People's education printing plate sixth grade mathematics second volume midterm examination paper

Must recite the formula that defines the theorem?

Volume and surface area?

Area of triangle = base × height ÷2. ? Formula? S=？ a×h÷2？

Area of a square = side length × side length? Formula? S=？ a2？

Area of rectangle = length × width? Formula? S=？ a×b？

Area of parallelogram = base × height? Formula? S=？ a×h？

Trapezoidal area = (upper bottom+lower bottom) × height ÷2? Formula? S=(a+b)h÷2？

Sum of internal angles: sum of internal angles of triangle = 180 degrees. ?

Surface area of cuboid = (length× width+length× height+width× height? )? ×2? Formula: S=(a×b+a×c+b×c)×2?

Surface area of cube = side length × side length ×6? Formula:? S=6a2？

The volume of a cuboid = length × width × height? Formula: v? =? abh？

Volume of cuboid (or cube) = bottom area × height? Formula: v? =? abh？

Volume of cube = side length × side length × side length? Formula: v? =? a3？

Circumference = diameter × π? Formula: l = π d = 2π r?

Area of circle = radius × radius× π? Formula: s = π 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 = π DH = 2π RH?

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+2πr2?

Volume of cylinder: the volume of cylinder is equal to the bottom area multiplied by the height. Formula: V=Sh?

Volume of cone = 1/3 bottom× product height. Formula: V= 1/3Sh?

arithmetic

1, additive commutative law: Two numbers are added to exchange the position of addend, and the sum is unchanged. ?

2. additive associative law: a? +? b？ =? b？ +? Answer?

3. Multiplicative commutative law: A? ×? b？ =? b？ ×? Answer?

4. the law of multiplicative association: a? ×? b？ ×? c？ =? Answer? ×(b？ ×? c)？

5. Multiplication and distribution law: A? ×? b？ +? Answer? ×? c？ =? Answer? ×? b？ +? c？

6. the nature of division: a? ÷? b？ ÷? c？ =? Answer? ?(b？ ×? c)？

7. 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 o to get o? 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. ?

8. Division with remainder:? Dividend = quotient × divisor+remainder?

Equations, algebras and equations?

Equation: An equation in which the value on the left of the equal sign equals 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. ?

Equation: An equation with an unknown number is called an equation. ?

One-dimensional linear equation: including an unknown number, the number of unknown numbers? One of the equations whose number is once is called a linear equation with one variable. Example method and calculation of learning linear equation of one variable. That is, an example is given to illustrate that the formula is replaced by χ and calculated. ?

Algebra: Algebra means replacing numbers with letters. ?

Algebraic expression: Expressions expressed by letters are called algebraic expressions. Like 3x? =ab+c？

Scores?

Fraction: divide the unit "1" into several parts on average, and the number representing such a part or points is called a fraction. ?

Comparison of fraction size: Compared with the fraction of denominator, the numerator is large and the numerator is small. Compare the scores of different denominators, divide them first and then compare them; If the numerator is the same, the denominator is big and small. ?

Addition and subtraction of fractions: add and subtract fractions with the same denominator, only add and subtract numerators, and the denominator remains the same. Fractions of different denominators are added and subtracted, first divided, then added and subtracted. ?

Fraction multiplied by integer, numerator is the product of fractional and integer multiplication, denominator remains unchanged. ?

Fractions are multiplied by fractions, the product of numerator multiplication is numerator, and the product of denominator multiplication is denominator. ?

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 unchanged. Fractions of different denominators are added and subtracted, first divided, then added and subtracted. ?

The concept of reciprocal: 1 If the product of two numbers is 1, we call one of them the reciprocal of the other. These two numbers are reciprocal. The reciprocal of 1 is 1, and 0 has no reciprocal. ?

A fraction divided by an integer (except 0) is equal to this fraction multiplied by the reciprocal of this integer. ?

The basic nature of a fraction: the numerator and denominator of a fraction are multiplied or divided by the same number (except 0). What is the size of the score?

The law of division of fractions: dividing by a number (except 0) is equal to multiplying the reciprocal of this number. ?

True fraction: The fraction with numerator less than denominator is called true fraction. ?

False fraction: Fractions with numerator greater than denominator or numerator equal to denominator are called false fractions. False score is greater than or equal to 1. ?

With a score: write a false score as an integer, and a true score is called with a score. ?

The basic nature of the fraction: the numerator and denominator of the fraction are multiplied or divided by the same number (except 0) at the same time, and the size of the fraction remains unchanged. ?

What is the formula for calculating the quantitative relationship?

Unit price × quantity = total price? 2. Single output × quantity = total output?

Speed × time = distance? 4. Work efficiency x time = total workload?

Appendix+Appendix = sum? One addend = and+ another addend?

Minus-Minus = Difference? Subtraction = minuend-difference? Minus = Minus+Difference?

Factor × factor = product? One factor = product ÷ another factor?

Dividend = quotient? Divider = Divider? Dividend = quotient × divisor?

Length unit:?

1 km = 1 km? 1 km = 1000 m？

1 m = 10 decimeter? 1 decimeter =10cm? 1 cm = 10 mm？

Area unit:?

1 km2 = 100 hectare? 1 ha =10000m2?

1 m2 = 100 square decimeter? 1 square decimeter = 100 square centimeter? 1 cm2 = 100 mm2？

1 mu = 666.666 square meters. ?

Unit of volume?

1 m3 = 1000 cubic decimeter? 1 cubic decimeter = 1000 cubic centimeter?

1 cm3 = 1000 cm3?

1 liter = 1 cubic decimeter = 1000 ml? 1ml = 1cm3？

Weight unit?

1 ton = 1000 kg? 1 kg =？ 1000g =? 1 kg =？ 1 kg?

Than?

What is the ratio? When two numbers are divided, it is called the ratio of two numbers. Such as: 2÷5 or 3:6 or 1/3? The first and second items of the ratio are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged. ?

What is proportion? Two formulas with equal ratios are called proportions. Such as 3: 6 = 9: 18?

The basic property of proportion: in proportion, the product of two external terms is equal to the product of two internal terms. ?

Solution ratio: the unknown term in the proportion is called solution ratio. Such as 3: χ = 9: 18?

Proportion: two related quantities, one of which changes and the other changes. If the ratio (i.e. quotient k) corresponding to these two quantities is constant, these two quantities are called proportional quantities, and the relationship between them is called proportional relationship. For example: y/x=k (? K must) or kx=y?

Inverse proportion: two related quantities, one of which changes and the other changes accordingly. If the product of the corresponding two numbers in these two quantities is certain, these two quantities are called inverse proportional quantities, and their relationship is called inverse proportional relationship. ? Such as: x×y? =? k(？ K) or k? /? x？ =? y？

Percentage?

Percentage: a number that indicates that one number is a percentage of another number, which is called percentage. Percentages are also called percentages or percentages. ?

To convert decimals into percentages, just move the decimal point two places to the right and add hundreds of semicolons at the end. In fact, to convert a decimal into a percentage, just multiply this decimal by 100%. To convert percentages to decimals, simply remove the percent sign and move the decimal point two places to the left. ?

When a fraction is converted into a percentage, the fraction is generally converted into a decimal (three decimal places are generally reserved when it is not used up), and then the decimal is converted into a percentage. In fact, to turn a fraction into a percentage, you must first turn the fraction into a decimal and then multiply it by 100%. ?

Divide the percentage into components, and rewrite the percentage into components first, so that the quotation that can be lowered can be made into the simplest score. ?

We should learn to decompose fractions into components and fractions into decimals. ?

Multiplication and reduction?

Maximum common divisor: The common divisor of several numbers is called the common divisor of these numbers. There is a finite common factor. The largest one is called the greatest common divisor of these numbers. ?

Least common multiple: The common multiple of several numbers is called the common multiple of these numbers. There are infinite common multiples. The smallest one is called the least common multiple of these numbers. ?

Prime number:? The common divisor is only 1, which is called a prime number. Two adjacent numbers must be prime numbers. Two consecutive odd numbers must be coprime. 1 and any number coprime. ?

Comprehensive score: the difference between scores of different denominators is changed into the same denominator score equal to the original score, which is called comprehensive score. (General division uses the least common multiple)?

Decrement: divide the numerator and denominator of a fraction by the common divisor at the same time, and the fraction value remains unchanged. This process is called dropping points. ?

Simplest fraction: The numerator and denominator are fractions of prime numbers, which are called simplest fraction. At the end of the score calculation, the score must be converted into the simplest score. ?

Prime number (prime number): If a number only has 1 and its two divisors, it is called a prime number (or prime number). ?

Composite number: a number. If there are other divisors besides 1 and itself, such numbers are called composite numbers. 1 is neither prime nor composite. ?

Prime factor: If a prime number is a factor of a certain number, then this prime number is the prime factor of this number. ?

Prime factorization: Representing a composite number in a complementary way of prime factors is called prime factorization?

Multiplication characteristics:?

Characteristics of multiples of 2: You are 0, 2, 4, 6, 8. ?

Characteristics of multiples of 3 (or 9): The sum of the numbers on each digit is multiples of 3 (or 9). ?

Characteristics of multiples of 5: You are 0, 5. ?

Characteristics of multiples of 4 (or 25): The last two digits are multiples of 4 (or 25). ?

Characteristics of multiples of 8 (or 125): the last three digits are multiples of 8 (or 125). ?

Characteristics of multiples of 7 (1 1 or 13): the difference (big-small) between the last three digits and other digits is a multiple of 7 (1 1 3). ?

Characteristics of multiples of 17 (or 59): the difference (big-small) between the last three digits and the rest digits is a multiple of 17 (or 59). ?

Characteristics of multiples of 19 (or 53): the difference (big-small) between the last three digits and other seven digits is a multiple of 19 (or 53). ?

Characteristics of multiples of 23 (or 29): The difference (big-small) between the last four digits and the other five digits is multiples of 23 (or 29). ?

Of the two numbers in the multiple relation, the greatest common divisor is smaller and the smallest common multiple is larger. ?

The coprime relation between two numbers, the greatest common divisor is 1, and the least common multiple is the product. ?

When two numbers are divided by their greatest common divisor, the quotient is coprime. ?

The product of two numbers and the least common multiple is equal to the product of these two numbers. ?

The common divisor of two numbers must be the greatest common divisor of these two numbers. ?

1 is neither prime nor composite. ?

A prime number greater than 3 divided by 6 must get 1 or 5. ?

Odd and even numbers?

Even numbers: Numbers are numbers of 0, 2, 4, 6 and 8. ?

Odd number: The number is not 0, 2, 4, 6 or 8. ?

Even = even? Odd odd = odd? Odd even number = odd number?

Even numbers add up to even numbers, and odd numbers add up to odd numbers. ?

Even × even = even? Odd × odd = odd? Odd × even = even?

The sum of two adjacent natural numbers is odd, and the product of adjacent natural numbers is even. ?

If one number in the multiplication is even, then the product must be even. ?

Odd ≠ even?

Can be divided?

If c | a,? C | b, then c | (a b)?

If, then b | a,? c|a？

If b | a,? C | a, and (b, c)= 1,? So BC | a?

If c | b,? b|a，？ So c | a?

Decimal?

Natural number: an integer used to represent the number of objects, called natural number. 0 is also a natural number. ?

Pure Decimal: Decimal in units of 0. ?

With Decimal: Decimal with more than 0 digits. ?

Cyclic decimal: a decimal, starting from a certain bit of the decimal part, and one or several numbers are repeated in turn. Such decimals are called cyclic decimals. Like 3. 14 14 14?

Acyclic decimal: a decimal, starting from the decimal part, without one number or several numbers appearing repeatedly. Such a decimal is called acyclic decimal. Like 3. 14 1592654?

Infinite cycle decimal: a decimal, from the decimal part to the infinite digits, and one or several numbers are repeated in turn. Such decimals are called infinite cyclic decimals. Like 3. 14 14 14……?

Infinite acyclic decimal: a decimal, from decimal part to infinite digits, is called infinite acyclic decimal without one number or several numbers appearing repeatedly. Like 3. 14 1592654……?

Profit?

Interest = principal × interest rate× time (time is usually in years or months, which should correspond to the interest rate)?

Interest rate: The ratio of interest to principal is called interest rate. The ratio of one year's interest to principal is called the annual exam description: this question 15, full mark 120, and the answer time is 90 minutes. ?

1. Fill in the blanks:?

1, two digits. Divided by 58+2, 73+3, 85+ 1. This two-digit number is 14.

2. 173□ is a four-digit number. The math teacher said, "I filled in three numbers one by one in this □, and the three four-digit numbers I got were divisible by 9, 1 1 and 6 in turn." Then the sum of the three numbers filled in in turn is 19. ?

3. What's the score? A in is a natural number, in order to make this score reducible,? A the minimum value is 1 1.

A five-digit number plus 200,000, after tripling, the result is exactly the same as that of the right-hand side of the five-digit number plus 2. This five-digit number is _ _ _ _ _ _ _. ?

5. A worker put the parts into two kinds of boxes, each big box contains 12 parts, and each small box contains 5 parts, which is just finished. If the number of parts is 99 and the number of boxes is greater than 10, it is 8 and 5 boxes respectively. ?

6. When the goods with the unit price of 40 yuan are sold in 50 yuan, the profit per piece is 10 yuan, but only 500 pieces can be sold. It is known that the sales volume of this kind of goods will decrease by 1 0 for every price increase of1yuan. In order to make the biggest profit, the selling price should be set at? Yuan. ?

7. Two cups are filled with 40% and 10% salt solution respectively, and the concentration is 30% after being poured together. If you add 300 grams of 20% salt solution, the concentration will become 25%. What about the original 40% salt solution? Dick. ?

8. At a certain moment, the hour hand of the clock is between 10 and 1 1. Six minutes later, the minute hand is exactly opposite to the hour hand three minutes ago and is in a straight line. What is the time indicated by the clock at the moment? . ?

9. Grandpa is six times older than Xiaoming this year. In a few years, my grandfather will be five times as old as Xiaoming. In a few years, my grandfather will be four times as old as Xiaoming. Q: How old is my grandfather this year? ?

10, the film crew had a one-day trip from city a to city b, and planned to walk more in the morning than in the afternoon 100 km to go to city c for lunch. Because of the traffic jam, they arrived at a small town at noon, only one third of the original plan was opened. After crossing the town, the car traveled 400 kilometers and then stopped to have a rest in the evening. The driver said, from C City to here, we have to walk half way. Kilometers?

Second, answer the question:?

1 1. As shown in the right figure, AD, BE and CF divide △ABC into six small triangles, and the areas of the four small triangles have been marked on the figure. Try to find the area of △ABC. (unit: square centimeter)?

12. My mother gave Honghong some money to buy New Year cards. There are three kinds of New Year cards: A, B and C. The first card is 0.50 yuan each, and the third card is 1.20 yuan. Using this money to buy a card is more than 8 cards for B card, and 6 cards for B card. How much did mom give Hong Hong? How much is the second card? ?

13. The escalator runs from bottom to top at a constant speed. Two impatient children thought that the escalator was running too slowly, so on the escalator, the boy walked up 1 step every second and the girl walked 2 steps every 3 seconds. As a result, boys go upstairs in 50 seconds and girls go upstairs in 60 seconds. How many steps does this escalator have? ?

14. A workshop plans to finish the task of processing a batch of parts in five days. What happened on the first day? Too much 120, and the rest will be handled the next day? 150 pieces are missing, and the rest will be handled on the third day? More than 80, and the rest will be dealt with on the fourth day? 20 pieces were missing, and finally 1800 pieces were processed on the fifth day. How many parts are there in this batch?

15, a and b from? 、? After driving in opposite directions for 6 hours, the two cities can meet somewhere on the way. A car failed to track on the way, and it took 2.5 hours to continue driving. So it took 7.5 hours from departure to meeting. So, where did it come from? Where is the city? How many hours are there in this city? ?

Interest rate. The ratio of interest to principal in January is called monthly interest rate. ?

Mid-term examination questions of sixth grade mathematics in primary school?

Class:? Name:? Grade:?

Fill in the blanks. ?

1、0.7÷5? =? 7:(? )? =? =(? )%。 ?

2.5A=4B(A and B are not equal to 0). A: B = (? ):(? )。 ?

3、? :? The ratio of the simplest integer is (? )。 ?

4. What if? =? Then a and b become (? ) proportional relationship. ?

5. What is the volume of a cylinder whose bottom diameter and height are 6 decimeters? )。 ?

6. The radius of the cylinder bottom is 5m, the volume is157m3, and the height is (? ) meters. ?

7. In proportion, two internal terms are reciprocal and one external term is? Another external project is (? )。 ?

8. a rectangular piece of land, 75 meters long and 30 meters wide, is there? Draw it on the picture, draw it long (? ), widely painted (? )。 ?

9. The radius of the bottom of the cylinder is 2 cm and the height is 2 cm. Its side expansion diagram is (? ) shape, the circumference of this figure is (? ) cm, with an area of (? ) square centimeters. ?

10、? : The ratio of 8 is (? ), if you use it to write a ratio, this ratio can be (? )。 ?

1 1. It is known that the relationship between A, B and C is A ÷ B = C. If A is certain, then B and C become (? ) proportional relationship, if c is certain, a and b become (? ) proportional relationship. ?

12, what is the proportion of those who passed the math contest in grade six to those who failed? The passing rate of sixth-grade students in this competition is (? )。 ?

13, the sum of the minuend, subtraction and difference is 40, the ratio of subtraction and difference is 3:2, and the minuend is (? ), the subtraction is (? )。 ?

14, a kind of brine, is made by mixing salt and water at the ratio of 1: 100. Now prepare 8008 grams of salt water, salt (? ) kg. ?

15, the two external terms of a ratio are 5 and 6 respectively, and their ratio is 3, then (? )。 ?

16. On the map of China with the scale of 1: 400000, the distance between the two places is 30 cm. What is the actual distance between the two places? ) kilometers. ?

17、(? ) The statistical chart can not only show the quantity, but also clearly show the change of quantity. ?

18, a certain length of iron wire is divided into several sections on average, and the length of each section is equal to the number of sections (? ) proportion. ?

Second, choose. ?

1, the following ratios can be compared? :? The ratio is (? )。 ?

①3:4? ②4:3? ③? :? ④? :3?

2. Put 1 g salt into100g water, and the ratio of salt to brine is (? )。 ?

① 100: 10 1? ② 1: 10 1? ③ 1:99? ④ 1: 100?

3. In proportion, the product of two external terms is certain, and the two internal terms become (? )。 ?

1 ratio? ② Inverse proportion? 3 disproportionate? 4 can't judge?

4, the existing three numbers 9, 3,? , select (? ) can form a proportion. ?

①? ②? ④4? ④2?

5. Solution ratio? =2: 1,χ=(? )。 ?

①6? ② 1.5? ③0.7? ④9?

6. Two reciprocal numbers, they must be (? )。 ?

1 ratio? ② Inverse proportion? 3 out of proportion? 4 can't judge?

7. What is the height-to-weight ratio of Xiao Wang? )。 ?

1 ratio? ② Inverse proportion? 3 out of proportion? 4 can't judge?

8, small circle radius of 2 cm, big circle radius of 3 cm, the ratio of small circle area to big circle area (? )。 ?

①2:3? ②3:2? ③4:9? ④9:4?

9. For a project, the ratio of completed projects to this project is 3:5, and (? )。 ?

①60%? ②40%? ③20%? ④ 166.6%?

10, the distance on the map is 3cm, the actual distance is 1.5mm, and the scale is (? )。 ?

① 1:20? ② 1:2? ③ 1:200? ④20: 1?

1 1, the class size is certain, and the number of attendees and absentees (? )。 ?

1 ratio? ② Inverse proportion? 3 disproportionate? 4 can't judge?

12, a cylinder, if the height is constant, the bottom area will be expanded by 3 times and the volume will be expanded (? )。 ?

①3 times? 26 times? ③9 times? ④27 times?

Third, the judge. ?

1. The total amount of money subscribed to Little Torch is directly proportional to the number of copies ordered. ? (? )?

2. Legends should be used to make composite bar charts. (? )?

3. What is the scale? On the map, 1cm indicates that the actual distance is 20km. ? (? )?

There are 55 students in the class, the ratio of male to female is 5:6, so there are 30 boys in this class. (? )。 ?

5. The lateral area of two cylinders is equal, and their bottom perimeters are equal. ? (? )?

6. In proportion, the product of two external terms is 10? One is 5, and the other is 5. (? )?

7、? =B, then a and b are inversely proportional. ? (? )?

8. The circumference and diameter of a circle must be in direct proportion. ? (? )?

Fourth, the solution ratio. ?

=? :? =? :χ? =?

40:χ=2.5: 15? :χ=5: 16? :? =20:χ?

Five, according to the following data, calculate the pass rate of each class to participate in the competition, and then make statistics. ?

Six (1) classes 16 students, 12 students passed; ? 6 (2) class 15 students, 13 students passed; ?

Class 6 (3) 1 1 person, 8 people passed. ?

Interviewee:? xyywendy？ -? Assistant? Level two? 4- 10? 8: 30 p.m.

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