Seventh grade mathematics final examination paper I. Multiple choice questions (3 points for each small question, 30 points for * * *):
The reciprocal of 1 -2 is ()
A.﹣·c.﹣2
2. Alibaba data shows that 20 15 Tmall Mall? Double 1 1? The global carnival transaction volume exceeds 901.200 million yuan, and the data of 901.200 million is expressed as () by scientific notation.
A.9 12？ 108 B.9 1.2？ 109 C.9. 12？ 10 10 D.0.9 12？ 10 10
3. The following survey, suitable for sampling survey is ().
① Test the air quality in Shenzhen;
(2) To understand the health status of passengers on the same plane as the patients with Middle East respiratory syndrome;
3 as a guarantee? Shenzhou 9? Successfully launched and inspected its components;
④ The eyesight of 50 students in a class was investigated.
A.① B.② C.③ D.④
4. The following geometry is rectangular when viewed from the front (front view) ().
A.B. C. D。
5. In the following operations, the correct one is ().
A.﹣2﹣ 1=﹣ 1 b.﹣2(x﹣3y)=﹣2x+3y
C.D.5x2﹣2x2=3x2
6. When a carpenter saws wood, he usually draws two points on the board first, and then a chalk line pops up after these two points. This is because ()
A. between two points, the line segment is the shortest
B. Two points determine a straight line
C. one point, there are countless straight lines.
D. The line segment connecting two points is called the distance between two points.
7. It is known that 2x3y2m and ﹣xny are similar items, so the value of mn is ().
65438 AD+0 BC
8. As shown in the figure, it is known that point C is on the AB line, point M and point N are the midpoint of AC and BC respectively, and AB=8cm, then the length of MN is () cm.
A.2 B.3 C.4 D.6
9. The positions of rational numbers A and B on the number axis are shown in the figure. The following option is correct ().
a . a+b & gt； A-b company 0 C. | b-1| < 1 d.|a﹣b|>； 1
10. Of the following statements, the correct one is ().
A. a number whose absolute value is equal to itself is a positive number.
B. The absolute value of any rational number is not negative.
C. If line segment AC=BC, point C is the midpoint of line segment AB.
The size of angle D is related to the length of both sides of the angle. The longer the side, the bigger the angle.
Two. Fill in the blanks (3 points for each small question, *** 18 points):
1 1. The coefficient of the monomial is.
12. as shown in the figure, take any point o on the straight line AD, and the point crossing o is ray OB, and OE is equal? DOB, OC split equally? AOB，？ BOC=26？ What time? The degree of BOE is.
13. For rational numbers A and B, define a new operation and stipulate that A ☆ B = A2 | B |, then 2 ☆ (| 3) =.
14. A store will increase the cost price of a certain garment by 20%, then price it and sell it at a 10% discount. In this way, each piece of clothing can still make a profit in 8 yuan, so the cost of each piece of clothing is.
15. As shown in the figure, it is a chess piece (a>b) rectangular clearing with a length of A and a width of B, and the shaded part is afforested, with a shaded area of.
16. As shown in the figure, wooden sticks with equal length are arranged into a set of patterns according to certain rules. The first pattern needs 6 pieces, the second pattern needs 1 1, and the third pattern needs 16 pieces? Then the nth pattern needs a stick.
Three. Problem solving (***52 points, including 17 8 points, 18 9 points, 19 9 points):
17. Calculation
( 1) 10﹣(﹣5)+(﹣9)+6
(2)(﹣ 1)3+ 10? 22? ( ).
18.( 1) Simplify (2m+ 1)-3 (m2-m+3)
⑵(﹣4x2+2x﹣8y)﹣(﹣x﹣2y)
19. Solving equations
( 1)3(2x﹣ 1)=5x+2
(2) .
20. What is it? Welcome the New Year and celebrate New Year's Day? During this period, a shopping mall launched four different types of gift boxes * * 1000 boxes for sale. In figure 1, it is the percentage of all types of gift boxes. It is known that 50% of my four types of gift boxes have been sold, and the sales volume of each type of gift box is shown in Figure 2:
(1) There are boxes in the Class D gift box in the mall.
(2) Please find out that the central angle corresponding to Part A is equal to the degree in the sector statistical chart of Figure 1.
(3) Please complete the statistical chart in Figure 2.
(4) Through calculation, it is concluded that the sales volume of gift boxes is the best.
2 1. Solving application problems with column equations
One weekend, Xiaoming went to Xiwan Park from home to play. It is known that he goes to Xiwan Park by bike, and the speed of cycling is 8 kilometers per hour. When he goes home, he chooses to take the bus, which runs at a constant speed of 40 kilometers per hour. Results Cycling was more 1.6 hours than taking the bus. How many kilometers is it from his home to Xiwan Park?
22. We have learned the concept of angular bisectors, so will you use them to solve related problems?
(1) As shown in figure 1, fold the loose-leaf paper of a rectangular notebook into an angle, so that the vertex A of the angle falls on A? Where BC is the crease. What if? ABC=55？ , beg? Answer? Degree of BD.
(2) Under the condition of (1), what if the other corner of it is also obliquely folded and the BD side is connected with BA? Coincidentally, the crease was found, as shown in Figure 2. 2 and? CBE degree.
(3) What if Figure 2 is changed? The size of ABC, what about BA? The position has also changed, so what about ②? Will the scale of CBE change? Please explain.
The answer to the seventh grade mathematics final examination paper 1. Multiple choice questions (3 points for each small question, 30 points for * * *):
The reciprocal of 1 -2 is ()
A.﹣·c.﹣2
Test center countdown.
Analysis can be solved according to the definition of reciprocal.
Solution: The reciprocal of 2 is-.
So choose: a.
2. Alibaba data shows that 20 15 Tmall Mall? Double 1 1? The global carnival transaction volume exceeds 901.200 million yuan, and the data of 901.200 million is expressed as () by scientific notation.
A.9 12？ 108 B.9 1.2？ 109 C.9. 12？ 10 10 D.0.9 12？ 10 10
Scientific counting of test sites? Represents a bigger number.
Analytical scientific notation is expressed as? 10n, where 1? | a |< 10, n is an integer. Determining the value of n is an error-prone point. Since 9 1 1 is in 91200 million, it can be determined that n =1-1=10.
Solution: 91200 million = 9 12000000 = 9. 12? 10 10.
So choose C.
3. The following survey, suitable for sampling survey is ().
① Test the air quality in Shenzhen;
(2) To understand the health status of passengers on the same plane as the patients with Middle East respiratory syndrome;
3 as a guarantee? Shenzhou 9? Successfully launched and inspected its components;
④ The eyesight of 50 students in a class was investigated.
A.① B.② C.③ D.④
Comprehensive survey and sampling survey of test sites.
The survey results obtained from the analysis and census are more accurate, but more manpower, material resources and time are needed, while the survey results obtained from the sampling survey are similar.
Solution: ① Take sampling survey to detect the air quality in Shenzhen;
② In order to understand the health status of passengers on the same plane with confirmed Middle East respiratory syndrome patients, it is of great significance and a comprehensive investigation should be taken;
3 as a guarantee? Shenzhou 9? The successful launch is of great significance to the inspection of its parts and components, and comprehensive inspection should be adopted;
④ Investigate the eyesight of 50 students in a class, and the number is small, so a comprehensive survey should be adopted.
So choose: a.
4. The following geometry is rectangular when viewed from the front (front view) ().
A.B. C. D。
Three views of simple geometry in test sites.
Front view analysis is a graph obtained by looking at the front of an object respectively.
Solution: The front view of the cone is an isosceles triangle.
The front view of the cylinder is rectangular,
The front view of the frustum is trapezoidal,
The front view of the ball is round,
So choose B.
5. In the following operations, the correct one is ().
A.﹣2﹣ 1=﹣ 1 b.﹣2(x﹣3y)=﹣2x+3y
C.D.5x2﹣2x2=3x2
Mixed operation of rational numbers in test sites; Merge similar projects; Remove brackets and add brackets.
By analyzing the value of the calculation formula in each option, we can judge which option is correct.
Solution: Because ﹣2﹣ 1=﹣3, ﹣2(x﹣3y)=﹣2x+6y, 3? 6? =3? ,5x2﹣2x2=3x2，
So choose D.
6. When a carpenter saws wood, he usually draws two points on the board first, and then a chalk line pops up after these two points. This is because ()
A. between two points, the line segment is the shortest
B. Two points determine a straight line
C. a little, there are countless straight lines.
D. The line segment connecting two points is called the distance between two points.
The nature of the straight line in the test center: two points determine a straight line.
The analysis can be answered by determining a straight line based on two points.
Solution: Draw two points on the board, and then pop up a chalk line after these two points. The basis of this operation is that two points determine a straight line.
Therefore, choose: B.
7. It is known that 2x3y2m and ﹣xny are similar items, so the value of mn is ().
65438 AD+0 BC
Test sites are similar projects.
Analysis According to the definition of similar terms (including the same letters and the same index), the equations 2m= 1 and n=3 are listed, the values of n and m are calculated, and then substituted into algebraic formulas.
Answer: 2x3y2m and ∫﹣xny are similar terms.
? 2m= 1，n=3，
? m=，
? mn=( )3=。
So choose D.
8. As shown in the figure, it is known that point C is on the AB line, point M and point N are the midpoint of AC and BC respectively, and AB=8cm, then the length of MN is () cm.
A.2 B.3 C.4 D.6
The distance between two points in the test center.
The analysis can be solved by MN=CM+CN= AC+ CB= (AC+BC)= AB.
Solution: ∫M and n are the midpoint of AC and BC respectively.
? CM= AC，CN= BC，
? MN=CM+CN= AC+ BC= (AC+BC)= AB=4。
So choose C.
9. The positions of rational numbers A and B on the number axis are shown in the figure. The following option is correct ().
a . a+b & gt； A-b company 0 C. | b-1| < 1 d.|a﹣b|>； 1
The test center counts the shafts.
According to the number axis, we can get b <-1< 0
Solution: it can be obtained from the number axis B.
Then a+b 1, | a | b | > 1,
So choose D.
10. Of the following statements, the correct one is ().
A. a number whose absolute value is equal to itself is a positive number.
B. The absolute value of any rational number is not negative.
C. If line segment AC=BC, point C is the midpoint of line segment AB.
The size of angle D is related to the length of both sides of the angle. The longer the side, the bigger the angle.
Absolute value of the test site; The distance between two points; The concept of angle.
Analysis can be judged according to the definition of absolute value, midpoint of line segment and angle.
Solution: A, the number whose absolute value is equal to itself is non-negative and wrong;
B, the absolute value of any rational number is not negative, correct;
C, line segment AC=BC, then point C on the line segment is the midpoint of line segment AB, which is wrong;
D, the size of the angle has nothing to do with the length and error on both sides of the angle;
So choose B.
Two. Fill in the blanks (3 points for each small question, *** 18 points):
1 1. The coefficient of single item is ﹣.
Test center singleton
The analysis is based on the concept of single coefficient.
Answer: the coefficient of a single item is.
So the answer is:
12. as shown in the figure, take any point o on the straight line AD, and the point crossing o is ray OB, and OE is equal? DOB, OC split equally? AOB，？ BOC=26？ What time? The degree of BOE is 64? .
Definition of bisector of test center angle.
This analysis is based on the properties of angular bisector. The degree of AOB, and then use the angle to find it? BOD degrees, divided by OE equal parts? Dobby, you can answer.
Solution: ∫OC split equally? AOB，？ BOC=26？ ,
AOB=2？ BOC=262=52？ ,
BOD= 180？ ﹣? AOB= 180？ ﹣52? = 128? ,
? OE split? Dobby,
BOE= BOD=64？ .
So the answer is: 64? .
13. For rational numbers A and B, define a new operation, and stipulate that A ☆ B = A2 | B |, then 2 ☆ (| 3) = 1.
Mixed operation of rational numbers in test sites.
According to the given operation method, the formula is transformed into a mixed operation of rational numbers, and the answer can be obtained by further calculation.
Solution: 2 ☆ (-3)
=22﹣|﹣3|
=4﹣3
= 1.
So the answer is: 1.
14. A store will increase the cost price of a certain garment by 20% and then price it, and then sell it at a 10% discount. In this way, each garment can still make a profit in 8 yuan, so the cost of each garment is 100 yuan.
The application of one-dimensional linear equation in examination center.
Let's assume that the cost of each piece of this kind of clothing is X yuan, and list a linear equation according to the meaning of the question (1+20%)? 90%? X-x = 8, find the value of X.
Solution: Suppose the cost of each piece of this dress is X yuan.
Judging from the title: (1+20%)? 90%? x﹣x=8，
Solution: x= 100.
The cost of each piece of this kind of clothing is 100 yuan.
So the answer is: 100 yuan.
15. As shown in the figure, it is a rectangular clearing of chess pieces (a>b) with a length of A and a width of B. The shaded part is afforested, and the shaded area is AB.
Algebraic expression of test center.
According to the meaning of the problem and the figure, the area of the shadow part can be expressed by the corresponding algebraic expression.
Solution: From the figure,
The area of the shaded part is: ab? =ab﹣，
So the answer is: AB.
16. As shown in the figure, wooden sticks with equal length are arranged into a set of patterns according to certain rules. The first pattern needs 6 pieces, the second pattern needs 1 1, and the third pattern needs 16 pieces? , the nth pattern needs 5n+ 1 branch.
Regularity of test sites: diversity of graphics.
By analyzing the change of the pattern, we can see that the pattern at the back has five more sticks than the previous one. Combined with the data of 6, 1 1, 16, the number of sticks needed for the nth pattern can be obtained.
Solution: Pattern (2) has five more than Pattern (1), and Pattern (3) has five more than Pattern (2). According to the transformation law of mode:
Each pattern has five more sticks than the previous pattern.
The first pattern needs 6 sticks, 6=5+ 1,
? The nth pattern needs 5n+ 1 branch.
So the answer is: 5n+ 1.
Three. Problem solving (***52 points, including 17 8 points, 18 9 points, 19 9 points):
17. Calculation
( 1) 10﹣(﹣5)+(﹣9)+6
(2)(﹣ 1)3+ 10? 22? ( ).
Mixed operation of rational numbers in test sites.
Analysis (1) can be simplified first, and then classified calculation;
(2) Calculate the power first, then multiply and divide, and finally add.
Solution: (1) Original formula = 10+5-9+6.
= 12;
(2) The original formula =- 1+ 10? 4?
=﹣ 1+
=﹣ .
18.( 1) Simplify (2m+ 1)-3 (m2-m+3)
⑵(﹣4x2+2x﹣8y)﹣(﹣x﹣2y)
Addition and subtraction of algebraic expressions.
Analysis (1) and (2) Remove brackets first, and then merge similar items.
Solution: (1) Original formula = 2m+ 1-3m2+3m-9.
=5m﹣3m2﹣8；
(2) The original formula =-x2+x-2y+x+2y.
=-x2+X.
19. Solving equations
( 1)3(2x﹣ 1)=5x+2
(2) .
Try to solve the one-dimensional linear equation.
Analyze the (1) equation, remove the brackets, merge the shift terms, and change the x coefficient into 1, and the solution can be obtained.
(2) The equation can be solved by naming, removing brackets, shifting terms and merging, and transforming the x coefficient into 1.
Solution: (1) without brackets: 6x-3 = 5x+2,
Transfer and merger: x = 5；;
(2) denominator:10x+15-3x+3 =15,
Transfer and merger: 7x =-3,
Solution: x=﹣.
20. What is it? Welcome the New Year and celebrate New Year's Day? During this period, a shopping mall launched four different types of gift boxes * * 1000 boxes for sale. In figure 1, it is the percentage of all types of gift boxes. It is known that 50% of my four types of gift boxes have been sold, and the sales volume of each type of gift box is shown in Figure 2:
(1) There are 250 D gift boxes in the mall.
(2) Please find out that the central angle corresponding to Part A is equal to 1 26 degrees in the fan-shaped statistical chart of Figure1.
(3) Please complete the statistical chart in Figure 2.
(4) Through calculation, it is concluded that category A gift boxes have the best sales volume.
Bar chart of test center; Department statistical chart.
Analyze (1) the percentage of D-shaped gift boxes obtained from the department statistics chart, and then multiply this percentage by 1000 to get the number of D-shaped gift boxes in the mall;
(2) Get the percentage of Class A gift boxes from the fan map, and then multiply this percentage by 360? You can get the degree of the central angle corresponding to part a;
(3) Subtract the sales of Category A, Category B and Category D from the total sales volume to obtain the number of category C gift boxes, and then complete the histogram;
(4) According to the histogram, we can get the type of gift box with the largest sales volume, so that we can judge the type with the best sales volume.
Solution: (1) What is the number of category D gift boxes in the mall 1000? 25%=250 (box);
(2) The degree of the central angle corresponding to Part A is 36035%= 126? ;
(3) The sales volume of part C gift box is 500-168-80-150 =102 (box);
As shown in the figure,
(4) Gift Box A sells the most, so Gift Box A sells the best.
So the answer is 250, 126, a.
2 1. Solving application problems with column equations
One weekend, Xiaoming went to Xiwan Park from home to play. It is known that he goes to Xiwan Park by bike, and the speed of cycling is 8 kilometers per hour. When he goes home, he chooses to take the bus, which runs at a constant speed of 40 kilometers per hour. Results Cycling was more 1.6 hours than taking the bus. How many kilometers is it from his home to Xiwan Park?
The application of one-dimensional linear equation in examination center.
According to analysis, the distance from Xiaoming's home to Xiwan Park is X kilometers. Does it take 1.6 hours longer to ride a bike than to take a bus? Just list the equations and solve them.
Solution: Suppose Xiaoming's home is X kilometers away from Xiwan Park.
According to the meaning of the question: =+1.6,
Solution: x= 16.
A: The distance from Xiaoming's home to Xiwan Park is 16 km.
22. We have learned the concept of angular bisectors, so will you use them to solve related problems?
(1) As shown in figure 1, fold the loose-leaf paper of a rectangular notebook into an angle, so that the vertex A of the angle falls on A? Where BC is the crease. What if? ABC=55？ , beg? Answer? Degree of BD.
(2) Under the condition of (1), what if the other corner of it is also obliquely folded and the BD side is connected with BA? Coincidentally, the crease was found, as shown in Figure 2. 2 and? CBE degree.
(3) What if Figure 2 is changed? The size of ABC, what about BA? The position has also changed, so what about ②? Will the scale of CBE change? Please explain.
Definition of bisector of test center angle; Calculation of angle; Folding transformation (folding problem)
Analysis (1) can be obtained from the properties of folding? Answer? BC=？ ABC=55？ Can you get it through the definition of right angle? Answer? BD= 180？ ﹣? ABC﹣？ Answer? BC, available results;
(2) The conclusion from (1)? DBD？ =70? , can be obtained from the nature of folding = =35? , from the nature of the angle bisector? CBE=？ Answer? BC+？ d？ BE=？ 180? =90? ;
(3) From the nature of folding,? 2=? EBD=？ DBD？ , you can get the result.
Solution: (1)∵? ABC=55？ ,
Answer? BC=？ ABC=55？ ,
Answer? BD= 180？ ﹣? ABC﹣？ Answer? B.C.
= 180? ﹣55﹣55?
=70? ;
(2) The conclusion from (1)? DBD？ =70? ,
? = =35? ,
From the nature of folding,
CBE=？ Answer? BC+？ d？ BE=？ 180? =90? ;
(3) unchanged,
From the nature of folding,
,? 2=? EBD=？ DBD？ ,
1+? 2= = =90? ,
Constant, always half a right angle.