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I. Multiple choice questions (*** 10 small questions, 3 points for each small question, out of 30 points)
1.
three
The absolute value of is ()
A.
three
B.-
three
C.3 D.-3
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2. The Xihanggang Economic Development Zone in Shuangliu County was officially recognized by the Ministry of Science and Technology as the "National New Energy Equipment High-tech Industrialization Base", and it is one of the five 50 billion yuan parks cultivated by "1525 Project", of which 50 billion yuan is represented by () billion yuan.
a . 0.5× 103 b . 5× 102 c . 0.5× 104d . 5× 103
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3. In the following operations, the correct one is ()
A.2m2+3m3=5m5 B.a2？ a3=a6
C.(-x2)3=x6 D.(a+b)(a-b)=a2-b2
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4. Among the following Chinese characters, which can be regarded as an axisymmetric figure is ()
A. double B. you C. eyes D. axis
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5. As shown in the figure, a∨b, ∠ 1 = 100, then ∠2= ()
a . 80 b . 90 c . 100d . 1 10
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6. A geometric three-view as shown in the figure, which is ().
A. triangular prism B. triangular pyramid C. quadrangular prism D. quadrangular pyramid
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7. In the grid paper as shown in the figure, the small tree rotates and translates from position A to position B, so the following statement is correct ().
A. rotate 90 counterclockwise around point a, and then translate 7 squares to the right.
B. Rotate 45 counterclockwise around point A, and then translate 7 squares to the right.
C. rotate 90 clockwise around point a, and then translate 7 squares to the right.
D. Rotate 45 clockwise around point A, and then translate 7 squares to the right.
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8. The distance between A and B is 100 km, and a train travels from A to B at a speed of 50 km/h. Assuming that the distance between the train and B is S (km) and the travel time is t (hours), the function image of S about T is ().
A.B. C. D。
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9. As shown in the figure, in delta ABC, the bisector of ∠ABC and ∠ACB intersect at point D, and ∠ A = 50, then ∠D= ().
A. 15
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10. given the image of quadratic function y=ax2+bx+c as shown in the figure, in the same rectangular coordinate system, the linear function y=ax+b and the inverse proportional function Y =
c
x
The image is roughly ()
A.B. C. D。
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Fill in the blanks (***4 small questions, 4 points for each small question, full score 16)
1 1. There are three red balls and two white balls in a bag. These balls are identical in shape and size except for their different colors. Now, if you randomly draw a ball from this bag, the probability of touching a white ball is
2
five
.
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12. Decomposition coefficient: 2a2-8=
2(a+2)(a-2)
.
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13. Function y=
1
x+2
In, the value range of the independent variable x is
x>-2
.
☆☆☆☆☆
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14. As shown in the figure, if ∠ AOB = 80, ∠ACB=
140
.
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Iii. Answer questions (*** 1 small questions, full marks 12)
15.( 1) Calculation: (π? 3. 14)0? (?
1
2
)? 1+
eight
cos45。
(2) Simplify first and then evaluate: (
2x
x？ 1
x
x+ 1
)÷
x
x2？ 1
, where x =
2
3.
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Iv. Answering questions (3 small questions in this big question, 8 points for each small question, 24 points for * * *)
16. Shuangliu county Xincheng wetland park project headquarters plans to lay floor tiles in the leisure area 1600m2, which will be completed by two engineering teams. If Team A works alone for 5 days, the remaining projects will be completed by Team B for 2 days. If Team A works alone for 2 days and the rest is done by Team B for 4 days, which team is more efficient? How much higher?
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17. When the mathematics study group of a school measured the height of flagpole on the campus flag platform with a goniometer, the elevation of E at the top of flagpole was 30 at B, 45 at D, BD= 10 m, the height of goniometer AB was 1.5 m, and the height of flag platform MN was 0.
8m。 Find the height of flagpole EF (accurate to 0. 1m, reference data:
2
≈ 1.4 14,
three
≈ 1.732).
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18. Xiaogang hopes to visit the Shanghai World Expo after the senior high school entrance examination this year. His father, a math teacher, designed a roulette game for him: rotate the following two roulette wheels A and B (each roulette wheel is divided into five equal parts) once, and add the figures. If their sum is 12, they will be brought.
He went to Shanghai to visit the World Expo. Would you please use a tree diagram (or table) to help Xiaogang calculate the probability that he can visit the Shanghai World Expo?
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Verb (abbreviation of verb) solving problems (this big problem has two small questions, each with 9 points, *** 18 points)
19. As shown in the figure, the image of the linear function intersects with the X axis and the Y axis at point A and point B respectively, and the coordinates of point A and point B are (4,0) respectively.
),(0,3).
(1) Find the expression of a linear function.
(2) Point C is on the line segment OA, and it is folded along BC by △OBC, and point O just falls on D on AB, thus the expression of straight line BC is obtained.
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20. As shown in the figure, in quadrilateral ABCD, the images of AD < BC, diagonal AC and BD intersect at O point, AC=BD, ∠ ACB = ∠ AD 0 intersect at two points: A(x 1, y 1), B(x2, y2) (.
three
Time magazine.
(1) Find the value of y 1-y2.
(2) Find the function relation between k and m, and draw a sketch of the function image.
(3) Are there real numbers k and m that make the area of trapezoidal AEFB 6? If it exists, find the values of k and m; If it does not exist, please explain why.