1. Multiple choice questions: (This big question is a small question of *** 10, with 4 points for each small question and 40 points for * * *. Of the four options given in each small question, exactly one meets the requirements of the topic. Please fill in the code of the correct option in the corresponding position on the answer sheet. )
1. Among the following quadratic roots, the simplest quadratic root is ().
A.B C. D。
2. In the plane rectangular coordinate system, the number of times the parabola intersects the axis is ().
A.3 B.2 C. 1 D.0
3. The root of the equation is ()
A.B. C. D。
4. As shown in figure 1, in order to measure the width DE of a pond, find a point C on the shore, CD=30m, a point A on the extension line of DC, AC=5m, passing point A as AB‖DE, and crossing the extension line of EC at B, AB=6m, then the width DE of the pond is ().
a、25m B、30m
36 meters deep, 40 meters
5. In △ABC, the hypotenuse AB = 4° and ∠ B = 60. Rotate △ABC around point B by 60, and the routing length of vertex C is ().
A.B. C. D。
6. Rectangular ABCD, AB=4, BC=3. The lateral area of the cylinder obtained by rotating the straight line AB as the axis is
A.20л B.24л C.28л D.32л
7. The following proposition is wrong ()
A.you can make a circle after three o'clock.
The distance from the outer center of the triangle to each vertex of the triangle is equal.
C In the same circle or equal circle, the circular arcs with equal central angles are equal.
A straight line passing through the tangent point and perpendicular to the tangent line must pass through the center of the circle.
8. Zhang Hua wants his teacher Wang to send a message to pay a New Year call, but he can't remember the order of the last three digits of teacher Wang's mobile phone number at the moment, only the three digits of 1, 6 and 9, so the probability that Zhang Hua can send a message at one time is ().
A.B. C. D。
9. To celebrate the anniversary of Macao's return to the motherland 10, the fireworks factory specially designed and produced a new salute. The relationship between the lift-off height of this salute and the flight time is as follows: If this salute is detonated at the highest point, the time from ignition to lift-off is ().
(A) (B) (C) (D)
10. Xiaoming observed the following five pieces of information from the quadratic function image shown in the figure: ①; ② ; ③ ; ④ ; ⑤ ,
What is correct is that
1。
Fill-in-the-blank question: (Question ***6, you don't need to write the solution process of each small question 4***24, please fill in the final result in the corresponding position on the answer sheet. )
1 1. If, then.
12.in 2008, the per capita annual income of farmers in a county was 7 800 yuan, and it is planned that by 20 10, the per capita annual income of farmers will reach 9 100 yuan. If the average growth rate of per capita annual income is 0, the equation can be formulated.
13. What is the probability that two people make the same gesture in the game of "Rock, Paper and Scissors"?
14. The radii of two circles are 3 and 4 respectively, and the distance between the centers is 5. The positional relationship between these two circles is.
15. If a (), b () and c () are three points on the quadratic function image, the size relation of is
16 Let's relax and play a number game: Step 1: Take a natural number n 1=5 and calculate n 12+ 1 to get a1; Step 2: Calculate the sum of digits of a 1 to get n2, and calculate n22+ 1 to get A2; Step 3: Calculate the sum of all digits of a2 to get n3, and then calculate N32+ 1 to get A3; ........... and so on, then a2010 = _ _ _ _ _ _ _ _ _ _.
Third, the solution: this big question is ***9 small questions, with a score of ***86. When answering questions, write down the text description, proof process or calculation steps in the corresponding position on the answer sheet.
17. (4 points for each small question, ***8 points) (1)
(2) Solve the equation:
18.(6 points) It is known that the equation is about.
(1) proves that the equation has two unequal real roots;
(2) If one root of the equation is, find the other root and sum.
19.(8 points) An opaque pocket contains red, yellow and green balls of different colors, including two red balls and 1 yellow balls. The probability of randomly picking 1 ball is.
(1) Try to find the number of green balls in the bag; (2) Randomly take out the L ball from the bag for the first time 1 time (don't put it back), and then randomly take out the 1 ball for the second time. Please draw a tree diagram or list box and find the probability of hitting the red ball twice.
20.(8 points) As shown in the figure, E is a point on the AB side of the square ABCD (excluding points A and B), and F is a point on the extension line of the BC side. After rotation, △DAE can coincide with △DCF.
(1) What is the center of rotation?
(2) How many degrees has it rotated?
(3) If EF is connected, what kind of triangle is △DEF?
2 1. (The full mark of this question is 8) As shown in the figure, PA and PB are tangents of ⊙O, points A and B are tangents, AC is the diameter of ⊙O, and ∠ ACB = 70. The number of times to find ∠ p.
22. (This is entitled 10) As shown in the figure, when Xiaoming, whose street lamp (point) is 8 meters above the ground and whose height is 1.6 meters, walks from point A, which is 20 meters away from the bottom of the street lamp, to point B along the straight line where OA is located, does the figure become longer or shorter? How many meters has it become longer or shorter?
23.( 12) The pharmaceutical company introduced an anti-cold medicine. After listing at the beginning of the year, the company experienced a process from loss to profit. The quadratic function image shown in the figure (part) is the relationship between accumulated profit S (ten thousand yuan) and time (month) since the beginning of the year (that is, the relationship between total profit S and last month).
Answer the following questions according to the information provided in the picture:
(1) At what end of the month did the company start to turn losses into profits;
(2) the functional relationship between accumulated profit s and time;
(3) At the end of several months, the accumulated profit of the company can reach 300,000 yuan;
(4) What is the company's profit in the eighth month?
24. (The full mark of this question is 12) As shown in the figure, it is known that the diameter ⊙O is ab = 2, the straight lines M and ⊙O are tangent to point A, and P is a fixed point on ⊙O (not coincident with points A and B), and the extension line of PO intersects with ⊙O at point C and passes through point C.
(1) Verification: △APC∽△COD
(2) Let AP = x and OD = y, and try to express y with an algebraic expression containing x. 。
(3) When trying to find out what the value of x is, △ACD is an equilateral triangle.
25.( 14) The parabola is known to pass through points A (5 5,0), B (6 6,6) and the origin.
(1) Find the function relation of parabola;
(2) The intersection point C( 1, 4) is a straight line parallel to the X axis. At the intersection point D and the Y axis, choose any point P on the parabola below the straight line DC on the right side of the parabola symmetry axis. The intersection point P is a straight line PF parallel to the Y axis and intersecting with the X axis at point F, and intersecting with the straight line DC at point E. The straight line PF, the straight line DC and the two coordinate axes form a rectangular OFED (as shown in the figure). Is there a point p that makes OCD and two coordinate axes rectangular? If there is, find the coordinates of point P; If it does not exist, please explain why.
answer
The title is 1 23455 6789 10.
Option D B B C B B A A B D
18.( 1) ,
, 2 points
No matter what the value is, so, that is,
This equation has two unequal real roots. Three points
(2) Let another root exist,
Then, 4 points
Solution:,,
The other root of is that the value of is 1.
23.( 1) According to the image, the company began to turn losses into profits in ...................... after the fourth month (1).
(2) According to the image, its vertex coordinate is (2, -2),
Therefore, the functional relationship can be set as: y = a (t-2) 2-2 .................................................................................................... (2 points.
The image of the function relation is on (0, 0), so it is obtained.
A(t-2)2-2=0, A = ... (4 points)
∴ The functional relationship is: S= t-2)2-2 or s = t2-2t ............................................... (6 points).
(3) substitute S=30 into S= t-2)2-2 to get t-2) 2-2 = 30. .............................................................................................................................
The solution is t 1= 10, and t2=-6 (discarded) .................... (8 points).
A: By the end of 10, the accumulated profit of the company can reach 300,000 yuan ............................................................................................... (9 points).
(4) Substitute t=7 into the relational expression to get S = × 72-2× 7 =10.5 .................. (10 score).
Substituting t=8 into the relation, we get S= ×82-2×8= 16.
16- 10.5=5.5 …………( 1 1
A: In the eighth month, the company made a profit of 55,000 yuan ............................................ (12 points).
Hope to adopt it in time, thank you.