First, substitution exclusion method;
The second is the digital characteristic method;
Third, the proportional method;
Fourth, the method of assignment;
5. Cross method.
We can use the following five tricks to solve math problems:
First, the substitution exclusion method.
Substitution and exclusion method is the most intuitive and quick method to solve problems in line test. Consider using substitution exclusion in two situations: one is to see multiple numbers.
Question types, age questions, congruence questions and other questions are excluded by method of substitution; Second, when there is no idea and direction, consider substitution and exclusion.
There are four students, one of whom is just one year older than the other. Their age is multiplied by 93024.
How old is the oldest? ( )
A. 16 years old B. 18 years old C. 19 years old D.20 years old.
Answer c
It is troublesome to solve it directly by analytical method, so substitution exclusion method can be considered. Bringing in option A, the oldest person is 16 years old, and these people are 6.
15, 14, 13。 The mantissa of the product of four numbers is 0, and it is excluded if it does not match. Again, exclude BD. So the answer is C.
Second, the digital characteristic method
Example 1(2008- Guangdong-15) There are four classes in a certain grade, and the total number of the other three classes is131; Not counting the rest of Ding Ban.
The total number of students in three classes is134; The total number of students in Class B and Class C is less than that in Class A and Class D 1. Ask these four students. How many people are there in the class?
A. 177 B. 176 C.266？ D.265
Answer a
The odd and even features in digital feature method are considered analytically. The total number of students in Class B and Class C is less than that in Class A and Class D 1,
Using the parity feature, we can know the sum of B, C, A and D, that is, the total number of students in four classes must be odd, excluding B and C.
From the meaning of (b+c+d)+(a+b+c) =131+134 = 265, it can be concluded that the number of students in the four classes is less than 265.
So the answer is option a.
Third, the proportional method
Proportion is the contrast between numbers or physical quantities. Any form that conforms to the equation A=M×N, where a, m and n represent.
Different physical quantities, and one of the three quantities that must be determined, can be used in proportion. In practical applications, such as roads,
Process = speed × time, income = unit price × sales volume, etc. All meet the requirements. When a is fixed, m is inversely proportional to n;
When m is fixed, a and n are proportional.
20 12 There is an expressway between Zhejiang -53A and B, and Party A and Party B start from A and B respectively, heading in opposite directions. Party A will leave for half an hour first.
After 10: 00, B didn't start until an hour later. When they met, A's speed was 2/3 of B's. What is the ratio of the distance traveled by A and B?
A.5:6 B. 1: 1？ C.6:5 D.4:3
Answer b
Analyze the evaluation trip in this question. Distance = speed × time. V A: V B =2:3，T A: T B = 1.5: 1，
Then a: b = 2×1.5: 3×1=1:1. So, the answer is option B.
In 2008, two identical bottles in Shandong -43 were filled with alcohol solution, and the volume ratio of alcohol to water in one bottle was 3: 1.
The volume ratio of alcohol and water in the other bottle is 4: 1. If two bottles of alcohol solution are mixed, the mixed alcohol and water are the same.
What is the floor area ratio?
A.3 1:9？ B.7:2？ C.3 1:40？ D.20: 1 1
Answer a
Analyze the exam solution of this question. The two bottles have the same volume, and the volume ratio of alcohol to water is "3: 1" and "4: 1" respectively.
The bottles are divided into "3+ 1=4" and "4+ 1=5" respectively, so they should be in the proportional form of "and".
If the least common multiple of 4 and 5 is 20, then 3: 1= 15:5, 4: 1= 16:4,
The volume ratio of alcohol and water after mixing = (15+16): (5+4) = 31:9.
So, the answer is option a.
Fourth, the assignment method
Example 1 (National Examination 2012-71) The import price of a commodity in 2010 is 15 yuan/kg, and the import volume of the commodity in 201kloc-0/year is/kloc.
It has increased by half, and imports have increased by 20%. What is the import price of goods in 20 1 1 year?
10 b . 12 c . 18d . 24
Answer b
The import price, import quantity and import amount have changed in the two years of 20 10 and 20 1 1, so the value can be assigned to 20 10.
If the annual import volume is 2 kg, and the annual import volume of 201/kloc-0 is 3 kg, the unit price, quantity and amount within two years.
The relationship is shown in the following figure:
20 10, import volume = 15×2=30 yuan, 20 1 1, import volume =30×( 1+20%)=36 yuan.
Then the import price of 20 1 1 year is 36 ÷ 3 = 12 yuan, so the import price of goods in 20 1 1 year is 12 yuan/kg.
So the answer is option B.
Five, cross method
Cross method is widely used to solve problems, economic problems, engineering problems and differential ratio problems. .
Example 1(20 10 Guizhou -9) Two kinds of brine, A and B, with concentrations of 20% and 5% respectively, were mixed to make 15%.
900 grams of salt water. How many grams of 5% saline do you need? ( )
.250 caliber? B.285？ C.300？ D.325
Answer C.
reference data
Painting education. Tuhua Education Network [reference time 20 18-4- 13]