Grade 8 Mathematics 20 10. 1
This paper consists of three parts: multiple-choice questions, fill-in-the-blank questions and solution questions, with a total of 28 questions, with a full score of 100.
Examination time 120 minutes.
Precautions:
1. Before answering questions, candidates must fill in the school name, name, test number and other information in the corresponding position on the answer sheet.
2. Candidates' answers must be answered in the corresponding position on the answer sheet, and the answers on the test paper and draft paper are invalid.
First, multiple-choice questions (this topic is entitled * * 10 small questions, with 2 points for each small question and 20 points for each small question. Only one of the four options given in each small question meets the requirements of the topic, so fill in the correct answer in the corresponding position on the answer sheet)
The reciprocal of 1.2 is
a . 2b-2c . d
2. The following are the national flag patterns of some countries, among which the axisymmetric patterns are
3. The following statement is correct.
The square root of a.0 is 0b. 1 Yes 1.
The square root of C.- 1 is-1 D. The square root is-1.
4. There is a set of data: 10, 20, 80, 40, 30, 90, 50, 40, 50, 40, and their median is
30-90 A.D.
5. If the point P(m, 1-2m) is in the fourth quadrant, the range of m is
A.B.
C.D.
6. The characteristics that a square has but a diamond does not necessarily have are
A. diagonal bisection. B. Diagonal lines are perpendicular to each other.
C. Diagonal lines are equal. D. Diagonal lines bisect a set of diagonal lines.
7. Given a linear function, if y increases with the increase of x, the range of m is
A.B.
C.D.
8. As shown in the figure, in trapezoidal ABCD, AD‖BC, the median line EF intersects BD at point O, and if OE∶OF= 1∶4, AD∶BC is equal to.
1∶2 b . 1∶4 c . 1∶8d . 1∶ 16
9. As shown in the figure, in a regular triangle ABC with a side length of 2, it is known that point P is any point in the triangle, so the sum of the distances from point P to three sides of the triangle PD+PE+PF is equal to.
A.b.c.d is not sure.
10. As shown in the figure, find a point P on the symmetry axis L of rectangular ABCD, and make △PAB and △PBC isosceles triangles, then the point P that meets the conditions is
A. 1 B.3 C.5 D
2. Fill in the blanks (this big topic is ***8 small questions, each small question is 2 points, *** 16 points, please fill in the answer in the corresponding position on the answer sheet).
1 1. Calculation: ▲.
12. Over time, ▲.
The square root of 13. -27 is ▲.
14. Given that the sum of five data is 485 and one data is 85, the average value of the other four data is ▲.
15. given that point a (a, 2a-3) is on the image of linear function y=x+ 1, then a = ▲.
16. It is known that the circumference of an isosceles triangle ABC is 8cm and AB = 3cm ... If BC is the bottom of the isosceles triangle, then BC = ▲ cm.
17. As shown in the figure, point A and point B are on the same side of the straight line L, AB=4cm, point C is the symmetrical point of point B about the straight line L, AC intersects with the straight line L at point D, AC=5cm, so the circumference of △ABD is ▲ cm.
18. As shown in the figure, in △ABC, it is known that AB=AC, ∠ A = 36, BC=2, and BD is the angular bisector of △ABC, then AD = ▲.
Third, solve the problem (this big problem is 64 points * * *. When answering questions, you should write out the necessary calculation or explanation process, and fill in the answer process in the corresponding position on the answer sheet)
19. (The full mark of this question is 5) Calculation:.
20. (The full mark of this question is 5) Solve the inequality and express the solution set on the number axis.
2 1. (The full mark of this question is 5 points) As shown in the figure, each small square in the grid paper is a square with a side length of 1. Rotate △ABC 90 clockwise around point D to get the corresponding △ A 'b 'c'.
(1) Please draw △ a 'b 'c' on the grid paper;
(2) The length of cc' is ▲.
22. (The full mark of this question is 6) It is known that points O (0 0,0), A (3 3,0) and B are on the Y axis, and
The area of delta delta △OAB is 6. Find the coordinates of point B.
23. (The full mark of this question is 6) As shown in the figure, in the trapezoidal ABCD, it is known that AD‖BC, AB=DC, ∠ ACB = 40, ∠ ACD = 30.
( 1)∠BAC =▲；
(2) If BC=5cm, connect BD and find the length of AC and BD.
24. (The full mark of this question is 6 points) As shown in the figure, the midline AF of △ABC intersects with the midline DE at point O, are AF and DE equally divided? Why?
25. (Full mark for this question is 7) In order to know the daily electricity consumption of the company, a company randomly checks the electricity consumption of the whole company 10 day within one month. The data are as follows (in degrees):
Degrees 9010010210116120.
Days 1 1 2 3 1 2
(1) Find the mode and average of the data in the above table;
(2) According to the obtained data, estimate the company's electricity consumption this month (calculated by 30 days); If the price per kilowatt hour is 0.5 yuan, what is the electricity bill this month?
26. (The full mark of this question is 8) It is known: As shown in the figure, in the rectangular ABCD, point E is on the side of AD, AE >；; DE, BE=BC, and point O is the midpoint of line segment CE.
(1) Try to explain that CE bisects ∠ bed;
(2) If AB=3 and BC = 5, find the length of BO;
(3) Is there a point F on the straight line AD, so that the quadrilateral with B, C, F and E as its vertices is a diamond? If it exists, try to draw the position of point F and make an appropriate explanation; If it does not exist, please explain why.
27. (The full mark of this question is 8) It is known that the image of a function passes through a point and intersects with the image of the function at a point.
( 1);
(2) If the intersection of the image and the function axis is B and the intersection of the image and the function axis is C, find the area of the quadrilateral (where O is the coordinate origin).
28. (The full mark of this question is 8) As shown in the figure, the quadrilateral OABC is a rectangle with point D on the side of OC. With AD as the crease, △OAD is folded upwards, and the point O just falls on the point E on the side of BC. If the circumference of △ECD is 2, the circumference of △EBA is 6.
(1) The circumference of the rectangular OABC is ▲;
(2) If the coordinate of point A is, find the analytical formula of the straight line where the line segment AE is located.
Investigation on the final learning ability of junior middle school students
Grade 2 Grade 2 Mathematics +00. 1
Question 123, total score, rater and reviewer
1— 10 1 1— 18 19 20 2 1 22 23 24 25 26 27 28
score
A, multiple-choice questions (this topic is entitled *** 10 small questions, 2 points for each small question, 20 points for each small question. Only one of the four options given in each small question meets the requirements of the topic. Please fill in the corresponding box below)
The title is 1 23455 6789 10.
answer
Fill in the blanks (this topic is entitled ***8 small questions, 2 points for each small question, *** 16 points. Please fill in the answer on the horizontal line of the corresponding question number below)
1 1.； 12.； 13.； 14.； 15.； 16.； 17.； 18.。
Third, solve the problem (this big problem is 64 points * * *. When answering questions, you should write out the necessary calculation or explanation process, and fill in the answer process in the corresponding position on the answer sheet)
19. (The full score of this question is 5)
Solution:
20. (The full score of this question is 5 points)
Solution:
2 1. (The full score of this question is 5 points)
Solution: the length of C C' is.
22. (The full mark of this question is 6 points)
Solution:
23. (The full mark of this question is 6 points)
Solution: (1) ∠ BAC = 0;
(2)
24. (The full mark of this question is 6 points)
Solution:
25. (The full mark of this question is 7 points)
Solution:
26. (The full mark of this question is 8)
Solution:
=
27. (The full mark of this question is 8)
Solution:
28. (The full mark of this question is 8)
Solution: (1) The circumference of the rectangular OABC is;
(2)
Investigation and research on junior high school students' learning ability
Mathematics Answers and Grading Criteria of Grade Two in Junior High School
First, multiple-choice questions (this big question * * 10 small questions, 2 points for each small question, ***20 points)
1.B 2。 B 3。 A 4。 D 5。 D 6。 C 7。 An eight. B 9。 A 10。 C
Fill in the blanks (this topic is entitled ***8 small questions, with 2 points for each small question and *** 16 points)
1 1.9 12.0 13.-3 14. 100 15.4 16.2 17.9 18.2
Iii. Answering questions (this big question * * 10 small question, ***64 points)
19. (The full score of this question is 5)
Solution: Original formula ... (3 points)
=- 1 ...(5 points)
20. (The full score of this question is 5 points)
Solution: Turn the inequality into, that is ... (3 points)
Accurately draw the representation (sketch) of the solution set on the number axis ..... (5 points)
2 1. (The full score of this question is 5 points)
Solution: (1) Draw a corresponding point accurately with 1 point, and draw two corresponding points accurately with 2 points.
Three points correspond to three points (sketch) ... (3 points)
(2)C C'= (Note: write here, no penalty will be deducted) ... (5 points)
22. (The full mark of this question is 6 points)
Solution: Let the coordinate of point B be (0, b).
Point O (0 0,0), A (3 3,0), ∴ OA = 3...(2 points)
Point B is on the Y axis, ∴△OAB is a right triangle ... (4 points)
Judging from the meaning of the question,
That is to say, the coordinates of point B are (0,4) or (0,4) ... (6 points).
23. (The full mark of this question is 6 points)
Solution: (1) ∠ BAC = 70...(2 points)
(2)∫∠ABC =∠BAC = 70, ∴ AC = BC = 5cm ... (4 points)
In trapezoidal ABCD, ab = cd, ∴ BD = AC = 5cm...(6 points)
24. (The full mark of this question is 6 points)
Solution: AF and DE are equally divided ... (2 points)
Connect DF, EF. ∫AF and DE are the midline and midline of △ABC respectively,
∴D, E and F are the midpoint of AB, AC and BC respectively.
∴DF‖AE, AD ... (4 points)
∴ Quadrilateral ADFE is a parallelogram, ∴AF and Germany are equally divided ... (6 points)
25. (The full mark of this question is 7 points)
The mode of solving (1) this set of data is110; ..... (2 points)
The average value is
...... (4 points)
(2) It is estimated that the electricity consumption of the Company this month is108× 30 = 3240 (kWh); ..... (6 points)
Electricity expenditure is about 3240×0.5= 1620 (yuan) ... (7 points)
26. (The full mark of this question is 8)
The solution (1)∫ quadrilateral ABCD is a rectangle, ∴AD‖BC, ∴ BCE = ∠ dec...( 1 min).
∵ Bei = BC, ∴∠ BC = ∠ Bei ... (2 points)
∴ce ∴∠bec=∠dec∠ Bed ... (3 points)
(2) In the right triangle BAE, AB=3, BE=BC=5, ∴ AE = 4...(4 points).
In right triangle CDE, CD=3, DE= 1, ∴ EC =...(5 points).
In the right triangle BOC, BC=5, CO=, ∴ Bo =. (6 points)
(Note: You can also use the equal area method to find BO here, and you can write it here without deduction. )
(3) There is a point f on the straight line AD, which makes the quadrilateral with B, C, F and E as its vertices become a diamond.
Expand ED to f so that EF=BC. At this point, the quadrilateral BCFE is a diamond ... (7 points)
∵AE & gt； de,∴be>； CE，
So there is no point F on the extension line of EA, which makes the quadrangle BCEF a diamond ... (8 points)
27. (The full mark of this question is 8)
Solution (1) As can be seen from the meaning of the question, ... (2 points)
(2)∵ intersection of straight lines,
∴, the solution ... (4 points)
∴ Intersection point of function image and X axis, ... (5 points)
The intersection of function image and Y axis, ... (6 points)
Say it again, ... (7 points)
∴ ...(8 points)
(Note: There are many ways to find the quadrilateral ABOC area in the second sub-question, so score as appropriate.)
28. (The full mark of this question is 8)
Solution (1) The circumference of a rectangular OABC is 8...(2 points)
(2)∵, ∴ ...(3 points)
∴ ...(4 points)
∴, that is, the coordinates of point E are ... (5 points)
Let the analytical formula of straight AE be,
So, the solution is ... (7 points)
The analytical formula of linear acoustic emission is ... (8 points)
(Note: There are many ways to find the coordinates of point E in the second sub-question, so score as appropriate)