Mathematics application questions in Grade 7 Volume 1 (seeking questions and answers) Ask twenty questions about mathematics, application, solution and geometry (line segment) in grade seven! Kneel down and ask for ing, and, and the answers are casual, mainly questions, application questions, and evaluation questions of merging similar items! Help

Mathematics application questions in Grade 7 Volume 1 (seeking questions and answers) Ask twenty questions about mathematics, application, solution and geometry (line segment) in grade seven! Kneel down and ask for ing, and, and the answers are casual, mainly questions, application questions, and evaluation questions of merging similar items! Help

4、 (6 points for each small question, 18 points in total) 27. Simplify first, and then evaluate. Among them, 28. Solve the following equations and test them. Grade 7 mathematics page 3 of 1 five column equations solve application problems (6 points for each small question, 12 points in total) 30. Distribute a batch of books to the students of Grade 7 (11). If each student has 3 books, the remaining 20 books will be left

The rabbit sequence problem
Fibonacci, a famous Italian mathematician in the Renaissance, once proposed an interesting problem of rabbit reproduction: suppose that rabbits give birth to a pair of rabbits every month two months after they are born. Then, how many pairs of rabbits will there be in a year from the first pair of rabbits born at the beginning of the year?

1,1,2,3,5,8,13,…
From the third term, each term is the sum of the first two terms. Its general formula is: (1 / √ 5) * {[(1 + √ 5) / 2] ^ n - [(1 - √ 5) / 2] ^ n}. Therefore, 233 pairs of rabbits were born one year later

When a = 2, B = - 1, C = 3, find the square of the following algebraic value B - 4ac, the square of a + the square of B + the square of C + 2Ab + 2BC + 2Ac (a + B + C)
When a = 2, B = - 1, C = 3, find the algebraic values of the following expressions
The square of b-4ac
Square of a + square of B + square of C + 2Ab + 2BC + 2Ac
The square of (a + B + C)

They are:
-23
sixteen
sixteen
The calculation is as follows:
The square of b-4ac = (- 1) - 4 × 2 × 3 = 1-24 = - 23
The square of a + the square of B + the square of C + 2Ab + 2BC + the square of 2Ac = 2 + (- 1) + the square of 3 + 2 × 2 × (- 1) + 2 × (- 1) × 3 + 2 × 2 × 3 = 4 + 1 + 9-4-6 + 12 = 16
The square of (a + B + C) = the square of (2-1 + 3) = the square of 4 = 16

Summary and arrangement of mathematics knowledge points of PEP

Chapter 1: rational number 1, positive and negative number 2, rational number 3, addition and subtraction of rational number 4, multiplication and division of rational number 5, power of rational number Chapter 2: one variable linear equation 1, from formula to equation 2, from ancient algebra book 3, from "buy cloth problem" 4, re explore practical problems and one variable

Arrange in black and white in the following order: white white black white white black white white black white white black black white white black black white white black black white white black black white white black black black white white black black black white white black black black white white black black black white white black black black white white black black black white white black black black black white white black black
1. What is the 200th word in this column?
2. How many white? How many black in the first 104 words?
3. If there are 200 words, how many are black and white?

1. The 200th word is black
2. There are 63 white and 41 black in the first 104 words
If there are 200 words, there are 80 in black and 120 in white
I must be right
The other's answer to the second question is wrong

1ml =? Cubic centimeter 1L =? Cubic decimeter

One milliliter equals one cubic centimeter, and one liter equals one cubic decimeter

In the final exam, the average score of Xiaoqiang is 94 in Chinese and mathematics, 92 in mathematics and English, and 90 in Chinese and English
In this exam, how many points do Xiaoqiang get in each of the three subjects? List the formula, write out the process, and I'll give him or her 100 points
If you use an equation, you can only have one unknown number

94 + 92 + 90 = 186 + 90 = 276 (min) It is the total score of Chinese, mathematics and English
276-92 * 2 = 276-184 = 92 (min) The score of Chinese
276-90 * 2 = 276-180 = 96 (min) Marks in Mathematics
276-94 * 2 = 276-188 = 88 (min) English scores
A: Xiaoqiang scored 92 in Chinese, 96 in mathematics and 88 in English

For three consecutive even numbers, if the sum of squares of the first two numbers is 4 less than the product of the last two numbers, then the three numbers are?

Let these three even numbers be X-2, x, x + 2, then (X-2) ^ 2 + x ^ 2 + 4 = x (x + 2)
x^2-4x+4+x^2+4=x^2+2x
x^2-6x+8=0
X = 2 or x = 4
So these three numbers are
0,2,4
Or 2, 4, 6

How many liters is a kilogram of diesel and how many liters is a kilogram of gasoline

Usually, the density of diesel oil is calculated as 0.84, so a kilogram of diesel oil is about 1.19 liters
The density of gasoline is about 0.8kg/l, 1kg = 1kg, v = m / ρ = 1 / 0.8 = 1.25l~

The formula of unit 1 and unit 2
The first unit and the second unit
It's the people's education version of the trouble

1. Number of copies × number of copies = total number of copies / number of copies = total number of copies / number of copies = number of copies
2. 1 times × times = several times △ 1 times = several times △ 1 times
3. Speed × time = distance △ speed = time distance △ time = speed
4. Unit price × quantity = total price / unit price = total quantity / quantity = unit price
5. Work efficiency × work time = total amount of work △ work efficiency = total amount of work time △ work time = work efficiency
6. Addend + addend = sum - one addend = another addend
7. Subtracted - subtracted = difference subtracted - difference = subtracted difference + subtracted = subtracted
8. Factor × factor = product △ one factor = another factor
9. Divisor / divisor = quotient divisor / quotient = divisor quotient × divisor = divisor
Primary school mathematics figure calculation formula
1. Square C perimeter s area a side perimeter perimeter = side length × 4 C = 4A area = side length × side length s = a × a
2. Cube V: Volume A: edge length surface area = edge length × edge length × 6 s surface = a × a × 6 volume = edge length × edge length × edge length v = a × a × a
3. Rectangle
C perimeter s area a side length
Perimeter = (length + width) × 2
C=2(a+b)
Area = length × width
S=ab
4. Cuboid
5: Volume s: Area A: length B: width H: height
(1) Surface area (L × W + L × H + W × h) × 2
S=2(ab+ah+bh)
(2) Volume = length × width × height
V=abh
5 triangles
S area a bottom h height
Area = bottom × height △ 2
s=ah÷2
Triangle height = area × 2 △ bottom
Triangle bottom = area × 2 △ height
6 parallelogram
S area a bottom h height
Area = bottom × height
s=ah
7 trapezoid
S area a upper bottom B lower bottom h height
Area = (upper bottom + lower bottom) × height △ 2
s=(a+b)× h÷2
8 round
S area C perimeter Π d = diameter r = radius
(1) Perimeter = diameter ×Π = 2 ×Π× radius
C=∏d=2∏r
(2) Area = radius × radius ×Π
9 cylinder
v: Volume H: height s; bottom area R: bottom radius C: bottom perimeter
(1) Side area = perimeter of bottom surface × height
(2) Surface area = side area + bottom area × 2
(3) Volume = bottom area × height
(4) Volume = side area △ 2 × radius
10 cone
v: Volume H: height s; bottom area R: bottom radius
Volume = bottom area × height △ 3
Total number △ total number of copies = average number
The formula of sum difference problem
(sum + difference) △ 2 = large number
(sum difference) △ 2 = decimal
The problem of sum times
Sum (multiple-1) = decimal
Decimals × multiples = large numbers
(or sum - decimal = large)
Differential multiple problem
Difference (multiple-1) = decimal
Decimals × multiples = large numbers
(or decimal + difference = large)
The problem of tree planting
1. The tree planting problem on non closed lines can be divided into the following three cases
(1) if trees are to be planted at both ends of the non closed line, then:
Number of plants = number of segments + 1 = total length △ plant spacing-1
Total length = plant spacing × (number of plants - 1)
Plant spacing = total length (number of plants - 1)
(2) if trees are to be planted at one end of the non closed line and not at the other end, then:
Number of plants = number of segments = total length △ plant spacing
Total length = plant spacing × number of plants
Plant spacing = total length △ number of plants
(3) if trees are not planted at both ends of the non closed line, then:
Number of plants = number of segments-1 = total length △ spacing-1
Total length = plant spacing × (number of plants + 1)
Plant spacing = total length (number of plants + 1)
2. The quantitative relationship of tree planting on closed lines is as follows
Number of plants = number of segments = total length △ plant spacing
Total length = plant spacing × number of plants
Plant spacing = total length △ number of plants
Profit and loss
(profit + loss) △ the difference between the two distributions = the number of shares participating in the distribution
(big profit - small profit) △ the difference between the two distributions = the number of shares participating in the distribution
(big loss - small loss) △ the difference between the two distributions = the number of shares participating in the distribution
Encounter problem
Encounter distance = speed and X encounter time
Encounter time = encounter distance △ speed and
Speed sum = encounter distance △ encounter time
Follow up questions
Pursuit distance = speed difference × pursuit time
Pursuit time = pursuit distance △ speed difference
Speed difference = pursuit distance △ pursuit time
Flow problem
Downstream velocity = hydrostatic velocity + water velocity
Countercurrent velocity = still water velocity - water velocity
Hydrostatic velocity = (downstream velocity + countercurrent velocity) △ 2
Water flow velocity = (downstream velocity countercurrent velocity) △ 2
Concentration problem
Weight of solute + weight of solvent = weight of solution
Weight of solute / weight of solution × 100% = concentration
Weight of solution × concentration = weight of solute
Weight of solute △ concentration = weight of solution
Profit and discount
Profit = selling price cost
Profit margin = profit / cost × 100% = (selling price / cost-1) × 100%
Up and down amount = principal × up and down percentage
Discount = actual selling price △ original selling price × 100% (discount < 1)
Interest = principal × interest rate × time
After tax interest = principal × interest rate × time × (1-20%)
Length Conversion
1 km = 1 000 m 1 m = 10 decimeters
1 decimeter = 10 cm 1 meter = 100 cm
1 cm = 10 mm
Area Conversion
1 sq km = 100 ha
1 ha = 10000 M2
1 square meter = 100 square decimeter
1 square decimeter = 100 square centimeter
1 sq cm = 100 sq mm
Volume (volume) product unit conversion
1 cubic meter = 1000 cubic decimeter
1 cubic decimeter = 1000 cubic centimeter
1 cubic decimeter = 1 liter
1 cc = 1 ml
1 cubic meter = 1000 liters
Conversion of weight unit
1 ton = 1000 kg
1kg = 1000g
1kg = 1kg
Conversion of RMB units
1 yuan = 10 Jiao
1 jiao = 10 points
1 yuan = 100 points
time conversion
1 century = 100 years 1 year = December
Big month (31 days): January, March, may, July, August, October, December
Small month (30 days): April, June, September and November
The average year is 28 days in February and leap year is 29 days in February
There are 365 days in a normal year and 366 days in a leap year
1 day = 24 hours, 1 hour = 60 minutes
1 minute = 60 seconds 1 hour = 3600 seconds
There is only one straight line through two points
2 the shortest line segment between two points
The complements of the same or equal angles are equal
The remainder of the same or equal angle is equal
There is and only one line perpendicular to a known line passing through a point
Among all the line segments connected by a point outside the line and each point on the line, the vertical line segment is the shortest
The axiom of parallelism passes through a point outside the line, and there is only one line parallel to it
If both lines are parallel to the third line, the two lines are parallel to each other
The two lines are parallel
The internal stagger angles are equal and the two lines are parallel
The inner angles of the same side are complementary, and the two lines are parallel
The two straight lines are parallel and have the same angle
The two straight lines are parallel and the internal stagger angles are equal
The two lines are parallel, and the internal angles of the same side complement each other
Theorem 15 the sum of two sides of a triangle is greater than the third side
16 infer that the difference between the two sides of a triangle is less than the third side
The sum of the three internal angles of a triangle is 180 degrees
18 corollary 1 two acute angles of right triangle complement each other
Corollary 2 one exterior angle of a triangle is equal to the sum of two interior angles not adjacent to it
The outer angle of a triangle is greater than any inner angle not adjacent to it
The corresponding sides and angles of congruent triangles are equal
SAS has two congruent triangles whose two sides and their angles are equal
The 23 angle and side angle axiom (ASA) has two congruent triangles with two equal angles and their pinch sides
Inference (AAS) has two angles and the opposite sides of one of them corresponding to two equal triangles congruent
The 25 edge axiom (SSS) has two congruent triangles with three equal sides
The axiom of hypotenuse and right edge (HL) has hypotenuse and a right edge corresponding to two equal right triangles
Theorem 1 the distance from a point on the bisector of an angle to both sides of the angle is equal
Theorem 2 a point at the same distance from both sides of an angle is on the bisector of the angle
The bisection of 29 corners