On the second day, the final exam was math, multiple-choice questions (3 points for each small question, 30 points for * * *).
1. Given =, the value of is ().
A.B. C. D。
2. Among the following three-dimensional figures, the one whose top view is square is ().
A.B. C. D。
3. Among the following properties, what a diamond has but a rectangle does not necessarily have is ().
A. the diagonals are equal. B. Divide diagonally.
C. Diagonal lines are perpendicular to each other D. Adjacent sides are perpendicular to each other
4. When the quadratic equation x2+4x-3 = 0 is solved by collocation method, the original equation can be transformed into ().
A.B. C. D。
5. If the hyperbola passes through (-1,) and (-3,), then the relationship between the hyperbola sum is ().
A.& gtB. & lt
C.= D.y 1 and y2 cannot be determined.
6. If the function is an inverse proportional function, then ()
Morning? 0 B.m？ 0 and m? 1 C.m=2 D.m= 1 or 2.
7. As shown in the figure, the diagonal of rectangular ABCD intersects with point O, if? ACB=30？ , AB=2, then the length of OC is ()
A.2 B.3 C.2 D.4
8. As shown in the figure, on a rectangular ground with a length of 22m and a width of 17m, two perpendicular roads with the same width should be built (both roads are parallel to one side of the rectangle). If the lawn is planted in the remaining part to make the lawn area reach 300 meters, the width of the road to be built is () meters. ..
A.4 B.3 C.2 D. 1
9. When k>0, inverse proportional function y= and linear function y=kx+2, the image is roughly ().
A.B. C. D。
10. As shown in the figure, in the plane rectangular coordinates, square ABCD and square BEFG
Is a similar figure with the origin o as the similarity center, and the similarity ratio is, points a, b,
E On the X axis, if the side length of the square BEFG is 6, the coordinate of point C is ().
A.(3，2) B.(3， 1) C.(2，2) D.(4，2)
Fill in the blanks (3 points for each small question, *** 18 points)
1 1. Given that one root of the equation x2-3x+m= 0 is 1, then m=.
12. In the rhombic ABCD, diagonal AC=6 and BD= 10, then the area of rhombic ABCD is.
13. As shown in the figure, in △ABC, points D, E and F are on AB, AC, BC, DE//BC and EF//AB respectively. If AB = 8, BD = 3 and BF = 4, the length of FC is.
14. The side length ratio of the quadrilateral is 1: 2: 3: 4. If the minimum side length of another quadrilateral similar to it is 5 cm, then its maximum side length is 5 cm.
15. There is only one red ball and two yellow balls in the bag. These balls are all the same except the color. If you randomly draw a ball, put it back and mix it evenly, and then randomly draw another ball, the probability that the balls drawn twice are yellow balls is.
16. As shown in the figure, the straight line y =-x+b and the hyperbola y =-(x
If it intersects the X axis at point B, then OA2﹣OB2=.
Iii. Answering questions (***52 points)
17.(4 points) Solve the following equation:
18.(6 points) The price of a commodity is 400 yuan/piece, and the price after two price reductions is 324 yuan/piece, and the percentage of the two price reductions is the same.
(1) Find the percentage of each price reduction of this commodity;
(2) If the purchase price of the commodity is 300 yuan/piece, and after two price reductions, it will sell 100 pieces of the commodity, then the total profit of the two price reductions is not less than 32 10 yuan. How many pieces of this commodity should be sold at least after the first price reduction?
19.(6 points) There are two opaque pockets, pocket A contains three balls marked with the numbers 1, 2 and 3 respectively, and pocket B contains two balls marked with the numbers 4 and 5 respectively. They are exactly the same shape and size. Now, draw a ball randomly from pocket A and write down the number, and then draw a small ball from pocket B.
(1) Please use list or tree diagram (only choose one) to display all possible results of the graph obtained twice;
(2) Find the probability that the sum of two numbers can be divisible by 3.
20.(8 points) As shown in the figure, △ABC is an acute triangle, AD is the height on the side of BC, one side FG of the square EFGH is on BC, and vertices E and H are on AB and AC respectively. BC=40cm, AD=30cm.
(1) Verification: △ AEH ∽△ ABC;
(2) Find the side length and area of this square.
2 1.(8 points) As shown in the figure, there is a lamppost AB among the flowers. Under the light, the shadow length of Dahua at point D is DE = 3m, and it reaches point G along BD direction, DG = 5m. At this time, the shadow length of Dahua is GH = 5m. If the height of Dahua is 2 meters, find the height of lamppost AB.
22.(8 points) A pharmaceutical research institute has developed a new antibacterial drug, which has been used in clinical human trials for the first time after years of animal experiments. The functional relationship between the drug concentration y (μ g/ml) in the blood of adults after taking medicine and the time of taking medicine x hours is shown in the figure (when 4? x？ At 10, y is inversely proportional to x).
(1) According to the image, the functional relationship of y and x in the rising and falling stages of drug concentration in blood was obtained respectively.
(2) How many hours does the blood drug concentration last at least 2 μ g/ml?
23.( 12 points) As shown in the figure, in Rt△ABC,? ACB=90？ , AC=3, BC=4, and the intersection point b is ray BB 1 make bb 1∑AC. Moving point D starts from point A and moves at a speed of 5 units per second along the direction of ray AC, while moving point E starts from point C and moves at a speed of 3 units per second along the direction of ray AC. The intersection point D is DH? AB in h, a little e as EF? Ac crosshair BB 1 connects DG at the midpoint of f and g. Set point d moves for t seconds.
(1) When t is what value, AD=AB, and find the length of DE at this time;
(2) When △DEG is similar to △ACB, find the value of t. 。
Answers to the final exam questions of the second day of junior high school in mathematics 1. multiple-choice question
Two. Fill in the blanks11.212.3013.2.414.2015.3838+06.2.
Three. solve problems
17. Solution:
Or right away or? 4 points
18. Solution: (1) Let the price reduction percentage of this commodity be x%.
According to the question: 400? (1-x%) 2 = 324, the solution is: x= 10, or x= 190 (abbreviated).
A: The percentage of price reduction for this commodity is 10% each time. 3 points
(2) Assuming that M pieces of this commodity are sold after the first price reduction, (100-m) pieces of this commodity are sold after the second price reduction.
The unit profit after the first price reduction is: 400? (1 ~ 10%) ~ 300 = 60 (RMB/piece);
The unit profit after the second price reduction is: 324-300 = 24 (RMB/piece).
60m+24？ ( 100﹣m)=36m+2400？ 32 10,
Solution: m? 22.5.？ m？ 23.
A: In order to make the total profit of the two price reduction sales not less than 32 10 yuan, at least 23 pieces of this commodity must be sold after the first price reduction. Six points.
19. Solution: (1) The tree diagram is as follows:
? 3 points
(2)∫* * In six cases, the sum of two numbers can be divisible by 3 in two cases.
? The probability that the sum of two numbers can be divisible by 3 is that p (the sum of two numbers can be divisible by 3) =. 6 points
20. Solution: (1) Prove: ∵ quadrilateral EFGH is a square,? EH∨BC，
AEH=？ b，？ AHE=？ c，？ △AEH∽△ABC。 ? 3 points
(2) Solution: As shown in the figure, let AD and EH intersect at point m ∫? EFD=？ FEM=？ FDM=90？ ,
? The quadrilateral EFDM is a rectangle. EF=DM, let the side length of the square EFGH be x, ∫△AEH∽△ABC,
? = , ? = , ? x=，
? The side length of the square EFGH is cm, and the area is cm 2.8 minutes.
2 1. Solution: ∫CD∨AB,? △EAB∽△ECD，
? =, that is = ①,? 3 points
∫FG∨AB，？ △HFG∽△HAB，？ =, that is = ②,? 6 points
From ① ② =, BD=7.5,? =, solution: AB=7.
Answer: The height of lamppost AB is 7 meters. 8 points
22. Solution: (1) When 0? x？ 4. Let the analytical formula of the straight line be: y=kx, and substitute (4,8) to get: 8=4k.
The solution is: k=2, then the analytical formula of the straight line is: y=2x,? 2 points
When is 4? x？ At 10, let the inverse proportional decomposition function be: y=, and replace: 8= with (4,8).
Solution: a=32, so the inverse proportional decomposition function is: y =；;
Therefore, the functional relationship of the rising period of plasma concentration is y=2x(0? x？ 4),
The functional relationship in the descending stage is y= (4? x？ 10).？ 5 points
(2) When y=2, then 2=2x, the solution is: x= 1, when y=2, then 2=, the solution is: x= 16,
∫ 16- 1 = 15 (hours),? The duration of blood drug concentration is not less than 2 μ g/ml, 65438 05 hours. 8 points
23. Solution: (1)∵? ACB=90？ ，AC=3，BC=4，？ AB= =5。
∵AD=5t，CE=3t，？ When AD=AB, 5t=5, that is, t =1;
? AE=AC+CE=3+3t=6,DE=6﹣5= 1.？ 4 points
(2)∵EF=BC=4, g is the midpoint of EF,? GE=2。
Gongyuanshi
If △DEG is similar to △ACB, or,
? Or,? T= or t =;
When AD & gtAE (t>), DE = AD-AE = 5t-(3+3t) = 2t-3,
If △DEG is similar to △ACB, then,? Or,
The solution is t= or t =;
To sum up, when t= or or, △DEG is similar to △ACB. 12 point