The second grade math final examination paper 1, multiple-choice questions
1. The highest temperature in a place 12℃ and the lowest temperature -2℃, then the temperature difference in that place is ().
A.﹣ 10℃d.﹣ 14℃
2. It is reported that at present, China? Tianhe No.2? The computing speed of supercomputers ranks first in the world, reaching 338.6 trillion times per second. The figure of 338.6 billion can be simply expressed as () by scientific notation.
A.3.386？ 108 B.0.3386？ 109 C.33.86？ 107 D.3.386？ 109
3. Place a machine part as shown in the figure (Figure 1). If the figure viewed from the front is as shown in Figure 2, then the figure viewed from above is ().
A.B. C. D。
4. The following statement is true ()
A. rational numbers are divided into positive numbers and negative numbers.
B. the reciprocal of rational number must be less than 0.
C. two numbers with equal absolute values are not necessarily equal.
D. the absolute value of rational number must be greater than 0.
5. The coefficient and order of Monomial--23a2b3 are () respectively.
A.﹣2,8 B.﹣8,5 C.2，8 D.﹣2,5
6.if A+B
A.a & lt0，b & gt0 B.a & lt0，b & lt0
C.a>0, b<0 D.a and B have different symbols, and the absolute value of negative numbers is large.
7. Straightening a curved road can shorten the distance, and the mathematical principle involved is ().
A. there are countless straight lines outside a point b, and two points determine a straight line.
C.the shortest line segment d between two points. The line segment is a part of a straight line.
8. A brand of goods can still get a profit of 10% if they are sold at a 20% discount. If the price of the commodity is 275 yuan, the purchase price of the commodity is ().
A 192.5 Yuan B 200 yuan C 244.5 Yuan D 253 Yuan.
9. As shown in the figure, the vertical vertex angles o of two right-angled triangular plates coincide. What if? BOC=？ Then go to AOD. The degree of BOC is ()
.30 caliber? B.45？ C.54？ D.60？
10. The integer A suitable for | 2a+5 |+2a | 3 | = 8 has ().
A.4 B.5 C.7 D.9
Second, fill in the blanks
The reciprocal of 1 1. -Yes.
12. Pass through all diagonals of a vertex of a polygon and divide it into six triangles. This polygon is a polygon.
13. As shown in the figure, the numbers corresponding to points A, B and C on the number axis are A, B and C respectively. Simplify | A |+C | B | | A+B | =
14. As shown in the figure, P 1 is a semicircular cardboard with a radius of 1. Cut a semicircle with radius at the left lower end of P 1 to get figure P2, and then cut a smaller semicircle in turn (the diameter of semicircle is the radius of the semicircle cut in front) to get figures P3, P4,? ，Pn，？ Remember that the area of cardboard Pn is Sn. Try to calculate S 1, S2, and guess Sn- 1-Sn = (n? 2).
Third, answer questions.
15. Calculation problem
( 1)30? ( ﹣ ﹣ );
(2)﹣ 14﹣( 1﹣0.5) [ 1﹣(﹣2)3].
16. Solve the equation:
( 1) ﹣ = 1
(2) ﹣ =0.5.
17. As shown in the figure, given line segments A and B, make a line segment AB with a ruler, so that AB = 2A-B (no writing, but drawing lines).
18. Simplify first and then evaluate (﹣x2+3xy﹣ y2)﹣(﹣ x2+4xy﹣ y2), where x=2 and y= 1.
19. The New Year is coming. Children in poor mountainous areas want to write a letter to Mr. Wang who has helped them. When folding rectangular stationery into a standard envelope, they found that, as shown in Figure ①, if the stationery is folded in half twice and loaded along the edge of the envelope, the width is 3.8cm. If the letter paper is folded into three equal parts as shown in Figure ②, the width is 1.4 cm when it is loaded in the same way. Try to find out the length of the letter paper and the width of the envelope.
20. Smog weather seriously affects the quality of life of citizens. During the New Year's Day this year, the students in Class One, Grade Seven, of a school were right. What are the main causes of haze weather? A random survey was conducted on the public's views, and the survey results were sorted out, and an incomplete statistical chart (as shown below) was drawn, and the following problems were observed and analyzed.
Percentage of the main causes of haze weather in the population
Industrial pollution 45%
B automobile exhaust emission m
The flue gas emission of boiler C is 15%.
D others (deforestation, etc. )n
(1) This time, * * * citizens were investigated;
(2) completing the bar graph;
(3) The central angle of the sector corresponding to area B in Figure 2 is degrees.
2 1. As shown in the figure, you know? COB=2？ AOC, OD split equally? AOB, and COD=25? , beg? Degree of AOB.
22. Warehouse A has 65,438+000 tons of cement, and Warehouse B has 80 tons of cement. They all need to be transported to the places A and B. It is known that the place A needs 70 tons, and the place B needs 1 10 tons. The freight charges from warehouse A to the places A and B are 140 yuan/ton and 150 respectively.
(1) The cement transported from warehouse A to site A is X tons. Please use x to represent other unknowns in the table below.
A warehouse b warehouse
Site x
B site x+ 10
(2) The algebraic expression containing X indicates that the freight for transporting100t cement in warehouse A is RMB. (Write simplified results)
(3) Inquire about the tonnage of cement transported from warehouse A to site A. 。
23. Given that the line segment AB= 12 and CD=6, the line segment CD moves on the straight line AB (A is on the left side of B and C is on the left side of D).
(1) When point D coincides with point B, AC =；;
(2) Point P is any point on the extension line of AB line. Under the condition of (1), find the value of PA+Pb-2pc;
(3)M and N are the midpoint of AC and BD, respectively. When BC=4, find the length of MN.
Analysis of Reference Answers and Test Questions in the Final Examination Paper of Mathematics in Grade Two of Junior High School I. Multiple-choice Questions
1. The highest temperature in a place 12℃ and the lowest temperature -2℃, then the temperature difference in that place is ().
A.﹣ 10℃d.﹣ 14℃
Test center rational number subtraction.
The analysis uses the highest temperature 12℃ to subtract the lowest temperature -2℃ according to the meaning of the question, and the answer can be obtained according to the fact that subtracting a number is equal to adding the inverse of this number.
Solution:12 ~ (~ 2) =14 (℃).
2. It is reported that at present, China? Tianhe No.2? The computing speed of supercomputers ranks first in the world, reaching 338.6 trillion times per second. The figure of 338.6 billion can be simply expressed as () by scientific notation.
A.3.386？ 108 B.0.3386？ 109 C.33.86？ 107 D.3.386？ 109
Scientific counting of test sites? Represents a bigger number.
Analytical scientific notation is expressed as? 10n, where 1? | a |< 10, n is an integer. When determining the value of n, it depends on how many digits the decimal point moves when the original number becomes a, and the absolute value of n is the same as the number of digits the decimal point moves. When the absolute value of the original number >; 1, n is a positive number; When the absolute value of the original number
Solution: The number 338 600 000 can be simply expressed as 3.386 by scientific notation. 108.
So choose: a.
3. Place a machine part as shown in the figure (Figure 1). If the figure viewed from the front is as shown in Figure 2, then the figure viewed from above is ().
A.B. C. D。
Three views on simple combination of test sites.
According to analysis, the picture from above is a top view, and the answer can be obtained.
Solution: Seen from above, it is three rectangles with the same width.
Therefore, choose: d.
4. The following statement is true ()
A. rational numbers are divided into positive numbers and negative numbers.
B. the reciprocal of rational number must be less than 0.
C. two numbers with equal absolute values are not necessarily equal.
D. the absolute value of rational number must be greater than 0.
Reasonable number of test sites; Countdown; absolute value
According to the classification of rational numbers and the nature of absolute values, we can get the answer.
Solution: a, rational numbers are divided into positive numbers, zero numbers and negative numbers, so a does not meet the meaning of the question;
B, the reciprocal of a negative number is greater than zero, so b does not meet the meaning of the question;
C, the absolute value of the reciprocal number is equal, so c meets the meaning of the question;
D, the absolute value is not negative, so D does not meet the meaning of the question;
So choose: C.
5. The coefficient and order of Monomial--23a2b3 are () respectively.
A.﹣2,8 B.﹣8,5 C.2，8 D.﹣2,5
Test center singleton
According to the definition of single coefficient and times, the analysis problem is solved The numerical factor in the monomial is called the coefficient of the monomial, and the sum of the indices of all letters is called the degree of the monomial.
Solution: The coefficients and degrees of monomial--23a2b3 are -8 and 5 respectively.
So choose B.
6.if A+B
A.a & lt0，b & gt0 B.a & lt0，b & lt0
C.a>0, b<0 D.a and B have different symbols, and the absolute value of negative numbers is large.
Test site rational number multiplication; Addition of rational numbers.
The analysis is based on a+b.
Solution: ∫A+B
? A>0, b<0 and | a |
That is to say, the signs of a and b are different, and the absolute value of negative numbers is large.
So choose D.
7. Straightening a curved road can shorten the distance, and the mathematical principle involved is ().
A. there are countless straight lines outside a point b, and two points determine a straight line.
C.the shortest line segment d between two points. The line segment is a part of a straight line.
The nature of the test center line segment: the line segment between two points is the shortest.
According to the nature of the line segment, we can get the answer.
Solution: Straightening the curved road can shorten the distance. The mathematical principle is that the line segment between two points is the shortest.
So choose: C.
8. A brand of goods can still get a profit of 10% if they are sold at a 20% discount. If the price of the commodity is 275 yuan, the purchase price of the commodity is ().
A 192.5 Yuan B 200 yuan C 244.5 Yuan D 253 Yuan.
The application of one-dimensional linear equation in examination center.
If the purchase price of a commodity is X yuan, you can still get a profit of 10% if you sell it at a 20% discount on the basis of the known price tag. It can be seen that the selling price is (1+ 10%)x yuan, and the commodity price is 275 yuan, so the selling price is 275 yuan. 80% yuan, and its equivalent relationship is the equivalent price. Therefore, the equations are listed and solved.
Solution: Let the purchase price of goods be X yuan. According to the meaning of the question, we can get:
( 1+ 10%)x=275？ 80%,
1. 1x=220，
x=200。
Therefore, the purchase price of goods is 200 yuan.
Therefore, choose: B.
9. As shown in the figure, the vertical vertex angles o of two right-angled triangular plates coincide. What if? BOC=？ Then go to AOD. The degree of BOC is ()
.30 caliber? B.45？ C.54？ D.60？
Calculation of test center angle.
Analyze this problem? Two right triangles? Do you know? DOC=？ BOA=90？ Can it be proved according to the equivalence of the complementary angle of the same angle? DOB=？ AOC, set by the meaning of the question? BOC=x？ And then what? AOD=5x？ It can be solved by combining the diagram equation.
Solution: From the coincidence of the vertical vertex angles o of two right-angled triangular plates, we can know that DOC=? BOA=90？
DOB+？ BOC=90？ ,? AOC+？ BOC=90？ ,
DOB=？ AOC，
Settings? BOC=x？ And then what? AOD=5x？ ,
DOB+？ AOC=？ AOD﹣？ BOC=4x？ ,
DOB=2x？ ,
DOB+？ BOC=3x？ =90?
Solution: x=30
So choose a.
10. The integer A suitable for | 2a+5 |+2a | 3 | = 8 has ().
A.4 B.5 C.7 D.9
Absolute value of test center.
Analyzing this equation can be understood as the sum of the distances from 2a to -5 and 3, from which the value of 2a can be obtained, and then the answer can be obtained.
Solution: As shown in the figure, it can be concluded that when 2a is -4, -2, 0, 2, A takes an integer * * * four values.
So choose: a.
Second, fill in the blanks
The reciprocal of 1 1. -Yes.
The number of test sites is opposite.
To find the inverse of a number by analysis is to add it before this number? ﹣? Number.
The inverse of the solution: ﹣ is ﹣ (﹣) =.
So the answer is:
12. Pass through all diagonals of a vertex of a polygon and divide it into six triangles. This polygon is octagonal.
Test the diagonal of the central polygon.
According to the diagonal formula of N polygon, we can get the answer.
Solution: Let the polygon be N-sided, which is obtained by diagonal formula.
n﹣2=6.
The solution is n=8,
So the answer is: eight.
13. As shown in the figure, the numbers corresponding to points A, B and C on the number axis are A, B and C respectively. Simplified | A |+C | B | | A+B | = 0.
Addition and subtraction of algebraic expressions of test sites; Number axis; absolute value
According to the position of the point on the number axis, the positive and negative expressions in the absolute value are judged, and the result is obtained by simplifying the algebraic meaning of the absolute value, removing the brackets and merging.
Solution: according to the meaning of the question: a
? a & lt0,c﹣b>； 0,a+b﹣c<； 0,
? |a|+|c﹣b|﹣|a+b﹣c|=﹣a+(c﹣b)+(a+b﹣c)=﹣a+c﹣b+a+b﹣c=0.
So the answer is 0.
14. As shown in the figure, P 1 is a semicircular cardboard with a radius of 1. Cut a semicircle with radius at the left lower end of P 1 to get figure P2, and then cut a smaller semicircle in turn (the diameter of semicircle is the radius of the semicircle cut in front) to get figures P3, P4,? ，Pn，？ Remember that the area of cardboard Pn is Sn. Try to calculate S 1, S2, and guess Sn- 1-Sn = () 2n- 1? . (n？ 2).
Calculation of sector area of test center.
The analysis shows that P 1 is a semicircular cardboard with a radius of 1. After cutting a semicircle with radius at the left lower end of P 1, the graph P2, S 1= 12=? ，S2=？ () 2. Similarly, we can get Sn- 1 =? ﹣ ( )2﹣ [( )2]2﹣? ﹣ [( )n﹣2]2,Sn=？ ﹣ ( )2﹣ [( )2]2﹣? [() n ﹣ 2] 2 ﹣ [() n ﹣ 1] 2, and the difference between them can be obtained.
Solution: according to the meaning of the question, n? 2.
S 1= 12=？ ,
S2=？ ﹣ ( )2,
?
Sn﹣ 1=？ ﹣ ( )2﹣ [( )2]2﹣? ﹣ [( )n﹣2]2，
Sn=？ ﹣ ( )2﹣ [( )2]2﹣? ﹣ [( )n﹣2]2﹣ [( )n﹣ 1]2，
? sn﹣ 1﹣sn=()2n﹣2=( )2n﹣ 1？ .
So the answer is () 2n- 1? .
Third, answer questions.
15. Calculation problem
( 1)30? ( ﹣ ﹣ );
(2)﹣ 14﹣( 1﹣0.5) [ 1﹣(﹣2)3].
Mixed operation of rational numbers in test sites.
Analyze the original formula (1) and get the result by multiplication and division.
(2) The original formula calculates the power operation first, then the multiplication operation, and finally the addition and subtraction operation to get the result.
Solution: (1) Original formula =15-20-24 =15-44 =-29;
(2) The original formula =- 1-9 =-.
16. Solve the equation:
( 1) ﹣ = 1
(2) ﹣ =0.5.
Try to solve the one-dimensional linear equation.
The general steps to understand a linear equation with one variable are analyzed: removing the denominator, removing brackets, moving terms, merging similar terms, and converting the coefficient into 1, so as to find the solution of each equation.
Solution: Divide (1) by the denominator to get 2 (5+2x)-3 (10-3x) = 6.
Without parentheses, we get 10+4x-30+9x = 6.
Move the term to 4x+9x = 6- 10+30.
Combining similar projects, we get 13x=26.
The coefficient is 1 and x=2.
(2) Divide by the denominator to get1.5x-0.3 (1.5-x) = 0.5? 0.6
Without brackets, you get 1.5x+0.3x-0.45 = 0.3.
When the term is shifted, it is 1.5x+0.3x=0.3+0.45.
Combining similar projects, we get 1.8x=0.75.
The coefficient is 1, and x=
17. As shown in the figure, given line segments A and B, make a line segment AB with a ruler, so that AB = 2A-B (no writing, but drawing lines).
Test site mapping? Complex drawings.
X-ray first, then intercept AD=DC=a, then intercept BC=b, and AB = 2A-B can be obtained.
Solution: As shown in the figure, the line segment AB is the demand.
18. Simplify first and then evaluate (﹣x2+3xy﹣ y2)﹣(﹣ x2+4xy﹣ y2), where x=2 and y= 1.
Addition and subtraction of algebraic expressions? Simplify the assessment.
Firstly, simplify (﹣x2+3xy﹣ y2)﹣(﹣ x2+4xy﹣ y2), and then substitute x=2 and y= 1 into the simplified formula to find the value of the formula.
Solution: (﹣x2+3xy﹣ y2)﹣(﹣ x2+4xy﹣ y2)
=﹣x2+3xy﹣ y2+ x2﹣4xy+ y2
=﹣0.5x2﹣xy+y2
When x=2 and y= 1,
Original formula =-0.5? 22﹣2? 1+ 12
=﹣2﹣2+ 1
=﹣3
19. The New Year is coming. Children in poor mountainous areas want to write a letter to Mr. Wang who has helped them. When folding rectangular stationery into a standard envelope, they found that, as shown in Figure ①, if the stationery is folded in half twice and loaded along the edge of the envelope, the width is 3.8cm. If the letter paper is folded into three equal parts as shown in Figure ②, the width is 1.4 cm when it is loaded in the same way. Try to find out the length of the letter paper and the width of the envelope.
The application of one-dimensional linear equation in examination center.
If the paper length of the stationery is 12cm, the width of the envelope is (4x+ 1.4)cm. According to the folding method of stationery, a linear equation about x can be obtained if the width of the envelope is unchanged, and a conclusion can be drawn by solving it.
Solution: If the paper length of stationery is 12cm and the width of the envelope is (4x+ 1.4)cm.
According to the meaning of the question: 3x+3.8=4x+ 1.4,
Solution: x=2.4,
? 12x=28.8，4x+ 1.4= 1 1。
A: The paper length of stationery is 28.8cm, and the width of the envelope is 1 1cm.
20. Smog weather seriously affects the quality of life of citizens. During the New Year's Day this year, the students in Class One, Grade Seven, of a school were right. What are the main causes of haze weather? A random survey was conducted on the public's views, and the survey results were sorted out, and an incomplete statistical chart (as shown below) was drawn, and the following problems were observed and analyzed.
Percentage of the main causes of haze weather in the population
Industrial pollution 45%
B automobile exhaust emission m
The flue gas emission of boiler C is 15%.
D others (deforestation, etc. )n
(1) There are 200 citizens in this survey;
(2) completing the bar graph;
(3) The central angle of the sector corresponding to area B in Figure 2 is 108 degrees.
Bar chart of test center; Statistical table; Department statistical chart.
Analysis (1) According to the information of histogram and pie chart, the number and percentage of people in group A are obtained, and the number of citizens under investigation is calculated;
(2) According to the percentages of group A and group C, the number of people in group D can be obtained from the sum of the number of people in each group to complete the histogram;
(3) The proportion of citizens holding the main reasons of Group B multiplied by 360? Find the answer.
Solution: (1) According to the bar chart and fan chart, there are 90 people in group A, accounting for 45%.
? The citizens of this survey are: 90? 45%=200 people,
So the answer is: 200;
(2) There are 200 people in Group A? 45%=90 people, and there are 200 people in Group C? 15%=30 (person),
? The number of people in group D is 200-90-60-30 = 20.
Complete the bar chart as follows:
(3) The percentage of Group B is 60? 200=30%,
? 30%? 360? = 108? ,
That is, the degree of the central angle of the sector corresponding to area B is: 108? ,
So the answer is: 108.
2 1. As shown in the figure, you know? COB=2？ AOC, OD split equally? AOB, and COD=25? , beg? Degree of AOB.
Calculation of test site angle; Definition of angular bisector.
Analyze first? So AOC=x? COB=2？ AOC=2x, and then according to the definition of angular bisector? AOD=？ BOD= 1.5x, and then according to? COD=25？ List the equations, solve the equations to get the value of x, and then you can get the answer.
Solution: Settings? So AOC=x? COB=2？ AOC=2x。
∫OD split? AOB，
AOD=？ BOD= 1.5x。
COD=？ AOD﹣？ AOC= 1.5x﹣x=0.5x.
∵? COD=25？ ,
? 0.5x=25？ ,
? x=50？ ,
AOB=3？ 50? = 150? .
22. Warehouse A has 65,438+000 tons of cement, and Warehouse B has 80 tons of cement. They all need to be transported to a place and b place. It is known that a place needs 70 tons, b place needs 1 10 tons, and the freight from warehouse A to a place and b place is 140 yuan/ton and 150 respectively.
(1) The cement transported from warehouse A to site A is X tons. Please use x to represent other unknowns in the table below.
A warehouse b warehouse
Site x70-x
B site 100 x x+ 10
(2) The algebraic expression containing X indicates that the freight for transporting 100 tons of cement in warehouse A is-10x+ 15000 yuan. (Write down the simplified results)
(3) Inquire about the tonnage of cement transported from warehouse A to site A. 。
The application of one-dimensional linear equation in examination center.
Analysis (1) Just fill in the form according to the meaning of the question;
(2) According to the data in the table and the known freight, the total freight can be expressed;
(3) According to the total transportation cost of cement this time, the simplified equation needs 25,900 yuan.
Solution: (1) If the tonnage of cement transported from warehouse A to site A is x tons, then the tonnage of cement transported to site B is tons.
The tonnage of cement transported from warehouse B to site A is (70-x) tons, and that transported to site B is (x+ 10) tons.
Fill in the form as follows:
A warehouse b warehouse
A site x 70-x
B site 100 x x+ 10
So, the answer is: 70-x; 100﹣x；
(2) The freight for transporting100t cement in warehouse A is140x+150 =-10x+15000;
So the answer is:-10x+15000;
(3) 140x+ 150+200(70﹣x)+80(x+ 10)=25900，
Sorted:-130x+3900 = 0.
The solution is x=30.
Answer: The tonnage of cement transported from warehouse A to site A is 30 tons.
23. Given that the line segment AB= 12 and CD=6, the line segment CD moves on the straight line AB (A is on the left side of B and C is on the left side of D).
(1) When point D coincides with point B, AC = 6；;
(2) Point P is any point on the extension line of AB line. Under the condition of (1), find the value of PA+Pb-2pc;
(3)M and N are the midpoint of AC and BD, respectively. When BC=4, find the length of MN.
Sum and difference of test site line segments.
Analysis (1) can draw a conclusion according to the meaning of the question;
(2) AC= AB and CD= AB are obtained from (1), and the conclusion can be drawn according to the sum and difference of line segments;
(3) Need to discuss by classification: ① As shown in figure 1, when point C is on the right side of point B, according to? M and n are the midpoint of line segments AC and BD, respectively? , first calculate the length of AM and DN, and then calculate Mn = ad-am-dn; ② As shown in Figure 2, when point C is located on the left side of point B, the length of MN can be obtained by using the sum-difference relationship between line segments.
Solution: (1) When point D coincides with point B, AC = AB-CD = 6;
So the answer is: 6;
(2) AC= AB comes from (1),
? CD= AB，
Point p is any point on the extension line of line segment AB,
? PA+PB=AB+PB+PB，PC=CD+PB= AB+PB，
? pa+pb﹣2pc=ab+pb+pb﹣2( a b+ Pb)= 0；
(3) As shown in figure 1, ∵M and n are the midpoints of line segments AC and BD respectively.
? AM= AC= (AB+BC)=8，
DN= BD= (CD+BC)=5，
? mn=ad﹣am﹣dn=9；
As shown in fig. 2, ∫M and n are the midpoints of line segments AC and BD, respectively.
? AM= AC= (AB﹣BC)=4，
DN= BD= (CD﹣BC)= 1
? mn=ad﹣am﹣dn= 12+6﹣4﹣4﹣ 1=9.