First, multiple-choice questions (7 points for each small question, ***42 points)
1. If A, B and C are three arbitrary integers, then? 、? 、? Medium ().
(a) None of them are integers; (b) at least one integer; (c) They are all integers; (d) At least two integers.
2. As shown in the figure, E and F are points on the sides of the rectangle ABCD AD and BC respectively, and the areas of △ABG and △DCH are 15 and 20 respectively. Then the area of the shaded part in the figure is ().
(A) 15(B)20？ 35 years old? 40 people
3. The condition that the quadrilateral ABCD is rhombic is ().
(a) diagonal AC bisects diagonal BD and AC⊥BD.
(b) diagonal ∠A=∠C bisects diagonal BD, and ∠ a = ∠ c.
(c) Diagonal AC bisects diagonal BD and bisects ∠A and ∠ C.
(d) diagonal AC bisects ∠A and ∠C, and ∠ a = ∠ c.
4. When x-y= 1, the value of x4-xy3-x3y-3x2y+3xy2+y4 is ().
(A)- 1(B)0？ (C) 1？ (D)2
5. Let B take an even number from 1 to1,and C take any four players of A, B, C and D to play the game of passing the ball to each other. The first time A was passed to one of the other three people, and the second time was passed to one of the other three people by the person with the ball. This level has been passed four times. Then it was passed for the fourth time.
(A)(B)(C)(D)
Fill in the blanks (7 points for each small question, 28 points for * * *)
1. known a+b+c=0, A >；; B>c. So the range of c/a is.
2. Calculation:?
=.
3. As shown in the figure, three sides of Rt△ABC are taken as sides, and semi-circles, squares and regular triangles with areas of S 1, S2 and S3 are respectively made outward. Obviously, S 1=S2+S3. Three sides of Rt△ABC are respectively used to make any three triangles with areas of S 1, S2 and S3, and S 1=S2+S3. By analogy with the above conclusion, what are the conditions that these three triangles meet?
.
4.5 Football teams play round robin (one game for every two teams). It is known that Team A played three games, Team B played more than Team A, Team C played less than Team A, Team D played as much as Team E, and Team Dante and Team E never played. So, the total number of games is.
A second attempt
(20 points) It is known that t is the root of the unary quadratic equation x2-x- 1=0. For any rational number A, rational numbers B and C satisfy (at+ 1)(bt+c)= 1.
(1) Find B and C (expressed by the algebraic expression of A);
(2) Whether there is such a rational number A that at least one of B or C is equal to it, and if so, find such a value; If it does not exist, explain why.
Two. (25 points) If you buy tickets for a park, the fare is shown in table 1:
How many people buy tickets? 1~50? 5 1~ 100? /kloc-above 0/00
How much is the fee per person? 13 yuan? 1 1 yuan? 9 yuan
There are two tour groups A and B today. If tickets are purchased separately, the total ticket fees payable by the two groups are 1? 3 14 yuan; If you buy tickets in a group, the total ticket fee is 1? 008 yuan. How many people are there in each of these two tour groups?
Three. (25 points) As shown in Figure 3, △ABC is divided into six small triangles by three * * * straight lines AD, BE and CF. If the areas of △BPF, △CPD and △APE are all 1, find the areas of △APF, △DPB and △EPC.