First, multiple-choice questions (this big question is ***8 small questions, each small question has only one correct option, each small question is 3 points, out of 24 points)
1. The following calculation is correct (b) A.B.C.D.
2. This figure is a three-dimensional figure composed of four identical cubes, and its left view is (b).
3. Since last autumn, Chuxiong Prefecture has suffered from the once-in-a-century drought. As of April 20th,10, 19, Chuxiong prefecture * * * has received all kinds of drought relief funds 1080 14500 yuan, which is expressed by scientific notation (D).
A.B. C. D。
4. The solution of the unary quadratic equation is (A)
A. in BC,
5. It is known that the radii of ⊙O 1 and ⊙O2 are 2cm and 3cm respectively, and the distance between the centers of two circles is 5cm, then the positional relationship between the two circles is (a).
A. externally cut.
6. It is known that one internal angle of an isosceles triangle is 70, then the degrees of the other two internal angles are (c).
A.55, 55 B.70, 40 C.55, 55 or 70, 40 D are all incorrect.
7. The following statement is incorrect (D)
A. In the election, the data that people are usually most concerned about is Mode B, and rolling the dice, and 3 o'clock up is an uncertain event.
C the median of data 3, 5, 4, 1, -2 is 3d. Two triangles with two proportional sides and an equal angle must be similar.
8. As shown in the figure, the quadrilateral OABC is a diamond, and the points B and C are on the arc EF centered on the point O, and ∠ 1=∠2,
If the area of fan-shaped OEF is 3π, the side length of rhombic OABC is (c)
A.B.2 C.3 D.4
Fill-in-the-blank question (this big question ***7 small questions, 3 points for each small question, out of 2 1 point) 9. The reciprocal is -2.
10. If the point (-2,3) is on the image of the inverse proportional function, the expression of the inverse proportional function is.
1 1. Given that the sum of the inner angles of a polygon is twice the sum of its outer angles, the number of sides of this polygon is 6.
12. In the function, the range of independent variables is.
13. As shown in the figure, in □ABCD, diagonal AC and BD intersect at point O, without any auxiliary lines and letters, please add a condition to make □ABCD rectangular. The condition to be added is (AC=BD or ∠ ABC = 90). Just write one.
14. According to the program in the figure, when input x=2, the output result is 2.
15. As shown in the figure, put a row of square patterns with matchsticks. In this way, put 2n(n+ 1) or 4( 1+2+3+…n) matchsticks on the nth pattern (represented by an algebraic expression containing n).
Third, answer the question (this big question ***9 small questions, out of 75 points)
16. (6 points in this small question) Simplify first, then evaluate:, in which.
Solution: The original formula = =...5 points.
When, the original type =……6 ... 6 points.
17. (7 points in this small question) As shown in the figure, the points are on the same straight line.
Please discuss the relationship between BC and EF. And explain why.
Solution: BC∨EF. The reasons are as follows: ........................... 1 min.
Ae = db (known) ∴AE+EB=DB+BE (properties of the equation)
That is ab = de ............................................ 2 points.
And ∵AC∨df (known) ∴∠A=∠D (two straight lines are parallel with equal internal angles) ... 3 points.
In △ABC and △DEF,
∵∴△ ABC△ def (SAS) ......................................... 5 points.
∴∠ABC=∠DEF (congruent triangles's corresponding angles are equal) ... 6 points ∴∥ BC ∥ ef (internal dislocation angles are equal and two straight lines are parallel). .............................................................................................
18. The position of (7 points in this small question) in the plane rectangular coordinate system is shown in the figure.
(1) make it symmetrical and write the coordinates of the point;
(2) Rotate point O clockwise 180.
Solution: (1) Draw ... (3 points)
................. (4 points)
(2) Draw lots ... as shown (7 points)
19. Xiaoming and Xiaohua want to buy a ticket for the 20 10 Shanghai World Expo.
Tickets, they each designed a plan:
Xiao Ming's plan is: rotate the turntable as shown in the figure, and when the turntable stops rotating,
If the pointer stops in the shadow area, Xiao Ming gets the ticket; If the pointer stops at white
Area, Xiaohua gets the ticket (the turntable is divided into six sectors on average, and if the pointer stops at the boundary, the turntable rotates again).
Xiaohua's plan is: there are three cards marked with the numbers 1, 2 and 3 respectively. After washing, let their backs face up, take out a card, write down the numbers on the card, put it back, wash it again, and take out another card. If the sum of the numbers on the two cards is odd, Xiao Ming will get the ticket. If the sum of the numbers on the two cards is even, Xiaohua gets the ticket.
(1) In Xiao Ming's scheme, calculate the probability that Xiao Ming will get the ticket, and explain whether Xiao Ming's scheme is fair.
(2) List all possible results in Xiaohua's design scheme with tree diagram or list method, calculate the probability of Xiaohua getting tickets, and explain whether Xiaohua's scheme is fair.
Solution: (1) The probability that Xiao Ming gets the ticket is that Xiao Ming's scheme is fair, because both parties have the probability of getting the ticket ... (3 points)
(2)
1 2 3
1 2 3 4
2 3 4 5
3 4 5 6
Or ... five points.
The probability of Xiaohua getting the ticket is that Xiaohua's scheme is unfair, because the possibility of both parties getting the ticket is different.
The possibility of Xiaohua getting the ticket is that the possibility of Xiaoming getting the ticket is 8 points.
20. As shown in the figure, PQ and MN on both sides of the river are parallel to each other, and there is a row of small trees on PQ on the river bank. It is known that the distance between two adjacent trees is CD = 50m. Someone measured ∠ Dan = 35 at A of the river bank MN, and then walked along the river bank 120 meters to reach B, and measured ∠ CBN =
(Reference data: SIN35 ≈ 0.57, COS35 ≈ 0.82, TAN35 ≈ 0.70 SIN70 ≈ 0.94, COS70 ≈ 0.34, TAN70 ≈ 2.75).
Solution: the intersection of point c is CF//DA and AB is at point F.
MN//PQ，CF//DA
∴ Quadrilateral AFCD is a parallelogram.
∴ AF = CD = 50m，CFB=35。
∴ FB = AB-AF = 120-50 = 70...3 points.
And CBN = CFB+BCF ∴ BCF = 70-35 = 35 = CFB.
∴ BC = BF = 70 minutes and 5 minutes.
In Rt△BEC, sin70 = ∴ ce = BC? Sin 70 ≈ 70 0.94 = 65.8 66 ......................................................................................................................................................
A: The width of this river is about 66 meters. ................................................................ takes eight minutes.
2 1. (9 points in this small question) During the "Torch Festival" housing fair in Chuxiong in 2009, a real estate company conducted a random questionnaire survey on the consumers who participated in this housing fair, and * * * distributed 1000 questionnaires, all of which were recovered. According to the questionnaire, the annual income of consumers is sorted out and made into the following table:
Annual income (ten thousand yuan)1.21.83.05.010.0
Number of consumers surveyed (persons) 200 500a 70 30
According to the questionnaire, after sorting out the situation of the housing area that consumers intend to buy, make some frequency distribution histograms and fan-shaped statistical charts. According to the above information, answer the following questions:
(1) According to the table, a = _ _ _ _ _ _, and the average annual income of the surveyed 1000 consumers is 10000 yuan.
(2) Complete frequency distribution histogram and sector statistics.
(3) If there are about 40,000 people planning to buy a house in Chuxiong, please estimate how many people will buy a house of 80 to 120 square meters?
Solution: (1) According to the table, a = 200, and the average annual income of the surveyed 1000 consumers is 23,900 yuan ... (3 points)
(2) The answer is shown in ..................................... (6 points).
(3)
A: It is estimated that there are about 24,000 people who buy houses with an area of 80 to 120 square meters. .......................................................................................................................................
22. (8 points in this small question) As shown in the figure, the parabola intersects with the axis at two points, A (1 0) and B (3 3,0), and intersects with the Y axis at point C (0 0,3).
(1) Find the function relation of parabola;
(2) If point d (,m) is a point on a parabola, find the value of m and the area of △ABD at this time.
Solution: (1) is known by
................................., 3 points.
The solution is ... 4 o'clock.
∴ ...........................................................................................................................................................................
(2)∵ is the point∴on the parabola. ......................................................................................................................................................
......................................................, 8 points.
In April this year, Uncle Li harvested 30 tons of onions and 13 tons of cucumbers. Now he intends to rent two kinds of trucks * * * 65,438+00 to transport all these two vegetables to other places for sale. It is known that a truck can carry 4 tons of onions and 1 ton of cucumbers. A B-class truck can hold 2 tons of onions and 2 tons of cucumbers.
(1) How many schemes does Uncle Li have for arranging trucks A and B? Please help design it;
(2) If each class A truck has to pay 2,000 yuan, and each class B truck has to pay 1300 yuan, please ask Uncle Li to help you think about which scheme to choose with the least freight. What's the lowest freight?
Solution: (1) Let's assume that Uncle Li arranges an A-class truck, and the B-class truck has (10-) trucks, but there are none.
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
Because it should be a positive integer, so take 5, 6, 7 ... 5 points.
The scheme is as follows: ① Arrange five A-class trucks and five B-class trucks;
② Arrange 6 A-class trucks and 4 B-class trucks;
③ Arrange 7 A-class cars and 3 B-class cars for ........................ to score 6 points.
(2) Scheme ①: 5× 2000+5×1300 =16500 (yuan)
Scheme 2: 6× 2000+4×1300 =17200 (yuan)
Scheme ③: 7× 2000+3×1300 =17900 (yuan)
Therefore, Uncle Li should choose scheme ①, with the minimum freight rate of 16500 yuan. ...........................................................................................................................................
24. (Sub-topic 13) It is known that ⊙A intersects the axis at two points C and D, the coordinate of the center of a circle is (1 0), the radius is ⊙A, and the tangent of ⊙A passing through point C intersects the axis at point B (-4, 0).
(1) Analytical formula for finding the tangent line BC;
(2) If point P is a point on ⊙A in the first quadrant, the tangent passing through point P intersects BC line at point G, and ∠ CGP = 120, find the coordinates of point G;
(3) Move ⊙A to the left (the center of the circle is always on the axis) and intersect with the straight line BC at E and F. Is there a point during the movement, so that △AEF becomes a right triangle? If it exists, find the coordinates of point A; If it does not exist, please explain why.
Solution: (1) as shown in figure 1, if AC is connected, then AC=
In Rt△AOC, AC=, OA= 1, then the coordinate of point oc = 2∴c is (0,2).
Let the analytical expression of tangent BC be that it passes through points C (0 0,2), B (? 4,0), and then there is
Get a solution
....................................................., 4 points.
(2) As shown in figure 1, the coordinate of point G is (a, c), the passing point G is GH⊥ axis, and the vertical foot is H point.
Then oh = a, GH = c = a+2 5 points.
Connect AP, AG
Because AC = AP, Ag = Ag, Rt△ACG≌Rt△APG (HL).
So ∠AGC= × 1200=600.
At Rt△ACG, ∠AGC= 600, AC=
∴ sin600 = ∴ ag = .........................................................................................................................................................
In Rt△AGH, ah = oh-OA = a- 1, GH= a+ 2.
+ = ∴ + =
Solution: =, = (Give up) Ahhh.
(3) As shown in Figure 2, there is a point A during the movement, so that △AEF is a right triangle. ........................................................................................................................................
Make △AEF a right triangle
AE=AF
∴∠AEF=∠AFE 900
Only ∠EAF=900.
When the center of circle A is on the right of point B, the intersection point A is formed.
AM⊥BC, the vertical foot is point M.
In Rt△AEF, AE=AF=, then EF=, AM= EF=
In Rt△OBC, OC=2, OB=4, then BC=2.
∠BOC= ∠BMA=900，∠OBC= ∠OBM∴△BOC∽△BMA
∴ = ∴ AB = ∴ OA = Ob-AB = 4-∴ The coordinates of point A are (-4+0) ...1.
When the center of the circle is to the left of point B, let the center of the circle be a', and let A' M' ⊥ BC pass through point A' at point M', we can get
△A′M′B?△AMB
a′B = AB =
∴ OA ′ = Ob+A ′ B = 4+∴ A ′ The coordinate of the point is (-4-0).
To sum up, the coordinates of point A are (-4+0) or (-4-0). ...........................................................................................................................................