Error-prone knowledge points in xiaoshengchu mathematics exam
12. How to read large numbers: the problem of reading a few zeros.
Related example10,0070,0008 How many zeros did you read? Wrong answer 2 Other correct answers
Comment on examples
Reading large numbers is a knowledge point in grade four, especially reading a few zeros, which is easy to make mistakes.
13. Approximation problem
Related examples The approximate value of a number is 10000, and the maximum number is _ _ _ _ wrong answer 9999 correct answer 14999.
Comment on examples
The approximate value obtained by rounding may be not only "five inputs" but also "four inputs".
14. Number size sorting problem: pay attention to the size order required by the topic.
For related examples, put 3. 14,? On 22nd/7th, _ _ _ _ _ _ wrong answers are arranged in descending order. 3. 14.
Comment on examples
Ask any questions you want, and don't fool around. And be sure to write the original number sorting.
15. Scale problem: pay attention to the scale of the area.
Related examples On the sand table with the scale of 1:2000, the ecological park with an actual area of 800,000 square meters is _ _ _ _ square meters. Wrong answer 400, correct answer 0.2.
Comment on examples
Many students directly use 800 thousand? In 2000, I got the wrong answer. Remember, scale = distance on the map: the actual distance is the scale of the length, that is, the length unit of 1 on the map is the actual length unit of 2000. But this problem involves area and needs to be converted into the proportion of area. The ratio of square length is required, that is, the area unit of 1 on the drawing is the actual area unit of 4000000.
16. Positive-negative ratio problem: the meaning of positive-negative ratio is not clear.
True or false: The area of a circle is proportional to its radius. Wrong answer? Correct answer?
Comment on examples
If the product of two quantities is a constant value, it is inversely proportional; If the quotient of two quantities is a constant value, then it is proportional. Strict definition, originally changed to "the area of a circle is proportional to the square of the radius", is correct.
17. Comparison question: Pay attention to the order of the previous items.
Related examples
When the side length of a square increases by 1/3, the ratio of the area of the original square to the area of the new square is _ _ _ _ _ _ _.
Wrong answer 16:9 correct answer 9: 16
Comment on examples
Who is the first item and who is the second item? Be sure to open your eyes and see clearly!
18. Ratio problem: the difference between ratio and ratio
Related examples
When the side length of a square increases by 1/3, the ratio of the area of the original square to that of the new square is _ _ _ _ _.
Wrong answer 9: 16 correct answer 9: 16 example evaluation ratio is a result, a number.
19. Unit problem: Don't leave out the unit.
Related examples
The area of a square with a side length of 4 cm is _ _ _ _ _ _.
Wrong answer 16 correct answer 16 cm2.
Comment on examples
Area problem, the result is correct, but the unit that should be written is not written, just like a traveler in the desert, dying of thirst by the river near at hand. What a pity! Pathetic! Ridiculous! Alas!
20. Unit problem: Pay attention to the consistency of the unit.
Related examples
A flour bag is marked with (25kg plus or minus 50g), and the heaviest weight of this flour is ___kg.
Wrong answer 75 correct answer 25.05
Comment on examples
Many students didn't see that the units of kg and g were inconsistent, and directly gave the wrong answer of 75.
2 1. leap year, flat year problem: the concept of leap year is unclear.
Related examples
1900 is a leap year or a normal year?
Wrong answer leap year correct answer flat year
Comment on examples
Jump in four years, not in a hundred years, and jump again in four hundred years. If a year is a multiple of 4, it is a leap year; Otherwise it will be a normal year. But if it is a whole hundred years (for example,1900,2000), then it must be a multiple of 400 to be considered as a leap year, otherwise it is a flat year.
22. Solve the equation problem: the minus sign is in front of the brackets, and the number should be changed if the brackets are removed! Move the item to change the logo!
Related examples
6? 2(2X？ 3)=4
Wrong answer Other correct answers x=2
Comment on examples
Remove the bracket. If there is a minus sign in front of the bracket, please change it! Move the item (a number moves left and right on both sides of the equal sign) to change the symbol, remember!
23. Calculation problem: Keep in mind the operation order.
Related example 20? 7? 1/7 wrong answer 20 correct answer 20/49
Comment on examples
In the 530 exam, the trend of "de-technicalization" of calculation questions is obvious. This paper focuses on the basic calculation skills such as the operation of four fractions, the operation sequence and the extraction of common factors.
24. The average speed problem
Related examples Xiaoming's climbing speed is 1 m/s, and his downhill speed is 3 m/s, so Xiaoming's average climbing speed is _ _ _ wrong answer (1+3)? 2=2 (m/s) The correct answer is that the whole journey up the mountain is 3 meters, and the average speed is: (3? 2)? (3? 1+3? 3)= 1.5 (m/s)
The definition of average speed is: total distance? total time
25. There are many topics.
Related examples The degree of an angle of an isosceles triangle is 50 degrees, so its vertex angle is _ _ _ _ 80 degrees, which is the wrong answer, and 50 degrees or 80 degrees is the correct answer.
Comment on examples
Many types of problems usually have more than one result. Students must pay attention to the rigor of thinking, sum up more when doing problems at ordinary times, and try to take all the situations into account. Don't give an answer and think you're done.
26. Pay attention to the integrity of expression.
Related examples The ratio of three internal angles of a triangle is 1: 1:2, which is a _ _ _ _ _ triangle. Wrong answer isosceles triangle correct answer isosceles right triangle
Comment on examples
This kind of topic, only when training at ordinary times, think more and summarize more, can ensure that the exam will not make mistakes.
Knowledge points of mathematics compulsory examination in Xiaoshengchu
Definition, Theorem and Formula of Necessary Memory
Area of triangle = bottom? Tall? 2。 Formula S= a? h？ 2
Area of a square = side length? The side length formula S= a? a
Area of rectangle = length? The broad formula S= a? b
Area of parallelogram = bottom? High formula S= a? h
Area of trapezoid = (upper bottom+lower bottom)? Tall? 2 formula S=(a+b)h? 2
Sum of internal angles: sum of internal angles of triangle = 180 degrees.
Volume of cuboid = length? Wide? High formula: V=abh
Volume of cuboid (or cube) = bottom area? High formula: V=abh
Volume of cube = side length? Side length? Side length formula: V=aaa
Circumference = diameter formula: L=? d=2？ r
Area of circle = radius? Radius formula: S=? r2
Surface (side) area of cylinder: The surface (side) area of cylinder is equal to the perimeter of bottom multiplied by height. Formula: S=ch=? dh=2？ right hand
Surface area of cylinder: the surface area of cylinder is equal to the perimeter of the bottom multiplied by the height plus the area of the circles at both ends. Formula: S=ch+2s=ch+2? r2
Volume of cylinder: the volume of cylinder is equal to the bottom area multiplied by the height. Formula: V=Sh
The volume of the cone = 1/3 bottom? Cumulative height formula: V= 1/3Sh.
Law of fractional addition and subtraction: Fractions with the same denominator are added and subtracted, only the numerator is added and subtracted, and the denominator remains the same. Fractions of different denominators are added and subtracted, first divided, then added and subtracted.
The multiplication of fractions is: use the product of molecules as numerator and the product of denominator as denominator.
The law of division of fractions: dividing by a number is equal to multiplying the reciprocal of this number.
Arithmetic aspect
1, additive commutative law: Two numbers are added to exchange the position of addend, and the sum is unchanged.
2. Law of additive combination: When three numbers are added, the first two numbers are added first, or the last two numbers are added first, and then the third number is added, and the sum remains unchanged.
3. Multiplication and exchange law: when two numbers are multiplied, the position of the exchange factor remains unchanged.
4. Multiplication and association law: When three numbers are multiplied, the first two numbers are multiplied, or the last two numbers are multiplied first and then the third number, and their products are unchanged.
5. Multiplication and distribution law: When two numbers are multiplied by the same number, you can multiply the two addends by this number respectively, and then add the two products, and the result remains unchanged. Such as: (2+4)? 5=2? 5+4? five
6. Nature of division: In division, the dividend and divisor are expanded (or reduced) by the same multiple at the same time, and the quotient remains unchanged. Divide by any number that is not.
Simple multiplication: multiplication of multiplicand and multiplier with O at the end. You can multiply 1 before o first, and zero does not participate in the operation, and add a few zeros at the end of the product.
7. What is an equation? An equation in which the value on the left of the equal sign is equal to the value on the right of the equal sign is called an equation.
Basic properties of the equation: When both sides of the equation are multiplied (or divided) by the same number at the same time, the equation is still valid.
8. What is an equation? A: Equations with unknowns are called equations.
9. What is a linear equation with one variable? A: An equation with an unknown number of degree 1 is called a linear equation with one variable.