First, multiple-choice questions (2 points for each small question, *** 16 points)
1. Investigate the following questions, which ones do you think are suitable for sampling survey (▲)
(1) Whether the content of an additive in a certain food in the market meets the national standard.
② Investigate the annual income of all employees in a certain unit.
(3) Detecting the air quality in a certain area.
(4) Investigate the study time of your students in one day.
A.①②③ B.①③ C.①③④ D.①④
2. The following calculation is correct (▲)
A.B. C. D。
3. As shown in the figure, among the identified angles, the congruence angle is (▲).
A.∠ 1 and ∠2b∠ 1 and ∠3c∠ 1 and ∠4d∠2 and ∠3.
4. In order to know the weight of 300 junior one students, the school selected 30 students to measure. The following statement is true (▲).
A. The population is 300 b. The sample size is 30 c. The sample size is 30 students. D. the individual is every student.
5. If the sum of the inner angles of a polygon is equal to twice the sum of its outer angles, the number of sides of the polygon is (▲).
a6 b . 7 c . 8d . 9
6. Party A and Party B play marbles. A said to B, "Give me half of your marbles and I will have 10", and B said, "Just give me yours and I will have 10". If the number of marbles of B is X and the number of marbles of A is Y, then all listed in the equation are correct.
A.B. C. D。
7. As shown in the figure, △ ACB △, then the degree is (▲).
A.20 B.30 C.35 D.40
8. As shown in the figure, OA=OB, ∠A=∠B, with the following three conclusions:
①△AOD?△BOC，②△ACE?△BDE，
③ Point E is on the bisector of ∠O,
The correct conclusion is (▲)
A. only1b. Only 2C. Only1d. ③ There are 12.
2. Fill in the blanks (2 points for each small question, 20 points for * * *)
9. The diameter of an influenza virus is about 0.00000008 meters, which is expressed as ▲ meters by scientific notation.
10. There are 45 students in a class in the final exam of academic situation analysis, and the frequency of appearance is 0.2 in the score range of 120 ~ 130, so the class is at this score.
There are ▲ students in the paragraph.
1 1. As shown in the figure, when workers build doors, they usually use wooden strips EF to fix the rectangular door frame ABCD to prevent deformation.
The basis of this practice is ▲.
12. If, then ▲.
13. As shown in the figure, AD and AE are the bisector and height of △ABC, ∠ B = 60, ∠ C = 70, and 1 1 respectively.
Then ∠ EAD = ▲
14. As shown in the figure, the square ABCD with a side length of 3cm is first translated to the right by 1 cm, and then translated by 1 Crn to get the square.
EFGH, the shadow area is ▲ cm2.
15. As shown in the figure, in △ABC, ∠ c = 90, DB is the bisector of △ ABC, and point E is the midpoint of AB.
And DE⊥AB, if BC=5cm, then AB= ▲ cm.
16. It is known that x=a and y=2 are a solution of the equation, then a= ▲.
17. The lengths of two sides of the triangle are 2 and 6 respectively, and the length of the third side is even, so the perimeter of the triangle is ▲.
18. As shown in Figure A, it is a rectangular paper tape with ∠ def = 25. Fold the paper tape into Figure B along EF and then into Figure C along BF, so the paper tape in Figure C is
∠ The degree of ∠CFE is ▲
Third, calculation and solution.
19. (4 points for each small question, ***8 points) Calculation:
( 1) ; (2) .
20. (4 points for each small question, ***8 points) Decomposition factor:
( 1) ; (2) .
2 1. (6 points in this small question) Simplify first and then evaluate:, in which.
22. (6 points in this small question) Solve the equation:
Four. Operation and explanation.
23. (6 points for this small question) As shown in the figure, in △ABC, CD⊥AB, the vertical foot is D, the point E is on ef⊥ab BC, and the vertical foot is F.
(1) Are CD and EF parallel? Why?
(2) If ∠ 1=∠2 and ∠ 3 = 1 15, find the degree of ∠ACB.
After learning statistics, Xiaoming's math teacher asked each student to adjust the way his classmates went to school.
Check the statistics, as shown in the figure, two incomplete statistical charts drawn by Xiao Ming after collecting data.
Please answer the following questions according to the information provided in the picture:
(1) There are _ _ _ _ _ _ _ _ students in this class;
(2) Complete the "cyclic" bar chart;
(3) In the fan-shaped statistical chart; Find out the degree of the central angle corresponding to the "ride" part;
(4) If there are 600 students in the whole grade, try to estimate the number of students who go to school by bike in this grade.
25. As shown in the figure, line segments AC and BD intersect at point O, OA=OC, OB=OD.
(1)△OAB and △OCD are congruent? Why?
(2) Make an arbitrary intersection of a straight line MN and O, and the intersection points are as follows
Are m, n, OM and ON equal? Why?
Five, solve the problem (this question out of 8 points)
26. Xiao Li, an employee of a hamburger shop, sent hamburgers and orange juice to two families. The first one sent three hamburgers and two glasses of orange juice, and accepted the customer 32 yuan. The second one gave two hamburgers and three glasses of orange juice, and accepted the customer 28 yuan.
(1) If an employee of a hamburger shop gave four hamburgers and five glasses of orange juice, how much should he owe the customer?
(2) If customers buy hamburgers and orange juice at the same time, and the purchase cost happens to be 20 yuan, how should the hamburger shop deliver them?
Six, exploration and thinking (this question out of 8 points)
27. As shown in the figure, it is known that in △ABC, AB=AC=6 cm, BC=4 cm, and point D is the midpoint of AB.
(1) If point P moves from point B to point C at the speed of 1 cm/s on BC line, and point Q is on CA line.
Move from point c to point a.
① If the moving speed of point Q is equal to that of point P, are △BPD and △CQP equal after 1 s?
Please explain the reasons;
(2) If the moving speed of point Q is not equal to the moving speed of point P, what is the moving speed of point Q?
△BPD and△△ CQP are congruent?
(2) If point Q starts from point C with the moving speed in ②, and point P starts from point B with the original moving speed at the same time, both of them.
Move counterclockwise along the triangle of △ABC, and find out on which side of △ABC point P and Q meet for the first time.
Nanjing No.39 Middle School 20 1 1-20 12 school year seventh grade next semester final exam mathematics volume.
Reference answers and grading standards
First, multiple-choice questions (2 points for each small question, *** 16 points)
Title 1 2 3 4 5 6 7 8
Answer C D C B A D B D
2. Fill in the blanks (2 points for each small question, 20 points for * * *)
9.8× 10-8; 10.9; 1 1. Stability of triangle; 12.6; 13.5;
14.4; 15. 10; 16.； 17. 14; 18. 105;
Three. Calculation and solution
19. Solution: (1) Original formula = ... 2 points.
= ... 3 points.
= ... 4 points.
(2) The original formula = ... 3 points.
= 9: 04
20. Solution: (1) Original formula = ……………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
............................., 4 points.
(2) Deduct 2 points for the original formula ................
............................., 4 points.
2 1. solution: ............................ scored 3 points for the original formula.
.........................., 4 points.
Five points.
When, the original type = 9........................6 points.
22. Solution:
①× 10, score ③... 1.
②-③, 2 points.
∴ ............................................... 3 points.
If you substitute ③, you get ... 4 points.
Five points.
The solution of the original equation is 6 points.
Four. Operation and interpretation
23.( 1). The reasons are as follows: .................... 1.
∵ , ,
∴ ................................... 2 points.
∴ ............................................. 3 points.
(2)∵ ,
.........................................., 4 points.
∵ ,
∴ .
∴ ........................................ 5 points.
∴ ................................ 6 points.
24. (1) 40 ...........................1min.
(2) Missing 3 points.
③5 points.
(4)600×20%= 120 (name) .......................... 6 points.
25.( 1)△OAB and △OCD are congruent. The reasons are as follows: ...1min.
In delta △OAB and delta obsessive-compulsive disorder,
∴△OAB?△OCD(SAS)。
(2)OM equals ON. The reasons are as follows: ... The reasons are as follows: The reasons are as follows
∵△OAB?△ obsessive-compulsive disorder,
∴ ................................ 6 points.
In delta △OAB and delta obsessive-compulsive disorder,
Seven points
∴△mob?△nod(asa)。
....................................., 8 points.
26. Solution: (1) Let each hamburger be X yuan and each glass of orange juice be Y yuan .................... 1 minute.
According to the meaning of the question, get 3 points.
If it is solved, it will be 4 points.
So ..................................... scored five points.
Answer: He owes the customer 52 yuan money and ..................................................... 6 points.
(2) Set up a distribution hamburger and B cups of orange juice.
According to the meaning of the question, score 7 points
∴ .
And ∵ a and b are positive integers,
∴ , ; , .
Answer: There are two delivery methods for hamburgers:
Delivery 1 hamburger, 3 cups of orange juice or 2 hamburgers, and 1 cup of orange juice ............................................. 8 points.
27.( 1)①△BPD and△△△ cqp are congruent. The reason for this is the following：
∫D is the midpoint of AB,
∴ .
1 sec later.
∵ ,
∴ .
At △BPD and △CQP,
∴△ BPD△ CQP (SAS) ..................................................... scored 3 points.
② the moving speed of point q is x cm/s, and after t seconds △ bpd △ cqp.
Then,.
Get a solution
That is, when the moving speed of Q point is cm/s, △BPD and △CQP can be made equal to 5 points.
(2) suppose that points p and q meet for the first time after y seconds,
So, the solution is ... 7 o'clock.
At this time, the moving distance of point P is 24 cm.
The circumference of ∫△ABC is 16,
,
Points p and q meet at the edge ..................................................................................................................................................................