mathematics
This paper is divided into two parts: the first volume (multiple choice questions) and the second volume. Volume 1 has 1 to 2 pages, and volume II has 3 to 8 pages. * * * 120 points.
Examination time 120 minutes.
The first volume (multiple choice questions ***24 points)
Precautions:
1. Before answering the first volume, candidates must fill in their admission ticket number and exam subjects on the answer sheet with 2B pencil.
2. After selecting the answer to each question, black the answer label of the corresponding question on the answer sheet with 2B pencil. If you need to change it, clean it with an eraser and choose another answer. You can't answer them on the test paper.
Of the four options in the following question, only one is correct.
First, multiple-choice questions (2 points for each small question, ***24 points)
1. If the sum of and is O, then it is-().
The second century BC.
2. The result of calculation is-().
A.B. C. D。
Last year, Nanjing received about 876,000 inbound tourists, which can be expressed by scientific notation as-() A.B.C.D.
The square root of 4.9 is-().
A.b . 3c . 3d 8 1
5. The daily maximum and minimum temperatures in a certain place from June 5438 to1October 65438 to April 4 this year are as follows:
date
65438+ 10 month 1
1.2
65438+1October 3rd
65438+1October 4th
maximum air temperature
5℃
4 ℃
0℃
4 ℃
minimum air temperature
0℃
℃
℃
℃
Among them, the biggest temperature difference is-().
A.65438+1October1b.65438+1October 2nd C.65438+1October 3rd D.65438+1October 4th.
6. The Municipal Meteorological Bureau predicts that the probability of precipitation in this city will be 70% tomorrow.
A. It will rain 70% of the time in this city tomorrow, and it won't rain 30% of the time.
B: It will rain in 70% of the city tomorrow, and it won't rain in 30%.
C.it will definitely rain in this city tomorrow.
D: The probability that it will rain in this city tomorrow is 70%.
7. In the figure below, the figure with center symmetry is-().
A. diamond B. isosceles trapezoid C. equilateral triangle D. isosceles right triangle
8. As shown in the figure, points A, B and C are on ⊙O, AO∨BC, ∠ OAC = 20,
Then the degree of ∠AOB is-().
1O B.20 C.40 D.70
9. At △ABC, ∠ C = 90, AB=2, AC= 1, then the value of Sin B is ().
A. The second century BC
10. As shown in the figure, the light P is directly above the crossbar AB, and the shadow of AB under the light is CD.
AB∑CD, AB=2m, CD=5m, and the distance from point P to CD is 3m.
Then the distance from P to AB is-().
A.B.
C.D.
Vertices a, b and d of1.□ ABCD in the plane rectangular coordinate system.
The coordinates of are (0, 0), (5, 0) and (2, 3) respectively, then the vertex C.
The coordinates are-().
A.(3，7) B.(5，3)
C.(7，3) D.(8，2)
12. The following is a statistical chart of the annual expenditure of two families.
According to the statistical chart, the following judgment about the proportion of education expenditure of two families in the total annual expenditure is correct ().
A. household a is bigger than household B. Household b is bigger than household a.
C.a is as big as B. D. I can't determine which is bigger.
Nanjing 2OO6 Junior High School Graduates' Academic Examination
mathematics
Volume II (*** 9 6 points)
Small plan
Title number
two
three
four
five
six
seven
eight
Take the lead
Precautions:
1. Book 2, page ***6, use a pen or ballpoint pen (blue or black) to answer directly on the test paper.
2. Fill in the items in the sealing line and table number clearly before answering the question.
Fill in the blanks (3 points for each small question, *** 12 points)
13. As shown in the figure, in △ABC, ∠ ABC = 90, ∠ A = 50,
BD∨AC, then the degree of ∠CBD is 0.
14. The service life of a lamp is 1000 hours, and the average number of days it can be used.
The relationship between the hours used every day is.
15. Write a rational number and an irrational number so that they are both negative numbers greater than.
16. As shown in the figure, the rectangular ABCD intersects with ⊙O with the center on AB at points G, B, F, E,
GB=8cm, AG= 1cm, DE=2cm, then EF= cm.
Three. (6 points for each small question, ***24 points)
17. Calculation:.
18. Solve the inequality group and write the positive integer solution of the inequality group.
19. Known: As shown in the figure, in □ABCD, e and f are the midpoint of AB and CD respectively.
Verification: (1) △ AFD ≌ CEB;
(2) The quadrilateral AECF is a parallelogram.
20. In order to know the sales of canned drinks in our store in the first half of the year, the beverage store randomly investigated the daily sales of this kind of drinks for 8 days. The results are as follows (listening): 33, 32, 28, 32, 25, 24, 365, 438+0, 35.
(1) What is the average daily sales for these eight days?
(2) According to the above calculation results, how many cans of this beverage can this store sell in the first half of the year (calculated by 18 1 day)?
Four, (6 points for each small question, *** 12 points)
2 1. The charging standards of a parking lot are as follows: 6 yuan for medium-sized cars and 4 yuan for small cars.
At present, there are 50 small and medium-sized cars in the parking lot, and these cars pay parking fees. 230 yuan asked how many small and medium-sized cars there are.
22. A school has three restaurants, A, B and C, and each of the three students chooses one at random.
(1) Find the probability that students A, B and C eat in the same restaurant;
(2) Find the probability that at least one of the three students A, B and C will dine in the B restaurant.
Verb (abbreviation of verb) (7 points in question 23, 8 points in question 24, *** 15 points)
23. In the plane rectangular coordinate system, a straight line passes through point m (3,0) and is parallel to the axis.
(1) If the coordinates of the three vertices of △ABC are A (-2,0), B(- 1 0) and C (- 1 2), then the symmetry diagram of △ABC about the axis is △ A1b/kl.
The graph is △A2B2C 1, and the coordinates of three vertices of △A2B2C 1 are written;
(2) If the coordinate of a point is (,0), where point P is about
The symmetry point of an axis is the symmetry point of a point about a straight line,
I asked for a long time.
24. In an experimental field, the relationship between daily water demand (kg) and crop growth time (days) is shown in the graph. The daily water requirements of these crops were 2000 kg and 3000 kg on 10 and 30 days respectively, and the daily water requirements after 40 days increased by 100 kg compared with the previous day.
(1) Find the relationship between ≤40 and ≥40 respectively;
(2) If the daily water demand of these crops is greater than or equal to 4,000 kg,
If artificial irrigation is needed, when will it be started?
Six, (8 points for each small question, *** 16 points)
25. As shown in the figure, in the rectangular ABCD, AB=2AD and the line segment EF= 10. Take a point m on EF, and take EM and MF as.
Make rectangle EMNH and rectangle MFGN, so that rectangle MFGN∽ rectangle ABCD. Let MN= What is the value? What is the maximum area s of the rectangular EMNH? What is the maximum value?
26. Watermelon business owners bought a batch of small watermelons at the price of 2 yuan/Jin and sold them at the price of 3 yuan/Jin, which can sell 200 Jin every day. In order to promote sales, the business owner decided to reduce the price. After investigation, it is found that every time the price of this kind of small watermelon is reduced by 0. 1 yuan/kg, they can sell 40 kg more every day. In addition, the daily rent and other fixed costs are ***24 yuan. If the business owner wants to sell this small watermelon every day,
Seven, (this question 8 points)
27. As shown in the figure, Island A is 45 degrees southwest of Port P and 8l nautical miles away from the port. Ship a leaves from a,
Sail to the port at the speed of 9 knots in the direction of AP, and ship B will leave from Port P and follow the direction of 6 O in the southeast.
Depart at the speed of 18 knots. Now both ships leave at the same time.
(1) How many hours after the departure, are the distances between the two ships to Port P equal?
(2) A few hours after leaving Hong Kong, is the B ship due east of the A ship? (The result is accurate to 0. 1 hour)
(Reference data:)
Eight, (this question 9 points)
28. Given the rectangular paper ABCD, AB=2, AD= 1, fold the paper so that the vertex A coincides with the point E on the edge CD.
(1) If the crease FG intersects with AD and AB at points F and G respectively (as shown in figure 1), find the length of DE;
(2) If the crease FG intersects with CD and AB at points F and G respectively (as shown in Figure 2), the circumscribed circle of △AED is tangent to the straight line BC.
Find the length of the crease FG.
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