mathematics
There are 8 big questions and 23 small questions in this paper, with full score of 150 and examination time of 120 minutes.
First, multiple-choice questions (this big question * *10 small questions, 4 points for each small question, out of 40 points)
Each item gives four options, code A, B, C and D, and only one is correct. Please write the code name of the correct option in brackets after the item, and get 4 points for each option. If you don't choose, choose wrong or choose more than one code (whether written in brackets or not), you will get 0 point.
1. In the following figures, the sum with -3 is 0 ........................ ().
3rd century BC to 3rd century BC.
2. In the following geometry, the front (front) view is a triangle ().
A.B. C. D。
3. The result of calculation is ()
A.B. C. D。
4. Among the following polynomials, the one that can be factorized is ().
A.B.
C.D.
5. The output value of an enterprise in March this year was10,000 yuan, which decreased by 65,438+00% in April and increased by 65,438+05% in May, so the output value in May was ().
A.(- 10%) (+ 15%) ten thousand yuan B. (1-10%) (1+15%) ten thousand yuan.
C.(- 10%+ 15%) ten thousand yuan D. (1-10%+15%) ten thousand yuan.
6. The result of simplification is ()
A.+ 1 B. - 1 C .
7. In order to increase the green area, the original square floor tiles were replaced by regular octagonal grass-planting bricks, as shown in the figure. After replacement, the shaded area in the figure is grass planting area, and the shaded area is ()
A.2 B. 3
C.4 D.5
8. Call A, B and C. If the call order is arbitrary, the probability of calling A first is ()
A.B. C. D。
9. As shown in the figure, point A is on ⊙O with a radius of 2, point P on the line segment OA is a straight line, which intersects with the tangent of ⊙O passing through point A at point B, and ∠ APB = 60, and let OP=, then the function image about the area y of △PAB is roughly ().
10. Take one point from each right-angled edge of a right-angled triangular piece of paper and cut off two triangles along the connecting line between the midpoint of the hypotenuse and these two points. The rest is a right-angled trapezoid as shown in the figure, in which the three sides are 2, 4 and 3 respectively, so the length of the hypotenuse of the original right-angled triangular paper is ().
A. 10 B. C. 10 or D. 10 or
2. Fill in the blanks (4 small questions in this big question, 5 points for each small question, out of 20 points)
The annual cotton output in Anhui province11.201/kloc-0 is about 378,000 tons, and the scientific statistics show that 378,000 tons should be _ _ _ _ _ _ _ _.
12.A, b and c have 7 members each, and the average weight data of the members of the three groups are all 58, and the variance is 0,0 respectively, so the group with the least data fluctuation is _ _ _ _ _ _ _ _.
13. As shown in the figure, points A, B, C and D are on ⊙O, point O is within ∠D, and the quadrilateral OABC is a parallelogram, then ∠ oad+∠ OCD = _ _ _ _ _ _ _ _ _ _ _ _ _ _
14. As shown in the figure, p is any point in the rectangular ABCD, and △PAB, △PBC, △PCD and △PDA are obtained by connecting PA, PB, PC and PD. Let their regions be S 1, S2, S3 and S4 respectively, and give the following conclusions:
①s 1+S2 = S3+S4②S2+S4 = s 1+S3
③ If S3=2 S 1, S4=2 S2 ④ If S 1= S2, the point P is on the diagonal of the rectangle.
The serial number of the correct conclusion is _ _ _ _ _ _ _ _ _ (fill in the serial number of all correct conclusions on the horizontal line).
Three. (This topic is entitled ***2 small questions, with 8 points for each small question, with a full score of 16).
15. Calculation:
Solution:
[Source: Xue&; Departments and networks & ampX & ampX & ampK]
16. Solve the equation:
Solution:
Four. (This topic is entitled ***2 small questions, with 8 points for each small question, with a full score of 16).
17. In a rectangular grid composed of m× n (m× n > 1), the number f of small squares crossed by a diagonal line is studied.
(1) When m and n are coprime (m and n have no common factor except 1), observe the following figure and complete the following table:
1
2
three
2
1
three
four
three
2
three
five
four
2
four
seven
three
five
seven
Conjecture: When m and n are coprime, in the rectangular grid of m×n, the relationship between the number f of small squares crossed by a diagonal line and m and n is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (without proof);
Solution:
(2) When m and n are not prime numbers, please draw a picture to verify whether the relationship you guessed still holds.
Solution:
[Source: Z &；; xx & ampk.Com ]
18. As shown in the figure, in the grid composed of small squares with the side length of 1, the grid point △ABC (the vertex is the intersection of grid lines) and the point A 1 are given.
(1) Draw a grid point △ A 1 b1to make it congruent with △ABC and A and A1are corresponding points;
Map number 18