Mathematics Test
(Full volume * * *, five major questions, full score 150, examination time 129 minutes)
Topic one two three four five Total score total score person
score
Reference formula: the coordinate of parabola vertex is and the formula of symmetry axis is.
1. Multiple-choice questions: (There are 10 small questions in this big question, with 4 points for each small question and * * 40 points) Four answers with code names A, B, C and D are given under each small question, and only one is correct. Please put the code of the correct answer in brackets after the question.
The reciprocal of 1 -5 is ()
The fifth century BC
2. The result of calculation is ()
A.B. C. D。
3. The independent variable range of the function is ()
A.B. C. D。
4. As shown in the figure, a straight line intersects a point, and if, it is equal to ().
Point 70? B.80？ C.90？ D. 100？
5. Among the following surveys, () is suitable for a comprehensive survey (census).
A. investigate the service life of a batch of new energy-saving light bulbs
B. investigate the water pollution situation in the Yangtze river basin
C. Vision survey of junior middle school students in Chongqing
In order to ensure the successful launch of Shenzhou VII, check its parts.
6. As shown in the figure, the circumscribed circle of ⊙ is the diameter, and if, it is equal to ().
.60 caliber? B.50？ C.40？ D.30？
7. The picture shows an aggregate of four cubes with the same size, so its left view is ().
A B C D
8. Observe the following figure. The number of triangles in the first figure is ().
……
A.B. C. D。
9. As shown in the figure, in the rectangular ABCD, AB=2, BC= 1, and the moving point P starts from point B and moves at a constant speed along the route B→C→D, then the function image between the area S of △ABP and the moving distance of point P is roughly ().
A B C D
10. As shown in the figure, in the isosceles Rt△ABC, ∠C=90? , AC=8, F is the midpoint on the side of AB, and points D and E move on the sides of AC and BC respectively, keeping AD=CE to connect de, DF and EF. In the process of this movement change, the following conclusions are drawn:
①△DFE is an isosceles right triangle; ② Quadrilateral CDFE cannot be square; ③ The minimum value of DE length is 4; ④ The area of quadrangular CDFE remains unchanged; ⑤ ⑤ The maximum CDE area is 8.
The correct conclusion is ()
A.①②③ B.①④⑤ C.①③④ D.③④⑤
Fill-in-the-blank question: (There are 6 small questions in this big question, with 4 points for each small question and * * 24 points) Please fill in the correct answer directly on the horizontal line after each small question.
1 1. According to the data released by Chongqing Municipal Bureau of Statistics, the city's gross national product in the first quarter of this year was about 78.4 billion yuan, so 78.4 billion yuan was expressed as 10,000 yuan by scientific counting method.
12. The solution of the fractional equation is.
13. It is known that △ABC and △DEF are similar, and the area ratio is 4∶25, so the similarity ratio of △ABC and △DEF is.
14. It is known that the radius of ⊙ is 3cm, the radius of ⊙ is 4cm, and the distance between the centers of two circles is 7cm, so the positional relationship between ⊙ and ⊙ is.
15 In the plane rectangular coordinate system, a straight line and two coordinate axes form a delta delta δ△AOB. Now, five cards with the same backs, numbered 1, 2, 3, and, are washed evenly, with their backs facing up. Take any card from it, take the number on the card as the abscissa of point P, the reciprocal of the number as the ordinate of point P, and the probability that point P falls within △AOB is.
16.A company sells three products, A, B and C. In last year's sales, the sales amount of high-tech product C accounted for 40% of the total sales amount. Due to the impact of the international financial crisis, the sales amount of products A and B this year will be reduced by 20% compared with last year, so high-tech product C is the focus of this year's sales. If the total sales this year is the same as last year, then the sales of high-tech product C this year should increase by% compared with last year.
3. Solution: (There are 4 small questions in this big question, each with 6 points and * * * 24 points) When answering questions, each small question must give the necessary calculus process or reasoning steps.
17. Calculation:
18. Solving inequality groups:
19. Drawing: Please draw an equilateral △ABC with line segment AB as one side in the figure below. (Requirements: Draw with a ruler, and write what is known and desired, keep the traces of painting, and don't write methods and conclusions)
Known:
Looking for a job:
In order to build a "forest Chongqing" and green the environment, Class 1, Grade 7 of a middle school actively participated in tree planting activities. In April this year, some statistics of the students' tree planting in this class are shown in the following figure:
(1) Please fill in the following table according to the information in the above statistical chart:
The median number of trees planted in this category and the mode number of trees planted.
(2) Please complete the bar chart.
4. Solution: (There are 4 small questions in this big question, each of which is 18 ***40 points) When solving the problem, each small question must give the necessary calculus process or reasoning steps.
2 1. Simplify first and then evaluate:, where
22. It is known that, as shown in the plane rectangular coordinate system, the straight line AB intersects the axis at points B and A respectively, and intersects the image of the inverse proportional function at points C and D respectively, and the CE⊥ axis is at point E, OB=4 and OE=2.
(1) Find the analytical expression of the inverse proportional function;
(2) Find the analytical formula of straight line AB.
23. There is a turntable that can rotate freely, which is divided into four identical sectors and marked with the numbers 1, 2, 3 and 4 respectively (as shown in the figure). In another opaque pocket, there are three balls marked with the numbers 0, 1 and 3 (except the numbers are the same). Xiao Liang turns the turntable once. After stopping, the pointer points to a certain sector, and the number in the sector is Xiao Liang's lucky number. Xiaohong randomly touches a small ball, and the number on the ball is Xiaohong's lucky number, and then calculates the product of these two numbers.
(1) Please find the probability that the product of these two numbers is 0 by drawing a tree diagram or a list;
(2) Liang Xiao and Xiaohong play games. The rule is: if the product of these two numbers is odd, Liang Xiao wins; Otherwise Xiaohong won. Do you think this game is fair? Why? If it is unfair, please modify the rules of the game to make the game fair.
24. It is known: As shown in the figure, in the right-angled trapezoidal ABCD, AD‖BC, ∠ABC=90? , DE⊥AC at point F, intersection BC at point G, intersection AB extending at point E, AE=AC.
(1) verification: BG = FG
(2) If AD=DC=2, find the length of AB.
25. The price (yuan) of a brand TV set sold by a TV production enterprise in rural areas last year meets the functional relationship with the month, and the monthly sales volume (10,000 sets) last year is the functional relationship with the month. The sales situation in two months is as follows:
June 65438+ October May
The sales volume was 39,000 units and 43,000 units respectively.
(1) What month did this brand of TV set have the largest sales amount in the countryside last year? What's the highest?
(2) Due to the impact of the international financial crisis, the price of this brand TV set sold to rural areas in February and June this year was lower than that in February last year, and the monthly sales volume was lower than that in February last year. The state implements the policy of "home appliances going to the countryside", that is, rural families buy new home appliances, and the state gives financial subsidies at 13% of the product price. Affected by this policy, from March to May this year, the average monthly sales volume of this kind of TV set sold by this manufacturer in rural areas increased by 6.5438+0.5 million units compared with February this year, while maintaining the price in February this year. If the state gives a financial subsidy of 9.36 million yuan to the sales of this TV set from March to May this year, what is this value (keep one decimal place)?
(Reference data:,,,)
26. As shown in the figure, in the plane rectangular coordinate system, the edge OA of the right-angle OABC is on the positive semi-axis of the shaft, OC is on the positive semi-axis of the shaft, OA=2, OC=3. The bisector passing through the origin O is ∠AOC passes through AB at point D, connecting DC, passing through D is DE⊥DC, and passing through OA is at point E.
(1) Find the analytical formula of parabola passing through points E, D and C;
(2) After rotating ∠EDC clockwise around point D, one side of the angle intersects with the positive semi-axis of the shaft at point F, and the other side intersects with the line segment OC at point G ... If DF intersects with the parabola in (1) at another point M, is it true that the abscissa of point M is, EF=2GO? If yes, please give proof; If not, please explain the reasons;
(3) For point G in (2), is there a point Q on the parabola located in the first quadrant, so that the △PCG formed by the intersection point P of straight lines GQ and AB and points C and G is an isosceles triangle? If it exists, request the coordinates of point q; If it does not exist, please explain why.
The picture can't be uploaded, sorry.