The text of "Grandma's paper cut" in the sixth grade of primary school

In the small village supported by the great plain, on the windows of the neighbors, there are the ingenious work of grandma
A pair of ordinary scissors and a piece of ordinary colored paper are folded in grandma's hand, and you can have whatever you want. People, animals, plants and utensils can do anything. I have heard people tut tut tut praise since I was a child: "your grandma is God, cutting cat like cat, cutting tiger like tiger, cutting hen can lay eggs, cutting Rooster can sing."
Naturally, this is an exaggeration, but it reflects the popularity of grandma's paper-cut skills. The kind-hearted grandma has a good relationship with everyone. She can do whatever she wants. She lifts up her blue apron and wipes her hands: "come on, what's the use? Where are you going?" she goes happily, and then she does her work: washing clothes, taking shoes, choosing vegetables, panning rice, feeding pigs, weeding
I used to remember grandma's mind and body when she cut paper. The sound of the scissors brushing on the paper was very pleasant. I was a famous naughty guy who often changed the pattern to make trouble for grandma. One day, I covered grandma's eyes with both hands and let her touch the window flowers. Unexpectedly, when the worker was not big, a picture of "magpie climbing on the branch" was finished, The size and density are impeccable. I took it, but I still cheated: "grandma, you've peeked out from my fingers!"
"You almost pushed grandma's eyes out!" grandma pointed at my nose with her finger, "practice makes perfect, always cutting, hands are accurate!"
Yes, farmers are lucky. Grandma is very familiar with "magpie climbing branches". In the middle of winter, in summer, in the sun, in the moonlight, in the light, even in the dark. Grandma's hands are eyes, so that the scissors are like her two extended fingers
In the midsummer of dense clouds and rainy days, grandma was afraid that I would slip into the river and swim out of danger, so she tied me to the eaves with paper-cut. She tore a page from the old exercise book, brushed it a few times, and then cut out a picture. I grabbed it and saw that it was a naughty little rabbit riding on the back of a docile old cow. I asked, "why do cattle carry rabbits?"
Granny laughed: "who let the cow be the granny of the rabbit?"
Well, grandma's zodiac is a cow, and I'm a rabbit. I yell for more. Grandma cut out another picture: an old cow and a rabbit eating grass on the grass. Grandma asked, "do you understand?"
I thought about it and said, "I know. It means that grandma and I are eating in the same pot."
Grandma held me in her arms and boasted, "smart ghost!"
From then on, I always pestered my grandmother to cut rabbits and cows - jumping rabbits, running rabbits, sleeping rabbits; old cows pulling carts, old cows ploughing Rabbits are always playing, and old cows are always working. I fiddle with all kinds of window decorations, and I have a good feeling for lively rabbits and honest old cows
I went to school, primary school, middle school, University - I went farther and farther. But I still received the paper cuts from my grandmother. One of them was like this: an old cow was standing still, gazing at a little rabbit that was jumping away happily. What connected them was an open grassland. I knew that this was grandma's expectation for me. In fact, no matter how far and how long I walked, My dream always reflects my hometown's window flowers and the four seasons fields on both sides of the village road. Whenever and wherever I remember the refreshing sound of paper cutting, my mood and dream will immediately become vivid and colorful

Answers to grandma's paper cutting exercises and tests in sixth grade Chinese of Jiangsu Education Press
What does grandma expect from me

I hope I can go to a wider world and learn more

Conditions: Let f (x) = log base be 1 / 2, exponent (1-ax) / (x-1) be an odd function, and a be a constant
It is proved that f (x) increases monotonically in the interval (1, positive infinity)

Logarithms don't have exponents, they only have real numbers
It is found that (1-ax) / (x-1) > 0
1. If a > 0, the function holds on (1 / A, 1) or (1,1 / a), which is contradictory to the meaning (1, positive infinity)
2. If a

High school absolute value inequality
There's a problem that I can't figure out
For example: | X & # 178; - 3x-4 | x + 2, why don't we discuss three cases when ① x + 2 > 0, ② x + 2 < 0, ③ x + 2 = 0
It is directly equivalent to X & # 178; - 3x-4 ＞ x + 2 or X & # 178; - 3x-4 ＜ - X-2, and then the solution set is obtained
There are trees and gods to explain

LZ study dizzy... We discuss, because the absolute value is not an algebraic formula, can not be directly transferred out of the solution
No matter what the value of X + 2 is, it is always x + 2
In fact, there are only two cases of | a | B, either a > = 0, then a > b or AB, AB is equivalent to - B

The radius of the big circle is equal to the diameter of the small circle. It is known that the area of the big circle is 9.42 square decimeters more than that of the small circle, and the area of the small circle is______ ．

Let the radius of the small circle be r, then the radius of the big circle is 2R, the area of the big circle is: π (2R) 2 = 4 π R2, and the area of the small circle is: π R2, so the area of the big circle is 4 times of that of the small circle, then the area of the big circle is 4-1 = 3 times larger than that of the small circle, 9.42 △ 3 = 3.14 (M2). A: the area of the small circle is 3.14dm2

It is known that the four numbers a, B, C and D are proportional, and a and D are external terms. Verification: the point (a, b), (C, d) and the coordinate origin o are on the same line

It is proved that: let the straight line passing through points o and (a, b) be y = KX, then B = AK, then k = Ba, let the analytic formula of the straight line passing through points o and (C, d) be y = MX, then d = cm, and the solution is: M = DC, ∵ a, B, C, D are proportional, ∵ AB = CD, ∵ Ba = DC, ∵ k = m, then the straight line y = KX and the straight line y = MX are the same straight line, that is, the point (a, b), (C, d) and the coordinate origin o are on the same straight line

Write a quadratic polynomial with only the letter X, and find the value of this polynomial when x = - 2

For example, X2 + 1, when x = - 2, the original formula = 4 + 1 = 5

Given that the radius of the sector is R and the area is s, the arc length of the sector is ()
Given that the radius of the sector is R and the area is s, the arc length of the sector is ()
（a)2sr (b)rs/2
(c)2s/r (d)2r/s

s=Cr/2
C=2s/r
If the radius of the sector is R and the area is s, the arc length of the sector is (2S / R)

Note that the sum of the first n terms of the equal ratio sequence {an} is SN. Given S4 = 1, S8 = 17, find the general term formula of {an}
S(8)=S(4)+S(4)(q^4)=S(4)(1+q^4)
I don't understand this step
The two answers are different
The following is the second answer to the wrong first method
an=（-1）^n * 2^（n-1)/5

Let the common ratio of {an} be Q. from S4 = 1, S8 = 17, we know that Q ≠ 1
a1(q^4-1)/(q-1)=1,①
a1(q^8-1)/(q-1)=17.②
Q ^ 4 + 1 = 17, Q ^ 4 = 16
Ψ q = 2 or q = - 2
Substituting q = 2 into Formula 1, A1 = 1 / 15, so an = 2 ^ (n-1) / 15;
Substituting q = - 2 into Formula 1, A1 = - 1 / 5 is obtained,
So an = (- 2) ^ n / 10
Comments: This paper examines the general term formula, the first N-term sum formula, the equation idea and the overall idea of the equal ratio sequence. Special attention should be paid to the two cases of Q ≠ 1 and q = 1 when using the first N-term sum formula
The second method
S(4)=a1+a2+a3+a4=a1×(1+q+q^2+q^3)
S(8)=S(4)+a1q^4+a1q^5+a1q^6+a1q^7
=S(4)+a1×q^4(1+q^2+q^3+q^4)
=S(4)+a1×(1+q^2+q^3+q^4)×q^4
=S(4)+S(4)×(q^4)=S(4)×(1+q^4)
Do you understand the change process?
1 + Q ^ 4 = 17 / 1 = 17, Q ^ 4 = 16, q = 2, or q = - 2
a1*(1+2+4+8)=a1*15=1---> a1=1/15,a(n)=(2^n)/30
a1*(1-2+4-8)=a1*(-5)=1---> a1=-1/5,a(n)=(-2)^n/10

According to the following conditions, it is not necessary to calculate the quotient of (1) 17.28 divided by X, which is 3.6 (2) 16.2 minus 2 times of X, the difference is 12 times of 8.2 (3) x and 7.6, which is equal to 4 times of 20 (4) x, and the increase of 15 is 95

（1）17.28÷x=3.6 17.28÷x×x=3.6x 3.6x=17.28 3.6÷3.6=17.28÷3.6 x=4.8；（2）16.2-2x=8.2 16.2-2x+2x=8.2+2x 2x+8.2-8.2=16.2-8.2 2x=8 2x÷2=8÷2 x=4；（3）12x-7.6=20 12x-7.6+7.6=20+7.6 12x÷12=27.6÷12 X = 2.3; (4) 4x + 15 = 95 & nbsp; 4x + 15-15 = 95-15 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 4x = 80 & nbsp; & nbsp; & nbsp; 4x △ 4 = 80 △ 4 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; X = 20. So the answer is: 17.28 △ x = 3.6; 16.2-2x = 8.2; 12x-7.6 = 20; 4x + 15 = 95.6

The text of "Grandma's paper cut" in the sixth grade of primary school