, then 14700÷80= 183.75 people, which is irrelevant.
If there are more than 200 people, then 14700÷70=2 10 people.
The total is 2 10. ..... 2 points
The number of tourists from A and B schools is X and Y respectively.
..... 2 points
Solution ... 1 min.
Answer: A school 160, B school 80 ... 1.
24. The topic is 6 points.
Solution:1:BC ∨ OA,
∴∠ B+∠ O = 180, and ∠B=∠A,
∴∠A+∠O= 180，
∴ob∥ac； .................. 1 point
2≈b+∠BOA = 180，∠B= 100，
∴∠BOA=80，
∫OE segmentation∠ ∠BOF,
∴∠BOE=∠EOF, and ∠∠foc =∠AOC,
∴∠eof+∠foc=∠BOF+∠FOA =∠boa = 40； .................. 1 point
Conclusion: The value of OCB remains unchanged. The reason is:
∫BC∨OA，
∴∠FCO=∠COA，
And ? ≈FOC =∠AOC,
∴∠FOC=∠FCO，
∴∠OFB=∠FOC+∠FCO=2∠OCB，
∴∠ocb:∠ofb= 1:2； .........................., two points.
4 from 1:OB∑AC,
∠OCA=∠BOC，
Can be set to 2: ∠BOE=∠EOF=α, ∠FOC=∠COA=β,
Then ∠OCA=∠BOC=2α+β,
∠OEB=∠EOC+∠ECO=α+β+β=α+2β，
∠∠OEC =∠ ∠∠ OCA,
∴2α+β=α+2β,
∴α=β,
∫∠AOB = 80，
∴α=β=20 ,
∴∠∠∠ Orca = 2α+β = 40+20 = 60. ....................................................................................................................................
25. Additional questions are not included in the total score:
1 ...8 points
B = 8...2 points.
You can buy up to 5 A-level pens ... 10 point.