Seventh grade mathematics
The seventh grade mathematics second semester final examination questions.
Note: The full mark of this article is * * *120; Answer time is 90 minutes.
1. Multiple-choice questions (3 points for each minor question 1-6, 4 points for each minor question/7- 12, and * * * 42 points).
1. Among the following numbers: 3. 14, 0,,, ... (add a 4 between every two 1), and the number of irrational numbers is ().
A.3 B.4 C.5 D.6
2. The estimated value is in
Between A.7 and 8, B.6 and 7, C.3 and 4, D.2 and 3.
3. The coordinate of the symmetrical point of point P(-2, 1) about the X axis is ().
A.(2， 1) B.(-2，- 1) C.(2，- 1) D.( 1)，)-2
4. At present, 46 tons of drought-resistant materials are transported to the disaster area by two kinds of transport vehicles. The load of transport vehicle A is 5 tons, and the load of transport vehicle B is 4 tons. If the arrangement does not exceed 10, at least one transport vehicle should be arranged ().
A.4 B.5 C.6 D.7
5. When three straight lines intersect at the same point, there are m pairs of vertex angles, and when they intersect at different three points, there are n pairs of vertex angles, then m
The relationship with n is ()
A.m > nb.m = n.c.m < n.d. Not sure.
6. If point A(x, y) is on the coordinate axis, then ()
A.x=0 B.y=0 C.xy=0 D.x+y=0
7. Inequality 2 (x+ 1)
8. The sailing speed of the ship is akm/h, and the sailing speed is bkm/h, so the speed of the board drifting in the water is ().
a-a-b b-c-d。
9. Form a triangle with three line segments of length 1, 2, 3, 4 and 5. There are different methods ().
A.5 B.4 C.3 D.2
10. As shown in the figure, D and E are the midpoint of AB and AC on both sides of △ABC, and △ABC will be.
Fold along the line segment DE so that the point A falls on the point F, if ∠ b = 55,
Then ∠BDF ()
A.55 B.60
C.70 D. Not sure
1 1. It is known that the vertex coordinates of a graph are,
,, such as point to the right translation 2 single.
If set, the point will be reached after 4 units of translation.
The area of is, and the area of is, then
The size relationship of is ()
A.B.
C.d. is not sure
12. As shown in the figure, in the plane rectangular coordinate system, O (0 0,0), A (1, 1),
B (3 3,0) is the vertex, and a parallelogram is constructed. In the following points,
Can't as parallelogram vertex coordinates is ()
A.(-3， 1) B.(4， 1)
C.(-2， 1) D.(2，- 1)
Fill in the blanks (4 points for each small question, 20 points for * * *)
13. If (x-y-1) 2+| 3x+2y-1| = 0, then point P(x, y) is in the fourth quadrant.
14. If any inequality holds, then the range is,
15. Given that x is an integer and satisfies, then x =.
16. Law exploration: Connect the midpoints of three triangles in the graph (1) to get graph (2), then connect the midpoints of three triangles in the middle of the graph to get graph (3), and so on, then there is a triangle in the nth graph.
17. As shown in the figure, the real numbers corresponding to point A and point B on the number axis are m and n respectively, so the distance between a and b is. (expressed by a formula containing m and n).
Iii. Answering questions (***58 points)
18.(8 points) It is known that the solution of the equation about x and y is a value.
19.(8 points) Solve inequalities and express the solution set on the number axis.
20.( 10) As shown in the figure, in the quadrilateral ABCD, diagonal AC is connected. If ∠BAD =∠BCD∠B =∠D, what is the relationship between ∠ 1 and ∠2, and why?
2 1.( 10 minute) It is known that the solution of the equation satisfies that x is non-positive and y is negative.
(1) Find the range of m;
(2) Simplification: ∣ m-3 ∣-∣ m+2 ∣;
(3) In the range of m, when m is an integer, the solution of the inequality 2mx+x < 2m+ 1 is x > 1.
22.( 12) In June this year, a fruit farmer in our city harvested 30 tons of litchi and 0/3 tons of banana/kloc. Now I plan to rent two kinds of trucks *** 10 to transport all these fruits to Shenzhen. It is known that a truck can hold 4 tons of litchi and 1 ton of banana, and a truck can hold 2 tons of litchi and banana respectively.
(1) How many schemes do fruit farmers have when arranging two kinds of trucks? Please help design it.
(2) If each truck of Class A has to pay 2,000 yuan and each truck of Class B has to pay 1300 yuan, which scheme will the fruit farmers choose? Minimize freight? What's the lowest freight?
23.( 10) "Equation" is a very important mathematical model in real life. Please write an application problem of binary linear equations based on your real life, zero the listed binary linear equations, and write out the solution process.
Reference answer
First, multiple choice questions
BCB 6- 10:CDDCC 1 1- 12:BA
Second, fill in the blanks
13.4 14. 15.- 1，0， 1 16.4n-3 17 . n-m
Third, answer questions.
18. Solution 1: Add the two known formulas and get: 3a+3b = 10. ∴ A+b =。
Solution 2: From what is known, we can get the solution, Ⅷ.
19. Solution: ...
The solution set is correct. 20.∠ 1 = ∠ 2,
∠∠BAD =∠BCD，∠D=∠B
∴∠BAD+∠D=∠BCD+∠B
∫(∠BAD+∠D)+(∠BCD+∠B)= 360？ ,
∴∠BAD+∠D= 180？ ,
∴AB‖CD
∴∠ 1=∠2.
2 1.( 1) ; (2) 1-2m； (3)m=- 1
22.( 1) If X class A trucks are arranged, X class B trucks are arranged (10-x).
To solve this set of inequalities, you must
Is an integer, and x can be 5, 6, 7,
There are three schemes for trucks A and B: ① 5 trucks A and 5 trucks B; ② There are 6 Class A trucks and 4 Class B trucks; ③ There are 7 Class A trucks and 3 Class B trucks;
(2) Scheme ① needs 2000× 5+1300× 5 =16500 yuan, Scheme ② needs 2000× 6+1300× 4 =17200 yuan, and Scheme ③ needs 2000 yuan.
Fruit farmers should choose ① the least freight, the lowest freight 16500 yuan;
23. Application problem: There are 60 trees in my home, of which poplar is twice as big as willow. How many willows are there?
Solution process: set poplar and willow.
According to the meaning of the question: get
A: There are 40 poplars and 20 willows in my family.