(The full mark of this question is 120, and the examination time is l20 minutes)
The first volume (multiple choice questions ***l5)
1. Multiple choice questions (This big question is ***5 small questions, each with 3 points, *** 15 points. Of the four options given in each small question, only one meets the requirements of the topic)
1, the reciprocal of a number is 8, and this number is ().
A. 1/8 B.- 1/8 c.8 D.-8
2. The geometric figure shown in the figure consists of three cubes with the same size. Its top view is ().
3. It is appropriate to use () to reflect the daily maximum temperature change of a city in a week.
A, bar chart b, line chart c, fan chart d, frequency distribution histogram
4. The approximate images of functions y=ax2-a and y=a/x(a≠0) in the same plane rectangular coordinate system are ().
5. As shown in the figure, the O P with a radius of 5 intersects the Y axis at two points, M(0, -4) and N(0, -lO), so the coordinate of the center of the circle P is ().
A.(5.-4) B.(4，-5) C.(4，-7) D.(5，-7)
Volume 2 (multiple choice questions * * 105)
Fill in the blanks (3 points for each small question, 30 points for each small question. Please fill in the answer on the line in the question)
6. Calculation: =.
7. The inverse proposition of the proposition "Two angles whose sum is L 80 are complementary angles" is.
8. Decomposition factor: A3b-AB =.
9. As shown in the figure, points A, B and C are three points on ⊙ O. If ∠ AOB = 56, the degree of ∠C is.
10. The range of function Y= is.
1 1. The modes and average values of a set of data l0, 13,9, 16, 13, 10,13 are
12. If the image of the inverse proportional function y= passes through two points (a, 3) and (2, 6), the size relationship between A and B is
13. In △ABC, ∠A and ∠B are acute angles. If |tanA- 1|+( =0，∠C=
Wang Hong and Liu Fang are playing roulette, as shown in the picture. Divide roulette A and roulette B into three equal parts and number each part. The rules of the game are as follows: when the sum of the two numbers pointed by the pointer is 7, Wang Hongsheng; When the sum of these numbers is 8, Liu. So who is more likely to win?
15. The side development of the cone is a sector with a radius of 16 cm and a central angle of120, so the radius of the energy surface of the cone is.
Third, the solution (this big question is ***9 small questions, ***75 points. The solution should be written in the calculus step of explaining and proving the process)
16. (The full score for this short question is 7)
Simplify first, then find the value of algebraic expression.
Where m=+1 and n=-1.
17. (Full score for this small question)
Solving inequality system
Word, and write its integer solution.
18. (Full score for this small question)
As shown in the figure, in the parallelogram ABCD, e and f are the midpoint of AB and CD, respectively. Prove:
( 1)△AFD?△CEB。
(2) The quadrilateral AECF is a parallelogram.
19. (Full score for this small question)
There is a river between Village A and Village B. Originally, going back and forth from Village A to Village B needs to go through the bridge CD and take the broken line A-D-C-B or B-C-D-A. In the construction of "civilized new village", the two villages have built a new bridge EF on the river, which is the same length as CD, and can directly go back and forth from Village A to Village B along the straight line AB. Known AD=24 km, \. (The results are accurate to 0. 1 km, ≈ 1.4 1, ≈ 1.73).
20. (The full score for this short question is 8)
Wetland Park plans to build a mixed forest of A and B trees, and it needs to buy 2000 seedlings of these two trees. Information about planting two kinds of seedlings, A and B, is as follows:
Variety unit price (yuan/plant) Survival rate labor cost (yuan/plant)
Answer 20 99% 4
b 15 95% 3
Suppose you buy seedlings of X tree species A, and the total cost of building this forest is Y yuan. Answer the following questions:
(1) Write the functional relationship between Y (element) and X (tree) and the value range of X. 。
(2) Assuming that these saplings just survive 65,438+0,960 trees after planting, how much will it cost to build this forest?
2 1. (Full score for this small question)
A company booked a sightseeing tour in Hainan, Yunnan and Jiuzhaigou in a travel agency, and now the relevant information is drawn into the following two charts:
Tourist route price (yuan/person)
Hainan 1 600
Yunnan x
Jiuzhaigou 1 000
Please answer the following questions:
(1) Among them, some people have booked a route to Hainan; The number of people going to Yunnan accounts for% of the total number of people online.
(2) The company decided to allocate these three routes to 100 employees by random lottery. Without knowing anything, each employee draws a sign with a travel route (assuming that all signs are the same in shape, size and texture). ) and ask the employee Xiao Li the probability of drawing the route out of Jiuzhaigou.
(3) If the sum of the money of all the routes to Yunnan accounts for 3/8 of the sum of the money of all the routes, try to find the price for everyone to travel to Yunnan.
22. (The full score for this short question is 9)
There are 480 sets of old tables and chairs in a unit that need to be repaired by a carpenter. It takes 10 days for Master A to repair these tables and chairs alone than Master B; Master b repairs 8 sets more than master a every day; Master A's daily repair fee is 80 yuan, and Master B's daily repair fee is l20 yuan. Excuse me:
(1) How many sets of desks and chairs do carpenters A and B repair every day?
(2) In the process of repairing tables and chairs, the unit shall assign a staff member to supervise the quality and give him a daily transportation subsidy of 10 yuan. There are three repair schemes to choose from:
(1) is repaired separately; ② Maintenance by Party B alone; (3) Both parties shall repair * * *. Which scheme do you think saves time and money? Try to compare and explain.
23. (The full score for this short question is 9)
As shown in the figure, AB is the diameter ⊙O, CB=CD, AC and BD intersect at F, CF=2 and FA = 4.
(1) Verification: △ BCF ∽△ ACB.
(2) Find the length of BC.
(3) Extend AB to E, make BE=BO, connect EC, try to judge the positional relationship between EC and ⊙O, and explain the reasons.
24. (The perfect score for this little question is l0)
In the plane rectangular coordinate system xOy, the right-angle AOCB is rotated counterclockwise by α angle around point A, and the right-angle ADEF is obtained. Let AD and BC intersect at G point, A (-9,0) and C (0 0,6), as shown in Figure A. 。
(1) When α = 60, please guess the shape of △ABF and prove your guess.
(2) When GA=GC, find the analytical formula of straight line AD.
(3) When α = 90, as shown in Figure B, please explore whether the parabola with point B as the vertex passes through the symmetrical central day of the rectangular ADEF, and explain the reasons.
Reference Answers to Mathematics Examination Questions in Guangyuan City, Sichuan Province in 2009
1.D 2。 C 3。 B 4。 A 5。 C
6.-4 7. The sum of two complementary angles is l80.
8 . ab(a+ 1)(a-l)9.28 10 . x & lt； 1 1 1.25 12 . a & gt； b
13. 105 L4。 Wang Hong 15. 16/3cm
16.。 ,-
17. The solution of this inequality group is: 3.
Its integer solution is: 4,5,6,7.
18. Omit
19. The distance is about 20.5km less than before. ..
20. Solution: (1) y = 6x+36000 (0
(2) The total cost of building this forest is 45,000 yuan.
2 1. solution: (1) 50 30%
(2) 1/5 (3) The price of the tourist route to Yunnan is 2,000 yuan/person.
22. That is, Master A repairs L sets every day and Master B repairs 24 sets every day.
(2) (1) The time and expenses required for Master A's independent maintenance are as follows
480÷ 16=30 (days), (80+10) × 30 = 2,700 (yuan).
(2) The time and expenses required for independent maintenance of main equipment B are as follows
480÷24=20 (days), (120+ 10)×20=2 600 (yuan).
(3) The time and expenses required for Party A and Party B's cooperative repair are respectively
480÷( 16+24)= 12 (days), (80+120+10) ×12 = 2,520 (yuan).
Option 3 saves time and money. (9 points)
23.( 1) Omit (2)BC=2 or BC=-2 (Omit).
(3) Connect OC
24. Solution: (1)△ABF is an equilateral triangle.
(2) The coordinate of point G is (-13/2,6).
The analytical formula of AD is: y = x+.
(3) The analytical formula of parabola is y =-(x+9) 2+6. h (- 12，9/2)。
The parabola passes through the symmetry center h of the rectangular ADEF.