Find 50 Mathematical Algebra Problems ... (Simple)

1 Try to find the pairwise coprime of three different natural numbers, so that the sum of any two of them can be divisible by the third number.

Analysis: There are three unknowns in the question. We try to get some equations and then work out these unknowns.

Let x < y<z so y | (y+2x), so y | 2x.

These three numbers are 1, 2, 3.

Question: Party A and Party B buy grain in the same grain store at the same time (assuming that the unit price of grain purchased twice is different). Party A needs 100 kg for every grain purchase, and Party B needs 100 yuan for every grain purchase.

We assume that the unit price of grain purchased by Party A and Party B for the first time is X yuan per kilogram, and the unit price of grain purchased for the second time is Y yuan per kilogram.

(1) is expressed by an algebraic expression containing xy: Party A needs to pay _ _ _ yuan of grain twice, and Party B needs to buy _ _ _ kg of grain twice. If the average unit price of grain purchased twice by Party A is Q 1 yuan, and the average unit price of grain purchased twice by Party B is RMB, then Q 1.

(2) If it is stipulated who buys grain twice and whose average unit price is low, then the way to buy grain is more cost-effective. Please judge which way is more cost-effective for both parties and explain the reasons.

(1) is expressed by an algebraic expression containing xy: Party A needs to pay 100(x+y) yuan of grain in two installments. Party B buys (100/x+ 100/y) kilograms of grain in two times. If Party A buys grain twice,

(2)q 1-q2=(x+y)/2-2xy/(x+y)=[(x+y)^2-4xy]/[2(x+y)^2]=(x-y)^2/[2(x+y)^2]>； 0

B cost-effective.

3 Are the following categories correct? If not, how to correct it?

( 1)(a^2-2ab+b^2)÷(b-a)=a-b

(2) (x^2+2xy+y^2)÷(x+y)^3=x+y

(1).B is not equal to a, and the answer should be b-a.

(2). It should be 1/(x+y).

4 Calculate (xy-x 2) ÷ (x-y/xy)

Equal to -x 2y

5 factorization, please write down the detailed process.

9(x+y)^2-4(x-y)^2

Original formula = (3x+3y) 2-(2x-2y) 2 = (5x+y) * (5y+x)

6 If x*x+x- 1=0, what is the value of the algebraic expression x*x*x+2x*x-7?

Because x*x+x- 1=0.

So (x+1) * (x * x+x-1) = x * x * x+2x * x-1= 0.

So x*x*x+2x*x= 1.

So the answer is -6.

7 if a < b < 0 < c

Simplify a-b+a+b-c-a+2-b-c.

丨 a-b 丨+丨 a+b 丨 c-a 丨 +2 丨 b-c 丨 = (b-a)+(-a-b)-(c-a)+2.

The x power of 8 is 25 =2000, and the y power of 80 is 2000. Found 1/x+ 1/y=?

According to the meaning of the question:

2000^( 1/x)=25

2000^( 1/y)=80

Available deformation:

2000^( 1/x+ 1/y)=25*80

So the result is: 1/x+ 1/y= 1.

Merchants mix a kind of milk candy (30kg) with a kind of milk candy (20kg) at the price of B yuan /kg when buying new year's goods. What is the reasonable price of this mixed sugar?

One yuan for 30 kilograms, one 30 yuan.

20 kilograms of B yuan, A * * * 20 yuan.

So a ***30a+20b yuan, 30+20kg.

So (30a+20b)/(30+20)=(3a+2b)/ 5 yuan per kilogram.

10 it is known that a+1/b (one of b) = 1, b+ 1/c= 1 find c+1/a.

a = 1- 1/b； c= 1- 1/a

Therefore, c =1-1/(1-1/b); And1/a =1/(1-1/b).

Finally, c+1/a =1-1(1-1/b)+1/(1-1/)

Two 1/( 1- 1/b) are rounded, and c+ 1/a= 1.

1 1 if a and b are positive integers and a×b= 1, find a/a+ 1(a plus 1 a) +b/b+ 1.

From the meaning of the question, A and B are positive integers, ab= 1, so a=b= 1.

The original formula =1(1+1)+1(1+1) = 0.5+0.5 =1.

12 In a fund-raising activity, each student donated an average of A yuan, and as a result, a * * * donated B yuan, so the formula B divided by A can be interpreted as the number of people (a * * *).

13 If the side length of a square is a, the square of algebraic expression 6a can be interpreted as ().

One third x- 1 stands for (the area of 36 such squares).

/kloc-the square of 0/4ω x-the square of b (what is the area of a circle with an outer diameter of x and an inner diameter of b).

Note: ω means pie.

In addition, I'll give you some junior high school math synchronization questions:

The following is the first grade:

The first set: junior high school grade one (two) mathematics final simulation test paper

First, multiple-choice questions:

1. At that time, the value of the algebraic expression was 4. So, when the value of this algebraic expression is ().

(A)-4； (B)-8； (C)8; (D)2 .

2. The number of positive integer solutions of the equation is ()

(A)4； (B)3； (C)2； 1

3. In the equation, when, ().

23; (B)- 13； (C)-5； (D) 13

4. In a math test, 10 papers were randomly selected, and the results are as follows:

85,8 1,89,8 1,72,82,77,8 1,79,83。

Then the mode, average and median of this set of data are () respectively.

A.8 1，82，8 1 B. 8 1，8 1，76.5 C. 83，8 1，77 D. 8 1，8 1，8 1

5. The original cost of manufacturing a product is 65,438+000 yuan. Because the cost has been reduced twice in a row, the current cost is 865,438+0 yuan, so the average cost reduced each time is ().

A.8.5% B. 9% C. 9.5% D. 10%

6. In order to make people feel the impact of discarded plastic bags on the environment, six students of an environmental protection group recorded the number of discarded plastic bags at home in one class in a week. The results are as follows: 33 25 28 26 25 3 1. If there are 45 students in this class, according to the data provided, it is estimated that the total number of plastic bags discarded by the class this week is about ().

A.900 b . 1080 c . 1260d . 1800。

(5) Assuming everyone's work efficiency is the same, it takes _ _ _ _ days for an individual to make a teddy bear.

(4) If it is a binary linear equation, then the numbers are = _ _ _ _ _ _, = _ _ _ _ _.

(2) It is composed of _ _ _ _ _ _ _ and _ _ _.

(3) If so _ _ _ _ _.

(5) Buy 27 stamps with face value of 20 cents and 30 cents respectively, and use 6.6 yuan. Buy _ _ _ _ 20 cent stamps and _ _ _ 30 cent stamps.

In the statistical analysis of a class's math test score, the number of people in each score segment is shown in Figure 3 (the score is a positive integer, and the full score is 100). Please observe the chart and answer the following questions:

(1) There are students in this class;

(2) The frequency of 69.5 ~ 79.5 is, and the frequency is;

(3) Please estimate the average score of this exam in this class.

3. Answer: (***48 points)

(1) Solving equation: (8 points)

In the sales of clothing cabinets in Huanggang Department Store, it is found that "Baole" brand children's wear can sell an average of 20 pieces every day, and each piece makes a profit in 40 yuan. On International Children's Day, shopping malls decided to take appropriate price reduction measures to expand sales, increase profits and reduce inventory. According to market research, if the price of each children's wear is reduced by 4 yuan, you can sell an average of 8 more children's wear every day. If the average profit of selling this kind of children's clothes every day is 1200 yuan, how much will each child's clothes be reduced?

A melon farmer planted an acre of excellent watermelons with greenhouse cultivation technology, and there were about 600 watermelons in this acre. Before watermelons went on the market, melon farmers randomly selected 10 ripe watermelons, and weighed them as follows:

Watermelon quality (unit: kg) 5.5 5.4 5.0 4.9 4.6 4.3

Number of watermelons (unit: one) 1 2 3 2 1 1

Calculate the average quality of this 10 watermelon, and estimate the watermelon yield of this mu of land according to the calculation results.

If the average value of a set of data 6, 7, 5, 6, x, 1 is 5, then the mode of this set of data is _ _ _ _ _.

In order to understand the physical quality of the junior three graduates, a school selected some junior three graduates to take a one-minute skipping test, and after sorting out the obtained data, drew a histogram of frequency distribution. As shown in the figure, the area ratio of each group of small rectangles from left to right is 2: 4:17:15: 9: 3, and the frequency of the second group is 12.

(1) Fill in the blanks: the frequency of the second group is _ _ _ _ _, and the sample size of this question is _ _ _ _ _.

(2) If the number of times is greater than 1 10 (including 1 10), try to estimate the success rate of junior three graduates in our school.

(3) In this test, which group does the median number of students skipping rope belong to? Please explain the reason.

As shown in the figure, a square with a size of 4×4 is divided into four parts with the same shape and size, and the whole figure after division is axisymmetric, for example, figure 1 Please draw several different squares in the picture below, and divide the square with the size of 4×4 into four parts with the same shape and size.

A school held a "May 4th" cultural performance, and five judges graded the performances of each class. Among the 12 judges at home, remove the highest score, then remove the lowest score, and take the average score as the actual score of the program. For the performance of a program, the score is as follows: 8.9 9. 1.9.3 9.49.2, so the actual score of the program is ().

a、9.4 B、9.3 C、9.2 D、9. 18

(5) There is a pool filled with two water pipes. If the first pipe is opened, the pool will be filled in 2 hours and 30 minutes; If the second test tube is opened, the pool will be filled after 5 hours. (10)

(1) If both pipes A and B are injected with water for 20 minutes at the same time, then B will inject water separately. How long does it take to fill the swimming pool?

(2) Assuming that a drain pipe C is installed under the pool, it is only necessary to open the pipe C for 3 hours to discharge the water full of the pool. How many hours does it take to fill an empty pool with water if three pipes are opened at the same time?

Second set

First, multiple-choice questions (2 points for each question, ***20 points)

1, the following statement is true ()

A, the same angle is equal to b, on the same plane, if a⊥b, b⊥c, then a ⊥ c.

C, the equal angle is the diagonal D, in the same plane, if a‖b, b‖c, then A ‖ C.

2. Observing the following patterns, among the four patterns A, B, C and D, () can be obtained by translating the patterns (1).

( 1) A B C D

3. There is the following statement:

(1) irrational number is an inexhaustible number;

(2) Irrational numbers are infinitely cyclic decimals;

(3) Irrational numbers include positive irrational numbers, zero irrational numbers and negative irrational numbers;

(4) Irrational numbers can be represented by points on the number axis.

The correct statement is ()

a、 1 B、2 C、3 D、4

4. A quadrilateral, the sum of the external angles of the new polygon obtained after cutting a knife is ()

A, increase 180? B, minus 180? C, constant d, all of the above are possible.

Someone went to the tile shop and bought a polygonal tile with seamless floor. The shape of the tile he bought can't be ().

A, equilateral triangle B, square C, regular octagon D, regular hexagon

6, as shown in the figure, the following reasoning, the correct is ()

a、∠A+∠D= 180 ,∴AD‖BC

b、∠C+∠D= 180 ,∴AB‖CD

c、∠A+∠D= 180 ,∴AB‖CD

d、∠A+∠C= 180 ,∴AB‖CD

7. In,, 3. 14,1.01.0001…, 2+,-,0, the number of irrational numbers is ().

a，3 B，4 C，5 D，6

8, the solution set of inequality group is ()

A, x & lt-3 B, x & lt-2℃, -3℃<x<- 2, no solution.

9. If the solution set of inequality group is x>2, then the value range of X is ().

a、x & gt2 B、x & lt2 C、x 2 D、x 2

10, in order to protect the ecological environment, a city responded to the national call of "returning farmland to forests" and changed part of cultivated land into forest land. After the change, the forestland area and cultivated land area * * * are 180 square kilometers, and the cultivated land area is 25% of the forestland area. In order to find out how many square kilometers the forestland area and cultivated land area are after the change. Let the changed cultivated land area be x square kilometers and the forestland area be y square kilometers. According to the meaning of the question, list the following four equations, of which the correct one is ().

A B C D

Fill in the blanks (2 points for each question, 20 points for * * *)

1, No.2 in the fifth row of the theater can be represented by (5,2), followed by (7,4).

2. The positive integer solution of inequality -4x ≥- 12 is

3. In order to make it meaningful, the value range of x is.

In order to prevent the deformation of an old wooden door, the carpenter nailed a batten on the back of the wooden door. The reason for this is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

5. As shown in the figure, if ∠ A = 60 and ∠ B = 30, then ∠BCD=.

6. If one side of an isosceles triangle is equal to 5 and the other side is equal to 8, then the circumference is _ _ _ _ _ _ _.

7. As shown in the figure, please add a condition to make AD‖BC, E.

8. If the cube root of a number is itself, then the number is.

9. The coordinates of the point P (-2, 1) moving up by 2 units are.

10. Last year, a school had 1000 students, an increase of 4.4% over last year, of which 6% were boarding students and 2% were day students. How many boarding students and day students were there in this school last year? Suppose there were x boarding students and y day students last year, then the equation can be listed as follows.

Iii. Answering questions (***60 points)

1, Xiaoming's home is in A, and he needs to build a road to get water by the river. Please help him design the shortest route and find out the distance from Xiaoming's home to the river (the ratio is 1: 20000) (3 points).

This is a schematic diagram of classroom seats. Try to design a method to describe the positions of three students and draw a picture to illustrate. (3 points)

3. Fill in the blanks with reasoning (4 points)

As shown in the figure, ef ‖ ad, ∠ 1 = ∠ 2, ∠ BAC = 70. Complete the process of finding ∠AGD.

Because EF‖AD,

So ∠ 2 = _ _ _ _ _ (_ _ _ _ _ _ _ _).

Because ∠ 1=∠2

So ∠1= ∠ 3 (_ _ _ _ _)

So AB \\_ _ _ _ _ _(_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

So ∠ BAC+_ _ _ _ _ =180 (_ _ _ _ _ _ _ _ _ _ _ _ _)

Because < BAC = 70.

So ∠ AGD = _ _ _ _ _ _

4. As shown in the figure, in △ ABC, AD and AE are bisectors of the height and angle of △ ABC respectively. If ∠ b = 30,

∠ C = 50 (4 points)