First, multiple-choice questions (***42 points)

1, it is known that the image of the linear function y = ax+b passes through the point (0, 1), and the figure enclosed by it and the coordinate axis is an isosceles right triangle, so the value of a is _ _.

A, 1 B,-1 C, 1 D, uncertain.

2. As shown in the figure, there is a point P in the equilateral triangle ABC. Point P is perpendicular to three sides when it passes, and the vertical feet are S, Q, R, PQ = 6, PR = 8, PS = 10, then the area of ABC is equal to _ _.

a、 190 B、 192 C、 194 D、 196

3. If the polynomial 2x4-3x3+ax2+7x+b is divisible by x2+x-2, then = _ _.

a 、-2 B 、- C、D、0

4. A line has a number of 1000, in which the middle number of any three adjacent numbers is equal to the sum of the two numbers before and after it. If the first two digits of 1000 are both 1, then the sum of 1000 is equal to _ _.

a、 1000 B、 1 C 、- 1 D、0

5.a and B are real numbers. If -3 = 0 and B4+B2-3 = 0 are known, the value of is _ _.

a、6 B、7 C、8 D、9

6. The acute triangle * * * with the perimeter of three consecutive positive integers not exceeding 60 has _ _.

a， 15 B， 16 C， 18 D，20。

Two. Fill in the blanks (***28 points)

1, calculation: (2+1) (22+1) (24+1) ... (232+1)+1= _ _.

2. Let the graphic area enclosed by two coordinate axes KX+(k+ 1) y = 1 (k is a positive integer) be SK (k = 1, 2,3, …, 2005), then S 1+S2+S3+.

3. As shown in the figure, the areas of Δ δFBE, FDC and Δ δFCB are 5, 8 and 10 respectively, so the area of quadrilateral AEFD is S = _ _.

4. As shown in the figure, take the sides AC and BC of ABC as one side, make square ACDE and CBFG outside the triangle, and point P is the midpoint of EF.

PH⊥AB, vertical foot is H. If AB = 10, then

PH=__ .

Iii. (Full score for this question is 20 points)

It is known that three numbers A, B and C which are not equal to zero satisfy.

Prove that at least two numbers in A, B and C are opposite.

Four, (this question out of 25 points)

There are four schools, A, B, C and D, with 15, 8, 5 and 12 color TV sets respectively. In order to make the number of color TVs in each school the same, these schools are allowed to adjust each other, but only the color TVs can be transferred to neighboring schools (or to color TVs). How to allocate to minimize the total amount of color TV calls? Try to find out all possible schemes to minimize the total number of transferred color TVs, and find out the total number of transferred color TVs.

Five, (this question out of 25 points)

There is a rectangle ABCD, AB = A, BC = Ka. Now fold this paper so that vertex A and vertex C coincide. If the area of the non-overlapping part of the folded paper is a2, try to find the value of K. ..

Answer: 1. 1，C 2，B 3，A 4，B 5，B 6，B。

Second, 1, 264; 2、 ; 3、22 4、5

3. The factorization factor of denominator is: (a+b) (a+c) (b+c) = 0, which is proof.

4. Four schemes, at least 10 sets.

V. k = 1, k