Math test questions
(Full volume * * *, five major questions, full score 150, examination time 120 minutes)
Precautions:
1. The answers to the questions are written on the answer sheet (volume) and may not be answered directly on the test paper.
2. Read the notes on the answer sheet (volume) carefully before answering the questions.
3. At the end of the exam, the invigilator will take back the test questions together with the answer sheet (volume).
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 black the box corresponding to the correct answer to the right of the question number on the answer sheet (or fill in the code of the correct answer in the corresponding table of the answer sheet).
1. A 3, a 1, 0,2, the smallest number is ().
A.3b. 1c.0d.2
2. In the figure below, the axis symmetry is ().
3. The result of calculation is ()
In 2ab AD.
4. It is known that OA and OB are two radii of ⊙O, and both OA⊥OB and C are on ⊙O, then the degree of ∠ACB is ().
45 BC to 35 BC
5. Among the following surveys, () is suitable for a comprehensive survey (census).
A investigate the quality of old yogurt in the market, and b investigate the service life of a certain brand of ballpoint pen core.
C. Investigate whether the passengers on the plane carry dangerous goods. D. Investigate the awareness rate of the citizens of our city about the mascots of the London Olympic Games.
6. As shown in the figure, BD bisects ∠ABC, with point E on BC and ef//ab. If ∠ cef = 100, then the degree of ∠ABD is ().
A.60 B.50 C.40 D.30
7. It is known that the solution of equation 2x+a-9=0 about X is x=2, so the value of A is ().
A.2 B.3 C.4 D.5
August 2012 "International Rock Climbing Competition" was held in Chongqing. On the way, Xiaoli found that she forgot to bring her ticket, so she immediately called her mother to send it from home. At the same time, Xiaoli also drove back, chatted with her mother for a while, and then continued to drive to the competition site. Let the time for Xiaoli to leave home be T and the distance from Xiaoli to the competition venue be S. The following can reflect the approximate functional relationship between S and T.
9 The following figures are all composed of pentagrams with the same size according to certain rules. The first figure * * * has two pentagrams, the second figure * * * has eight pentagrams, and the third figure * * has 18 pentagrams, …, so the number of pentagrams in the sixth figure is ().
10. The image symmetry axis of the known quadratic function is shown in the figure. Among the following conclusions, the correct one is ()
A.abc & gt0b . a+b = 0c . 2b+c & gt； 0 D.4a 10 c
2. Fill in the blanks: (There are 6 small questions in this big question, with 4 points for each small question and 24 points for * *) Please fill in the answer to each small question directly on the corresponding horizontal line of the answer sheet (volume).
1 1. It is reported that in 20 1 1 year, there are nearly 38,000 private cars in the main city of Chongqing. The number 380,000 is expressed as _ _ _ _ _ by scientific notation.
12. Given △ABC∽△DEF, the perimeter of △ABC is 3, and the perimeter of △DEF is 1, then the ratio of the area of ABC to △DEF is _ _ _ _ _ _.
13. Chongqing rural medical insurance has been fully implemented. The number of reimbursement for hospitalization expenses in seven villages in a county is 20, 24, 27, 28, 3 1, 34, 38 respectively, so the median of this set of data is _ _ _ _ _ _.
14. If the central angle of a sector is 120 and the radius is 3, then the area of this sector is _ _ _ _ _ _ _ _ _ _ _ _ _ (the result is π).
15. Cut an 8 cm long wooden stick into three sections, each of which is an integer centimeter. If the lengths of three pieces of sticks are the same and are counted as the same cutting method (such as 5,2, 1 and 1, 5,2), then the probability that three pieces of sticks can form a triangle is _ _ _ _ _.
16. Party A and Party B play card games and get cards from a sufficient number of cards. It is stipulated that each player has at most two ways to get cards, with Party A taking four or (4k) cards at a time and Party B taking six or (6k) cards at a time (k is a constant, 0
3. Solution: (There are 4 small questions in this big question, each with 6 points and * * 24 points) When answering each small question, you must give the necessary calculus process or reasoning steps. Please write the answer in the corresponding position on the answer sheet (volume).
17. Calculation:
18. Known: as shown in the figure, AB=AE, ∠ 1 = ∠ 2, ∠ B = ∠ E. Proof: BC=ED.
19. Solve the equation:
20. As we all know, as shown in the figure,
2 1, as shown in the figure, at Rt△ABC, ∠ BAC = 90, point D is on the side of BC, and△ △ABD is an equilateral triangle. If AB=2, find the circumference of △ABC. (Results Retain the root number)
Iv. Answer: (There are 4 small questions in this big question, and each small question is 10 ***40 points)
When answering each question, the necessary calculus process or reasoning steps should be given. Please write the answer in the corresponding position on the answer sheet (volume).
2 1, simplify first, then evaluate:, where is the integer solution of the inequality group.
22. As shown in the figure, in the plane rectangular coordinate system, the image of the linear function and the image of the inverse proportional function intersect at points A and B in the first and third quadrants, and intersect with the X axis at point C. The coordinate of point A is (2, m), the coordinate of point B is (n, -2), and tan∠BOC= =.
(l) Find the analytical expressions of inverse proportional function and linear function;
(2) There is a point E (except point O) on the X axis, so that the areas of △BCE and △BCO are equal, and the coordinates of point E are obtained.
23. The high school enrollment index is an important measure for the reform of the enrollment system of the senior high school entrance examination in our city. A junior high school has made statistics on the number of students admitted to the school in the past four years, and made the following two incomplete statistical charts:
(1) The enrollment range of this school in recent four years is _ _ _ _ _ _ _ _ _. Please complete the broken line statistical chart;
(2) In 2009, there were only 1 girls in the whole school, and the school plans to randomly select two students from them to learn about their study in senior high school. Please find out the probability that the two selected students happen to be 1 male students and 1 female students by table method or tree drawing method.
24. As shown in the figure, in the rhombic ABCD, f is the midpoint of the side BC, DF intersects with diagonal AC at point M, and if m crosses, it is ME⊥CD at point E, ∠ 1=∠2.
(1) If CE= 1, find the length of BC; (2) verify AM=DF+ME.
Verb (abbreviation of verb) solution: (This big problem has two small problems, the 25th small problem is 10, the 26th small problem is 12, the first ***22). When you answer every small question, you must give the necessary calculus process or reasoning steps. Please write the answer in the corresponding position on the answer sheet (volume).
25. There are two ways for enterprises to treat sewage, one is to send it to a sewage plant for centralized treatment, and the other is to treat it through the enterprise's own equipment. Last year, the monthly sewage discharge of an enterprise was 12000 tons. Because the sewage plant was in the debugging stage at that time and the sewage treatment capacity was limited, the enterprise invested in self-built equipment to treat sewage, and the two treatment methods were carried out at the same time. From 1 to June, the functional relationship between the sewage quantity (ton) delivered by the enterprise to the sewage plant and the month (and integer) is as follows:
65438+The quadratic function relationship between the sewage volume (tons) and the month (and integer) from July to June in February is as follows. Its image is shown in the figure. From 1 to June, the functional relationship between (yuan) and X month is satisfied, and the functional relationship between (yuan) and X month is satisfied. From July to 65438+February, the cost per ton of sewage treated by sewage plants was 2 yuan, and the cost per ton of sewage treated by enterprises was 1.5 yuan. (l) Please observe the tables and images in the question, and use the knowledge of the learned linear function, inverse proportional function or quadratic function to directly write the functional relationship between and respectively;
(2) Please find out the month in which the enterprise spent the most on sewage treatment last year, W (yuan), and find out the maximum cost;
(3) Since the beginning of this year, since the self-built sewage treatment equipment has been put into full operation, the enterprise has decided to expand its production capacity and treat all the sewage by itself. It is estimated that after the expansion of production capacity, the monthly sewage volume this year will increase by a% on the basis of last year's monthly, and the sewage treatment cost per ton will increase by (A-30)% on the basis of last year's 65438+February. In order to encourage energy saving and reduce the burden on enterprises, the financial department will treat 50% of the sewage.
(Reference data:)
26. It is known that in right-angled trapezoidal ABCD, AD//BC, ∠ B = 90, AD = 2°, BC = 6° and AB = 3. E is a point on the side of BC, and BE is a square BEFG, so that both the square BEFG and the trapezoidal ABCD are on the same side of BC.
(l) Find the length of BE when the vertex f of the square just falls on the diagonal AC;
(2) Translate the square BEFG in question (L) to the right along BC. Note that the square BEFC in translation is a square B'EFG. When point E coincides with point C, stop translating. Let the translation distance be t, and the side EF of the square B'EFG intersects with AC at point M, connecting B'D, B'M and DM. Is there such a t △B'DM that is a right angle? If it exists, find the value of t; If it does not exist, please explain the reason;
(3) In the translation of question (2), let the area of the overlapping part of square B'EFG and △ADC be S, please directly write the functional relationship between S and T and the range of independent variable T. 。