(A) position, statistics, mathematics wide angle
I. Place
The origin is divided into (0,0) and (1, 1).
1, represented by a number pair (column, row)
2, direction: go to the column first, then go. The column (east-west) line (north-south) increases eastward and northward, and decreases westward and southward.
3. translation: the line changes from north to south, and the column remains the same. The contents of the column change, but the rows remain the same. (point-to-point translation)
4. Axisymmetry: the distance between the left and right figures and the axis of symmetry is equal.
Second, statistics.
1, the difference between statistical charts:
(1) Bar chart: indicates quantity.
(2) statistical chart of broken lines: indicating the changing trend.
(3) Department statistical chart: it shows the relationship between part and whole.
2, vermicelli map
(1) Calculate the central angle of 360×? %
(2) Precautions for raising questions *: unit "1"
Third, mathematics wide angle (chicken and rabbit in the same cage)
1. Hypothesis: chicken to rabbit, rabbit to chicken. Note *: It is easy to answer the number of chicken feet into the number of rabbit feet.
2. Equation: Note *: Set the number of feet to x to avoid subtracting negative numbers.
(2) Calculation
I. Significance
1, multiplication: ① Fraction multiplied by integer: What is the sum of several identical addends?
② Score multiplied by score: Find the score of a number.
2. Division: the operation of finding another factor by knowing the product of two factors and one of them.
3. Percentage: A number is the percentage of another book.
Second, the law
1. multiplication: numerator multiplies numerator, denominator multiplies denominator, score as many points as you can, and then calculate.
2. Division: A divided by B equals the reciprocal of A divided by B (except "0").
Divider ÷ Divider = Divider: Divider A ÷ B = A=A:B(B≠0)
Fourth, the law of change.
1, multiplication: original number × original number less than 1
2. Division: dividend ÷ number greater than 1 > dividend; Dividend ÷ Number less than 1 > Dividend
Verb (abbreviation for verb) counts down to seconds.
1, definition: the product is 1, and the two numbers are reciprocal.
2. Find the number (1) score: the numerator and denominator of the score are exchanged. (2) Integer: A→ 1/A(0 has no reciprocal, and the reciprocal of 1 is 1). (3) Decimal (percentage): First convert the decimal (percentage) into the simplest fraction, and then find the reciprocal.
3. The reciprocal of the true score is greater than1; The reciprocal of the false score (except 1) is less than 1.
(3) ratio
I. Definition
1, ratio: the division of two numbers is also called the ratio of two numbers, indicating the relationship between two numbers.
2. The former and the latter: in the ratio of two numbers, the number before the comparison symbol is called the former, and the number after the comparison symbol is called the latter.
3. Ratio: The quotient obtained by dividing the former term of the ratio by the latter term is called the ratio.
Second, the basic nature of the ratio
1, the basic property of the ratio: the first term and the second term of the ratio are multiplied or divided by the same number (except 0) at the same time, which is inconvenient.
Third, simplify the ratio and find the ratio.
1. Simplify the ratio to the simplest integer ratio.
2. Simplify the ratio, and it is best to write the ratio in fractional form.
Fourth, the score in the game is just a way of integration, not comparison.
(d) application problems
First, the problem-solving steps
Step 1: Find the unit "1":A is closest to the score; B behind "Bi, Shi and Zhan"; C "Increase, decrease, increase, decrease ..." It's all the same.
Step 2: Find the key sentences and complete them.
Step 3: Find the equivalence relation.
The fourth step: column solution.
Second, the case analysis
Conditions: 32 boys, 24 girls, * * * with 168 books.
1. How many points are boys more than girls?
(Male-female) Male (32-24 years old) 24 years old
2. How many points are girls less than boys?
(Male and female) Female (32-24 years old) ÷32
3. What percentage of boys are in this class?
Male (female+male) 32 (32+24)
4. What percentage of girls are in the class?
Female (female+male) 24 (24+32)
5. How many copies can boys and girls get?
168÷(32+24)=3 (Ben) 3×32=96 (Ben) 3×24=72 (Ben)
First each, then a few.
6. Go back to an application question and ask who pays dividends.
300 Jin of peanuts can squeeze out 20 Jin of oil.
(1) How many kilograms of peanut oil can be squeezed per kilogram? 20 ÷ 300 =115 (kg)
② How many kilograms of peanuts do you need per kilogram of oil? 300÷20= 15 (kg)
Third, the percentage formula
1, student attendance = actual attendance/attendance × 100%.
2. Wheat flour yield = flour weight/wheat weight × 100%.
3. Peanut oil yield = oil weight/peanut weight × 100%.
4. Plant survival rate = number of surviving plants/total number of plants × 100%
5. Shooting percentage = hit times/total shooting times × 100%
6. Salt content of brine = salt weight/brine weight × 100%.
7. Product qualification rate = qualified products/product quantity × 100%
Four. Interest and available interest
1, interest = principal × interest rate× time
2. Available interest = principal × interest rate × time × (1-5%)
(5) circle
I. Concept and characteristics
1, concept: a point on the center of the circle is called the center of the circle, generally represented by the letter O, a line segment connecting the center of the circle with any point on the circle is called the radius, generally represented by the letter R, a line segment passing through the center of the circle with both ends on the circle is called the diameter, generally represented by the letter D, and π ≈ 3.14π = 3.1465448.
The ratio of the circumference to the diameter of a circle is a fixed number, which is called pi.
1, function
① A circle has countless symmetry axes, while a semicircle has only one.
② In the same circle, there are countless radii and diameters.
(3) In the same circle, all radii are equal in length and all diameters are equal.
① In the same circle, the diameter is twice as large as the radius, and the radius is 1/2(0.5) times as large as the diameter.
d=2r r= 1/2d
Second, the formula
① d = 2R2R = 1/2D3C circle = π d = 2π r4S circle =πr? ⑤s ring =π(R? -r？ )
⑥ Semicircle =πr ⑦ Semicircle =πr+d=π+2r
Third, painting.
1. Draw a circle: ① Determine the center of the circle ② Measure the radius ③ Draw a picture ④ Draw O, R, d ⑤ Mark O, R, D.
2. Draw a circle in the square: ① The center of the circle is at the intersection of diagonal lines; (2) the radius is half the length of a square.
③ The ratio of square area to circular area is 200: 175.
4. 1, radius ratio = diameter ratio = circumference ratio. 2. Area ratio = the square of radius ratio.
Verb (abbreviation of verb) π ≈ 3.142π = 6.283π = 9.424π =12.565π =15.76π =18.84.
7π=2 1.98 8π= 15. 12 9π=28.26
4? π= 16π=50.24 5? π=25π=78.5 6? π=36π= 1 13.04 7? π=49π= 153.86
8? π=64π=200.96 9? π=8 1π=254.34