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+A.

3. Multiplicative commutative law: a× b = b× a.

4. Multiplicative associative law: a × b × c = a ×(b × c)

5. Multiplicative distribution law: a× b+a× c = a× b+c.

6. The nature of division: a ÷ b ÷ c = a ÷(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.

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

Second, the equation, algebra and equality

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: An equation with an unknown number of degree 1 is called a one-dimensional linear equation. 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. For example 3x = AB+C.

Three. Volume and surface area

Area of triangle = base × height ÷2. The formula S= a×h÷2.

Area of 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.

The surface area of a 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.

Cuboid volume = 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=πd=2πr

Area of circle = radius × radius× π formula: S=πr2.

Surface (side) area of cylinder: The surface (side) area of cylinder is equal to the perimeter of bottom multiplied by height. Formula: S=ch=πdh=2πrh.

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

Fourth, the score.

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 properties of a fraction: the numerator and denominator of a fraction are multiplied or divided by the same number (except 0), and the size of the fraction.

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.

First, fill in the blanks. (28 points)

1. Party A and Party B each go a little way. Their speed ratio is 3: 4 and their distance ratio is 7: 3, so the time ratio they need is ().

2. Rounding 0.5395 to one thousandth is ().

3. If the length of a cuboid is 120cm and the ratio of length to width is 2: 2: 1, then at most () faces of this cuboid are equal in size.

4. A semicircle with a radius of r and a perimeter of ().

5. The sum of three numbers is l20, the number A is twice that of B, the number C is 20 more than that of B, and the number C is ().

6. When a number is divided by a number, the quotient is 4 and the remainder is 3. If this number,

Both of them are expanded by 10 times at the same time. The quotient is () and the remainder is ().

The reciprocal of 7 is greater than the reciprocal of 7, then (

) 。

8. An express train and a local train leave from A and B respectively at the same time, and meet after l2 hours. The express train will travel to B for another 8 hours, so the local train will still travel after meeting (

) arrive at a place in an hour.

9. The length-width ratio of a rectangle is 4: 3, with an area of 432 square centimeters and a circumference of () centimeters.

10. If the sum of the reciprocal of three prime numbers is, then these three prime numbers are (), () and () respectively.

1 1. As shown below, the rectangle ABCD is divided into two rectangles, AB: AE = 4: 1. The area of the shaded triangle in the figure is 2 square decimeters, and the area of the rectangular ABCD is (

) Square decimeter.

12. Close to a fence, use a bamboo fence with a length of18m to enclose a rectangular vegetable field (the side length is an integer), and the largest area of this vegetable field is () square meters.

13. build an 80-meter-long expressway, and the rest is repaired, and () meters have been repaired. 14. The sum of the number A and the number B is 60, and the number A is exactly equal to the number B. The sum of numbers a and b is ().

15. 100 grams of water and 20 grams of sugar, the sugar content of sugar water is about ()%.

16. Then: = (

):( )。

17. The diameter of the semicircle is 6 decimeters, the circumference is () decimeters, and the area is () square decimeters.

18. The height of a cube is increased by 3 cm, and a new cuboid is obtained. The surface area of this cuboid is increased by 60cm compared with the original cube, and the surface area of the original cube is (

) square centimeters.

19. If number A is equal to number B, number A is 18, number B is (), and number A is ()% more than number B..

20. If the length and width of a rectangle with a circumference of 46 decimeters increase by10cm, the area will increase by () square decimeters.

2 1. Divide a circle with a circumference of 628 cm into four parts with the same shape, and the circumference of each part is () cm.

22. Turn it into a cyclic decimal. The 50th digit of the decimal part of this cyclic decimal is ().

Second, the judgment question. (5 points)

1. The volume difference between a cylinder and a cone with equal bottom and equal height is 4.6 cubic centimeters. The volume of this cylinder is 6.9 cubic centimeters. ( )

If the length and width of a rectangle are increased by 5 meters and 4 meters respectively, its area will increase by 20 square meters. ( )

3. When two numbers are divided, the quotient is 0.96. If the dividend is enlarged by 10 times and the divisor is reduced by 100 times, their quotient is 9.6. ( )

4. Infinite decimal must be greater than finite decimal. ( )

5.5 is 25% more than 4, and 4 is 20% less than 5. ( )

Third, multiple choice questions. (5 points)

1. If the radius of the bottom surface of a cone is enlarged by 2 times and the height is reduced by half, then its volume is the original volume ().

A.2 times B. half C. constant D. uncertainty

2. There are five cards, the numbers on which are 0, 4, 5, 6 and 7 respectively, and the three digits divisible by 4 are ().

a . 1 1 b . 12 c . 10d . 15

A village produced 300,000 Jin of apples a year ago, which increased by 20% last year and decreased by 20% this year. This year's output is () ten thousand kilograms.

3 1

4. A two-digit number divided by 5 is greater than 3, and divided by 7 is greater than 5. The maximum value of this two-digit number is ().

A.72 B.37 C.33 D.68

5. There are more boys than girls in a certain class, and boys are equivalent to () in the whole class. University of California, Los Angeles.

Fourth, the oral calculation questions. (8 points)

Fifth, the calculation problem. (8 points)

1.

2.

3.

4.97×2000-96×200 1

Sixth, the graphic calculation problem. (8 points)

1. As shown below, the area of triangle ABC is 70 square centimeters, BD=CD=6 centimeters, and ∠ C = 45. Find the area of the shaded part.

2. As shown in the figure below, the side length of square ABCD is 4cm, AE=2BE, and the area of triangular CDF is found.

Seven, application questions. (26 points)

1. There are 48 floats in a row. Each float is 4 meters long and the float spacing is 6 meters. How many meters is this float? (3 points)

2. Xiao Ming reads story books and reads 18 pages every day. He only read half of the book in seven days. Since then, he has read three more pages every day. It took Xiaoming several days to finish reading this book. (3 points)

A container has just been filled with 65,438+00 liters of pure alcohol. Pour out 3 liters and fill it with water. Pour out 3.5 liters and fill it with water. What is the concentration of the solution in the container? (4 points)

4. Two engineering teams, A and B, the workload of team A for three days is equivalent to that of team B for four days. At present, Team A has completed 80% of the whole project in 24 days, and the rest will be done by two teams. How many days will it take? (4 points)

There are many square bricks. If you put them together into a big rectangle with an aspect ratio of 5: 4, there are 38 pieces left. If you change to a big rectangle with L pieces in length and width, it will be 53 pieces less. So, how many bricks are there in this batch? (4 points)

6. Zhao Ming read a book. On the first day, he read the whole book. On the second day, I read l2 pages more than the first day, and on the third day, I read 6 pages more than the second day. At this time, he only read half of the whole book. How many pages are there in this book? (4 points)

7. Five bottles contain the same amount of water. If you pour 3 grams into each bottle, the total amount of water left in five bottles is exactly the total amount of the original three bottles. How many kilograms of water are there in each bottle? (4 points)

Eight, expand thinking problems. (12)

1. Divide the following picture into five pieces with the same size and shape. (3 points)

2. A truck and a bus leave from two cities, A and B, respectively, and go in opposite directions. The truck returns immediately after arriving at B, and the bus returns immediately after arriving at A. It is known that the speed ratio of the truck and the bus is 4: 3, and the first meeting point of the two cars is 24 kilometers away from the second meeting point. How many kilometers are the two cities apart? (4 points)

The two ships keep a distance of 600 meters and sail from the upstream to the downstream of the river. Two people, A and B, are in the same place on the river bank. When the boat in front came to two people, A sailed upstream of the river at the same speed, and B sailed downstream of the river. In this way, 2 minutes later, A met the boat behind, and 3 minutes later, B was overtaken by the boat behind. Ask them how fast they walk. (5 points)

Reference answer

One,

1.28:9 2.0.540 3.4 4.R+2R 5.45

6.4,30 7.& lt8. 18 9.84 10.7, 1 1, 13 1 1.

l 2.40 13.30 14.78 15. 16.67

16. 10:7 17. 15.42, 14. 13 18. 150 19. 16, 12.5 20.24

2 1.357 22.8

Two. 1.√ 2.× 3.× 4.× 5.√

Three. 1.A2.D3.C4.D5.D。

Fourth,106.1.1.18.103, 0.03, 57.6,

Verb (abbreviation of verb) 1.

2.

3.

4.97×2000-96×200 1

6. 1.70÷2=35 (square centimeter) 6×(6÷2)÷2=9 (square centimeter) 35-9=26 (square centimeter)

2. Because AE=2BE, the area ratio of triangle AEF to triangle ADF is 2: 3 (F is on the diagonal, and the two triangles are equal in height).

The area of triangle AED is (square centimeter), the area of triangle ADF is (square centimeter), and the area of triangle CDF is (square centimeter).

Seven. 1.(m)

2.7+18× 7÷ (18+3) =13 (days)

3.

4.80%÷4= (days) 5. Let the sides of a large rectangle with an aspect ratio of 5: 4 be 5 and 4, then

Solution = 10

So this batch of bricks =2038 (block) 6. ( 12+ 12+6)÷(×3)= 240(page)。

7.3×5(5-2)= 5 (kg)

Eight, 1.

2.24÷2×(4+3)=84 (km) (Hint: suppose two cities are kilometers apart. The speed ratio of trucks to buses is 4: 3. When they first met, the truck traveled thousands of meters, that is, the place where they first met was far from Jiacheng.

Kilometers From the time of departure to the second meeting, the sum of the distance traveled by the truck and the bus was 3 kilometers, and the truck traveled kilometers. The second meeting place is kilometers away from Jiacheng. )

3. (meter)

180÷2=90 (m/min)

Tip: Let the speed of the boat be meters, and the walking speed of people be meters. The ship is opposite to A, which belongs to the problem of meeting on the way.

………①

The ship is traveling in the same direction as B, and the distance between the ship and B is 600 meters at first, which is a catching-up problem.

………②