(Examination time: 100 minutes, full mark: 120 minutes)
First, multiple-choice questions (2 points for each small question, 30 points for * * *)
The reciprocal of 1.2 is ()
A.-2 B.2 C.- D
2. In 2004, China's total fiscal revenue was 2170 billion yuan, which can be expressed as () by scientific notation.
A. 2 17× 103 billion yuan B.2 1.7× 103 billion yuan.
C.2.17×10.4 billion yuan D.2. 17× 10 billion yuan.
3. The following calculation is correct ()
A.+ = B .？ =
C.= d .≤=(≠0)
4. If the score is meaningful, it should satisfy ()
A.=0 B. ≠0
C.= 1d .Ͱ 1
5. Among the following radicals, the simplest quadratic radical is ().
A.B. C. D。
6. It is known that the radii of two circles are 3㎝ and 4㎝ respectively, and the center distance of the two circles is 10㎝, then the positional relationship between the two circles is ().
A. inscribed, intersected, circumscribed and separated
7. The solution set of inequality group can be expressed as () on the number axis.
8. Given k > 0, the image of function y= is roughly ().
9. In △ABC, ∠ c = 90, AC=BC= 1, then the value of Sina is ().
A. BC 1 year.
10. As shown in the figure, AB‖CD, AC⊥BC, the complementary angle with ∠CAB in the figure is ().
A. 1
C.3 D.4
1 1. On the map with the scale of 1: 600000, the distance from Nanjing to Beijing is 15㎝, and the actual distance between the two places is ().
a.0.9㎞·9㎞c.90㎞d.900㎞
12. If the side length of an equilateral triangle is 6, then the radius of its inscribed circle is ().
The third century BC.
13. Observe the following formula: 2 1=2, 22=4, 23=8, 24= 16, 25=32, 26=64, 27= 128, 28 = 250.
A.2 B.4 C.6 D.8
14. There is a square piece of land with a side length of, and the gardener has designed four different patterns, among which the shaded part is used for planting flowers and plants, and the largest area for planting flowers and plants is ().
15. As shown in the figure, OA and BA respectively represent the linear function images of two students' movements. In the figure, and respectively represent the distance and time of movement. Judging from the image, the speed of A and B is compared, and the following statement is correct ().
A.A is faster than B. A is slower than B.
C.a and b are the same. D. can't judge
Two. Fill in the blanks (2 points for each question, *** 12 points)
The square root of 16.9 is.
17. Decomposition factor:-=.
18. In the function, the range of independent variables is.
19. Among the geometric figures you have studied, there are (write two) that are both axisymmetric and centrally symmetric.
20. As shown in the figure, PA cuts ⊙O at point A, PC passes through point O, and at points B and C, if PA=6㎝ and PB=4㎝, then the radius of ⊙O is ㎝.
2 1. As shown in the figure, when,, =3㎝, =4㎝, taking the straight line where the edge is located as the axis, it will rotate once, then the lateral area of the obtained branch geometry is (the result keeps π).
Third, solve the problem (6 points for each small question, 30 points for * * *)
22. calculation?
23. Solving equations
24. It is known that, as shown in the figure, intersects with the point, ‖, =, and is the midpoint respectively. Prove that a quadrilateral is a parallelogram.
25. The voltage of the battery is constant. When using this power supply, the functional relationship between current and resistance is shown in the figure: write the expression of this function.
26. At the beginning of the year, a shipping company bought a transport ship for 6.5438+0.2 million yuan. After being put into transportation, the total annual income is 720,000 yuan, and the required expenses are 400,000 yuan.
(1) Q: After several years of transportation, the ship began to make a profit (profit means that the difference between the total income MINUS the ship purchase fee and all expenses is positive? )
(2) If the ship is scrapped after 15 years of transportation, 200,000 yuan can be recovered when the old ship is scrapped, and the average profit for this 15 years can be obtained (exactly 0. 1 10,000 yuan).
Four, (this question 6 points)
27. All 320 students in the third grade of a school took the same level exams before and after computer training, and the test scores were divided into three grades according to the same standard: failed, qualified and excellent. In order to understand the effect of computer training, 64 students' test scores were obtained by drawing lots. The statistical chart drawn is as shown in the figure. Try to answer the following questions with graphic information:
(1) The grades of the median test scores of these 64 trainees before training are:
(2) It is estimated that there are famous students with "excellent" results after training in the whole third grade of the school;
(3) Do you think the above estimate is reasonable? Why?
Answer: reason:.
V. (6 points for this question)
28. As shown in the figure, it is known that there are reefs within 7 nautical miles around Lighthouse A. A fishing boat measured Lighthouse A at point B at 60 north of due east, and after sailing 8 nautical miles east of C, it measured Lighthouse A at 30 north of due east. The fishing boat continued to sail eastward without changing course. Is there any danger of hitting the rocks? Please explain the reason by calculation (reference data 1.732).
Six, (this question 6 points)
29. as shown in the figure, d is a point on AC, BE‖AC, BE=AD, AE intersects BD and BC at f, g, ∠ 1=∠2 respectively.
Which triangle in the (1) graph is congruent with △FAD? Prove your conclusion;
(2) Explore the relationship among line segments BF, FG and EF, and explain the reasons.
Seven, (this question 6 points)
30. As shown in the figure, it is the diameter ⊙, the point is the midpoint of the radius, and the point moves on the line segment (not coincident with the point). The point moves on the upper semicircle, and always keeps the extension line of the tangent intersecting the point at this point.
(1) When, it is judged as a triangle;
(2) If yes, please guess the shape and give proof;
(3) It is further inferred from the conclusions of (1) and (2) that when a point moves to any position on a line segment, it must be a triangle.
Eight, (this question 7 points)
3 1. Read the article first, and then answer the questions at the back of the article:
In geometry, a point is usually used to indicate the position, the length of a line segment is used to indicate the distance between two points, and a ray is used to indicate the direction.
At the two endpoints of a line segment (as shown in the figure), if we specify an order: the starting point and the ending point, we say that this line segment has the direction of rays, and this line segment is called a directed line segment, and its length is called the length (or modulus) of the directed line segment, and it is called.
A directed line segment contains three elements, starting point, direction and length. The starting point of a directed line segment is known, and its ending point is uniquely determined by the direction and length.
Answer the following questions:
(1) Draw a directed line segment in the plane rectangular coordinate system (the length unit of the directed line segment is the same as that of the shaft), and the included angle with the positive semi-axis of the shaft is, and the included angle with the positive semi-axis of the shaft is;
(3) If the terminal coordinate is (3), find its modulus and the degree of included angle with the positive and semi-axis of the shaft.
Nine, (this topic 7 points)
32. After market research, a company decided to implement "limited production and limited storage" for products A and B from next year, and planned to produce 20 pieces of these two products throughout the year. The total output value of these 20 pieces is not less than 1 1.4 million yuan and not more than1/.7 million yuan. The known data are shown in the following table:
The output value of each product.
0.45 million yuan
0.75 million yuan
(1) suppose to produce x product A (X is a positive integer), and write the inequality group that x should satisfy;
(2) Please help design all the production schemes that meet the requirements.
Ten, (this question 10)
33. As shown in figure 1, in the isosceles trapezoid, the ‖ point moves along the edge at a speed of 3-s from the beginning, and the point moves along the CD edge at a speed of1-s from the beginning. If each point starts from and at the same time, when one of the points reaches the end point, let the movement time be.
At what value is (1), a quadrilateral is an equilateral quadrilateral?
(2) As shown in Figure 2, if the radii of ⊙ and ⊙ are both 2㎝, then why are ⊙ and ⊙ circumscribed?
In 2009, the entrance examination for senior high school entrance examination in mathematics was completely simulated (9).
I. 1. a2 . C3 . D4 . D5 . B6 . D7 . A8 . a9 . b 10。 B 1。 D 12。 B 13.C65438。
Two. 16.317.18.19. Rectangular and circular 20.2.5㎝ 2 1. 15π.
Third, 22. The solution of the original formula =
23. Solving the original equation can be transformed into. When the solution is found, the solution is the root of the original equation.
24. ∫ AC BD ∴∠ C = ∠ D ∠ Cao = ∠ DBAO = Bo ∴△ AOC △ BOD ∴∴ of = OD = OC = OE, and f is respectively The quadrilateral table AFBE with AO=BO and EO=FO ∴ is an equilateral quadrilateral.
25. The inverse proportional function that is feasible from the image is set by the expression of (2, 18) ∴ function: =.
26.( 1) Assuming that the shipyard starts to make profits after X years of transportation, and 72x-( 120+40x) > 0, x >, then the ship starts to make profits after 4 years of transportation. (2) (ten thousand yuan).
Four. 27.( 1) Unqualified (2) 80. (3) Reasonable reasons. Use the unfinished quantity of the sample to calculate the total unfinished quantity.
Verb (abbreviation of verb) 28. Let AD⊥BC cross the BC extension line at point D, and let AD=. In Rt△ACD, ∠ CAD = 30 ∴ CD =. In Rt△ABD, ∠Abd = 30∴BD =∫BC = 8∴ there is danger of hitting the rocks.
29. Solution: (1)△. Proof: (2) reason:. Once again, that is.
7.30. Solve (1) isosceles right triangle (2) as J equilateral triangle.
Prove; The tangent of the connecting line is an equilateral triangle. (3) isosceles triangle.
8 3 1. (1) Draw a sketch (2)
It's nine thirty-two ( 1) 1 140≤45x+75(20-x)≤ 170(2) 1 1≤x≤ 12。 20- 1 1=9 When = 12, 20- 12=8∴ Production 1 1 product A, 9 product B or1.
10.33. solution: (1)∵DQ//AP, ∴ when AP=DQ, the quadrilateral APQD is a parallelogram. At this time, 3t = 8-T. The solution is t=2(s). That is, when t is 2s, the quadrilateral APQD is a parallelogram.
(2) The radii of Φ ⊙ P and Φ ⊙ Q are both 2cm. When PQ=4cm, Φ ⊙ P and Φ ⊙ Q are circumscribed. When PQ=4cm, if PQ//AD, then the quadrilateral APQD is a parallelogram.
① When the quadrilateral APQD is a parallelogram, t=2(s) is obtained from (1).
② When the quadrilateral APQD is isosceles trapezoid, ∠A=∠APQ. ∵ In the isosceles trapezoid ABCD, ∠A=∠B, ∴∠ APQ = ∠ B. ∴PQ//BC. Quadrilateral parallelogram. At this time, CQ=PB. ∴t= 12-3t。 T3(s) is obtained.
To sum up, when t is 2s or 3s, ⊙P and ⊙Q are tangent.
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