1. Multiple choice questions: fill in the correct options in the corresponding boxes (3 points for each question, ***30 points).

1, as shown below: ① Triangle ② Quadrilateral ③ Pentagon ④ Regular Hexagon () can definitely be densely laid.

A. 1 B. 2 C. 3 D.4

2. Teacher Zhang went to the store to buy prizes for students and asked for 9 yuan for each prize. Now there are only three different commodities from 3 yuan and four different commodities from 6 yuan to choose from. There are () different options to combine into prizes from 9 yuan.

A. 12 B. 13 C. 14 D. 15.

3. A junior high school 12 volleyball team in a city will play a game. If the single round robin system is adopted, a * * * will hold () games.

A. 1 1b . 12c . 66d . 72

4. Use black and white hexagonal floor tiles to make several patterns according to the rules shown in the figure.

The 20th pattern has () white floor tiles.

A.120b.80c.82d. None of the above is correct.

5, cut a cake into four knives, and cut it into () pieces at most.

A.9 b . 10 c . 10d . 12

6. In the figure below, what cannot be folded into a cube is ().

7. There are two kinds of packaging for a kind of soap: large box 100, price 150 yuan; A small box of 50 yuan, priced at 80 yuan. Now I want to buy 920 bars of soap. What is the cheapest way to buy? Neither of these two packages of soap can be unpacked and retailed. )

A. 1500 b . 1380 c . 1520d . 1430

8. The candle is 20 cm long and burns 5 cm per hour after being lit. Four students drew the burning situation respectively, where Y represents the remaining height of the candle and X represents the time, so the correct one is ().

9. Choose two of the five candidates as mathematical representatives, and * * * has () different schemes.

A.20 B. 10 C. 30 D. 15

10, the following statement is wrong ()

A. the southeast direction is 45 degrees east of south;

B. A is in the northwest of B and B is in the southeast of A;

C.A is in the northwest of B, and C is also in the northwest of B, so A, B and C must be in a straight line;

D.a is in the southeast of B, C is in the south of B, and C is in the east of A.

Fill in the blanks (3 points for each question, 30 points for * * *)

1 1, estimated: 7.36+0.45+2.68+5.12 = _ _ _ _ _ _.

12. It is known that on a map of China with the scale of 1: 2700000, the straight-line distance between Beijing and Hongkong is 7. 1cm, so the actual distance between the two places is _ _ _ _ _ _ _ km.

13, the kitten ate 1 fish on the first day, 2 fish on the second day, 3 fish on the third day, 4 fish on the fourth day, ... 55 fish for the kitten to eat _ _ _ _ _ _.

14, a child of 12 needs 50 mg of vitamin C every day. It is known that every 25 grams of a fruit juice contains C 10 mg of vitamin C, and it takes _ _ _ _ _ _ grams of this fruit juice to meet the needs of vitamin C for one day.

15, two athletes run a 400-meter race, the runway width is 1.2 meters, and the curve is semicircular, so the difference between the starting lines of two adjacent runways is _ _ _ _ _ _ _ _ _.

16. There are _ _ _ _ _ _ different line segments in the picture below.

17, a computer is priced at 6000 yuan, and the computer company sells it at a 10% discount. It costs _ _ _ _ _ _ _ yuan to buy a computer.

18, the length, width and height of a rectangular carton are 10cm, 8cm and 5cm respectively, so the surface area of this carton is _ _ _ _ _ _ _ square cm.

19, a hectare of lush forest can absorb about 1 ton of carbon dioxide every day, and each person exhales 38 grams of carbon dioxide per hour on average. If you want to absorb the carbon dioxide exhaled by ten thousand people in one day, you need at least _ _ _ _ _ _ _ hectares of forest.

20. There are four students, and the number of apples they get is exactly 1 more than 1. The product of their apples is 5040, so the sum of their apples is _ _ _ _ _ _ _.

Third, answer questions (8 small questions, ***40 points)

2 1, (4 points in this question) Xiaoming went to the essence bookstore and bought two dictionaries for his classmates. It is known that the length, width and height of each dictionary are 26cm, 18cm and 3cm respectively. Now they are packaged into a package. How to save wrapping paper? How many square centimeters of wrapping paper do you need at least?

22. (5 points in this question) Naughty bag has a map with three places, A, B and C, but the map is polluted by ink. I can't see the exact location of C clearly, but I know that C is 30 degrees east of the north of A and 45 degrees east of the south of B. Can you help naughty determine the location of C?

(3: 23) Three young workers were newly transferred to a workshop, and the workshop director Zhao asked their ages:

Xiao Liu said, "I am two years younger than Chen Xiao."

Xiao Chen said, "Xiao Li and I are three years apart."

Xiao Li said, "I am younger than Xiao Liu, who is 23 years old."

Would you please help director Zhao analyze the ages of the three of them?

24. (4 points in this question) A middle school organizes students to visit museums 6 kilometers away from the school. Xiaoxiao can't take the school chartered bus because of something, and is going to take a taxi to the museum at the school gate. Taxi charges are as follows: 8 yuan will be charged when the mileage is less than 3km (including 3km); When the mileage exceeds 3km, each additional 1km will be charged 1.8 yuan. Xiaoxiao only has 14 yuan. Is it enough to go to the museum by taxi? Please provide a justification for the answer.

25. (4 points in this question) Xiaoming's home is 2 kilometers away from the school and 3 kilometers away from the Children's Palace. So the distance from the school to the Children's Palace must be 5 kilometers? Please provide a justification for the answer.

26. (6 points in this question) A car drives from A to B, with an average speed of 60 km/h; Return to A from B along the original road, with an average speed of 40 km/h, and find the average speed of the car.

27. (This question is 6 points) There are 44 students in 6 classes in a junior high school in a school. The teacher gave the students an assignment: Please design a contact network for the class and ask the following questions for the students to learn:

If a message is transmitted by telephone, do you call the same number of times for different schemes?

(2) If it takes 1 minute to make a phone call, a message will be delivered within 9 minutes from the beginning to the end. Please design a plan.

Practical test paper

1. Tell a short story with the following route.

2. If a family has two adults and a child aged 12, please design a week's nutritious meal for them and estimate the cost of a week's nutritious meal according to the food price.

3. Poems on Diophantine Tombstones

Dioplantes (about 246~330), a Greek mathematician, is said to have written an inscription on his tombstone and told his life in a poem. This poem is written like this:

Passerby! Five years later, my son was born,

Diophantu was buried here, but his son died four years before his father.

Please calculate the following figures, the age is only half of the father's death.

We can know how many winters and summers he has experienced in his life. Poor old man who lost his son in his later years,

One sixth of his life was a happy childhood, and he spent his old age in sorrow.

One twelfth are carefree teenagers,

One seventh of the journey of life,

He built a happy family.

Please communicate with other students in the class and calculate the age of Diophantine's life.

Test answer

A, 1, c can be a dense ordinary graph.

2, b food collocation

3. Number of C matches

4.c stack

5, C pancakes

6. Three-dimensional folding

7. Shopping plan

8.b image

9. Team A plan

10, d direction and position

Second, 1 1, 15 438+0 (true value) estimation

12, 19 17 scale

Arithmetic progression and 13 and 10.

14, 125 nutritional catering

15, 2.4π starting line

16 and 15.

17,5400 shopping guide

whitewash a wall

19,9.12 vitamins and calcium

20, 34 stack

Three. 2 1. Solution: (26×18+18× 3× 2+26× 3× 2 )× 2 =1464 (square centimeter).

A: When the largest surfaces overlap, wrapping paper is the most economical.

At least 1464 square centimeters of wrapping paper is required.

Note: If the formula is 1, the result is 1, the unit is 1, and the answer is 1. -Packaging knowledge

22. Solution:

The drawing of points A and B is 2 points each, and the intersection point is 1 point. -Direction and position

23. Solution: Xiao Liu is 23, Xiao Chen is 25 and Xiao Li is 22. -Logical reasoning

24. Solution: 8+ 1.8×(6-3)= 13.4 (yuan) ∵ 13.4 < 14 ∴ Enough.

Note: The formula is calculated as 2 points, the numerical comparison is 1 minute, and the answer is 1 minute. -Travel expenses

25. Not necessarily. Note: The answer is 2 points and the counterexample is 2 points. -How far is it?

26. Solution: 2 ÷ (1÷ 60+1÷ 40) = 48 (km/h).

Attendant: The average round-trip speed is 48 kilometers per hour. ..

Note: the formula is 2 points, the result is 2 points, the unit is 1 minute, and the answer is 1 minute. -Average speed

27.① Same. ② Remarks: 2 points for the answer and 4 points for the reasonable design scheme. -Liaison plan

Practice test paper