April 2006, 10: 30 to 10: 30.
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First, multiple-choice questions (4 points for each small question, 40 points for * * *)
1.a and b are rational numbers satisfying ab≠0. There are four propositions: ① the reciprocal is; ② The inverse number of A-B is the difference between the inverse number of A and the inverse number of B; ③ The inverse of AB is the product of the inverse of A and the inverse of B; ④ The reciprocal of AB is the product of the reciprocal of A and the reciprocal of B, and the true proposition is ()
1 (B)2 (C)3 (D)4。
2. In the figure below, it is () that is not the flat expansion diagram of the cube.
(A) (B) (C) (D)
3. In the algebraic expression xy2, if the values of x and y decrease by 25% respectively, the values of the algebraic expression decrease ().
50% (B)75% (C) (D)
4. if a < b < 0 < c < a, the following conclusion is correct ().
(a) A+B+C+D must be a positive number; (b) D+C-A-B may be negative.
D-C-B-A must be a positive number.
5. In figure 1, da = db = dc, then the value of x is ().
10 20 30 40
6. It is known that a, b and c are integers, and m = | A+B |+| B-C |+| A-C |, then ()
(A)m must be an odd number; (B)m must be an even number.
(c) Only when A, B and C are even numbers, the parity of M is uncertain.
7. The lengths a, b and c of three sides of a triangle are integers, [a, b, c] = 60, (a, B) = 4 and (b, C) = 3. (Note: [a, b, C] stands for the least common multiple of a, b, c, (a, b).
30 (B)3 1 (C)32 (D)33
8. As shown in Figure 2, the rectangular ABCD consists of 3×4 small squares. In this diagram, rectangles that are not squares have ().
40 (B)38 (C)36 (D)34。
9. Let [a] be a rational number, and use [a] to represent the largest integer not exceeding a, such as [1.7] = 1, [- 1] =- 1, [0] = 0, [-650].
(a) [a]+[-a] = 0 (b) [a]+[-a] equals 0 or-1.
(c) [a]+[-a] ≠ 0 (d) [a]+[-a] equals 0 or 1.
10. There are two points A and B on the number axis corresponding to numbers 7 and B respectively, and the distance between A and B is less than 10. Let m=5-2b, then the value range of m is ()