June 2003/15 full mark 120, examination time 100 minutes.
1. Multiple choice questions (this question 15, 3 points for each question, * * 45 points) Only one of the four options given in each question below is correct. Please fill in the letters before the correct option in the corresponding box on the answer sheet.
The image of 1. linear function fails ()
(a) the first quadrant (b) the second quadrant
(c) the third quadrant (d) the fourth quadrant
2. In the cube as shown in the figure, the plane perpendicular to the side BB 1 and the plane CD 1 has ().
1 (B)2 (C)3 (D)4。
3. A store holds a prize-winning sales activity, and the measures are as follows: whoever buys more than 100 yuan will get a lottery ticket, and the more you buy, the more you get. Every 10000 lottery tickets is a lottery unit, with a total of 1 grand prize, 50 first prizes and 100 second prizes. Then the winning probability of buying 100 yuan is ()
(A) (B) (C) (D)
4. Calculated ()
1 (B)- 1 (C) (D)
The area of Tiananmen Square is about 440,000 square meters. Please estimate that one millionth of it is equivalent to ().
(a) The area of the classroom floor (b) The area of the blackboard.
(c) the area of the desktop (d) the area of the surface of the pencil case.
6. The side development diagram of the cylinder is a rectangle with an area of 4 square units, so the functional relationship between the length of the generatrix and the bottom radius of the cylinder is ().
(a) Positive proportional function (b) Inverse proportional function (c) Linear function (d) Quadratic function
7. As we all know, then the value is ().
(A)3 (B)4 (C)5 (D)6
8. Judge that the area of ABC is several times that of ABC, and only use a ruler with scale, and the number of measurements is at least ().
(A)3 times (B)2 times (C) 1 time (D)3 times or more.
9. There is a rectangular aluminum sheet with a length of and a width of. Cut a square with the same side length at each corner and fold it to make a box without a cover. Then the expression of the volume v of this box should be ().
(A) (B)
(C) (D)
10. As shown in the figure, if point C is a point on the chord AB of ⊙O, point P is a point above ⊙O, and OC⊥CP, there is ().
(A)OC2 = Canada? OC2=PA？ PB (C)PC2=PA？ PB (D)PC2=CA？ Civil band
1 1. The analytical formula of the obtained image is, then there is ().
(1) and (2),
(C)、(D)，
12. Let, be two equations about, be two equations about, then, the values of are equal to () respectively.
(A) 1，-3 (B) 1，3 (C)- 1，-3 (D)- 1，3
13. A certain type of air conditioner is reduced by 30% for three times, and the average percentage of each price reduction (accurate to 1%) should be ().
(A)26.0%(B)33. 1%(C)8.5%(D) 1 1.2%
14. On the expressway, a car with a length of 4m and a speed of 1 10km/h is ready to overtake a truck with a length of 12m and a speed of 10km/h, so it takes about () for the car to catch up with and overtake the truck.
(A) 1.6 seconds (B)4.32 seconds (C)5.76 seconds (D)345.6 seconds.
15. For the following four propositions: ① If two sides of a right triangle are 3 and 4, the third side is 5; ② ; ③ If point P (,) is in the third quadrant, point Q (,) is in the first quadrant; ④ The median lines of two sides and the third side correspond to the congruence of two equal triangles. The correct statement is ()
(a) Only ① is wrong and everything else is right; (B)①② is wrong and ③ ④ is right.
(C)①④ Wrong, ② ③ Correct (d) Only ④ Wrong, others correct.
Fill in the blanks (there are 5 small questions in this question, each with 4 points and * * * 20 points)
16. According to the figures released by the Ministry of Information Industry in April 2003, the number of fixed-line and mobile phone users in China has increased significantly in recent years, and mobile phone users are close to fixed-line users. According to the picture on the right, the fixed-line telephone in China increased the most from _ _ _ _ to _ _ _ _. From _ _ _ _ _ to _ _ _ _ _ the annual increment of mobile phones is the largest.
17. As shown in the figure, the high lines CE and BF of the AB side and AC side of the acute triangle ABC intersect at point D. Please write two pairs of similar triangles in the figure: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (connected by similar symbols).
18. A main player of Zhejiang Wanma Basketball Team scored 28 points in a game with 22 shots 14. In addition to three three-pointers, he also hit _ _ _ _ _ two-pointers and _ _ _ _ free throws.
19. According to the instruction [s, a] (s ≥ 0,0o
20. To find the minimum value of a function, the appropriate mathematical method should be: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
3. Answer questions (6 small questions in this question, ***55 points). The answer should be clearly written about the process or deduction steps.
2 1. (The full score for this short question is 7)
There are five real numbers in the set circle on the right. Please calculate the difference between the sum of rational numbers and the product of irrational numbers.
22. (The full mark of this question is 8)
As shown in the figure, EF is the center line of trapezoidal ABCD, and AH bisects ∠DAB intersects EF in M, and extended DM intersects AB in N. ..
Prove: Triangle sum is isosceles triangle.
23. (The full score for this short question is 8)
As shown in the figure, ⊙C passes through the origin and intersects the two coordinate axes of point A and point B respectively. The coordinate of point A is (0,4), m is a point on the circle, and ∠ BMO = 120o. Find the radius of ⊙C and the coordinates of the center C.
24. (Full score for this small question 10)
Solve the equation:
25. (Full score for this small question 10)
Brown-red smoke from converter steelmaking will pollute the atmosphere. A device can reduce pollution by recovering iron oxide from brown-red flue gas, and the iron oxide recovery rate of the device is related to the current it passes through. The following data were obtained through experiments:
Passing current intensity (unit a)11.71.9 2.12.4
Iron oxide recovery rate (%) 75 79 88 87 78
As shown in the figure, a rectangular coordinate system is established, with the abscissa representing the current intensity and the ordinate representing the iron oxide recovery rate.
(1) The data obtained from the test are represented by points in the rectangular coordinate system given on the right (note: the intersection of coordinate axes in this drawing represents points (1, 70));
(2) Connect the points (1) drawn in the question with line segments from left to right. If this image is used to simulate the functional relationship between iron oxide recovery y and current x, try to write the expression of this function when 1.7≤x≤2.4;
(3) Using the function relation obtained in question (2), when the iron oxide recovery rate is greater than 85%, the current range that the device should control (accurate to 0. 1A).
26. (The full score of this short question is 12)
As shown in the figure, in rectangular ABCD, BD = 20, AD > AB, let ∠ AD>AB = α, and it is known that sinα is the real root of the equation, and points E and F are points on BC and DC respectively, EC+CF = 8, let Be = X, and the area of δδAEF is equal to Y.
(1) Find the functional relationship between y and x;
(2) When E and F are positioned, what is the minimum value of Y? Find this minimum.
Answer:
2 1.
22.
23.
24.
25.
26.