The third grade mathematics final investigation examination paper.
1. Multiple choice questions (this question is * *, 12, with 3 points for each question and * * * 36 points for each question, and only one option is correct).
1.sin60？ The value of is.
A. BC 1 year.
2. The graph 1 is a part of a sphere. Among the following four options, it is a top view.
3. Solve the equation by matching method. The following formula is correct.
A.B.
C.D.
4. Figure 2 is the inverse proportional function image we have learned, and its resolution function may be
A.B. C. D。
5. As shown in Figure 3, is it known? Bad =? CAD, the following conditions may not make
△ Abd△ ACD is
A.？ B=？ C B？ BDA=？ Command data interception (abbreviation for Command and Data Acquisition)
C.AB=AC D.BD=CD
6. Cars passing through the intersection can go straight, turn left or right. If these three possibilities are the same, then the probability that both cars will go straight after the intersection is
A.B. C. D。
7. Rectangles have characteristics that diamonds don't have.
A. diagonal bisection. B. Diagonal lines are perpendicular to each other.
C. the diagonals are equal. D is a central symmetric figure.
8. Regarding the quadratic function, the following statement is correct.
A. its opening direction is upward. B. When X
C. Its vertex coordinates are (? 2,3) D. When x = 0, the minimum value of y is 3.
9. as shown in fig. 4, it is known that a is an inverse proportional function (x >；; 0) One on the image
Moving point, b is the moving point on the x axis, AO=AB. Then when point a is in the diagram,
When the image moves from left to right, the area of △AOB
A. Increase B. Decrease C. Constant D. Uncertainty
10. As shown in Figure 5, it is known that AD is the height of △ABC and EF is the center line of △ABC.
What is wrong in the following conclusions is
A. ef? AD B.EF= BC
C.DF= AC D.DF= AB
1 1. A company has an output value of 2 million yuan this year, and now plans to expand production, so that the output value in the next two years will increase in the same proportion as that in the previous year, and the total output value in the next three years (including this year) will reach140,000 yuan. Let this percentage be x, and the equation can be listed as follows
A.
B.
C.
D.
12. As shown in Figure 6, it is known that the parabola and the X-axis intersect at point A and point B respectively, and the vertex is m. The parabola l 1 is folded along the X-axis, and then translated to the left to get parabola l2. If parabola l2 intersects with point B, the other intersection with X axis is C, and the vertex is N, then the area of quadrilateral AMCN is
A.32 B. 16 C.50 D.40
The second part (non-multiple choice questions, ***64 points)
Fill in the blanks (3 points for each small question, *** 12 points. Please fill in the answer sheet in the corresponding form.
13.20 1 1 During the Shenzhen Universiade, Xiaoming randomly surveyed 500 people in a community of 3,000 people and found that 450 people watched the evening news of the Universiade on Shenzhen TV. Ask anyone in the community, and the probability that he watches the Universiade evening news on Shenzhen TV is probably the answer. Please fill in the answer sheet.
14. If one root of the equation is 1, then the value of b is the answer. Please fill it in the answer sheet.
15. As shown in Figure 7, two street lamps A and B are 20 meters apart. One night, when Xiaogang
When you go straight from the bottom of lamp A to the bottom of lamp B16m, you find yourself at the top of the graph.
Part of it just touches the bottom of street lamp B. It is known that Xiaogang's height is 1.6 meters.
Then the height of street lamp A is the answer. Please fill in the answer sheet.
16. As shown in Figure 8, quadrilateral ABCD is a square with a side length of 2, and e is a point on the side of AD. Turn △CDE counterclockwise around point C to △CBF, and connect EF and BC at point G. If EC=EG, please fill in the answer sheet.
Third, answer the question (this topic is ***7 small questions, ***52 points)
17. (5 points for this question) Calculation:
18. (5 points for this question) Solve the equation:
19. (8 points in this question) As shown in Figure 9, ABCD, AB//CD, AD = BC = CD, diagonal BD? AD，DE？ AB, CF in e BD in F.
(1) Verification: △ ade △ CDF; (4 points)
(2) If AD = 4 and AE=2, find the length of EF. (4 points)
(1) Turn the dial once, and the probability that the pointer is in the red area is _ _ _ _ _ _ _ _;
(2 points)
(2) Turn the dial twice, if the color pointed by the pointer twice can be the same as that of purple (red
Color and blue together can become purple), then the player can win. Please use columns.
Find out the probability that the player can win by table method or tree drawing method. (6 points)
2 1. (8 points in this question) As shown in figure 1 1, there are three cities, A, B and C, where A is just west of B and C is 60? Direction, 30 east of B city? There are expressways l 1, l2 and l3 connecting these three cities. Liang Xiao starts from City A and travels along l2 Expressway to City C at an average speed of 80km per hour. Three hours later, Liang Xiao arrived in C city.
(1) Find the shortest distance from City C to Expressway l 1; (4 points)
(2) If Liang Xiao travels along C from C City at the same speed? b？ A's route is to return to A city from the expressway. So how long will it take him to return to a city? (The result is accurate to 0. 1 hour) (4 points)
22. (9 points for this question) Reading materials:
(1) For any real number A and B, there are,? Then it is concluded that the equal sign is true if and only if a = B.
(2) Any nonnegative real number can be written as the square of a number. That is, if, then. For example, 2=, etc.
Example: a > is known; 0, verification:.
Proof: ∫a > 0,?
? The equal sign is true if and only if.
Please answer the following questions:
A gardening company is going to build a rectangular garden, with one side against the wall (the wall is long enough) and the other three sides surrounded by fences (as shown in figure 12). Let the side perpendicular to the wall be x meters.
(1) If the fence used is 36m long, then:
① When the garden area is 144 square meters, what is the length of the side perpendicular to the wall? (3 points)
(2) Let the area of the garden be s m2. What is the maximum area of the garden when the length of the side perpendicular to the wall is several meters? Find this maximum area. (3 points)
(2) If you want to enclose a garden of 200 square meters, what is the minimum fence? (3 points)
23 (9 points) As shown in figure 13- 1, it is known that parabola (a? 0) intersects the x axis at (? 1, 0) and B (3 3,0) intersect the y axis at point C (0 0,3).
(1) Find the function expression of parabola; (3 points)
(2) If the vertices F and M of the right-angle EFMN are on the parabola above the X-axis, and one side EN is on the X-axis (as shown in figure 13-2), let the coordinates of point E be (x, 0) and the perimeter of the right-angle EFMN be L, and find the maximum value of L and the coordinates of point E at this time; (3 points)
(3) Under the premise of (2) (that is, when L reaches the maximum value), is there a point P on the parabola axis of symmetry, so that after the △PMN is folded along the straight line PN, the point M just falls on the Y axis? If yes, request the coordinates of all points P that meet the conditions; If it does not exist, please explain why. (3 points)
Answers to the examination paper of the third grade mathematics final survey.
First, multiple-choice questions (3 points for each small question, 36 points for * * *)
BCBAD ACBCD DA
Fill in the blanks (3 points for each small question, *** 12 points)
13.0.9; 14.4 ; 15.8 ; 16.
Third, answer questions.
17. solution: the original formula = 2 points (each function value 1 minute).
= 3? 1.4 points (every correct operation 1 point)
= 2 5 points
18. Scheme 1: Move the goods and get 1 points.
formulate
2 points
Which means it's still 3 points.
? , 5 points
Option 2: √,
? 1 point
? 3 points
? , 5 points
Solution 3: The original equation can be reduced to 1 point.
? x？ 1 = 0 or x? 3 = 0 3 points
? , 5 points
19.( 1) Proof: ∫DE? AB，AB//CD
? De? laser record
1+? 3=90? 1 point
∵BD？ advertisement
2+? 3=90?
1=? 2 2 points
∵CF？ BD，DE？ ab blood type
CFD=？ AED=90？ 3 points
AD = CD
? △ ade△ CDF 4 points
(2) solution: ∫DE? AB，AE=2，AD=4
2=30? , DE= 5 points
3=90? 2=60?
∫△ADE?△CDF
? DE=DF 6 point
? △DEF is an equilateral triangle
? EF=DF= 7 points
(Note: If you answer in other ways, please give points according to this standard as appropriate. )
20.( 1) 2 points
Red, yellow and blue
Red (red, red) (yellow, red) (blue, red)
Yellow (red, yellow) (yellow, yellow) (blue, yellow)
Blue (red, blue) (yellow, blue) (blue, blue)
(2) Solutions: List
Results * * * There are nine possibilities, two of which can be purple.
? P (winning) =
(Note: in item (2), if you can draw a tree diagram in the list, you will get 4 points; if you find the probability, you will get 2 points and ***6 points. )
2 1.( 1) Solution: Do you make a CD after C? If l 1 is at point d, the known score is 1.
AC=3？ 80=240 (km), CAD=30？ 2 points
? CD= AC=？ 240= 120 (km) 3 points.
? C city to expressway l 1 shortest distance 120km. 4 points
(2) solution: from known? CBD=60？
In Rt△CBD,
∵ sin? CBD=
? BC= 5 points
∵? ACB=？ CBDCAB=6030？ =30?
ACB=？ CAB=30？
? AB=BC= 6 points
? T = 7 points
After about 3.5 hours, he can return to City A .. 8 minutes.
(Note: If you answer in other ways, please give points according to this standard as appropriate. )
22.( 1) solution: score 1 from the meaning of the question.
Pursue simplification
Solution: 2 points
Answer: The length of the side perpendicular to the wall is 6m or 12m. 3 points
(2) solution: from the meaning of the question.
S = 4 points
= 5 points
∫a =？ 2 & lt0,? When x = 9, the maximum value of s is 162.
? When the length of the side perpendicular to the wall is 9m, the maximum value of S is obtained, and the maximum area is 162m2. 6 points
(3) Solution: Assuming that the required fence length is L meters, it is obtained from the meaning of the question.
7 points
Namely: 8 points
? If you want to enclose a garden of 200 square meters, you need a fence of at least 40 meters and 9 points.
23.( 1) solution: According to the meaning of the question, a parabola can be set to 1.
Parabolic intersection (0, 3)
Solution: a =? 1 2 point
The analytical formula of parabola is:
Namely: 3 points
(2) Solution: The parabola symmetry axis obtained by (1) is a straight line x = 1.
∫E(x，0)，
? F(x,), EN = 4 points.
?
Simplification, 5 points
∵? 2 & lt0,
? When x = 0, the maximum value of l is 10.
At this time, the coordinates of point E are (0,0) 6 points.
(3) solution: obtained from (2 2): e (0 0,0), f (0 0,3), m (2,3), n (2 2,0)
There is a point P( 1, y) that satisfies the condition.
And let the corresponding point of the folding point m be M 1.
? NPM=NPM 1=90，PM=PM 1
PG = 3？ y，GM= 1，PH = | y |，HN = 1
∵? NPM=90？
?
?
Solution:
? The coordinates of point P are (1,) or (1,) 7 points.
When the coordinate of point P is (1,), connect the PC.
∵PG is perpendicular bisector of CM. PC=PM
∫PM = PM 1，？ PC=PM=PM 1
M 1CM = 90？
? The point M 1 is eight points on the y axis.
Similarly, when the coordinate of point P is (1,), point M 1 is also nine points on the Y axis.
Therefore, there is a point P that meets the conditions, and the coordinates of this point P are (1,) or (1,).
(Description: You can correctly find the coordinates of a point, and explain that point M falls on the Y axis, so you get 2 points. )