The second exam of the first day of junior high school

April 2007, 15, 8: 30 am to 10: 30 am.

1. Multiple choice questions (this big question * * 10 small questions, 4 points for each small question, ***40 points) Only one of the following four options is correct. Please write the English letters of the correct answers in brackets after each question.

65438+

1440ml. (b) milliliters. (c) milliliters. (d) milliliters.

2. As shown in figure 1, the two sides of straight line L and ∠O intersect at point A and point B respectively, so the sum of the number of rays with O, A and B as endpoints in the figure is ().

(A)5。 (B)6。 (C)7。 (D)8。

3. Integers A and B satisfy: ab≠O and A+B = O, and the judgment is as follows:

○ 1a, b and b have no positive score; A. there is no negative score between 2a, b and b;

There is at most one integer between 3a and b; ○4a, b and b have at least one integer.

Among them, the number of correct judgments is ()

1。 (B)2。 (C)3。 (D)4。

4. The solution of the equation is x = ()

(A) (B) (C) (D)

5. As shown in Figure 2, a regular hexagonal paper with a side length of 1 is an axisymmetric figure, and the number of its symmetry axes is ().

1。 (B)3。 (C)6。 (D)9。

6.9 Numbers: -5, -4, -3, -2,-1, 0, 1, 2,3, the number that can accommodate inequality -3.

(1) 2. (B)3。 (C)4。 (D)5。

7. Teacher Han specially made four identical cubes and placed them as shown in Figure 3(a) and Figure 3(b) respectively. Then the sum of the points of the four bottom squares in Figure 3(b) is ().

(1) 1 1. (B) 13。 (C) 14。 16。

Figure 3

8. For three positive integers that are prime numbers, there are the following judgments:

(1) both are odd numbers; ② There must be even numbers; ③ If there is no common factor, there must be a common factor.

Among them, the number of false judgments is ()

1 (B)2 (C)3 (D)4

9. Put 42 cube building blocks with side length of 1cm together to form a solid cuboid. If the perimeter of the bottom of a cuboid is 18cm, then the height of the cuboid is ().

2 cm (B)3 cm (C)6 cm (D)7 cm

10, if 0 is less than c and b is less than a, then ()

(a) b+a in C+A is greater than or equal to c-a, a+c in b-a-C, a+c(C)c-a in B-A is greater than or equal to C+A, B+A (D) B+A+C.

II. Fill in the blanks (this big question * * 10 small question, 4 points for each small question, 40 points for * * *)

1 1, if the rational number is satisfied, then

12, today (Sunday, April/0/5, 2007) is the day of the second test of 18 "Hope Cup" national mathematics invitational tournament, so the day after a few days is a week.

13, Confucius was born on September 28th, 55 BC1year, so September 28th, 2007 is the birthday anniversary of Confucius. (Note: No AD 0)

14, in the figure. 4, ABCD is rectangular. , the area of the shaded rectangle is

15, the following table is the mathematical statistics of the final exam in the first semester of 2007 in Class 5, Senior One, a middle school:

Score 40-59 60-70 765 438+0-85 86-65 438+000.

No.5 19 12 14

The average math score of this class is not less than 0, not more than 0. (accurate)

16, known, represents a non-zero number, then

17. A city1100,000 households has a monthly water consumption quota of 5 tons. Due to the hot weather in June, July and August, each household uses more water 1 ton per month. In order not to exceed the annual water quota, the water consumption of each household in other months of the year should be controlled within the average monthly ton. If each household saves 2 kilograms of water every day, the water saved in one year (calculated by 365 days) accounts for about% of the annual water quota.

18, a, b and c are all prime numbers. If a+b+c+abc=99, then /a minus B /+/b minus c minus A/=(/…/ stands for absolute value).

19. A machining operation can be completed in five days with four A-type lathes; Use four A-type lathes and two B-type lathes in three days; It can be completed in 2 days with 3 B-type lathes and 9 C-type lathes. If one A-type, B-type and C-type lathe works together for 6 days, only one A-type lathe can continue to work, and the operation can be completed on the other day.

20, set four formulas, the maximum value is

The minimum value is

Third, the answer (this big question ***3 small questions, ***40 points) requirements: write out the calculation process.

2 1, (the full mark of this question is 10)

Xiao Ming marked 2007 points on the plane and drew a straight line L. He found that every symmetrical point of these 2007 points about the straight line L was still on these 2007 points. Please indicate that at least 1 of the points in 2007 are on the straight line L.

22. (The full mark of this question is 15)

Xiaoming and his brother are practicing long-distance running on the circular track. They start from the same starting point in the opposite direction at the same time and meet every 25 seconds. Now, they are heading in the same direction from the same starting point at the same time. After 25 minutes, my brother caught up with Xiaoming and ran 20 laps more than Xiaoming.

(1) How many times is Brother's speed faster than Xiao Ming?

(2) How many laps did Xiaoming run when his brother caught up with him?

23. (The full mark of this question is 15)

How many positive integers n*** satisfy 1+3n ≤ 2007, making 1+5n a complete square number?

Answer:

First, multiple-choice questions (4 points for each small question. )

The title is 1 23455 6789 10.

Answer B D A C C C D C B D

Second, fill in the blanks (4 points for each small question; Two empty questions, 2 points each. )

1 1: negative two thirds 12: three13: 225714:1815: 67; 9; 80; 9 16: 98 17: four and two thirds; 1.22 18: 17/ 19 19:2 20: 1/a； A+ one in B.

Three. solve problems

2 1. Suppose that all the 2007 points are not on the straight line L, because the symmetrical points of each point (I = 1, 2, ..., 2007) are still on the 2007 points about the straight line L, so they are not on the straight line L. ..

That is to say, points not on the straight line L (I = 1, 2, ..., 2007) appear in pairs with points symmetrical about the straight line L, that is, the total number of points marked on the plane should be even, which contradicts the total number of points 2007!

Therefore, the assumption that "these 2007 points are not on the straight line L" cannot be established, that is, at least 1 of these 2007 points are on the straight line L.

22. Let Brother's speed be m/s, Xiao Ming's speed is m/s ... The circular runway is 100 m long.

(1) I knew from "25 minutes later, my brother caught up with Xiaoming and ran 20 laps more than Xiaoming".

Minutes later, my brother caught up with Xiaoming and ran 1 lap more than Xiaoming. therefore

Tidy up, take,

So ...

According to the meaning of the question, you must

That is, the solution,

So after 25 minutes, Xiao Ming ran away.

(2) Another explanation is that every time Xiao Ming runs 1 lap, his brother runs 1 lap more than Xiao Ming, so when his brother runs 20 laps more than Xiao Ming, Xiao Ming also runs 20 laps more.

23. From the condition 1+3N ≤ 2007.

N ≤ 668, and n is a positive integer.

Let 1+5n = (m is a positive integer), then

This is a positive integer.

So m+ 1 = 5k, or m- 1=5k(k is a positive integer).

○ 1 When m+ 1=5k is,, by

，，k≤ 1 1

When k= 12, > 668.

Therefore, there are 1 1 positive integers n that satisfy the meaning of the question, so 1+5N is a complete square number;

2 when m- 1 = 5k,

Therefore, there are 1 1 positive integers n that satisfy the meaning of the question, so 1+5N is a complete square number.

So there are 22 positive integers n*** that satisfy 1+3n ≤ 2007, making 1+5n a complete square number.