6. A number of squares and isosceles right-angled triangles are spliced into a graph as shown in the figure. If the side length of the largest square is 7cm, then the sum of the areas of squares A, B, C and D is () (a)14cm2 (b) 42cm2 (c) 49cm2 (d) 64cm2 7. It is known that x.a ≤ (d) ≤ a <: 8. the number of intersections of graphs with function y= > and function y=kx(k≠0) is () (A)0 (B) 1 (C)2 (D)0 or 2.
9. A pharmaceutical research institute has developed a new drug, which is taken by adults at a prescribed dose. After taking the medicine, the functional relationship between the drug content y (mg) per milliliter of blood and the time t (hours) approximately satisfies the curve shown in Figure 3. When the drug content per milliliter of blood is not less than 0.25 mg, the treatment is effective. The effective time to treat the disease once is () (a) 16 hours (B) 15 hours (C) 15 hours (D) 17 hours 10. A company organized employees to go boating in the park, and fewer than 50 people signed up. Only 18 people didn't take the boat, and each boat took 10 people, so after the rest of the boats were full, only one boat was not empty. There are () (A)48 people (B)45 people (C)44 people (D)42 people who take part in rowing. ***40 points) 1 1. Given that A, B and C are the three sides of △ABC, the simplified result │a+b+c│+ is _ _ _ _ _ _ _. 12. Since the invention of scanning tunneling microscope, a new door has been born in the world. 1 micron = 1000 nm, then the length of 2007 nm is expressed as _ _ _ _ _ _ _ m.13 by scientific notation. If the range of the unknown x in the inequality set is-1
16. As shown in the figure, a kitten climbs up along the board standing obliquely in the corner, and the bottom of the board is 0.7 meters away from the corner. When the kitten climbs from the bottom of the board to the top, the bottom of the board slides to the left 1.3 meters, and the top of the board slides down by 0.9 meters. Then the kitten climbed _ _ _ _ _ _ meters on the board. 17. Xiaoming said to Xiaohua, my age plus your age. Plus my age, your age is 48. Xiaohua's age now is _ _ _ _ _. (English-Chinese dictionary: age; Add add; When when) 18。 The length, width and height of a cuboid are positive integers A, B, C, a+B+C+AB+BC+AC+ABC = 2006, so the volume of this cuboid is _ _ _ _ _ _.19. As we all know. Information transmission needs encryption, the sender changes from plaintext to ciphertext (encryption), and the receiver changes from ciphertext to plaintext (decryption). Now the encryption rules of 26 English letters are as follows: 26 letters correspond to integers from 0 to 25, such as English A, B, C and D, and write their plaintext (corresponding to integers 0, 1, 2, 3). 3x4 calculation, the ciphertext is obtained, that is, the ciphertext corresponding to letters A, B, C and D is 2, 3, 8 and 9 respectively. Now the ciphertext received by the receiver is 35, 42, 23, 12, and the decrypted English word is _ _ _ _ _ _ _. Third, answer the question (this big question * requirements: write out the calculation process. 2 1. (The full mark of this question is 10) As shown in the figure, the vertex of a big hexagonal star (thick solid line) is the center of six congruent small hexagonal stars (thin real number) around it, and two adjacent small hexagonal stars each have a common vertex. If the distance from the vertex C of the small six-pointed star to the center A is a, (2) the area of the large six-pointed star; (3) The ratio of the area of the big six-pointed star to the sum of the areas of the six small six-pointed stars. (Note: The six-pointed star in this question is formed by splicing 12 identical equilateral triangles). 22. (The full mark of this question is 15) A and B respectively transport a batch of goods from place A to place B and then return to place A. Figure 6 shows the image of the distance s (km) between two cars and place A changing with time t (hours). It is known that the B car will return at a speed of 30k m/ h after arriving at the B place. Please answer according to the data in the picture: (1) How long did it take for A car to be overtaken by B car? (2) How far away from A did car A and car B meet head-on? (3) What is the speed of car A returning from place A before car B can return to place A? 23. There are several points on the plane, and any three of them are not in a straight line. Divide these points into three groups and connect them with line segments according to the following rules: ① There is no line segment connection between any two points in the same group; ② There must be a line segment connection between any two points that are not in the same group. (1) If there are exactly 9 points on the plane, which are divided into three groups on average, how many line segments are there on the plane? (2) If there are exactly nine points on the plane and these points are divided into three groups: 2, 3 and 4, how many line segments are there on the plane? (3) If there are 192 line segments on the plane, how many points are there on the plane? Reference answers and grading standards of the 18th "Hope Cup" National Mathematics Invitational Tournament, grade two, test 1, multiple-choice questions (4 points for each small question) 1. C2 B3 . C4 . D5 . a6 . C7 . b8 . d9 . c 10。 A 2. Fill in the blanks (4 points for each small question, No.65438), 2 points for each blank, 19, and 2 points for a correct answer)11.2c12.2.007×10-4. -6 14.> 15.6; 1416.2.517.1618.88819.5-2 or -5-2 20. Hope three. Answer question 2 1. (65438+.∠ AOC = 30, so AO = 2ac = 2a. (3 points) (2) As shown in the figure, the area of a six-pointed star is 12 times that of an equilateral △AMN. Because AM2=, the solution is AM = A. So the area of the hexagonal star is S =12×××× a× a = 4a2. (7 points) (3) The distance from the vertex C of the small six-pointed star to its center A is A, and the distance from the vertex A of the big six-pointed star to its center O is 2a. So the area of the big hexagonal star is four times that of the small hexagonal star, so the area of the big hexagonal star: the sum of the areas of the six small hexagonal stars = 2: 3 (10 minute) 22. (1) As can be seen from the figure, it can be assumed that the resolution function of a car from A to B is s=kt, and (2.4,48). The solution is k = 20. Therefore, S = 20t. (2 points) As can be seen from Figure 2, car B overtook car A at 30km, so when S = 30km, T= = 1.5 (hours). That is, car A was overtaken by car B after 1.5 hours. (5 points) (2) From the figure, it can be assumed that the resolution function of car B from place A to place B is s=pt+m, and (1.0) and (650) so s=60t-60. (7 points) When the B car arrives at the B place, s = 48km, when it is substituted into s = 60t-60, t = 1.8h Let the resolution function of the B car returning from the B place to the A place be s=-30t+n, and substitute into (1.8,48) to get 48 =-30x/. Substituting s=20t, it is s = 40.8km That is, car A and car B meet head-on at 40.8km (12min). (3) When car B returns to place A, there is -30t+. The solution is t=3.4 hours. Car A will return to place A before car B, and the speed is greater than =48 (km/h). (15 minutes) 23. There are exactly nine points on the (1) plane, which are divided into three groups with three points in each group, and each point can be connected with six points in the other two groups. * * * There are line segments =27 (bars). (5 points) (2) If there are exactly 9 points on the plane and these points are divided into three groups: 2, 3 and 4, then there are line segments [2× (3+4)+3× (2+4)+4× (2+3)] on the plane. The third group has c points, so there is a line segment [A (b+c)+B (a+c)+C (a+b)] = AB+BC+CA (bar) on the plane. If the number of points in the third group remains unchanged, one point in the first group is classified into the second group. Then the number of line segments on the plane is (a-1) (b+1)+(b+1) c+(a-1) c = ab+BC+ca+a-b-1. It is the same as the original number of line segments. B, when a-b- 1≥0, the number of line segments on the plane will not decrease; When a≤b, a-b- 1 < 0, the number of line segments on the plane will inevitably decrease. In this way, when a point is drawn from a group with more points to a group with fewer points on the plane, the number of line segments on the plane does not decrease, so when there are as many points in the three groups (or basically average), the number of line segments on the plane is the largest. (13 points) Suppose there are x points in three groups, then the number of line segments is 3x2 = 6503. The solution is x = 8. So there are at least 24 points on the plane. (15) (Some topics can't be copied completely, I can send them to your email if necessary)