This paper consists of three types of questions: fill-in-the-blank questions, multiple-choice questions and solution questions. * * * 29 small questions. The perfect score is 130. Examination time 120 minutes.
Fill in the blanks: this big problem has its l 2 small problem. 3 points for each small question, 36 points for * * *. Fill the answer directly in the corresponding position on the answer sheet.
The reciprocal of 1 Yes.
2. Calculate =.
3. A school held "Sunshine Sports" at three o'clock in the afternoon. At 3 o'clock in the afternoon, the angle between the minute hand and the hour hand of the clock is equal to degrees.
4. In the function, the range of independent variables is.
5. Factorization: =.
6. As shown in the figure, the bottom of a horizontally placed cuboid is a rectangle with sides of 2 and 4, and its left view.
If the area of is 6, the volume of this cuboid is equal to.
7. Xiaoming's achievements in the 700-meter race are as follows:
The median of these seven grades is seconds.
8. In order to welcome the 2008 Beijing Olympic Games, Xiao Tian designed two kinds of table tennis, one with the Olympic rings printed on it and the other with the Olympic rings printed on it.
There are Olympic Fuwa patterns. If you put eight table tennis balls with Olympic rings and 12 table tennis balls with Olympic Fuwa patterns into one.
In an empty bag, each ball is the same size. Stir it and find a ball randomly in your pocket. Then touch the one printed with the Olympic rings.
The probability of the ball is.
9. If a quadratic equation with one variable has two real roots, the value range of m is.
10. Make a regular octagon with a side length of 1 into a square as shown in the figure.
The side length of this square is equal to (the result retains the root sign).
1 1.6 From June 1, a supermarket began to provide three kinds of reusable products for free.
Reusable shopping bags, each price is 1 yuan, 2 yuan, 3 yuan, each of these three reusable shopping bags can hold rice at most.
3 kg, 5 kg, 8 kg. On June 7th, Xiaoxing and her father bought three reusable shopping bags in the supermarket.
They bought 20 kilograms of bulk rice, and they had to pay at least RMB to the supermarket for three reusable shopping bags.
12. When drawing the image of quadratic function with "tracing point method" in the third grade mathematics textbook, the following table is listed:
Answer the questions according to the information in the table: when = subfunction =3, y =.
Second, multiple-choice questions: this big question ***6 small questions, 3 points for each small question, *** 18 points. Of the four options given in each small question, only one meets the requirements of the topic Please use 2B pencil to paint the answers to multiple-choice questions on the answer sheet.
13. The following operations are correct.
A.B. C. D。
14. In the function, the range of independent variables is
A.≠0 b ≠ c ≠ 1 d ≠1
15. According to Suzhou City Business Daily on May 26, 2008, it has been two weeks since the Wenchuan earthquake, but all walks of life have been devastated.
The love of donating money and materials in the district is still endless. As of May 25th, 2008, Suzhou Red Cross Society has received more than ten thousand donations.
Donation15 million yuan. 15000000 can be expressed by scientific notation as follows
a . 1.5× 106 b . 1.5× 107 c . 1.5× 108d . 1.5× 109
16. In the following figure, the axisymmetric figure is
17. If is, the value of is equal to.
University of California, Los Angeles or
18. As shown in the figure. AB is the diameter ⊙O, AC crosses ⊙O at point E, BC crosses ⊙O at point D, CD=BD, ∠ c = 70.
Now give the following four conclusions:
①∠A = 45； ②AC=AB:
③ ; ④CE？ AB=2BD2。
The number of the correct conclusion is
A.①② B.②③
C.②④ D.③④
Iii. Answer: This big question * * 1 1 small question, with a score of ***76. Write down the answer process in the corresponding position on the answer sheet. When you answer, you should write
Draw the necessary calculation process, derivation steps or text description. Sign the drawing with 2B pencil or black ink.
19. (5 points for this question)
Calculation:.
20. (5 points for this question) Simplify before evaluating:
, among them.
2 1. (5 points for this question)
Solve the equation:
22. (6 points for this question)
Solve the inequality group: and judge whether the inequality group is satisfied.
23. (6 points for this question)
As shown in the figure, diagonal lines AC and BD of quadrilateral ABCD.
Intersect at point O, ∠ 1=∠2, ∠ 3 = ∠ 4.
Verification: (1) △ ABC △ ADC;
(2)BO=DO。
24. (6 points for this question)
The factory produces a product. Figure ① is the statistical chart of the factory's output in the first quarter for three months, and Figure ② is the relationship between the output of these three months and the factory's output.
When making charts ① and ②, statisticians omitted some data in the statistical chart of the proportion distribution of total output in the first quarter.
According to the above information, answer the following questions:
(l) In which month was the highest output of this factory in the first quarter? Month.
The output of this factory in January accounted for% of the total output in the first quarter.
(3) The quality inspection department of this factory conducted sampling inspection on the products in the first quarter, and the qualified rate of the samples was 98%.
Please estimate: How many qualified products did this factory produce in the first quarter? (Write out the solution process)
25. (8 points for this question) As shown in the picture, sailing boat A and sailing boat B are training on the lake surface of Taihu Lake, with O as the fixed point on the lake surface, and the coach boat is waiting for O point. During training, the two ships A and B are required to be always symmetrical about the O point. With O as the origin, establish the coordinate system as shown in the figure, and the positive directions of the axis and the Y axis represent the due east and north directions respectively. Let two ships, A and B, be approximately regarded as moving on a hyperbola, and the lake. The double sails have a beautiful distant shadow. During the training, when the coach ship and the two ships A and B happened to be in a straight line, Minlang elegy also found the AC ship in distress on the lake. At this time, the coach ship measured that the C ship was 45 in the southeast, the angle between AC and AB measured by A ship was 60, and the position of C ship was also measured by B ship (assuming that the position of C ship will not change,
A, B and C Minlang's elegy can be represented by three points (A, B and C respectively).
(1) When the ship C was discovered, the position coordinates of Minlang's elegies A, B and C were respectively
A (,), B (,) and
c(，)；
(2) When the C ship was discovered, Minlang's elegy immediately stopped training and started training from A, O and B respectively.
Set out at three o'clock and go to the rescue along the shortest route at the same time, two ships, A and B.
The speed of the coach ship is equal, and the speed ratio of the coach ship to the A ship is 3: 4.
Ask the coach if the boat arrived first. Please provide a justification for the answer.
26. (8 points for this question)
As shown in the figure, in the isosceles trapezoid ABCD, AD‖BC, AB=DC=5, AD=6, BC = 12. The moving point p starts from point d.
The starting point moves along DC to the end point C at a speed of 1 unit per second, and the moving point Q starts from point C and moves along CB at a speed of 2 units per second.
The speed at which bit moves to point B starts at two o'clock at the same time, and when point P reaches point C, point Q stops moving.
(1) The area of trapezoidal ABCD is equal to;
(2) When PQ//AB, the time from point P to point D is equal to
Seconds;
(3) When P, Q and C form a right triangle, P leaves.
How long will it take at d?
27. (Question 9) As shown in the figure, in △ABC, ∠ BAC = 90, BM divides ∠ABC into m, A as the center, AM as the radius, OA into BM into N, AN's extension line into BC into D, straight line AB into OA at P and K, and MT⊥BC into T.
(1) Verify AK = mt
(2) Textual research: AD ⊥ BC;
(3) When AK=BD,
Verification:
28. (Question 9) In class, the teacher rotates the △AOB in Figure ① counterclockwise around point O, and finds that the shape and size of the figure remain unchanged during the rotation, but the position has changed. When △AOB rotates 90, △ A 1OB 1 is obtained. A (4 4,2) and B (3 3,0) are known.
The area of (1)△A 1OB 1 is;
The coordinates of point A 1 are (,; The coordinate of point B 1 is (,);
(2) After class, Xiaoling and Xiaohui continue to discuss this problem and reverse the time of △AOB near the AO midpoint C (2, 1) in Figure ②.
Rotate the needle by 90 to get △ a ′ o ′ b ′. Let o ′ b ′ and o ′ a ′ intersect at d, and o ′ a ′ intersects at e. At this time, the coordinates of a ′, o ′ and b ′ are (1, 3) and (3,-1) respectively.
(3) Under the condition of (2), the radius of the △AOB circumscribed circle is equal to.
29. (9 points for this question) As shown in the figure, the intersection of parabola and axis is m and n, and the straight line intersects the axis at p (-2,0). It intersects the y axis at C. If A and B are on a straight line and AO=BO=,
AO⊥BO.d is the midpoint of line segment MN. OH is the height on the hypotenuse of Rt△OPC.
The length of (1)OH is equal to; k=，b=。
(2) Whether there is a real number A, so that a point f on the parabola satisfies the vertices of d, n and e;
Is triangle similar to delta delta △AOB? If it does not exist, explain the reasons; If it exists, find the analytical expressions of all qualified parabolas. At the same time, it is explored whether there is a qualified E point on the obtained parabola (briefly explain the reasons), and further explored whether the intersection point G of the straight line ne and the straight line AB always satisfies PB for each qualified E point. PG 10, write the exploration process.