mathematics

First, fill in the blanks. (24 points)

1. At present, the total area of China and Hongkong is 1052 million square meters, and the unit of "ten thousand" is rewritten as (1052 million) square meters, and the mantissa after omitting "100 million" is about (11000 million) square meters.

2.4.25 hours =( 2) hours (4 minutes), 7 cubic meters and 40 cubic decimeters =(7.04) cubic meters.

3. Cut the 4-meter-long rope into 5 sections on average, each section is () meters, and each section accounts for () of the total length.

4.3 14%, 3. 1, 3.0 14, 3,3, the maximum number is (3), and the minimum number is (3.0 14).

5, (80)% = 4 ÷ 5 = = (8): 10 = (0.8) (decimal)

6. There are (6) simplest true fractions whose denominator is 18 and their sum is (3).

7. Glue three cubes 4 cm long together to form a cuboid. The cuboid has a volume of (192) cubic centimeters, and its surface area is reduced by (64) square centimeters compared with the sum of the original three small cubes.

8, more than 80 meters is (120) meters, below 12 kg is 15 kg (20)%.

9. The diagonal length of a square piece of paper is 4cm, and its area is (8) cm2. If cut into the largest circle, the area of the circle is (6.28) cm2.

The ratio of 10 to: is (), and the ratio of 4: 0.8 to the simplest integer is (5): (1).

The greatest common factor of 1 1, 12 and 30 is (6), and the smallest common multiple is (60).

12, observe the law of finding examples and answer questions as required.

( 120× 120)-( 1 19× 12 1)= 1, ( 120× 120)-( 1 18× 122)=4,

( 120× 120)-( 1 17× 123)=9, ( 120× 120)-( 1 16× 124)= 16,

……

( 1)( 120× 120)-( 1 12× 128)= ( 64)。

(2)( 120× 120)-( 108) × ( 132)= 144

Second, the judgment question. (5 points)

1, add 0 or go to 0 after the decimal point, and the size of the decimal point remains the same. (10)

2. The volume of the cone is equal to the volume of the cylinder. (10)

One ton of coal has been used up, and there are still several tons left. (10)

Time is fixed, and distance is directly proportional to speed. (√ )

The price of a commodity rises first and then falls. The current price of this commodity is the same as the original price. (√ )

Third, multiple choice questions. (6 points)

1, the divisor of two numbers is 2.4. The divisor is enlarged by 100 times, and the quotient of the divisor divided by 0.0 1 is (b).

a、2.4 B、24000 C、240

2, said a patient's temperature changes in a day, draw (a) statistical chart is more appropriate.

A, dotted line b, sector c, bar

3, an isosceles triangle, the ratio of a base angle to a vertex angle is 2: 1, then this isosceles triangle is also (a).

A, acute triangle b, right triangle c, obtuse triangle

Xiao Ming walked 20 kilometers in 3 hours, and rode back along the original road just 1 hour. The average speed of Xiao Ming's round trip is (b) per hour.

A, 5km b,10km c,13km.

5. A project was originally planned to be completed in 5 hours, but the task was actually completed in 4 hours, which improved the work efficiency (c).

A, B, C,

6, composed of five small cubes a three-dimensional figure, the shape is from the left, the shape is from the top, * * * has (a).

a、 1 B、2 C、3

Fourth, the calculation problem. (22 points)

1. Numbers written directly (10 points)

127+38 = 165 8.8÷0.2 = 44 568-278 = 290 58x 8× 1 = 464

1÷7+2 = 9 1- 1× 18 = 18 30X 12 = 360 1.02-0.43 = 0.59

2. Simple calculation. (12)

9-(3+0.4) = 51.8×+2.2× 25% = V. Graphics and operations. (8 points)

1, a part, as shown below, find its volume. (4 points)

2. The side length of each small square in the right square is 1 cm. Please draw this picture.

The trapezoid in the shape is divided into three triangles, A, B and C, so their area ratio is

1∶2∶3, and calculate the areas of the three triangles respectively. (4 points) A: 12÷( 1+2+3) =2.

B: 12÷( 1+2+3) ×2=4 (square centimeter) c: 12÷( 1+2+3)×3=6 (square centimeter).

Sixth, solve the problem. (3 1)

1, only counting the column type, not counting: (2 points for each question, ***8 points)

(1) A factory plans to produce 240 machine tools in 15 days, but in fact, it produces 4 more than planned every day. How many days will it actually take to complete? 240÷(240÷ 15+4) =

(2) The survival rate of a sapling is 95%. How many saplings must be planted at least to ensure 570 saplings? 570÷95=%

(3) The store delivered 20 baskets of pears and 0/6 baskets of apples, weighing 820kg. It is known that each basket of apples weighs 22.5 kilograms. How many kilograms does each basket of pears weigh? (Equation solution) 20x+ 16x22.5 = 820.

(4) ICBC introduced lump-sum deposit and withdrawal of education savings, and implemented interest tax relief. Xiao Qiang's parents went to the bank to deposit 8,000 yuan as a three-year lump-sum education savings in Xiao Qiang. It is known that the annual interest rate of lump sum deposit and withdrawal for three years is 3.24%. How much principal and interest can I get at maturity? 8000+8000×3×3.04%=

2. Xiaoming reads a story book. In the first four days, he read an average of 24 pages a day, and on the fifth day he read 34 pages. How many pages did Xiao Ming read every day for the first five days? (4 points), (24×4+34)÷5=

There is an 80-meter-long water pipe, which used 25% of the total length for the first time, 40% more than the first time. How many meters are left after two times? (4 points) 80-80× 25%-80× 25 %× (1+40%) =

4. A cylindrical barrel without a lid, measured from the inside, has a bottom diameter of 4 decimeters and a height of 6 decimeters. How many square decimetres of iron sheet does it take to make this barrel? The water depth in the bucket is 5 decimeters. How heavy is the water in the bucket? (1 liter weight 1 kg) (5 points), (4 ÷ 2) 2× 3.14+4× 3.14× 6 = 98.92 (square decimeter) (4 ÷ 3).

The distance between a and b is 264 kilometers. A takes a bus from A to B, with an average of 80 kilometers per hour. B rides a motorcycle from B to A with an average speed of 32 kilometers per hour. A travels 200 kilometers and meets B. How many hours does A have to leave before B? (5 points) 200 80-(264-200) 32 =

6. One day, Zunyi Evening News published a message: the monthly water fee for each household in a city was changed from per cubic meter 1.90 yuan to:

Water consumption is 20 cubic meters or more and 20 cubic meters or less.

The charging standard is 2.30 yuan per cubic meter per cubic meter of 3.5 yuan.

According to the above information, the water fee of the Wangs in May this year was paid to 24 yuan more than before according to the new charging standard. How many cubic meters of water did the Wangs consume in May this year? (5 points)

24×(2.3- 1.9)+(x-20)×(3.5- 1.9)= 24 x = 30

General review questions of mathematics

A, axisymmetric graphics

Only the figure of 1 symmetry axis is (isosceles triangle, isosceles trapezoid, semicircle).

A figure with two axes of symmetry is (rectangle)

A figure with three axes of symmetry is an equilateral triangle.

A figure with four axes of symmetry is (a square).

A figure with countless axes of symmetry is (circle, ring)

2. The figure of the circular symmetry axis is (the straight line where the diameter is located).

The symmetry axis is a straight line.

4. The circle is a (plane figure, curve, axis symmetry) figure.

Second, in the same circle or equal circle (an essential premise), the diameter is twice the radius, and the radius is half the diameter.

(d=2r 0 (r=d÷2)

3. In the same circle or in the same circle (an indispensable prerequisite), (the diameters are all equal and the radii are all equal. )

Fourth, the center of the circle determines the position of the circle, and the radius determines the size of the circle. The distance between two feet of a compass is the radius of a circle.

Five, the circumference of the circle

1, (the length of the circled curve is called a circle) perimeter.

2. The quotient of the circumference of a circle divided by the diameter (the ratio of circumference to diameter) is called pi, which is a (fixed number) and has nothing to do with the size of the circle. π>3. 14。 The circumference of a circle is about 3. 14 times the diameter.

3.c circle =(πd) c circle =(2πr)

4. The circumference of a rectangle = ((length+width) × 2 = (a+b) × 2)

The circumference of a square = (side length × 4 = 4a)

5. The unit of length and circumference is: (kilometers, meters, decimeters, centimeters and millimeters)

6. Find the diameter from the known circumference (d = c÷π).

Find the radius from the known circumference (r = c÷2)

Six, the circumference of a semicircle

C semicircle = (d+π d ÷ 2) C semicircle = (2r+π r)

Seven, circle area

1. Divide the circle into several parts evenly, and you can make a parallelogram or rectangle.

2.s circle = (π R2 = π (d÷2) x2)

3.s rectangle = (length× width = ab)

S squared = (side length × side length = A2)

S parallelogram = (base× height = ah)

S triangle = (base × height ÷ 2 = ah ÷ 2)

S trapezoid = ((upper bottom+lower bottom) × height ÷ 2 = (a+b) × h ÷ 2)

S semicircle = (π R2 ÷ 2)

S circle = (S great circle -S small circle = π (R2-R2))

4. The units of area and surface area are: (square kilometers, hectares, square meters, decimeters and square centimeters).

5. If the perimeter of a rectangle = the perimeter of a square = the perimeter of a circle, then the area between them (the circle) is the largest.

Eight, enlarge the radius by n times, enlarge the diameter by n times, enlarge the circumference by n times, and enlarge the area by (n2) times.

Second unit

First, yes, equality, equivalence, meaning (same).

2. How much = (how much discount)

2. What percentage do you want to increase, decrease, increase, decrease, save, increase and decrease? Both use: a-B.

3. The ratio of degrees of three internal angles of a triangle is 1: 2: 3 or 1: 1: 2. This triangle is a (right angle) triangle.

Four, the general steps to solve the problem of score application

1. (found unit "1")

2. (Judge whether the unit "1" is known or unknown)

3. (If the unit "1" is known, it is calculated by multiplication: unit "1"× corresponding score).

4. (If the unit "1" is unknown, it will be calculated by division: known quantity ÷ corresponding score = unit "1"; In addition, equation can also be used)

5. Subtraction = (subtraction) Divider = (Divider quotient)

Verb (abbreviation of verb) common quantitative relationship

1, (speed× time) = distance (distance/speed) = time (distance/time) = speed.

2. (unit price × quantity) = total price (total price/unit price) = quantity (total price/quantity) = unit price.

3. (work efficiency × working hours) = total workload (total workload ÷ work efficiency) = working hours.

(total amount of work ÷ working hours) = working efficiency

4. (number of copies × number of copies) = total number of copies (total number of copies/number of copies) = number of copies (total number of copies/number of copies) = number of copies.

Intransitive verb equality

1, (an equation with unknowns is called an equation).

2. (solving the equation) is "singing the devil's advocate"

Seven. Interest = (principal × interest rate× time)

Third unit

In graphic transformation and pattern design, we will use: (axis symmetry, translation and rotation).

1. (axisymmetric)

2. Translation: (Pay attention to whether it is up and down translation or left and right translation, especially how many grids have been translated)

3. Rotation: (pay attention to whether it is clockwise or counterclockwise, and pay attention to the angle of rotation)

4. Operating rules:

Additive commutative law and nature.

(a+b=b+a)

associative law of addition

a+b+c = a+(b+c)25+37+63 = 25+(37+63)

Commutative law of multiplication

a×b×c=a×c×b 25×9×4=25×4×9

Multiplicative associative law

a×b×c =(a×c)×b 128×3×8 =( 125×8)×3

Powder companion

Multiply the sum of two numbers by one number. You can multiply these two addends by this number respectively, and then add the two stages.

a×(b+c)= a×b+a×c 8×( 125+25)= 8× 125+8×25

2.37×99=2.37× ( 100- 1 )=2.37× 100-2.37× 1

Operational properties of subtraction

a―b―c = a-(b+ c) 14.29―3.9―6. 1 = 14.29―3.9+6. 1

Fourth unit

1. The division of two numbers is also called the ratio of these two numbers. Among them, the number before the comparison sign is the former item of the ratio, and the number after the comparison sign is the latter item of the ratio, and the former item ÷ the latter item = the ratio.

2. The relationship between ratio, division and fraction

A ÷ b = a: b = (b ≠ 0, divisor, denominator and postterm cannot be 0)

Simplified proportion

Simplifying a ratio is to change a ratio into the simplest integer ratio. That is, the first and last items of 9 are integers, and the first and last items can only have one common factor 1).

4. Note: The ratio is a number. (The result of simplifying the ratio is a ratio. )

5. Application of ratio

Key points: It is known that the circumference of a rectangle is 28 cm and the length-width ratio is 4: 3. Find the length, width or area of a rectangle.

6. The ratio of degrees of three internal angles of a triangle is 1: 2: 3 or 1: 1: 2. This triangle is a (right angle) triangle.

7. Mass unit: (tons, kilograms and grams)

8. unit of volume: (L ml)

9. unit of volume: (cubic meter cubic decimeter cubic centimeter)

10, RMB unit: (jiao yuan fen)

1 1, numbers greater than 0 are called (positive numbers), and numbers less than 0 are called (negative numbers). Positive and negative numbers can be used to represent quantities with opposite meanings. 0 is neither (positive) nor (negative).

12, positive and negative numbers can be offset, for example, (+5) and (-5) can be completely offset; (-8) and (+3) offset to get -5.

13. Statistical charts include: (composite) bar chart, (composite) line chart and fan chart.

14, bar graph: (It's easy to see the quantities of various quantities. )

15, broken line statistical chart: (Not only can you see the quantity, but you can also indicate the increase or decrease of the quantity. )

16, pie chart: (you can display the percentage and total of each part. )

.

Suggestion: When reviewing, avoid mechanical exercises, fill in forms and make statistical charts monotonously, and design some practical activities in combination with students' real life. In the activity, students can apply statistical knowledge, which not only consolidates knowledge, but also mobilizes students' enthusiasm and initiative, and gives play to students' practice and innovation ability.

For example, starting from students' study and life, according to the various characteristics of shopping discounts in shopping malls, let students design their own shopping plans and choose the best shopping plan, and complete the task of reviewing statistical knowledge in this process.

Be sure to learn well, the first volume of the first day of junior high school and the second volume of the first, second and seventh volumes can all be learned well!

Significance and nature of decimal exercise.

I. Fill in the blanks:

1. Add "0" or remove "0" at the end of the decimal, and the size of the decimal remains the same. This is the nature of the so-called decimal.

2. The second digit on the left of the decimal point is (ten) and the third digit on the right is (one thousandth).

3. 15 0.0 1 Yes (0. 15), 24 0. 1 Yes (2.4).

8% in 4.0.08 and 50% in 0.5.

5. A decimal consists of five thousandths and seven thousandths, and this decimal is (0.507).

6. Among the decimals of 0.9, 1. 1, 0.45 and 40.8, there are (0.9, 0.45) pure decimals.

7. Move the decimal point of decimal number three places to the left, and the decimal point will be reduced by (1000) times.

8. To enlarge a decimal by 100 times, just move the decimal point to the right (two places).

2. Judge right or wrong. Correct painting "√" and wrong painting "×"

(1) Add two zeros at the end of the decimal, and the size of the decimal remains the same. (×)

(2) Rewrite 400,000 meters into tens of thousands of meters, which should be written as: 400,000 meters. (×)

(3) Three decimal places must be greater than two decimal places. (×)

3. Simplify the following decimals:

( 1)0.500 (2) 18.00 (3)40.050

(4)70.00 (5) 1.8040 (6)5.240

4. Rewrite the following figures to three decimal places without changing the size of the figures:

( 1)0.9=0.900 (2)4.2500=4.250 (3) 10.5= 10.500

(4) 13= 13.000 (5)58.4=58.400 (6)0.80=0.800

(1) in 0.95 and 0.59,

(2) in 1.05 and 0.9985,

(3) At1.25m and 1. 19m,

(4) In 0.356, 0.635, 0.563 and 0.653,

The intransitive verb is changed by 0.35 as needed, as shown below:

(1) amplification 10 times, and (3.5) was obtained.

(2) Remove the decimal point (35)

(3) 10 times reduced (0.035)

(4) Rewrite it into a number of one thousandth, and get (0.350).

7. Fill in the appropriate decimal places in ():

(1) 27m =(0.027) km

(2)5 cm =(0.05) m

(3)8 tons 45 kg =(8.045) tons

4500m =(4.5) km

(5)42 square meters 70 square decimeters =(42.7) square meters

(6)2600 kg =(2.6) tons

700g =(0.7) kg

(8)4 yuan 8 jiao =(4.8) yuan.

Eight. Keep the following figures to one decimal place and approximate them:

( 1)3.877 (2) 10.349 (3)0.98

(4)3.446 (5) 16. 17 (6)63.6363

9.( 1) Rewrite the following figures into "ten thousand" figures:

& lt 1 & gt； 23.5 million = 23.5 million

(2) Rewrite the following figures into "100 million" figures; Keep another decimal place.

& lt 1 & gt； 397 million = 397 million

& lt2 & gt530700000 = 53070 million.