(Time: 120 minutes, total score: 120 minutes)
First, multiple-choice questions (3 points for each small question, 30 points for * * *)
1. In the formula,,+,9 x+, the number of fractions is ().
A.5 B.4 C.3 D.2
2. Among the following categories, the correct one is ()
A.B. C. D. =2
3. The following judgment about the score is correct ()
A. when x=2, the value of is zero. No matter what the value of x is, its value is always positive.
C. No matter what value X is, it is impossible to get the integer value D. When X is 3, it makes sense.
4. Enlarge X and Y of numerator denominator in the fraction to twice the original value at the same time, and the value of the fraction will be () of the original value.
A.2 times B.4 times C. half D. unchanged
5. The following triangle belongs to the right triangle is ()
A. the ratio of three sides is 5: 6: 7 B. three sides satisfy the relationship a+b = C.
The length of three sides of C is 9,40,41d. One side is equal to half of the other side.
6. If the three sides of △ABC are respectively, where is a positive integer greater than 1, then ()
A.△ABC is a right triangle with the hypotenuse B. △ABC is a right triangle with the hypotenuse B.
C.△ABC is a right triangle with the hypotenuse d △ABC is not a right triangle.
7. A right-angled triangle has one right-angled side of 6 and the other two sides are continuous even numbers, so the circumference of the triangle is ().
A.20 B. 22 C. 24 D. 26
8. It is known that the image of a function passes through points (2, 3), and the following statement is true ().
A.y increases with the increase of X. B. The image of the function is only in the first quadrant.
C when x < 0, there must be y < 0 D. The point (-2, -3) is not on the image of this function.
9. there are three points A 1(x 1, y 1), A2(x2, y2), A3(x3, y3) on the image of function (k > 0), and x 1 < x2 < 0 < x3.
a . y 1 < y2 < y3 b . y3 < y2 < y 1 c . y2 < y 1 < y3 d . y3 < y 1 < y2
10. As shown in the figure, the functions y = k (x+ 1) and (k < 0) are in the same coordinate system, and the image can only be () in the following figure.
Fill in the blanks (2 points for each small question, 20 points for * * *)
1 1. Without changing the value of the fraction, the first coefficient of the numerator and denominator is positive, then.
12. Simplification: = _ _ _ _ _ _; =___________.
13. Given -= 5, the value of is.
14. If the diagonal of a square is 4, its side length AB=.
15. If the bottom of the ladder is 9 meters away from the building, then the height that the ladder with the length of 15 meters can reach the building is _ _ _ _ _ meters.
16. A sailboat sailed due to the wind 160km, and then sailed north 120km. At this time, it is _ _ _ _ _ _ _ kilometers away from the starting point.
17. As shown in the figure below, given OA=OB, the number represented by point A on the number axis is _ _ _ _ _ _ _ _ _ _.
18. An edible oil factory wants to make a cylindrical oil drum with a volume of 5 liters (1 liter = 1 cubic decimeter). The functional relationship between the bottom surface area s of the oil drum and the height h of the oil drum is as follows.
19. If points (2,) and (-,a) are in the image of the inverse proportional function.
Up, then a =
20. As shown in the figure, let A be a point and a rectangle ABOC on the inverse proportional function image.
The area of is 3, the inverse ratio of the resolution function is 0.
Iii. Answering questions (***70 points)
2 1. (4 points for each small question, *** 16 points) Simplify the following categories:
( 1) + .(2) .
(3) .(4)( - )? ÷( + ).
22. (4 points for each small question, ***8 points) Solve the following equation:
( 1) + =3.(2) .
23.(6 points) The snail god who lives next door met the ant king and set off together at 8 o'clock the next morning to attend the micro-animal summit under the ginkgo tree, which is 16 meters apart. The snail god thought of the old saying "stupid birds fly first", so he left a note for the ant king and went alone two hours in advance. The ant king set out at the scheduled time, and as a result, they arrived at the same time. The known speed of the queen ant is.
24.(6 points) As shown in the picture, someone wants to cross the river. Due to the influence of the current, the actual landing point C is 50 meters away from the expected landing point B. As a result, the distance he actually swims in the water is much wider than the river 10 meter. What is the width AB of this river?
25.(6 points) As shown in the figure, a ladder AB is 2.5 meters long, and the top A leans against the wall AC. At this time, the distance from the bottom B of the ladder to the corner C is 1.5 m, and the ladder slides and stops at the position of DE, and the measured BD is 0.5 m long. How many meters did the top A of the ladder drop?
26.(8 points) The assembly workshop of an air-conditioning factory originally planned to assemble 150 air conditioners every day for 2 months (calculated as 30 days per month). (1) Since the air conditioner was assembled, the number of units assembled every day is m (unit: units/day), and the production time is t (unit:
What is the functional relationship between heaven and earth?
(2) As the temperature rises ahead of schedule, the manufacturer decides to put the air conditioners on the market ten days in advance, so how many air conditioners should the assembly workshop assemble at least every day?
27.( 10 points) As shown in the figure, the square OABC has an area of 9, point O is the coordinate origin, point B is on the image of function (k > 0, x > 0), point P(m, n) is any point on the image of function (k > 0, x > 0), and the intersection points P are X axis and Y respectively.
(1) Find the coordinates of point B and the value of k; (2) When S = 92, find the coordinates of point P; (3) Write the functional relationship between S and M. 。
28.( 10) As shown in the figure, a water pump station will be built along the river to supply water to Zhang Cun A and Lizhuang B respectively. It is understood that Zhang Cun A and Lizhuang B are 2km and 7km away from the river respectively, and the distance between Zhang Cun and Li Er Village is 13km. ..
(1) Where should the water pump be built to make the water pipe use the shortest? Please design the location of the pump station on the drawing;
(2) If the cost of laying water pipes is per kilometer 1500 yuan, what is the most economical cost of laying water pipes?
Temporary comprehensive test
1.B 2。 A 3。 B 4。 C 5。 C 6。 C 7。 C 8。 C 9。 C 10。 B 1 1。 12., 13. 1 14. 15. 12 16.200 17. 18. 19.-2 20.2 1.( 1) ; (2) ; (3) ; (4) 22.( 1) ; (2) It is not the root of the original equation, and the original equation has no solution. 23. The speed of the snail god is 6 meters per hour, and the speed of the ant king is 24 meters per hour. 24.1200m. 25. First use Pythagorean theorem to find AC = 2m, CE =1.5m, so AE = 0.5m 26. ( 1).(2) 180 27.( 1)B(3，3)，k = 9； (2)(32 ,6),(6,32 ); (3) S = 9-27m or S = 9-3m28. (1) As point A' is the symmetrical point of point A relative to the straight line L where the river is located. Connect point A' b with point P, and point P is the location of the water pump station. At this time, the sum of the lengths of PA+PB is the shortest, that is, the laid water pipe is the shortest; (2) Let point B be the vertical line of L and point A' be the parallel line of L, and let these two lines intersect at point C, then ∠ c = 90. Let point A be AE⊥BC in E. According to the meaning of the question, BE=5, AB= 13, ∴ AE2 = AB2-BE2. In rt △ ba ′ c, ∫BC = 7+2 = 9, a ′ c =12, ∴ a ′ b ′ = a ′ C2+bc2 = 92+122 = 225, ∴ a.