Summary of knowledge points that must be tested in junior high school mathematics exam and are most prone to mistakes
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
Follow the topic you asked, don't be silly. 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
The 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 close 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.
Xiaoshengchu mathematical formula summary, the exam is necessary!
Geometric formula
? ? The circumference of a rectangle = (length+width)? 2
C=(a+b)？ 2
? Area of rectangle = length? extensive
S=ab
? ? Perimeter of a square = side length? four
C=4a
? Area of a square = side length? Length of side
a=a
? ? Area of triangle = bottom? Tall? 2
S = huh? 2
? The sum of the internal angles of the triangle = 180 degrees.
? ? Area of parallelogram = bottom? high
S = ah
? ? Area of trapezoid = (upper bottom+lower bottom)? Tall? 2
S=(a+b)h？ 2
? ? Diameter of a circle = radius? 2(d=2r)
? Radius of a circle = diameter? 2(r=d？ 2)
? Circumference = pi? Diameter = pi? Radius? 2
C=？ d =2？ r
? Area of a circle = pi? Radius? radius
S=？ r？ r
? ? Volume of cuboid = length? Wide? high
V=abh
? ? Volume of cube = side length? Side length? edge
V=aaa
? ? Lateral area of a cylinder: the lateral area of a cylinder is equal to the perimeter of the bottom multiplied by the height.
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.
S=ch+2s=ch+2？ r？ r
? Volume of cylinder: the volume of cylinder is equal to the bottom area multiplied by the height.
V=Sh
? ? The volume of the cone = 1/3 bottom? High skill
V= 1/3Sh
Unit conversion
? 1 km = 1 km =1000m
1 m = 10 decimeter
1 decimeter = 10/0cm
1 cm = 10/0mm
? 1 m2 = 100 square decimeter
1 square decimeter = 100 square centimeter
1 cm2 = 100 mm2
? 1 m3 = 1000 cubic decimeter
1 cubic decimeter = 1000 cubic centimeter
1 cm3 = 1000 cm3
? 1 ton = 1000 kg
1 kg = 1 000g =1kg =2 kg
? 1 ha = 1 10,000 m2
1 mu =666.666 m2
? 1 l = 1 decimeter cubic = 1000 ml
1 ml = 1 cm3
? 1 yuan = 10 angle.
1 angle = 10 point
1 yuan = 100 integral.
? 1 century = 100 year
1 year = 65438+ February.
The big month (3 1 day) is: 65438+August.
Abortion (30 days) is April.
February 28th in a normal year and February 29th in a leap year.
There are 365 days in a normal year and 366 days in a leap year.
1 day =24 hours
1 hour =60 minutes =3600 seconds
1 min =60 seconds
magnitude relation
? Per share? Number of copies = total number
Total? Number of copies = number of copies
Total? Number of copies = number of copies
? Multiply by 1? Multiple = multiple
How many times? 1 multiple = multiple
How many times? Multiplication = 1 multiplication
? Speed? Time = distance
Distance? Speed = time
Distance? Time = speed
? Unit price? Quantity = total price
Total price? Unit price = quantity
Total price? Quantity = unit price
? Work efficiency? Working hours = total amount of work
Total amount of work? Working efficiency = working hours
Total amount of work? Working hours = working efficiency
? Appendix+Appendix = Sum
And-one addend = another addend
? Negative-negative = difference
Negative difference = negative
Difference+Minus = Minus
? Factor? Factor = product
Product? One factor = another factor
? Dividend? Divider = quotient
Dividend? Quotient = divisor
Business? Divider = dividend
special problem
? encounter a problem
Meeting distance = speed and? Meeting time
Meeting time = meeting distance? Speed sum
Speed sum = meeting distance? Meeting time
? Catch up with the problem
Chasing distance = speed difference? Catch up with time
Catch-up time = catch-up distance? speed difference
Speed difference = catching distance? Catch up with time
? Tap water problem
(1) general formula:
Downstream velocity = still water velocity+current velocity
Countercurrent velocity = still water velocity-current velocity
Still water velocity = (downstream velocity+countercurrent velocity)? 2
Water velocity = (downstream velocity-countercurrent velocity)? 2
(2) Formula for two ships sailing in opposite directions:
Downstream speed of ship A+downstream speed of ship B = still water speed of ship A+still water speed of ship B.
(3) Formula for two ships sailing in the same direction:
Hydrostatic speed of rear (front) ship-Hydrostatic speed of front (rear) ship = the speed of narrowing (expanding) the distance between two ships.
? Concentration problem
Solute weight+solvent weight = solution weight.
The weight of solute? The weight of the solution? 100%= concentration
The weight of the solution? Concentration = weight of solute
The weight of solute? Concentration = solution weight
? Profit and discount problem
Profit = selling price-cost
Profit rate = profit? Cost? 100%= (price? Cost-1)? 100%
Upper and lower amount = principal? Percentage of increase and decrease
Discount = actual selling price? Original price? 100% (discount
Interest = principal? Interest rate? time
Interest after tax = principal? Interest rate? Time? ( 1-5%)
? Engineering problems
Work efficiency? Working hours = total amount of work
Total amount of work? Working hours = working efficiency
Total amount of work? Working efficiency = working hours
1? Working time = how much is the total workload completed in unit time?