初一数学奥数题（First Mathematical Olympiad）

初一数学奥数 题 快递公司问题件快递公司问题件货款处理关于圆的周长面积重点题型关于解方程组的题及答案关于南海问题 （First Mathematical Olympiad） 初一数学奥数题(First Mathematical Olympiad) Math Olympiad First, fill in the blanks: 1. Calculation: (1). One of the +3*4 points of +2*3 is one of the +4*5 points of one of the 1*2 points. The value of one of the +2001*2002 2. There are two strings arranged according to some law, please fill in the number of vacancies according to the law. (1) 15, 20, 10, (), 5, 30, (), 35. 3, there are A, B, c three, known A, B, B, C, and a two number of the average is 40, 46, 43, then the average of a, B, c three number is _____43______. 4, the bottom of the addition of the vertical type of Shen, office, Austria, shipped four Chinese characters, respectively, representing four different figures, I ask: bid for the Olympic Games, respectively, the number of the formula was established. =______, =______, =______, =______ 5, Class A students 48 people, of which 1/2 are girls, Class B has 45 students, of which 1/3 are girls, then two classes of boys have ___54___ people. 6, the configuration 3% of glucose 50 kilograms, the need for 1% and 6% of glucose respectively ______ kg, ___ kg. 7, five people belong to the dragon, their age product is 589225, these five people's age and is __________. 8, processing a batch of parts, if the master first processing 20 days later, the remainder of the Apprentice processing 30 days just completed, if the Apprentice first processing 37 days, the rest by the master processing 17 days also just completed. Now master, apprentice processing a few days together, the remainder of the Apprentice processing 40 days just completed. Q: The Master and Apprentice processed the day together. 9, with two of the same length 3 cm, width 2 centimeters, high 1 centimeters of cuboid, spelled into a large cuboid, its surface area is the largest ________ square centimeter. (i.e. cm2) Second, the comprehensive question: (6 points per small topic, a total of 30 points) 1, a store to buy puppies and teddy bear toys A total of 80, has sold the number of puppies only 1/5, the Cubs only 2/3 of the number, a total of 30. How many are the numbers of puppies and cubs? 2, there is a book, if the first day to read 35 pages, every day after reading 5 pages more than the previous day, the result of reading only 35 pages, read the end, or this book, if the first day read 45 pages, later every day than the previous reading 5 pages, the last day Read only 40 pages also finished. Q: How many pages are there in this book? 3, will a surface is red cuboid (3x4x5), cut into a number of small 1x1x1 cubes, ask the surface is only a small red cube and the surface of the small cube is not red how many pieces? 4, there are red, yellow, blue, white, purple five colors beads each one, placed in the numbered 1, 2, 3, 4, 5th, five boxes, a, B, C, D, e Five People's conjecture results are as follows: A: No. 2nd purple beads Inside, 3rd yellow beads. B: No. 2nd is filled with blue beads and No. 4th in red beads. C: No. 1th is packed with red beads and 5th white beads inside. D: No. 3rd is filled with blue beads and 4th white beads inside. E: No. 2nd yellow beads, 5th inside purple beads. And everyone guessed right. One, and only one person in each case guessed right, a, B, C, D, e what color is the color of the beads of the guessed pair? 1 A( Select the question (four of each of the following options, only one is correct) 1. -7 Absolute value () (a)-7 (b) 7 (c)-(d) 2. 1999-The value equals () (a) -2001 (b) $number (c) $number (d) 1999 3. Here are 4 propositions: ? exists and only a positive integer is the same as its inverse number. ? exists and there is only one rational number and its opposite number. ? exists and only a positive integer exists and its reciprocal is the same. ? exists and there is only one rational number and its reciprocal. The correct proposition is: () (a) ? and ? (b) ? and ? (c) ? and ? (d) ? and ? 4.4abc similar is () (a) 4BCA (b) 4cab (c) ACB (d) ACB 5. The production of a particular factory in July was 20% lower than in June, and if August products were to be produced in June, the production of August would increase () (a) $number (b) $number (c) $number (d) 75% 7. If X=―, $literal. 5, then x―y―??????? The value of 2X is () (A)0 (B) (C) (D) ― 8. Ax+b=0 and mx+n=0 on the same solution equation for unknown x, there are () (a) a+m>0. (b) Mb?an. (c) Mb?an. (d) Mb=an. 9. ( -1) + ( -1)-( -1) x (-1) = (-1) The result is () (a)-1 (b) 1 (c) 0 (d) 2 2 $number( In the following operation, the error is () (a) 2x+3x=5x (b) 2x-3x=-1 (c) 2X 3x=6x (d) 2x?4x= $number( Known a<0, simplify, get () (a) 2 (b) 1 (c) 0 (d)-2 $number( The result of the calculation (-1) + (-1) ?|-1| is () (a) 0 (b) 1 (c)-1 (d) 2 $number( In the following equation, the correct () (a) a a=a. (b) (x) =x. (c) 3=9. (d) 3b 3C=9BC. 14. Negative reciprocal of the-|-3| opposite number is () (a)-(b) (c)-3 (d) 3 $number( October 1 friends and relatives party, xiaoming statistics Everyone's average age is just 38 years old, Grandpa said, two years ago October 1 is these people together, then two years ago when the average age is () age. (a) Mr. (b) (c) (d) 35 $number( If a<0, then 4a+7|a| equals () (a) 11a (b) -11a (c) -3a (d) 3a $number( If the rational number x. Y satisfies |2x-1|+ (y+2) = 0, then x. The value of y equals () (a)-1 (b) 1 (c)-2 (d) 2 3 $number( Rational number A, B, C corresponds to the point on the axis as shown in the figure: then the following is the correct () (a) C + B > A + B. (c) AC > AB (b) CB AB. (d) CB > AB $number( The positive integer solution of the inequality of 1 is (). (a) 2 (b) 3 (c) 4 (d) 5 $number( A computer system can perform only one task at a time and complete the task to perform the next task, the existing U, V, W time is 10 seconds, respectively, 2 and 15, the relative wait time for a task is the ratio between the time that the task was submitted to the task and the time when the computer system performed the task, and the minimum execution of the three tasks in the following four order of execution was (). (a) U, V, W. (b) v, W, u (c) W, u, v. (d) U, W, v $number( Segments AD, AB, BC, and EF are 1, 8, 3, 2, 5 and 2, the area of the closed polyline Aebcfd is S, and the following four selections are correct () (a) s=7.5 (b) s=5.4 (c) 5.4 (d) y>- $number( The following four sentences are correct () A( Positive integers A and B are common greater than or equal to a. b( Positive integers A and b common greater than or equal to AB. C( The common of positive integers a and B is less than or equal to a. D( Positive integers A and b common greater than or equal to AB. 4 $number( Known a?2, B?-3, c?5, and a-b+c=10, the A+b+c value is equal to (). (a) (b) 8 (c) 6 (d) 4 $number( The result of 6 of the opposite number, excluding-6, is ___. $number( With scientific notation: 890000=____. $number( By rounding the approximate value of 1999.509 (accurate to single), the approximate number obtained is __. $number( Known two rational numbers-12.43 and-12.45. So, the difference between the large number and the decrease is __. 30. The sum of the negative reciprocal of |-4| and-|4| is equal to __. $number( The approximate number of 0, 1990 is __. $number( The sum of the number of a, B, C, Cyclobutanetetrone is equal to-90, a number minus-4, B plus-4, C-Number multiply-4, the number of Pebe is equal to 4, then the largest number in four numbers is larger than the smallest one. $number( It is known that the supplementary of angle a equals 3.5 times times the angle a, and the angular a equals __. $number( The known equation (1.9x-1.1)-() $number. 9 (3 x-1) + 0.1, the value of the solution x is _. $number( The first floor is 24.5 meters taller than C, and the second floor is 15.6 meters taller than C/F. $number( If the sum of four numbers in four small triangles is equal to zero, then the sum of the four numbers is equal to __. x-2y=1999 $number( The solution to the equation group {is ___. 2x-y=2000 5 $number( Xiao Ming bike from a ground by B, first uphill after the downhill, to reach the ground immediately after the return of a, a total of 34 minutes, known uphill speed is 400 meters/min, downhill speed is 450 m/min, then a to B to the distance is __ meters. $number( Father Bi Xiaoming 24 years old, and 1998 years of age is xiaoming 2000 Age 3 times times, then Xiaoming 1999 age is __ years old. $number( Are all two-bit positive floors, and they are known to have a common of 385, and the maximum value is __. $number( A bottle of salt water concentration of 8%, b bottle of salt water concentration of 12%, two bottles of salt water weighing 1000 grams, put a, b two bottles of salt after the concentration is 10.08%, then a bottle of salt water heavy ___ grams. $number( Known series 1, 1, 2, 3, 5, 8, 13, ..., each number from the 3rd is equal to the sum of the two adjacent to its front, then the 1999th number in the string is 3 minus the remainder of the number. $number( What is equal to the seven times of the seven-square + of the three-square + of X+y=-3 X's three-=-18? 44. At 12 o'clock clock, the three-pin coincidence, after how many minutes seconds for the first minute and the hour of the sharp-angle sandwiched between the two? 45. A taxi stop has 6 taxis, and after the first taxi departs, a taxi is opened every 4 minutes, and after 2 minutes of the first car, there is a taxi station, every 6 minutes thereafter there is a taxi pit stop, back to the taxi in the original taxi in turn out after each 4 minutes out of a, asked, after the first taxi out, after how many times the station can not be on schedule? 46. There are six straight lines 22 intersecting in the plane, and only 3 of them have crossed a little, then they have no overlapping segments (). Article 36 B. Article 33 C. 24 D. 21 C is a point on the line AB, D is the midpoint of the CB segment, the sum of all the segments on the AB is known to be 23, the length of the AC segment and the length of the CB is a positive integer, then the length of the segment AC is () 48.3 lines of 22 intersect, but the same point to 3 straight line equidistant points have (). 49. There is a definite line of three points A, B, C, straight line L satisfies the condition: A, B to l the distance is equal, and is equal to C to L's distance twice times, then such a straight line L has a (). 50. There is a point P and straight L in the plane, and the distance from point P to straight L is 3, with P as the center, and R for Radius circle. If the circle has exactly two points to a straight line distance equal to 2, the radius r range. 51. In the same plane there are 2002 straight A1, A2, ... a2002, if A1 vertical A2, A2 parallel A3, A3 vertical A4, A4 parallel a5 ... So the position of A1 and A2002 is () 52. There are 6 straight lines in the plane, of which only 3 are handed to one point, and the other 3 are parallel to each other, then the 6 lines divide the plane into () parts. 53. If the value of the polynomial 2x?2-x is equal to 1, what is the value of the polynomial 4x?4-4x?3+3x?2-x-1? 54. If m-1/m =-3, then m3-1/m3=? 55. If a, b are rational numbers, and A2-2ab +b2 +4a+8=0, then AB equals? $number( If the square of X-(m-1) x+4 is a completely flat way, then = () 57. The known equation for x 2a (x-1) = (-) x+3b has numerous solutions, then a=_____, b=_____. 58. What is the sum of all the possible four digits of the $number composed of the natural number, the four-digit numbers? 59, the absolute value of a rational number equals itself, and this number is () 6 A, positive B, non-negative C, 0 d, negative number 60, known X and 1 reciprocal number, and | a+x | Reciprocal with x to find the value of x sliding x2001. 61, a three-digit number, the number on the hundred is 1 larger than the number on the ten, the number on the single digit is 3 times times less than the number of the ten, 2, if the number of digits on the single and the Hundred is reversed, the three-digit and the original three-digit number and 1171, to this three-digit number. 62, set A, B, c for real numbers, and |a|+a=0, |ab|=ab, |c|-c=0, simplify algebra |b|-|a+b|-|c-b|+|a-c| 63, known (m+n) * (m+n) +|m|=m, |2m-n-2|=0, value of MN 64, the existing 4 rational number 3, 4,-6, 10 use 24 point game rules, so that its results 24. (Write 4 different) 65, because-(-(-6) = 6, so 1 small questions given in the four rational number and 3, 4, 6, 10, the same essence, please use Add, subtract, multiply, divide and bracket, write the result not more than 24 formula 66. Can the sum of the number and the original number of the digital sequence of a three-digit change be 999? Explain the reasons. 67, A, b two people respectively. Follow the railway in the opposite direction. At this time, a train at a constant speed to a head-on, the train in a side drive, with 15 seconds, and then in the next side of the drive, 17 seconds. Two people are known for their pace. 3.6km/h. How long is the train? 68, a rectangular, if the width is unchanged, the length of 3 meters, then its area reduced 24 square meters, if the length is unchanged, width increased 4 meters, then its area increased by 60 square meters, the original area of the rectangle is how many square meters? 69, a rectangular, if the width does not change, the length increases 5 meters, then its area increases 30 square meters, if the length does not change, the width increases 3 meters, then its area increases 48 square meters, this rectangular area originally is how many square meters? 70, a rectangle, if its length is reduced by 3 meters, or its width is reduced by 2 meters, then it's area is reduced by 36 square meters, the original area of the rectangle? 71, red to long 40000km it can be seen as a girdle of the Earth, If you assume that a new belt grows 10m then how much m does it leave the surface void of the Earth? Judge if you and your classmate can walk under a new belt. 72, Xiao Qiang asked how old uncle, Uncle said: "I am as big as you are, you are only four years old." When you were my age, I was 40 years old. How old is Xiao Qiang and uncle? 73, a number of stools and chairs in the room, each stool has 3 legs, each chair has 4 legs, when they are all seated, a total of 43 legs (including 2 legs per person) asked how many people in the room? 74, at the station start checking tickets, there is a (a>0) passengers waiting. After the ticket began, there were still passengers to come in line. The speed of the ticket check-in is fixed as the passenger increases at a fixed rate. If a openings are opened, it will take 30 minutes to complete the check-in of all the passengers in the queue, and 10 minutes if the two wicket is opened. If you have to check out all the passengers in the queue in 5 minutes so that the passengers arriving later will be able to follow the inspection, at least a few ticket gates will be opened at the same time. 75. A two-digit, 10-digit is x, and the figures are x-1, what are the two digits of the 10 digits after the figures are exchanged? 7 76. Small mother with M yuan money to buy vegetables, she bought meat to go to one-second, to buy vegetables to use the remaining One-third, then how many yuan she left? 77 The following figure, the 5th number in line 100th? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 ... 78. Calculate the value of the 1+3+5+7+ +1997+1999. 79. If the value of the 2x+|4-5x|+|1-3x|+4 is constant, the condition of x and the value of this constant are obtained. 80, known 1 2 3 --- + --- + --- = 0 ? X y Z 1 6 5 --- - --- - --- = 0 ? X y Z X y Z 试求 --- + --- + --- 的值 Y z X 8 81, in 1, 2, 3, ..., each of the number of 1998 before adding a "+" or "-" then the final calculation of the result is odd or even? 82, a school junior high school one grade mathematics competition, the participation is 3 times times the number of participants, and if the grade is reduced by 6 and the number of students who have not participated increases by 6, then the participation of participants in the competition is 2:1 of those who have not participated in the competition and the level of the junior middle School in one years. $number( Set A, B, C is a real number, and |a|+a=0, |ab|=ab, |c|-c=0, to find the value of algebraic |b|-|a+b|-|c-b|+|a-c|. $number( If m<0, n>0, |m|<|n|, and |x+m|+|x-n|=m+n, calculate the range of X. $number( Set (3x-1) 7=a7x7+a6x6+ ... +a1x+a0, try to find the value of A0+A2+A4+A6. $number( The solution equation is 2|x+1|+|x-3|=6. $number( Solution Inequality | |x+3|-|x-1| |>2. $number( X, Y, Z are both non-negative real numbers and satisfy: x+3y+2z=3, 3x+3y+z=4, u=3x-2y+4z maximum and minimum value. $number( X4-2x3+x2+2x-1 divided by the quotient and remainder of the x2+x+1. $number( Small pillar live in Jia Cun, grandmother live in the village, Sunday small pillar to visit Grandma, first in the North Hillside dozen grass, and in the South Hillside chop a bundle of firewood to grandma sent. May I ask: what kind of route should the pillar choose to make the shortest distance? $number( AOB is a straight line, OC, OE is ?aod and ?dob, respectively, the split line, ?cod=55?. ?doe Supplementary. $number( Be equally ?abc, ?cbf=?cfb=55?, ?edf=70?. Verification: Bc‖ae. $number( In ABC, EF?AB, Cd?ab, ?cdg=?bef. Verification: ?AGD=?ACB. $number( A, B, C, D, e five digits, and 8, The sum of squares is 16, and the maximum value of E is obtained. 9 $number( In ABC, E is the midpoint of the AC, D on BC, and BD: dc=1:2, AD and be in F. The ratio of the area of BDF to the quadrilateral Fdce. $number( The quadrilateral ABCD two pairs of sides extend intersect in K and L, diagonal ac‖kl, BD extension line KL in F. Verification: KF=FL. $number( Can the sum of the number and the original number of the digital sequence of any three digits change be 999? Explain the reasons. $number( With a 8-row, 8-column box of paper, the 32 squares are painted black, and the remaining 32 squares are painted white. The following on the color of the square paper "operation", each operation is arbitrary or vertical column on the various squares change color. Q Can you finally get a checkered paper with a black square? $number( If positive integers p and p+2 are prime numbers greater than 3, verify: 6| (p+1). $number( There are a number of stools and chairs in the room, each with 3 legs, 4 legs per chair, and 43 legs (including two legs of each person) when they are all seated, how many people are there in the room? $number( The integer solution of the indefinite equation 49x-56y+14z=35. $number( The 8 men and women danced the choreography. (1) If men and women stand in two rows; (2) If the men and women stand in two columns, regardless of priority, only consider how men and women form partners. How many different kinds of situations are there? $number( From 1, 2, 3, 4, 5 these 5 digits of the number of five digits, how many of them are greater than 34152? $number( A train length 92 meters, b train length 84 meters, if the opposite and row, after meeting after 1.5 seconds (s) Two cars missed, if the same with the row after 6 seconds after the two cars missed, the speed of the two trains. $number( A B Two production team together vegetables, plant 4 days later, by the team a alone to complete the rest, and 2 days to complete. If a alone complete the task than B to complete the full 3 days. How many days does it take to complete each individual? 10 $number( A ship to a port 240 nautical miles away, 48 nautical miles before reaching its destination, the speed of 10 nautical miles per hour, the total time spent at the same time as the original speed of less than 4 nautical miles per hour, to the original speed. $number( A factory a B two workshop, last year plans to complete taxes 7.5 million yuan, the results of a workshop exceeded 15% completion plan, B workshop exceeded 10% completion plan, the two workshops together to complete taxes 8.45 million yuan, last year this two workshop to complete taxes How many million? $number( The sum of the original price of two kinds of goods is known to be 150 yuan. As a result of market changes, a commodity price reduction of 10%, b commodity prices 20%, after the price adjustment of the two commodity prices and the sum of the original unit price and lower than 1%, the original price of the first two commodity is how much? $number( Xiao Hong last summer in the store bought 2 children's toothbrush and 3 toothpaste, just take the money to run out. It is known that each toothpaste is 1 yuan more than each toothbrush, this summer vacation she brought the same money to the store to buy the same toothbrush and toothpaste, because this year's toothbrush every rise to 1.68 yuan, toothpaste each price of 30%, Red had to buy 2 toothbrushes and 2 toothpaste, the result of the return of 4 cents. How much does each toothbrush cost last summer? How much does each toothpaste cost? $number( A shopping mall if the purchase price of 8 yuan of goods, according to 12 yuan per piece sold, 400 per day, according to experience, if each piece sold less than 1 yuan, then can sell more than 200 pieces per day, ask how many per piece should be reduced to get the best results? $number( The distance from a town to B town is 28-kilometer, with a bike riding 0. 4-kilometer/min Speed, starting from a town to B town, 25 minutes later, B bike, with 0. 6-kilometer/min Speed chasing a, how many minutes after the nail? $number( Existing three kinds of alloys: the first copper 60%, manganese 40%, the second manganese 10%, containing nickel 90%, the third containing copper 20%, manganese 50%, containing nickel 30%. Now each of these three alloys of appropriate weight, A new alloy containing 45% nickel with a weight of 1 kilograms. (1) The weight of the first alloy in the new alloy is used to indicate the weight of the second alloy; (2) The weight range of the second alloy is contained in the novelty alloy; (3) The weight range of manganese contained in the novelty alloy. $number( Known 3x2-x=1, 6x3+7x2-5x+2000 value. 11 $number( A store sells a commodity, sells 100 pieces every day, each piece can profit 4 yuan, now they use to raise the price, reduces the quantity of stock to increase the profit, according to experience, this commodity each price rises 1 yuan, sells 10 pieces every day. How many dollars will the price of each item be raised in order to achieve maximum profit? What is the maximum profit? $number( Known Cb?ab, ce split ?bcd, de equally ?cda, ?1+?2=90?. Verification: Da?ab. $number( The integer solution of the equation |xy|-|2x|+|y|=4. $number( Wang Ping bought an annual interest rate of 7.11% three-year and an annual interest rate of 7.86% of five-year Treasury bills totalling 35000 yuan, if the three-year Treasury bill expires, the principal and interest in a continuous period of two one-year regular savings, five years later and five years of Treasury bills and principal and interest sum of 47761 yuan, asked Wang Ping buy three-year and five-year Treasury bills how many? (known one-year term savings annual interest rate is 5.22%) $number( The integer solution of the indefinite equation 3x+4y+13z=57. $number( Xiao Wang used 5 yuan to buy 40 fruit to entertain five friends. Fruit has three kinds of apples, pears and apricots, each of which is 20, 8, and 3. Wang hoped that he and five friends can share the apple, and each person obtains the number of apples is not the same, ask if he can realize his wish? $number( The sum of the coefficients in the expansion of (8X3-6X2+4X-7) 3 (2x5-3) 2. $number( Liquid pesticide A barrels, poured out after 8 liters of water filled, and then pour out mixed solution 4 liters, then filled with water, then the concentration of pesticides 72%, the volume of barrels. $number( Meet [ -1.77X]=-2X's natural number x total? Here [x] represents the largest integer that does not exceed X, for example [ -5.6]=-6, [3]=3. $number( P is one points within ABC. The distance between the three vertices of P to ABC and the range of the ratio of the circumference of the triangle. $number( A B two people at the same time from two points to walk, meet, a more than B line 24-kilometer, a after 9 hours to the East station, b after 16 hours to the West station, two station distance. $number( The blackboard is written with three digits, wiping away one of them, changing it to the other two and minus 1, so as to continue, finally get the $number, 1999, ask the original three number can be 2, 2, 2? $number( With n real x1, x2, ..., xn, each of which is not +1 or 1, verify that n is a multiple of 4. $number( A, B, C, D are known to be positive and a+d