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/kloc-the answer and explanation of the second test in the second day of the 0/8 th Mathematics Hope Cup Competition.
Answers to the 18th "Hope Cup" National Mathematics Invitational Tournament (Grade Two)

First, multiple-choice questions:

Title number

1

2

three

four

five

six

seven

eight

nine

10

answer

B

C

A

B

C

C

A

A

C

C

Hint: 1, omitted

2. The original formula can be changed to: m( 1-m)=0, m=0 or m= 1.

3. What does △ BPP mean from the topic? Is an isosceles right triangle, and PP is obtained from Pythagorean theorem? =2

4. To solve these equations:

∵x & gt; 0,y & lt0

Get 4

∴a=5.

5. When k>4 o'clock direction, 2k & gtk2 & gt2k & gtK+2, so choose C.

6. A quadrilateral obtained by connecting the midpoints of four sides of the quadrilateral in turn is a quadrilateral with an area of:

(

× 10)×(

×8)=20

7.s is positive =

Aortic second sound

S diamond =

Bc, ∫b:a = a:c, that is, a2=bc, ∴S is positive.

: s diamond

= 1: 1

8. Let the other two sides be A and B, then a2+b2= 1 12.

(irrelevant) or 1 12=

Aortic second sound

-

b2

=(a+b)(a-b)= 12 1

= 12 1× 1;

A and b are natural numbers.

∴a+b= 12 1,

∴ The circumference is121+1=132.

9.∫x2-9x+ 18 = 0, that is, (x-6)(x-3)=0.

, ∴x=6 or x=3, ∴ the three sides of the triangle are:

Three, three, three or six, six, six or six, six, three. Perimeter: 9 or 15 or 18.

10, omitted

Two. Fill in the blanks in Group A:

Tip:

1 1

Accelerated business collection and delivery system (adopted by the United States post office)

B.C.

//BM

The circumference is 12.

12.

Simplified as (a-b)(a+b-9)=0.

13. From the meaning of the question,

solve

14 AB=5.

BC= 12

15 is 7a+ 196=2 13.

a=

When b is the smallest.

A+b value is the largest.

That is, a+b=27.

16.

Draw a figure, which is composed of symmetry and equilateral.

The nature of the triangle can assume that the distance from f to BC is 4.

17

The sum of the outer angles of the polygon is 360.

, the outer corner is

,

Let the polygon be 360.

=

= 18 polygon

The sum of all integer solutions is 0+ 1+2+3=6.

18.

19 is set to 2=

a=2

20.

Five triangles

10 quadrilateral

five

Third, fill in the blanks in group B.

Hint: 2 1. The denominator is set to 2 (x-1)-5 (x+1) = m.

When x= 1

m=- 10

When x=- 1

m=-4

23. Set the first book as X yuan.

The second x+700 yuan

Solution: x=3800

x+700=4500

A: The first book costs 3,800 yuan.

The second one is 4500 yuan.

24. From the meaning of the question.

solve

Or (

)

Or (-2,0)

The analytical formula is y=

Or y=

25. 1 1; 3 1