Four types of application problems in junior high school mathematics compulsory examination
Classic example 1
A philatelist bought stamps of 10 and 20 cents *** 100, with a total value of180 cents in 8 yuan. How many stamps did this stamp collector buy?
Analysis:
Suppose every 100 stamp bought is 20 cents, then the total value should be 20? 100=2000 (minutes), which is 2000- 1880= 120 (minutes) more than the original total value. And this extra 120 points means that every point of 10 is regarded as 20 points, and every point is 20- 10= 10 (points), so how many points can you get from 10 points?
Formula: (2000- 1880)? (20- 10) = 120? 10 = 12 (sheets)? 10, the number of sheets per sheet.
100- 12=88 (Zhang)? First 20 minutes or 20 minutes, then 10 minutes. The method is as above. Please note that the total value is less than the original total value.
Classic example 2
The price of five toy cars is equal to the price of three airplane toys, and each airplane toy is more expensive than each toy car, 8 yuan. What is the unit price of these two toys?
Analysis:
Because each toy plane is more expensive than each toy car, 8 yuan, so three toy planes are 8? 3=24 yuan. Because the price of five toy cars is equal to the price of three toy planes.
So this 24 is equivalent to the price of (5-3) toy cars, and each toy car is 24? 2= 12 yuan, and the price of each toy plane is 12+8=20 yuan.
Classic example 3
Pump water with two pumps, small pump for 6 hours, large pump for 8 hours, and one pump for 3 12 cubic meters. The pumping capacity of a small pump for 5 hours is equal to that of a large pump for 2 hours. How many cubic meters of water can these two pumps pump per hour?
Analysis:
Because the pumping capacity of a large pump for 2 hours is equal to that of a small pump for 5 hours, the pumping capacity of a large pump for 8 hours should be equal to that of a small pump for 8 hours. 2? 5=20 hours of pumping capacity.
So 3 12 cubic meters of water is equivalent to the pumping capacity of a small pump (6+20) hours. Is the hourly pumping rate of small water pump 3 12? (6+20)= 12 cubic meters, and the water pump pumps water every hour 12? 5? 2=30 cubic meters.
Classic example 4
A work will be completed by B after 5 hours, and it can be completed in 3 hours; After B has done it for 9 hours, A can do it, or it can be done in 3 hours. So how many hours can B do after A does 1 hour?
Analysis:
Comparing the two sets of known conditions in the question, if A does less (5-3) hours, B will do more (9-3) hours, that is, the workload of A 2 hours is equal to B 6 hours, and A 1 hour is equal to B 3 hours.
A Does it take 5+3 to do all this work? 3=6 hours, now A does it first 1 hour, B does the remaining 5 hours, and B must use 5? 3= 15 hours to complete.
Seven Arithmetic Rules Necessary for Elementary School Mathematics Examination Calculation
I. additive commutative law
When two numbers are added, the positions of the two addends are exchanged and the sum remains unchanged, which is called additive commutative law.
a+b=b+a
Second, the law of additive association.
When adding three numbers, add the first two numbers and then the third number, or add the last two numbers and then the first number, and the sum remains the same. This is the so-called law of additive association.
a+b+c=(a+b)+c=a+(b+c)
Third, the essence of subtraction.
In subtraction, the minuend and the minuend add or subtract a number at the same time, and the difference remains the same.
a-b=(a+c)-(b+c) ab=(a-c)-(b-c)
In subtraction, how much the minuend increases or decreases, the minuend remains the same, and the difference increases or decreases. On the other hand, how much is reduced, how much is increased, the minuend is unchanged, and the difference increases or decreases with the decrease.
In subtraction, the minuend subtracts several minuends, which can be added first, and the difference is unchanged.
Answer? b - c = a - (b + c)
Fourthly, multiplicative commutative law.
Multiplication of numbers, where the positions of two factors are exchanged and the product remains unchanged, is called the commutative law of multiplication.
Answer? b = b？ a
Fifth, the law of multiplication and association.
Multiply three numbers, multiply the first two numbers and then the third number, or multiply the last two numbers and then the first number, and the product remains the same. This is the so-called law of multiplication and association.
Answer? b？ c = a？ (b？ c)
Sixth, the law of multiplication and distribution
Multiplying the sum (or difference) of two numbers with a number is equivalent to multiplying these two numbers with this number respectively, and then adding (or subtracting) the two products. This is the so-called law of multiplication and division.
(a + b)？ c= a？ c + b？ C (a-b)? c= a？ c - b？ c
Other operational properties of multiplication
If one factor is multiplied several times, the other factor must be reduced by the same multiple, and its product remains the same.
Answer? b = (a？ c)？ (b？ c)
VII. Operability of Division of Labor
Quotient is constant. When two numbers are divided, the dividend and divisor expand or shrink the same number at the same time (except 0), and the size of the quotient remains the same.
Answer? b=(a？ c)？ (b？ c) a？ b=(a？ c)？ (b？ c)
A number is divided by two consecutive numbers. You can multiply the last two numbers first, and then divide this number by their product, and the result is still the same.