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20 1 1 National Mathematics
20 1 1 National Junior High School Mathematics Competition Examination Time: 20 1/March 20th 9: 30-1:30 Full marks: 150 Note:/kloc-. 2. Don't exceed the binding line when writing the solution; 3, the draft paper was not handed in. A, multiple-choice questions (***5 small questions, 7 points for each small question, ***35 points. Each small question is given four options code-named A, B, C and D, of which one and only one option is correct. Please put the code of the correct option in parentheses after the question. If you leave it blank, you will get 0) 1. If it is set, the algebraic value is () a, 0 B, 1 C,-1D, 2 2. For any real number a, b, c, d, if (u, v) △ (x, y) = (u, v) for any real number u, v, then (x, y) is () a, (0, 1) B, (1. Then the sum of all possible values of the real number t is () a, b, c, 1 D, 4. As shown in the figure, point D and point E are on the AB side and AC side of △ABC respectively, and be and CD intersect at point F. Let,,, and then the relationship with the size is () A, ﹤ B, = C, ﹤. 20 1 1), the number of right-angled triangles with the hypotenuse length of b+ 1 is .7, and the numbers on the six faces of a cube with uniform texture are 1, 2, 2, 3, 3 and 4 respectively; The numbers on the six faces of another cube with uniform texture are 1, 3, 4, 5, 6 and 8 respectively. When these two dice are thrown at the same time, the probability that the sum of the two upward numbers is 5 is .8. As shown in the figure, the hyperbola () intersects with the sides BC and BA of the right-angled OABC at points E and F, respectively, and AF = BF connects EF, then the area △OEF of ⊙O divided by three different inscribed regular triangles is 0.9 and the number of ⊙O regions is 0. So this four-digit number is. 3. Solve problems (***4 questions, each with 20 points and * * 80 points) 1 1. It is known that the two integer roots of the unary quadratic equation about x are just larger than the two roots of the equation by 1, and the value obtained is. 12. extend the intersection of AD and CH at point p, and prove that point p is the midpoint of CH. 13. If you choose five pairs of integers with different prime numbers from 1, 2, 3, ..., n, one of which is always a prime number, so find the maximum value of n, as shown in figure, △

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