Question number one two three four five Total score

Score (1) (2) (3) (4)

(This paper is full of 100 points, in 90 minutes to complete. I believe you will do a great job)

I. There are a lot of traps, be careful!

Fill in the blanks: (2 points per question, ***26 points)

1. Figure (1) is a schematic diagram of a numerical conversion machine, you are asked to input a rational number, think about what number will be output. You decide to input __2_________,and finally it will output _______0_____.

2. The *** in figure (2) below has _____6_______ line segments.

3. China's forest area has 128 million hectares, which is 1.28*10(9) hectares in scientific notation.

4. Compare the size: > . (fill in " = , > , < ")

5. A submarine has risen from 50 meters below sea level to -50 meters, and now it has risen 20 meters, so the depth of the water in which the submarine is now

is recorded as -30 meters.

6. There is a wrong equation in the workbook of Xiaoxin, please add the symbols of "addition, subtraction, multiplication, division, parentheses" (each operation symbol can be used more than once) directly in the equation to make the equation hold: 3 * 6 + 4 + 2 = 24.

7. It is known that x=3 is the solution of the equation ax-6 = a + 10, then a = ____8_____________.

8.There is a column of numbers: 1, , , , , , ...... and the ninth number is .

9. The figure on the right is a calendar for January 2003, now any four numbers are boxed in the calendar , please use an equation table

show the quantitative relationship between: ______.

10. A store can still make a profit of 20% by selling a detergent at 90% off the list price. If the purchase price of the detergent is 21 yuan, then the list price is yuan.

11. Do you like ramen? The master of the ramen shop, with a very thick noodle, pinched the two ends together and stretched, then pinched again, then stretched again, and repeated a few times, the very thick noodle into many thin noodles. As shown in the picture: this pinch together after the first time, you can pull out 128 thin noodles, try at home after class.

After the second pinch, after the third pinch, after the fourth pinch

12. Our country is a serious shortage of water, we should cherish water resources, water conservation. According to the test, the unscrewed faucet drips about cubic meters of water per hour. Xiaoming students after washing hands, did not tighten the tap, when Xiaoming left a day after the tap dripped cubic meters. If a year of leakage of water, it can supply a school that uses 146 cubic meters of water per day for days.

13. Xiaohong and Xiaomei are playing a calculation game, the rules of calculation is =ad-bc, now it is Xiaohong's turn to calculate

the value of the, please help you calculate a how much? Solution: =_________________________.

II. The questions are not difficult, you can do it! Multiple choice questions: (2 points each, ***20 points, fill in the answers directly in the table below)

Question No. 1 2 3 4 5 6 7 8 9 10

Answers

1. Observe the following equation, the correct one is ( )

(A) (B)

(C) (D)

2. The following figure is a side expansion of a triangular prism

A. B. C. D.

3. You think the following events are inevitable ( )

(A) It will rain tomorrow; (B) Xiao Ming scored 99 marks in his math exam;

(C) Today is Monday, tomorrow will be Tuesday; (D) There are 370 days in the next year.

4. The following statements about operations with rational numbers are correct ( )

(A) Subtracting a number is the same as adding the inverse of that number; (B) The sum of two negative numbers must be greater than each of the addends;

(C) Multiplying several rational numbers, one of which is negative ****, results in a negative product;

(D) Multiplying two numbers together results in a positive product, and a negative product results in a negative product. (B) If two numbers are multiplied together, the product is negative if they have the same sign.

5. It is known that: as shown in Figure (3) ∠DBE = . If BE bisects ∠CBD , then the degree of ∠ABC ( )

(A) (B) (C) (D)

6. If , then the value of ( )

(A) (B) 7 (C) 12 (D) -12

7. Xiaoming went to his grandma's house for a visit, and she took out a box of candies (candies of the same shape exactly. And in the fruit box outside can not see any candy) which has 3 pieces of chocolate candy, 5 pieces of sesame seed crisp candy, 7 pieces of fudge, Xiaoqiang once out of a piece of chocolate candy the possibility of the size ( )

(A) (B) (C) (D)

8. >

(B) the winning rate of a lottery ticket is one in a thousand, buy this ticket 1001 must win;

(C) a two-digit number of digits is , the tenth digit is 7, then it can be expressed as ;

(D) A, B, two people's speed is 3 km / h and 5 km / h, respectively, from the distance of 4 kilometers away from the same time

same direction, set They after x hours B catch up with A, then the equation can be 3x + 5x = 4 .

9. Observatory measured a ship in the north by east 35 ° 20′, then the ship on the observation station bearing is ( )

A south by south-east 54 ° 40′ B south by east 35 ° 20′

C south by west 35 ° 20′ D south by west 54 ° 40′

10. Xiaoming according to the regular two-year savings of 1500 yuan to the bank (the annual interest rate of 3 %), when the maturity of the withdrawal, after deducting the interest income tax (the tax rate is 20 %), Xiaoming real interest is ( )

(A) 1,272 yuan (B) 1,572 yuan (C) 36 yuan (D) 72 yuan

Three, you do the math! Don't make any mistakes! (4 points per question, ***20 points)

(1) ; (2 ) .

Solution: Solve:

(3) 5 (xy-2z) - 2 (-xy + 3z) (4) Solve the equation:

Solution: Solve:

(5) Simplify first and then find the value : , where .

Solution:

Four, mindfulness, hands-on drawing,

Drawing questions (4 points for the first sub-topic, 3 points for the second and third sub-topics, *** 10 points)

(1) The following figure, Xiaogang is ready to take the cow at C to the river AB to drink.

①Make the shortest route for Xiaogang (without considering other factors) and intersect with the river AB at point E.

②If Xiaogang finds a way to the river by going upstream or downstream parallel to the river from point C, make a straight line n parallel to the river AB through point C.

③If Xiaogang is leading a cow to the water at river AB and must go to river D to observe the water quality of the river, make the shortest route for Xiaogang to walk (without considering other factors) and explain the reason.

(2) Draw the top view of the geometry built from five small cubic blocks with prongs of 1 centimeter as shown in the figure below left.

(3) Please put together a pattern with the following shapes and describe this scene in short words

V. Mathematics and our life:

Solutions: (6 points for sub-topics 1 and 2, 7 points for sub-topic 3, 5 points for sub-topic 4, ****24 points)

(1) There are 8 bags of rice, with each bag being based on 30 kilograms, and more than one kilogram is recorded as a positive number, which are respectively are: -2, +1, +4, +6, -3, -4, +5, -3. How much do these 8 bags of rice **** weigh?

Solution:

(2) The following questionnaire was given to 400 seventh-grade students at a school to find out the main ways in which they use computers.

Ways of use Study Finding information Chatting on the Internet Playing games

Number of people 40 60 200 100

①Make an appropriate statistical chart based on the data above. Indicate the percentage of the total number of students who use computers in various ways.

Solution:

②Based on the results of this survey, please briefly write down your thoughts or suggestions for those students who are obsessed with "chatting and playing games on the Internet".

Solution:

(3) a school organized by the seventh-grade students in the autumn tour, the original plan to rent a number of 45-seat bus, but there are 15 people do not have a seat, if you rent the same number of 60-seat bus, then more than one, and the rest of the bus happened to be full. Ask the school

What is the number of seventh-grade students?

Solution:

(4) Use the number of diagonals passing through a point in a polygon to find the formula for summing the interior angles of a polygon.

......

①Fill in the blanks according to the pattern shown in the figure:

Number of sides of the figure Trilateral Quadrilateral Pentagon Hexagon

Degree of the sum of the interior angles

(2) The degree of the sum of the interior angles of an n-sided figure is asked to be (expressed algebraically in terms of number of sides, n)

(3) According to (2) Based on ②, if the figure is 22-sided, find the degree of the sum of its interior angles.

Solution: