1. Among the following numbers: -(-2),-(-2 2), which is the reciprocal of the absolute value of-2, (-2) 2, where the number of negative numbers is ().
1。
2. Among the following propositions, the correct one is ()
(1) The opposite number is only equal to its own number 0; ② The number whose reciprocal equals itself is only1;
③ The number whose square equals itself is 1 and 0; (4) The numbers whose absolute values are equal to their own are only 0 and1;
A. only 3b. ① and 2c. Only1d. ③④。
On June 24th, 2007, the Long March 3A carrier rocket carrying China's first lunar exploration satellite Chang 'e-1 was successfully launched from xichang satellite launch center Tower III. Technicians designed Chang 'e-1 to adapt to the lunar environment. This is because the temperature difference between day and night on the surface of the moon can reach 3 10℃, and the place where the sun shines vertically during the day can reach 65438.
a . 437℃b . 183℃c .-437℃d .- 183℃
4. It is estimated that the daily economic loss caused by land desertification in China is about 65.438+0.5 billion yuan, and the total economic loss caused by land desertification in China in one year (calculated by 365 days) is expressed by scientific notation ().
a.5.475* 10^ 1 1·5.475* 10^ 10
C.0.547* 10^ 1 1·5.475* 10^8
5. Add two numbers, and the sum is less than one addend and greater than the other, then ()
A. The signs of these two addends are both positive.
C. the signs of these two addends cannot be the same. The signs of these two addends cannot be determined.
7. In the algebraic expressions 5abc, -7x 2+ 1, -2x/5, 1/3, (2x-3)/5, the monomial * * * has ().
1。
8. Xiaogang did a math problem: "Given that two polynomials are A and B, find the value of A+B." He mistook "A+B" for "A-B" and the answer was X-Y. If B=3x-2y is known, then the original value of A+B should be ().
A.4x+3y B.2x-y C.-2x+y D.7x-5y
9. In the following equation, the solution is-1/2 is ().
a . x-2 = 2-x b . 2.5x = 1.5-0.5x c . x/2- 1/4 =-5/4d . x- 1 = 3x
1 1. The distance between Party A and Party B is m kilometers. The original planned train speed was x kilometers per hour. If you travel at a speed of 50 kilometers per hour, the time required for the train to travel from A to B will be reduced by () hours.
A.m/50 b . m/x . c . m/x-m/50d . m/50-m/x
12. Our usual numbers are decimal numbers, such as 2639 = 2 * 103+6 */kloc-0+3 *10+9, which means that decimal numbers need10 digits (also called numbers) There are only two numbers: 0 and 1. If the binary number 10 1 =1* 2+0 * 21+1= 5, the binary number101is equal to the decimal number.
56 C.57 D.58
Fill in the blanks (2 points for each small question, *** 16 points)
13. Integer greater than -2 and less than 1 is _ _ _ _ _ _ _ _.
14. If the square of a number is 9, then the cube of this number is _ _ _ _ _.
15. Calculation:10+(-2) * (-5) 2 = _ _ _ _ _.
The divisor16.24,700 is accurate to _ _ _ _ _ _ _ _ _, with _ _ _ _ _ _ significant digits.
17. If the algebraic expressions 2x-6 and -0.5 are reciprocal, then x = _ _ _ _ _
18. If the sum of 2 * A 3N and -3 * A 9 is still a monomial, then A = _ _ _ _ _ _
Four, column equation to solve application problems (*** 13 points)
29. (4 points in this question) Party A and Party B each process a batch of parts with the same number in the workshop. Party A can process 25 parts per hour, and Party B can process 20 parts per hour. Because Party A went to the meeting first, he worked less than Party B 1 hour. As a result, both of them completed the task at the same time, and each person was required to process the total number of parts.
30. (Question 4) The opening of the Qinghai-Tibet Railway is the wish of several generations of China people. On this railway line, there is a long frozen soil between Golmud and Lhasa. The speed of the train is 100 km in frozen soil section and 120 km in non-frozen soil section. From Golmud to Lhasa, it takes about O.77 hours for the train to pass through the frozen section than the unfrozen section.
(1) How many kilometers is the unfrozen area longer than the frozen area expressed by the algebraic expression with t?
(2) If the total length of Golmud-Lhasa railway is118km, find t (accurate to O.O.1) and the length of frozen soil section (accurate to one place).
3 1. (5 points in this question) A grade used the summer vacation to organize students to travel abroad, 10 Parents' representatives traveled with the group. A travel agency said, "If all parents of 10 buy full tickets, the rest of the students can enjoy a half-price discount"; Travel agency B said, "Including 10 parent representatives, all air tickets are offered a 40% discount on the total ticket price". If the total fare is 40 yuan,
(1) If the number of students is 30, how much does the travel agency charge? If the number of students is 70, how much does the travel agency charge?
(2) When the number of students is what, are the charges of the two travel agencies the same?
(3) Which travel agency is more economical to choose?
V. Asking questions (***3 points)
32. Let A, B and C be rational numbers, and in the multiplication operation of rational numbers, satisfy;
(1) switching rule a * b = b * a(2) distribution rule of addition (A+B) * C = A * C+B * C.
Now let's have a&; B This operation is defined as follows: a &；; b=a*b+a+b
Discussion: Does this operation satisfy the (1) commutative law? (2) The distribution law of addition? Explain by calculation.
Six, additional questions (***6 points, recorded in the total score, but the total score does not exceed 100 points. )
33. (3 points for this question) Proof: 1/3
34. (3 points for this question)
Equation ||x-2|- 1|=a has three integer solutions about x, so find the value of a.