2. Let a, b and c be real numbers, and | a |+a = 0, | ab | = ab, | c |-c = 0, and find the value of the algebraic expression | b |-| a+b |-c-b |+| a-c |.
3. If m < 0, n > 0, | m |
4. Let (3x-1) 7 = A7X7+A6X6+…+A1X+A0, and try to find the value of A0+A2+A4+A6.
6. Solve equation 2 | x+ 1 |+x-3 | = 6.
8. Solve the inequality || x+3 |-x- 1 || > 2.
10.x, y and z are non-negative real numbers, which satisfy the following conditions: x+3y+2z = 3, 3x+3y+z = 4, and find the maximum and minimum values of u = 3x-2y+4z.
1 1. Find the quotient and remainder of x4-2x3+x2+2x- 1 divided by x2+x+ 1.
12. As shown in figure 1-88, Zhu Xiao lives in village A and grandma lives in village B. On Sunday, Zhu Xiao went to visit her grandmother. She first cut a bundle of grass on the north slope, and then cut a bundle of firewood on the south slope to send it to her grandmother. Excuse me, which route should Zhu Xiao take for the shortest journey?
13. As shown in figure 1-89, AOB is a straight line, OC and OE are bisectors of ∠AOD and ∠DOB, respectively, and ∠ COD = 55. Find the complementary angle of ∠DOE.
14. As shown in figure 1-90, the bisected line ∠ABC, ∠ CBF = ∠ CFB = 55, ∠ EDF = 70. Verification: BC ∠ AE.
15. As shown in figure 1-9 1. In △ABC, EF⊥AB, CD⊥AB, ∠ CDG = ∠ BEF. Verification: ∠ AGD = ∠ ACB.
16. As shown in figure 1-92. In △ABC, ∠B=∠C, BD⊥AC is in D.
17. As shown in figure 1-93. In △ABC, e is the midpoint of AC, d is on BC, BD∶DC= 1∶2, and AD and BE intersect at F. Find the ratio of the area of △BDF to the area of quadrilateral FDCE.
18. As shown in figure 1-94, two opposite sides of quadrilateral ABCD extend and intersect at K and L, and diagonal AC‖KL and BD extension lines intersect at F. Verification: KF = FL.
19. Can the sum of the number obtained by arbitrarily changing the order of a three-digit number and the original number be 999? Explain why.
20. There is a piece of paper with 8 rows and 8 columns, in which 32 squares are randomly painted black and the remaining 32 squares are painted white. Next, the color grid paper is operated, and each operation changes the color of each square in any horizontal or vertical column at the same time. Can you finally get a grid paper with only one black square?
2 1. If both positive integers p and p+2 are prime numbers greater than 3, then verify: 6 | (p+ 1).
22. Let n be the smallest positive integer satisfying the following conditions, which is a multiple of 75 and has exactly
23. There are several stools and chairs in the room. Each stool has three legs and each chair has four legs. When they are all seated, * * * has 43 legs (including everyone's two legs). How many people are there in the room?
24. Find the integer solution of the indefinite equation 49x-56y+ 14z=35.
25. Eight men and eight women dance in groups.
(1) If there are two substations, male and female;
(2) If men and women stand in two rows, in no particular order, only consider how men and women form partners. How many different situations are there?
26. 1, 2, 3, 4, 5, how many numbers are greater than 34 152?
27.A train is 92 meters long and B train is 84 meters long. If they travel in the opposite direction, they will miss each other after 1.5 seconds. If they travel in the same direction, they will miss each other in six seconds. Find the speed of two trains.
28. The two production teams of Party A and Party B grow the same vegetables. Four days later, Team A will finish the rest alone. It will take two more days. If Party A finishes all the tasks by itself three days faster than Party B, how many days does it take to ask Party A to finish it by itself?
29. A ship starts from a port 240 nautical miles apart, and its speed decreases by 65,438+00 nautical miles per hour before reaching its destination 48 nautical miles. The total time it takes after its arrival is equal to the time it takes for the whole voyage when its original speed is reduced by 4 nautical miles per hour, so that we can find out the original speed.
30. Last year, two workshops A and B of a factory planned to complete tax profits of 7.5 million yuan. As a result, workshop A exceeded the plan 15%, workshop B exceeded the plan 10%, and two workshops * * * completed tax profits of 8.45 million yuan. How many million yuan of tax profits did these two workshops complete last year?
3 1. It is known that the sum of the original prices of two commodities is 150 yuan. Due to market changes, the price of the first commodity decreased by 10%, and the price of the second commodity increased by 20%. After the price adjustment, the sum of the unit prices of the first and second commodities decreases by 1%. What are the original unit prices of the first and second commodities respectively?
Xiaohong bought two children's toothbrushes and three toothpastes in the shop last summer vacation, and just used up all the money she had with her. It is known that each toothpaste is more than each toothbrush 1 yuan. This summer, she took the same money to the store and bought the same toothbrush and toothpaste. Because each toothbrush rose to 1.68 yuan this year and the price of each toothpaste rose by 30%, Xiaohong had to buy two toothbrushes and two toothpastes, and she got back 40 cents. How much is each toothpaste?
33. If a shopping mall sells goods with a unit price of 8 yuan per piece 12 yuan, it can sell 400 pieces every day. According to experience, if each piece is sold less 1 yuan, you can sell more than 200 pieces every day. How much should each piece be reduced to get the best benefit?
34. The distance from Town A to Town B is 28 kilometers. Today, A rode his bike at a speed of 0.4km/min, and set out from Town A to Town B. After 25 minutes, B rode his bike to catch up with A at a speed of 0.6km/min. How many minutes does it take to catch up with A?
35. There are three kinds of alloys: the first contains 60% copper and 40% manganese; The second type contains manganese 10% and nickel 90%; The third alloy contains 20% copper, 50% manganese and 30% nickel. Now a new alloy containing 45% nickel is composed of these three alloys, and its weight is 1 kg.
(1) Try to express the weight of the second alloy by the weight of the first alloy in the new alloy;
(2) Find out the weight range of the second alloy in the new alloy;
(3) Find out the weight range of manganese in the new alloy.
hope this helps