(Examination time: 90 minutes; 100)

1. Multiple choice questions (4 categories 1, 5 points for each small question, otherwise 0 points, 50 points for this big question).

1. As we all know, and the value of. Equal to ().

A.； b； c； d。

2.( ).

A.； b； c； d。

3. If, then, the number of positive numbers is ().

A. I; B. one; C. one; D. it's all possible

4. There is a regular triangular prism with a side length of. Now cut off a part, and what remains is that the remaining volume is ().

A.； b； c； d。

5. It is known that the quartic equation with one variable has three equal real roots and one different real root, so there are () true propositions in the following three propositions.

(1) may be established; ② It may be established; (3) may be established.

A.； b； c； d。

6. Given that the decimal place of a square number is 7, then its single place is ().

A.； b； c； d。

7. If the two roots of the equation about are and, then the relationship with is ().

A.； b； c； D. uncertainty

8. All integer solutions of the equation have () groups.

A.； b； c； d。

9. Let the quadratic function satisfy: if, then the maximum value of. Yes ().

A.； b； c； d。

10 value. Yes ().

A.； b； c； d。

Fill in the blanks (5 points for each small question, otherwise 0 points. This big question is 50 points).

1 1. When the sum of the squares of four sides of a square with side lengths of,, and respectively is the smallest, its area is _ _ _ _.

12. The solution to inequality is _ _ _ _.

13. The equation about has two unequal real roots, and the average value of is, then the value range of is _ _ _ _.

14. The sum of all the real roots of the equation is _ _ _ _ _.

15. If this point is different from the sum on the arc of the circumscribed circle of a regular triangle, judge the relationship between the sum: _ _ _ _ _ _ (fill in the blanks).

16. As shown in the figure, the location is located on both sides of the river, the width of the river is 0, and the horizontal distance between them is m. If someone wants to use the route in the figure to get from the location to the location, it takes the least time when the included angle is _ _ _ _.

17. A straight line passing through a point on a plane is called a straight line cluster about that point, and at this time it is called the order of the straight line cluster (note: it can be considered that the straight line cluster degenerates to a point at this time). If the sum of the orders of two non-overlapping points on a plane and the straight line cluster about that point is, then the number of areas formed by all straight lines dividing the plane of these two straight line clusters is the largest.

18. It is called the largest integer that does not exceed. Remember, then _ _ _.

19. Known integer …, satisfying:

① , …, ; ② … ; ③ … .

The minimum value of ... is _ _ _ _, and the maximum value is _ _ _ _.

20. This is a function that takes a small number and a large number. For example, the solution of the equation is _ _ _ _.

The 20th "Wuyang Cup" Junior Middle School Mathematics Competition Grade Three Examination Questions

Model answer

1. Multiple choice questions (4 categories 1, 5 points for each small question, otherwise 0 points, 50 points for this big question).

Title 1 2345

Answer c d b c b

Title 6789 10

Answer c b b b c

Fill in the blanks (5 points for each small question, otherwise 0 points. This big question is 50 points).

Title:1121314151617.

Answer 2 4 > x≥ 12

C & lt2-3 or c & gt2+3

-2 = 30 degrees

3 1, 16

Title 18 19 20

Answer 2206 2008, 2008 35+2245 30 or 35-2245 30

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