1. Multiple choice questions (5 '× 10 = 50') Only one of the four options in each question below is correct. Please fill in the letters indicating the correct answers in the table below. Yangming education

Average value of odd prime numbers within 1.30.

The nearest number is

12 b . 13 c . 14d . 15

2. Stack 10 identical cubes as shown in the figure, and its appearance includes

Several small squares, as shown in the figure, remove a small cube marked with the letter a,

At this point, the number of small squares in the appearance is compared with that before moving.

A. neither increase nor decrease B. decrease 1.

C. reduce by 2 n. Reduce by 3

3. A TV series with ***8 episodes will be broadcast for 3 days, at least one episode every day, and then arranged.

There are _ _ _ _ _ broadcast methods.

2 1

Party A, Party B and Party C pay the same amount of money to buy the same notebook. In the end, Party A and Party B got three more notebooks than Party C, and both parties gave 2.4 yuan to Party C, so the price of each notebook was _ _ _ _ _ _ _.

A.0.8 B. 1.2 C.2.4 D.4.8

5. Use 0, 1, 2, 9 to form a four-digit number, a three-digit number, a two-digit number and a one-digit number. Each number can only be used once, so that the sum of these four numbers is equal to 2007, and the minimum value of the three digits is: c, 1736+204+58+9.

20 1

6. There are 2007 lights on, and each light is controlled by a pull switch. When you pull the cable switch, the light will change from bright to bright, and then from bright to bright. Now number the lights as 1, 2, …, 2007 in sequence, then pull out all the lights numbered as multiples of 2, then pull out all the lights numbered as multiples of 3, and finally pull out the lights numbered as multiples of 5.

1004 b 1002 c 1000d 998

7. It is known that the hundreds, tens and digits of a three-digit number are A, B and C respectively, and a×b×c=a+b+c, then the sum of the three digits satisfying the above conditions is

A. 1032 B， 1 132 c . 1232d . 1332

8. A math exam with ***5 questions, with 52 participants in the class. * * * Correct answer 18 1 question. It is understood that everyone answered the question 1 correctly at least. 1 Seven people answered correctly, as many people answered correctly 2 questions as 3 questions, and 6 people answered correctly 5 questions. So who answered four questions correctly?

3 1

9. One triangle divides the plane into two parts, and two triangles divide the plane into eight parts at most, …, so how many parts can five triangles divide the plane into at most?

5 12 D. 1024

10. There are five stations A, B, C, D and E on the single-track railway, and the distance between them is as shown in the figure. Two trains leave from two stations, A and E, at the same time. Station A is 60km per hour, and Station E is 50km per hour. As only the station on the single-track railway is paved with parking rails, it is necessary to stop at the station so that the opposite train can pass.

Fill in the blanks (5 feet × 12 2 60 feet)

1 1. Observation 5 * 2 = 5 ten 552 60, 7 * 4 = 7+77+777+7777 = 8638. It is inferred that the value of 9* 5 is _11168.

12. As shown in the picture, some 2m-wide cars are parked in an unmarked park 30m long.

At the roadside of the car compartment, _ _ _ _ cars can be parked in the best case, and _ _ _ _ cars can be parked in the worst case.

13. As shown in the figure, a circle is divided into four sectors by four radii, and the circumference of each sector is 7. 14cm, so the area of the circle is _ _ _12.56 _ _ cm2 (pi is 3. 14).

14. According to the following pattern, the number of people to be filled in the nth square is (n+1) (n+2) (n+3)-3n-7 _ _ _ _ _ _ _ _ _, where n is a non-zero natural number.

15. There are no more than 500 apples in the basket. If you take out two at a time, three at a time, four at a time, five at a time and six at a time, there will be an apple left in the basket. If you take out seven apples at a time, there are no apples, and there are apples in the basket * * _ _ _ 301_ _.

16. The residents of a country are either knights or rogues. Knights don't lie, rogues always lie. When we met residents A, B, C and A, we said, "If C is a knight, then B is a rogue." C said, "A is different from me. One is a knight and the other is a rogue." So among these three people, _ _ _ B _ _

17.a and B divide the same number by the remainder. A divided by 8, B divided by 9. Now it is known that the sum of the quotient obtained by A and the remainder obtained by B is 13, so the remainder obtained by A is _ _ _ _ _ _ _?

Yang Ming

18. As shown in the figure, two squares, BDEC and ACFG, are made with two sides of △ABC as side lengths. It is known that S△ABC:S quadrilateral BDEC = 2: 7, and the side length ratio of square BDEC to square ACFG is 3: 5. Then the simplest integer ratio of △CEF to the whole graphic area is _ _ _ _ 9: 137.

19. There are three identical balls in a pocket with the numbers 2, 3 and 4 written on them. If you take a ball out of your bag for the first time, write the number A on the ball and put it back in your bag. Take another ball out of the bag for the second time and write the number B on it. Then calculate their product.

Then the sum of the products obtained in all different situations with the ball is _ _ _ 53 _ _

20. As shown in the figure, A and B are two ends of a circle diameter, with Xiao Zhang at point A and Xiao Wang at point B, and they start counterclockwise at the same time. Meet at point C in the first week and at point D in the second. It is known that point C is 80 meters away from point A and point D is 60 meters away from point B, so the circumference of this circle is _ _ _ _ _ _ _ _ _.

2 1. Nine consecutive natural numbers, all greater than 80, so there are at most _ _ 4 _ _ prime numbers.

22. Arrange odd numbers 1, 3, 5, ... and group them continuously from 1, so that the nth group has n numbers, namely

( 1),(3,5),(7,9, 1 1),( 13, 15, 17, 19),…

Then 2007 is in the 45th group, which is the 27th group.

Iii. Answering questions (***40 points)

23.(20 minutes) As shown in the figure, the distance between A and B is 1 500 meters. The solid line indicates that A leaves from A to B at 8: 00 am, takes a short rest after arriving at B, and then leaves from B to return to A; The dotted line also shows B's walking from B to A at 8: 00 a.m., arriving at A and returning to B immediately.

(1) Observe this diagram and solve the following problems:

How long did A rest in B? Calculate, what is the walking speed before and after rest? 15 o'clock, 75,75

②B From B to A, what is the walking speed from A to B? 50、50

(2) Party A and Party B met twice on the way. Let's combine these figures to calculate. When did you meet for the first time and the second time? 8: 12,8:45

24.(20 points)

As shown above, 2008 squares are arranged in a row, and a chess piece is placed in the leftmost square. A and B move this piece alternately. After A moves first, everyone can move the chess pieces to the right a few squares at a time, but the number of squares moved cannot be a composite number. The person who moves the chess piece to the rightmost square wins.

(1) According to the number of squares each person moves, what are the four ways to move?

* * * The following four moves: 1, and the number of squares moved by two people is a number that is neither prime nor composite: 1.

2. Prime numbers with unit number of 2: 2

3. Prime numbers with units of 5: 5

4. Prime numbers with unit number 1, 3, 7, 9.

Some teachers think it is odd, even, even and odd. In other words, the parity of two people is divided. But I think this division is inconsistent with the following question, "Four paths for B".

Please express your opinions. How to divide it?

(2) If A walks 3 squares at the first 1 time, what countermeasures should A take to ensure that He (A) will win? And simply explain, why do you have to take such countermeasures and you must win?

A After moving 3 squares for the first time, there are 2004 left. Now it's B's turn to move. After B moved, it was A's turn again. In other words, A always comes last. So if A wants to win, he must leave at least four after every second countdown, so that B can't finish playing. In this way, A wins.

When b takes 1, a takes 3, or other prime numbers add up 1 to be a multiple of 4. This will leave a multiple of 4 squares. In the end, A will win.

B takes two, and A takes two. Make sure that a remains a multiple of 4.

The same is true when b takes quintic prime numbers. As long as A is taken at B every time, then taking it and B together is a multiple of 4. In this way, we always win in the end.