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Beg, the first day 100 math problem! ! ! !

Sorry, I made a mistake just now. Here are the answers. 1. Fill in the blanks: (5 points for each small question, * * * 30 points)

x+y=5

1, given the equation y+z=6, then 2002(x+y+z)= 1

z+x=7

2. When a2+a=0, the value of a200 1+a2002+ 12 is.

3. If the sum of two natural numbers is 100, the maximum value of the product is.

4. From 1: 45 to 2: 05, the turning angle of minutes is.

5. If the complementary angle of an angle is x0, then the complementary angle of this angle is degrees. (900 x > 0, then the value range of a is ().

2x-y= 1

a-3 < a < 2b 2 < a < 5c 1 < a < 4d-4 < a < 1

2. Calculation-= ()

D 250 a 62500 B 1000 C 500

3. Given that xn=2 and yn =3, the value of (x2y)2n is ().

A 48 B 72 C 144 D cannot be determined

4. In the following forms of numbers (no matter what natural number N takes), the one that is definitely not the square of a natural number is ().

a3(N2-n+ 1)b5(N2-n+ 1)C7(N2+n+ 1)d9(N2+n+ 1)

5. Observe the graph below and read the related text below the graph. Like this, the number of intersections where ten straight lines intersect the most is ().

Two lines intersect, three lines intersect, four lines intersect,

Up to 1 intersections. Three intersections at most. Six intersections at most.

A 40 B 45 C 50 D 55

6. As shown in the figure, if parallel straight lines EF and MN are in phase with intersecting straight lines AB and CD.

Cross, then the figure * * * has the same inside angle ()

A 4 to B 8 to C 12 to D 16.

Third, answer questions.

1, the known rational numbers x, y and z satisfy x-y=8, xy+z2=-16.

Verification: x+y+z=0 (in 10)

2. As shown in the figure, AB‖CD, the number of times to find ∠ 1+∠2+∠3+∠4. (in 10)

Read the following article first, and then answer the questions.

A food research department wants to mix A, B and C into 100 kg food, and it is stipulated that at least 44,000 units of vitamin A and 48,000 units of vitamin B are needed in the mixed food. The contents of vitamins A and B in the three foods are shown in the following table.

Table 1

A, B and C.

Vitamin A (unit/kg)

Vitamin B (unit/kg)

Table 2

Production cost per kilogram (yuan)

A species

B 12

C 8

Assume that the quality of three kinds of food developed and produced is X kg, Y kg and Z kg respectively.

① Try to list the equations and inequalities according to the meaning of the question, and prove that: y≥20, 2x-y≥40.

(2) Let the production costs of three kinds of food A, B and C be shown in Table 2, and try to express the total cost P of mixed food with X and Y; If the mass of food A in mixed food is limited to 40 kg, try to find out the range of total cost P at this time and determine the mass of food B and C when P is the minimum. (out of 20)

In 2004, the examination paper of Fuyang City Junior One Mathematics Competition.

First, multiple-choice questions (5 points for each small question, 30 points for * * *):

1, it is known that three points A, B and C on the number axis represent rational numbers, which are 1 and-1 respectively, so it means ().

(a) the distance between points a and b (b) the distance between points a and c.

2. Wang Laobo first bought five sheep in the market, with an average of RMB each, and later bought three sheep, with an average of RMB each.

Later, he sold all the sheep at the price of each sheep, only to find himself losing money. The reason for the loss is ()

(a) (b) (c) and (d) have nothing to do with size.

3. The sum of two positive numbers is 60, and their least common multiple is 273, so their product is ().

273(B)8 19(C) 1 199(D) 19 1 1

4. A class of ***48 people went boating on the West Lake in Hangzhou in the spring, with 3 people per boat, and the rent was 16 yuan, with 5 people per big boat.

People, rent 24 yuan, then this class should at least spend rent ().

(A) 188 yuan (B) 192 yuan (C)232 yuan (D)240 yuan.

5. It is known that the circumference of a triangle is, one side is twice as long as the other, and the range of the smallest side of the triangle is ().

Between (a) and (b) and (c) and between (d) and.

6. Two identical bottles are filled with alcohol solution. The volume ratio of a bottle of wine to water is 1. In another bottle,

The volume ratio of alcohol to water is 1. Mix two bottles of solution together, and the volume ratio of alcohol to water in the mixed solution is.

( )

(A) (B)

II. Fill in the blanks (5 points for each small question, 30 points for * * *):

7, known,,, and > >, then =;

8, set a polynomial, when known = 0,; When,,

Then when =;

9. Arrange positive and even numbers into 5 columns according to the table below:

Column 1 column 2, column 3, column 4 and column 5

The first line 2 4 6 8

The second line16141210

Line 3 18 20 22 24

The fourth line 32 30 28 26

…… … … … …

According to the rules in the table, even numbers 2004 should be arranged in rows and columns;

10, Party A and Party B set off at the same time with their backs to point A on the 400m circular runway. Eight minutes later, they met for the fifth time.

It is known that A walks 0. 1 m more than B every second. What is the shortest distance along the runway from where they met for the fifth time to point A?

Rice;

1 1. Someone asked Teacher Yang, "How many students are there in your class?" Teacher Yang said: "Now half of the students in our class are taking part in the math contest, one quarter are taking part in the music interest group, one seventh are in the reading room, and three female students are watching TV." . So the number of students in Teacher Yang's class is;

12. There are two red balls and two white balls in the box. Xiaoling touched the balls out of the box one by one, and red balls and white balls alternated.

The possibility of occurrence (which can be "red, white, red and white" or "white, red, white and red") is.

Third, answer questions:

13, (10) as shown in the figure, AB‖ED, ∠ c =, ∠ ABC = ∠ def, ∠ d =, ∠ f =,

Find the size of e.

14, (10 minute) The midline of an isosceles triangle divides the perimeter of the triangle into two parts, 14 and 18, and find three.

The length of each side of an angle.

15 and (10) have nine straight lines on the plane, and no three straight lines intersect at one point. What is the positional relationship of these nine straight lines, so that their intersection point is exactly 26, and all possible situations can be drawn (it is required to draw correctly with a ruler).

16, (10 minute) The three hands of the clock coincide at 12. How many minutes did it take the second hand to set the angle of the minute hand and the hour hand for the first time?

Acute angle) equally divided? (expressed in fractions)

Reference answers to the 2004 Fuyang Junior One Mathematics Competition

First, multiple-choice questions (5 points for each small question, 30 points * * *): BABCAD

II. Fill in the blanks (5 points for each small question, 30 points for * * *):

7,0 or -28,-179, 25 1, 3 10, 176 1 1 2,

Third, answer questions:

13, solution: extend DC and AB to G.

∫ed‖ab，∠D= ∴∠G=

∠∠BCD = =，∠ BCD = ∠ G+∠ CBG ∴∠ CBG =

∴∠ABC= = That is ∠∠ e =

14, solution: let the waist length of an isosceles triangle be and the bottom length be,

So or

Solve:, or,

The lengths of the three sides of a triangle are:,, or 12, 12, 8 respectively.

15, solution: There are two situations, as follows:

16, Solution: Obviously, the second hand bisected the angle between the minute hand and the hour hand for the first time after 1 minute.

When setting minutes, the second hand bisects the angle between the minute hand and the hour hand for the first time, so the angle of the hour hand is degrees, the angle of the minute hand is degrees, and the angle of the second hand is degrees.

So there are:

Solution: (Points)

A: Minutes later, the second hand bisects the angle between the minute hand and the hour hand for the first time.

Examination Paper of Mathematics Competition in Junior One (4)

Time: 100 minutes Total score: 100 minutes.

I. Multiple-choice questions: (2 points for each question, 20 points for * * *)

1. In the following categories, the correct calculation is ().

A.m2 m3 = M6 b . m2(-m3)= M5 c . m2+(-m)3 =-M5 d . m3(-m)4 = M7

2. Given that 2m=a, 2n=b and (m, n is a positive integer), 2m+n is ().

A.a+bb.abc.2ab.d None of the above is correct.

3. In the following categories, the wrong one is ()

A.(a3)m = a3+MB .[(a+b)2n]m =(a+b)2mn c .(am)3 = a3m d .(a+b)m(a+b)n =(a+b)m+n

4. If the length, width and height of a cuboid are 3x-4, 2x and x respectively, its volume is ().

5. If (x-2) (x+3) = x2+px+q, then the values of p and q are () respectively.

A.p = 5，q = 6 B. p = 1，q = -6 C. p = 1，q = 6 D. p = 5，q = -6

6. If a+b = 7, ab = 12, A2-AB+B2 = ()

A. 1 1 b . 13 c . 37d . 6 1

7. It is correct to express -0.00000 12 by scientific notation ().

A.- 1.2× 10-4 b .- 1.2× 10-5 c .- 1.2× 10-6d .- 1.2× 10-7

8.32n+ 1 equals ()

A.9n+ 1 b .(3n+ 1)2c . 3×9n d . 32×3n×3

9. (-0.25)11× 410 equals ()

A.-5 10 b . 18 c .-5.25 10d .-0.25

10. If the expansion of (x+3y) (2x-ky) does not contain the xy term, the value of k is ().

A.2b-2c . 6d . 3

Fill in the blanks: (3 points for each question, ***24 points)

1.x2 XM _ _ _ _ _ _ _ _ _ _ _ = x2m+3，(0.25a)2 (4b2)2 =____________。

2. Calculate199× 201= (_ _ _ _ _ _) (_ _ _ _ _ _) = _ _ _ _ _.

3. Expressed by scientific notation:-0.0000203 = _ _ _ _ _, 5720000 = _ _ _ _ _.

4. If (2x-5)-5 is meaningful, then the condition that X should have is _ _ _ _ _ _ _.

5.a2+B2 = _ _ _ _ _ _ _ _ _ _ _ _+(a-b)2 =(a+b)2+_ _ _ _ _ _ _ _。

7. If am = 4 and an = 8, then A3M-2n = _ _ _ _ _ _ and if 4x = 2x+3, then X = _ _ _ _ _ _ _

8. If (x+y )2 = 9 and (x-y) 2 = 5, then xy = _ _ _ _ _ _ _ _ _

Third, answer questions:

1. If A-B = 2 and A-C = 1, find the value of (B+C-2A) 2+(C-A) 2. (5 points)

2. Understand the following categories:

① Given x+y = 4 and xy = 3, find the value of 2x2+2y2. (5 points)

3. Simplify first, then evaluate.

4. Calculation:

① (XM+N) 2 (-XM-N) 3+3x2m-N (-x3) m (5 points)

② (x+4y-6z) (x+6z-4y)-(4y+6z+x) (4y-x+6z) (5 points)

6. If x2+y2-2x+2y =-2, try to find the value of x200 1+y2002. (5 points)

Can you use what you have learned to calculate the following values? If possible, please calculate their values.

If not, explain why.

1.(2+1) (22+1) (24+1) ... (232+1), try to find its value ... (8 points)

2. Given S =12-22+32-42+…+992-1002+1065438, try to find the value of S. (8 points)

Song Wan Middle School in Ruian City in 2003 junior high school mathematics competition examination paper.

Class: Name: Seat Number:

First, multiple-choice questions: This big question is a small question of *** 10, with 3 points for each small question and 30 points for * * *.

(1) Go west for 5 meters, and then go east for -5 meters. The result is ()

(a) Go west 10 meter; (b) Go west for 5 meters;

(2) The number whose reciprocal is not greater than itself is ()

Positive number; Negative number; (c) Non-positive numbers; (d) non-negative.

(3) If the sum of two numbers is 100, and one number is expressed in letters, then the product of these two numbers can be expressed as ().

(1); (b) and: (c) and: (4).

(4) If the radius of a circle is 3㎝, the area will increase after the radius increases () 2.

(1); (b) and:

(5) If, then the value of is ()

(A)3； (B) 1； 3 or1; (d) None of the above is true.

(6) and are similar projects, then ()

(1); (b) and: (c) and: (4).

(7) In the following categories, the wrong one is ()

(1); (b) and:

(8) The result of simplification is ()

(1); (b) and: (c) and: (4).

(9) For rational numbers, if < 0, < 0. Then the following statement is correct ().

(1) < 0, < 0; (b) > 0, < 0 and

(10) The number of kilometers traveled by the train per hour is known, so the wrong answer in the following answers is ().

(a) It takes several hours for a train to walk one kilometer; (b) Trains travel thousands of meters per hour;

Kilometers traveled by the train per minute; (d) It takes hours for the train to travel 1 km.

Fill in the blanks: This big question is ***8 small questions, with 4 points for each small question and 32 points for * * *. Please fill in the correct answer on the line.

(1 1) The number whose absolute value is not greater than 3 is

The reciprocal of (12) is

(13) Lalin Jettis is a Greek orator. He was born on July 4th, 30 BC and died on July 4th, 30 AD. He lived for several years.

(14) when 3 < < 4, simplify.

(15) 73 tons of a certain substance is planned to be transported by two trucks with a load of 7 tons and 5 tons respectively, and each truck should be filled. It is known that the freight for a truck with a deadweight of 7 tons is 65 yuan and that for a truck with a deadweight of 5 tons is 50 yuan, so the most economical freight is _ _ _ _ _ _ _ _.

(16) Bake cakes in a pan, and only two cakes can be placed at a time. It takes 2 minutes to bake a cake (one minute in front and one minute in the back), at least 3 minutes.

(17) Write the natural number from 1 and get the following column number:123456789101212.

(18) Given two numbers A and B, a new number C is extended according to the rule c=a+b+ab. This new number C is called "Spring Festival travel rush number". Take any two of the three numbers A, B and C, and according to the rules, a "Yingchun" can be expanded ... Every expansion of "Yingchun" is called an operation. The existing numbers are 1 and 4, and the maximum number of "Spring Festival" obtained after three operations according to the above rules is _ _ _ _.

3. Calculation problem: This big problem is ***4 small questions, each with 6 points and * * * 24 points.

( 19) ;

(20)

(2 1) It is known that the solution of the equation satisfies,

The value.

(22) If

4. This big question has ***2 small questions, each with 6+8 points, *** 14 points.

(23) Place cubes with all edges in the shape as shown in the figure, q:

① There is a cube;

(2) After being placed in the shape shown in the figure, the surface area is

(24) Five integers A, B, C, D and E, whose sums are 183, 186, 187, 190,19, respectively. A < b < c < d < e, x > 196 is known.

(1) Find the values of a, b, c, d, e and x;

(2) If y= 10x+3, find the value of y.

In 2003, the first semester of the school year, the first math final examination paper.

Title (1) (2)171819 202122 23 24 25 26 Total score.

Note: 1, you can use a calculator. It is suggested that according to the question type.

Seize the opportunity to use the calculator.

2. The full mark of this volume is 150, and it will be completed within 90 minutes. I believe you will do well!

Test your basic skills first (120)

(a), fill in a fill (every empty 3 points ***45 points)

1. Write the result directly: (-32) ÷ 4 =, =

The reciprocal of 2 and -5 is; The absolute value of -6 is

3. For example, there are parallel lines in your home.

4. A triangular prism has one face and a prism has 10 face.

5. When the pattern below is folded into a cube, the number _ _ _ will be on the plane opposite to the plane where the number 2 is located.

4 5 6

1 2 3

6. In a book called Mathematics and Imagination, the authors Edward Casner and James Newman introduced a large number called "Gugor", which is both large and good, and was quickly adopted by the author in the article "Mathematics Popularization". Googol is a number, followed by a hundred zeros after the number 1 If we use scientific notation to represent this number, it can be expressed as

7. If the diameter of a circle is d cm, then its circumference is cm and its area is cm; If the diameter of this circle increases by 1cm, then its circumference increases by cm;

8. If point A is represented on the number axis, then the number represented by the point three length units away from point A on the number axis is _ _ _ _ _ _ _ _.

9. In the calendar, the sum of two adjacent numbers on the vertical line is 27, so the smaller of these two numbers is

10, assuming that there are enough black and white Weiqi players to line up according to certain rules:

……

Excuse me, is 2003 black or white? A: _ _ _ _ _ _.

Second, choose one (3 points for each question, *** 15 points)

1 1, the school, home and bookstore are located in a north-south street in turn, with the school home 20 meters south and the bookstore home 0/00 meters north. Zhang Ming starts from home, walks 50 meters north, and then walks -70 meters north. At this time, Zhang Ming's position ().

A: At home, at school, at the bookstore and on the road.

12, the solution of equation 3x-6 = 2 (x+5) is ().

a、4 B、 1 1 C、 16 D、

Xin Chen said that his family just bought a 15 inch LCD computer monitor. When asked how thin it was, he couldn't say. underneath

Among these four data, please choose a more reasonable data to represent the thickness of LCD ().

A, 5mm b, 5cm c, 5cm d, 5m.

14, the following events, you think the inevitable event is ()

A, Huangyan New Year's Day weather is clear in Wan Li.

B, Xiao Ming said that there was a sudden power outage at home last night, because the light was not good and he accidentally bit his nose while eating.

C, New Year's Day happens to be 1+0.

D. A bag contains three white balls and seven red balls, all of which are the same except the colors. Reach out and touch a white ball.

15, Party A, Party B, Party C and Party D sit face to face at a square table. A number "9" is written on a piece of paper on the desk. A said he saw "6", B said he saw ",C said he saw", D said he saw "9", so the following statement is right ———————————————————————.

A.A is opposite to Ding, B is to the left of A, and C is to the right of Ding.

B.c and b are opposite, with a on the left and d on the right.

C.a and B are opposite, C is on the right and D is on the left.

D. A is opposite to D, B is to the right of A, and C is to the right of D..

(3) do it.

16, calculation (4 points for each question, *** 12 points):

( 1)-8+4÷(-2) (2)

(3) —2 —( 1— 0.2)÷(—2)

17, combining similar items (4 points for each question, 8 points)

( 1)5xy 2+2x2y-3xy 2-x2y(2)-2x+5(x+2y)-(x-3y)

18, (5 points) simplify before evaluation: 2 (x-y)-3 (x-2y)+5, where x= 1999 and y =-

19, (6 points) Draw the picture and fill in the blanks:

(1) POint P is the vertical line Po of the straight line L, and the vertical foot is O;

(2) connecting PA and Pb;

(3) Point out that there is a line segment in the drawing.

20.(6 points) Put a pair of triangular plates together as shown in the figure to draw an angle of120. What other angles can you draw with this set of triangles? If you can draw three different angles correctly and mark the corresponding degrees, you can get 6 points; If you can tell me other angles, so much the better. )

2 1, (6 points) Xiaoling solves the equation as follows:

(1) Remove the brackets to get;

(2) move the item and get it;

(3) merging similar items to obtain;

(4) finally.

But after testing, it is not the root of the original equation. Please check, what's wrong with the above problem-solving process? And correct it.

22.(8 points) The price of a commodity is 900 yuan per piece. In order to participate in the market competition, the store will give 40 yuan a 10% discount on the selling price and still make a profit of 10%. What is the purchase price of this commodity?

23.(9 points) The following table shows the temperature changes recorded by Xiao Ming at noon every day during the week of June 10 (the temperature increased to a positive value and decreased to a negative value compared with the previous day).

Start date 123456

Temperature change/? 0? 2C

Actual temperature/? 0? 2C

1) If the temperature of 12 at noon last Sunday was 10? 0? 2C, so what's the actual temperature every day this week? (Please fill in the above form)

2) What is the difference between the highest temperature and the lowest temperature this week?

3) If you want to show the temperature changes this week. What statistical chart would you choose? According to the above data, please draw a picture.

Second, learn to see the world from a mathematical point of view (each question 10 score ***30 score)

24. There is such a question: "Calculate the value, among which". A student mistakenly copied ""as "",but the final result of his calculation was the same as that of other students. Try to explain the reason and find out the result.

25. There is a piece of paper with a thickness of 0.1mm. If it can be folded in half continuously, then

(1) continuous folding 10 times. * * How many floors are there?

(2) After being folded in half for 20 times in a row, is it as high as the teaching building of our school? Please explain your answer.

26. Have you read The Journey to the West? If you are a careful reader, you will find that this literary masterpiece also contains many mathematical problems. The following is a plot in The Journey to the West: According to legend, the Monkey King, the Great Sage of Qitian, met an evil ghost on his way to escort Tang Priest to fetch Buddhist scriptures from the West. The evil spirit shouted, "I have practiced for hundreds of years to get where I am today." What is your age? Get out of my way! " At this moment, the Monkey King laughed and said, "You said I was blind when I was young. You can't even reach my grandson! Listen: I am king in Huaguoshan at the age of one quarter; Then I became the Monkey King for 290 days, which means you spent 290 years in the underworld. Because of the havoc in heaven, he was crushed under the Five Elements Mountain and spent half his life. Then I escorted Master to the Western Heaven for Buddhist scriptures. It has been ten years since then. You calculate how old I am! " ..... Students, can you find out the Monkey King's age at that time?

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