Mid-term examination questions in the second volume of junior high school mathematics 1. Multiple choice questions (***36 points)
1. Among the following statements, the one that does not belong to the proposition is ().
A. Two points determine a straight line B. The vertical line is the shortest.
C. the same angle is equal. D. make the bisector of angle a.
2. In the plane rectangular coordinate system, which of the following points is in the fourth quadrant ()
A.( 1，2)b.( 1,﹣2 c.(﹣ 1,2 d.(﹣ 1,﹣2)
3. In the following four figures? 1 and? 2 is the adjacent complementary angle, and 2 is ()
A.B. C. D。
4. The following are true ()
A.=3 B.(﹣ )2= 16 C. =？ Three dimensions =-4
5. The following statement is true ()
The cube root of a is 2b. -3 is the negative cube root of 27.
The cube root of D.(﹣ 1)2 is ﹣ 1.
6. Move point A (-2, -3) to the left by 3 unit lengths to get point B, and the coordinate of point B is ().
A. 1,﹣3 b.(﹣2,0 c.(﹣5,﹣3 d.(﹣2,﹣6)
7. What is the name of the mascot of China 20 10 Shanghai World Expo? Haibao? , that is to say? Treasure of the four seas? Through translation, the mascot in the picture can be changed. Haibao? Go to Figure ()
A.B. C. D。
8. As shown in the figure, AB∨CD, then? A+？ C+？ AEC=()
360? B.270？ C.200？ D. 180？
9. Real number: 3. 14 159,1.01001? , ,? , medium, irrational ()
1。
10. As shown in the figure, if the plane rectangular coordinate system is established on the China chessboard, it will make? Handsome? At point (-1,-2),? The horse is at point (2,-2), and then what? Soldiers? At point ()
A.﹣ 1, 1 b.(﹣2,﹣ 1 c.(﹣3, 1 d.( 1,﹣2)
1 1. As shown in the figure, the straight line AB and CD intersect at the point O, OT? AB in o, CE∑AB and CD in point c, if? ECO=30？ And then what? Point equals ()
.30 caliber? B.45？ C.60？ D. 120？
12. As shown in the figure, straight line AB and CD intersect at point O, OF? CO，？ AOF and? The ratio of BOD degrees is 3: 2, then? The degree of AOC is ()
A. 18？ B.45？ C.36？ D.30？
Two. Fill in the blanks (***24 points)
The antonym of13.3 is.
14. As shown in the figure, I want to build a bridge on both sides of the river, and the shortest time to build a bridge is PM. The reason is.
15. If it is known that real numbers A and B satisfy+| b |1| = 0, then a20 12+b20 13=.
16. The sum of all integers greater than and less than is.
17. the point a is on the left side of the y axis and on the upper side of the x axis, which is 4 unit lengths away from each coordinate axis, so the coordinate of the point a is.
18. as shown in the figure, AB∨CD,? B=40？ , CN is? The bisector of BCE, CM? CN，？ BCM is degrees.
Iii. Answering questions (***90 points)
19. Calculation
( 1) + ﹣( )2+
(2) +| ﹣ 1|﹣( + 1)
20. given | 20 16 |+= a, find the value of a | 20 162.
2 1. As shown in the figure, ADE=? b，？ 1=? 2、FG？ AB, Q: Is Q:CD perpendicular to AB? Try to explain why.
22. explain why
As shown in the figure, 1+? 2=230? , b∨c, then? 1、? 2、? 3、? How many degrees is four degrees?
Solution: ∵? 1=? 2 ( )
? 1+? 2=230?
1=? 2= (degree of filling)
∫b∑c
4=? 2= (degree of filling)
( )
? 2+? 3= 180? ( )
3= 180? ﹣? 2= (degree of filling)
23. Complete the following reasoning process:
As shown in the figure, it is known that DE∑BC, DF and BE are equally divided. Ade? ABC Can you give it a push? FDE=？ Debbie's reason is:
∫DE∨BC (known)
ADE=()
∫DF and BE split equally? Ade? ABC，
ADF=()
? ABE=()
ADF=？ Abe
? ∥ ( )
FDE=？ Debenture corporate bonds ()
24. As shown in the figure, AB∨CD, AE equally divided? No, CD and AE intersect at F. CFE=？ E. Verification: AD ∨ BC.
25. As shown in the figure, write the coordinates of the three vertices of the triangle ABC and calculate the area of the triangle ABC.
26. In the plane rectangular coordinate system, the positions of the three vertices of △ABC are shown in the figure (the side length of each small square is 1).
(1) Please draw △A after △ABC moves 3 unit lengths along the X axis and then 2 unit lengths along the Y axis. b？ c？ (where is a? 、B？ 、C？ They are the corresponding points of a, b and C.
2 write a directly? 、B？ 、C？ Coordinates of three points:
Answer? ( , );
b？ ( , );
c？ ( , ).
27. As shown in the figure, it is known that straight lines l 1∑l2, l3 and l 1, L2 intersect at point A and point B respectively, and point P is on AB.
(1) Try to find out? 1、? 2、? 3. The relationship of giving reasons;
(2) If point P moves between point A and point B, excuse me? 1、? 2、? Has the relationship between 3 changed?
(3) If point P moves beyond points A and B, try to explore? 1、? 2、? 3 (point p does not coincide with a and b)
The answer to the mid-term examination paper in the second volume of junior one mathematics 1. Multiple choice questions (***36 points)
1. Among the following statements, the one that does not belong to the proposition is ().
A. Two points determine a straight line B. The vertical line is the shortest.
C. the same angle is equal. D. make the bisector of angle a.
Propositions and theorems of test sites.
Analyze and judge each option according to the definition of the proposition.
Solution: two points determine a straight line, the shortest vertical line segment and the same angle are propositions, and the bisector of angle A is descriptive language, not a proposition.
So choose D.
2. In the plane rectangular coordinate system, which of the following points is in the fourth quadrant ()
A.( 1，2)b.( 1,﹣2 c.(﹣ 1,2 d.(﹣ 1,﹣2)
Coordinates of the test site.
The coordinate characteristics of a point in the plane coordinate system are: the first quadrant (+,+), the second quadrant (+), the third quadrant (+) and the fourth quadrant (+); According to this feature, we can know the answer to this question.
Solution: Because the abscissa of the point in the fourth quadrant is positive and the ordinate is negative, only B meets the conditions, so B is selected.
3. In the following four figures? 1 and? 2 is the adjacent complementary angle, and 2 is ()
A.B. C. D。
The test center is opposite to the vertex angle and the adjacent complementary angle.
Analysis According to the definition of adjacent complementary angles, two adjacent complementary angles are mutually adjacent complementary angles to judge.
Solution: a, b options,? 1 and? 2 has no common vertex and is not adjacent, so it is not an adjacent complementary angle;
C option? 1 and? 2 complementary and non-adjacent complementary angles;
Option d is complementary and adjacent, which is adjacent complementary angle.
So choose D.
4. The following are true ()
A.=3 B.(﹣ )2= 16 C. =？ Three dimensions =-4
Square root of arithmetic in test center.
Analysis is based on the definition of arithmetic square root: the positive square root of a non-negative number is the arithmetic square root of this number, from which the result can be obtained.
Solution: A =3, so this option is correct;
B, (-) 2 = 4, so this option is wrong;
C =3, so this option is wrong;
D. There is no arithmetic square root, so this option is wrong.
So choose: a.
5. The following statement is true ()
The cube root of a is 2b. -3 is the negative cube root of 27.
The cube root of D.(﹣ 1)2 is ﹣ 1.
Cubic root of test center.
According to x3=a, then x=, x2=b(b? 0) then x=, the answer is that there is only one cube root of a number and only two square roots of a number, and the answer can be obtained accordingly.
Solution: A =8, and the cube root of 8 is 2, so this option is correct.
B, -3 is the cube root of -27, and there is only one cube root of a number, so this option is wrong.
C, so this option is wrong.
The cube root of d,-1) 2 is 1, so this option is wrong.
So choose a.
6. Move point A (-2, -3) to the left by 3 unit lengths to get point B, and the coordinate of point B is ().
A. 1,﹣3 b.(﹣2,0 c.(﹣5,﹣3 d.(﹣2,﹣6)
Changes in coordinates and graphics of test sites-translation.
Subtract 3 from the abscissa and keep the ordinate unchanged, and you can get the coordinates of point B.
Solution: Point A(﹣2, ﹣3) is translated to the left by 3 unit lengths to get point B,
? The abscissa of point B is -2-3 =-5, and the ordinate is unchanged.
That is, the coordinates of point B are (-5, -3), so choose C.
7. What is the name of the mascot of China 20 10 Shanghai World Expo? Haibao? , that is to say? Treasure of the four seas? Through translation, the mascot in the picture can be changed. Haibao? Go to Figure ()
A.B. C. D。
Translation phenomenon in the life of test center.
According to the nature of translation, the shape and size of the figure have not changed before and after translation, but the position has changed.
Solution: A, B and C mascots? Haibao? It is obtained through the rotation of the original figure, so it is not translation, and only if D meets the requirements is translation.
So choose D.
8. As shown in the figure, AB∨CD, then? A+？ C+？ AEC=()
360? B.270？ C.200？ D. 180？
The nature of parallel lines in test sites.
After the analysis, the point E is EF∨AB. According to the properties of parallel lines,? A+？ C+？ AEC can be transformed into the sum of two pairs of internal angles on the same side.
Solution: the intersection e is EF∨AB,
A+？ AEF= 180？ ;
∫AB∨CD，
? EF∑CD，
C+？ FEC= 180？ ,
? (? A+？ AEF)+(？ C+？ FEC)=360？ ,
Namely:? A+？ C+？ AEC=360？ .
So choose a.
9. Real number: 3. 14 159,1.01001? , ,? , medium, irrational ()
1。
The number of test sites is unreasonable.
The analysis can be changed to 4. According to the definition of irrational number, irrational number is1.010010001? ,? .
Solution: ∫= 4,
? The irrational numbers are:1.01001001? ,? .
So choose B.
10. As shown in the figure, if the plane rectangular coordinate system is established on the China chessboard, it will make? Handsome? At point (-1,-2),? The horse is at point (2,-2), and then what? Soldiers? At point ()
A.﹣ 1, 1 b.(﹣2,﹣ 1 c.(﹣3, 1 d.( 1,﹣2)
The coordinates of the test center determine the location.
Analyze and use first? Handsome? Draw a rectangular coordinate system (-1, -2) on the point, and then write? Soldiers? The coordinates of this point.
Solution: As shown in the figure,
? Soldiers? At point (-3, 1).
So choose C.
1 1. As shown in the figure, the straight line AB and CD intersect at the point O, OT? AB in o, CE∑AB and CD in point c, if? ECO=30？ And then what? Point equals ()
.30 caliber? B.45？ C.60？ D. 120？
The nature of parallel lines in test sites.
From the analysis of CE∨AB, according to the fact that two straight lines are parallel and have the same angle, it can be concluded that? The degree of BOD, and by OT? AB, ask for it? The degree of BOT, and then by? DOT=？ BOT﹣？ DOB, you can get the answer.
Solution: ∫CE∨AB,
DOB=？ ECO=30？ ,
∵OT？ AB，
BOT=90？ ,
DOT=？ BOT﹣？ DOB=90？ ﹣30? =60? .
So choose C.
12. As shown in the figure, straight line AB and CD intersect at point O, OF? CO，？ AOF and? The ratio of BOD degrees is 3: 2, then? The degree of AOC is ()
A. 18？ B.45？ C.36？ D.30？
Vertical line of test site; Opposite vertex angle and adjacent complementary angle.
Is analysis available by vertical definition? FOC=90？ , and then according to? AOF and? Is there a ratio of 3: 2 BOD? AOF:？ AOC = 3: 2, and then we can get the answer.
Solution: ∫OF? CO，
FOC=90？ ,
∵? AOF and? The ratio of BOD degree is 3: 2,
AOF:？ AOC=3:2，
AOC=90 =36？ ,
So choose: C.
Two. Fill in the blanks (***24 points)
The reciprocal of 13.3 is 3.
Properties of real numbers in test sites.
According to the analysis, only the opposite number of two numbers with different signs can get the answer.
Solution: The reciprocal of 3 is 3.
So the answer is: -3.
14. As shown in the figure, I want to build a bridge on both sides of the river. The shortest time to build a bridge is PM, because the vertical line is the shortest.
The vertical section of the test center is the shortest.
You can populate the analysis according to the shortest nature of the vertical segment.
Solution:
∵PM？ MN，
? According to the shortest vertical line segment, PM is the shortest.
So, the answer is: the vertical segment is the shortest.
15. If it is known that real numbers A and B satisfy+| b |1| = 0, then a20 12+b20 13= 2.
The nature of non-negative number of test sites: arithmetic square root; The nature of non-negative number: absolute value.
The values of a and b can be obtained according to the non-negative property formula, and then substituted into the algebraic formula to solve.
Solution: according to the meaning of the question, A- 1 = 0, B- 1 = 0,
The solutions are a= 1 and b= 1.
Therefore, a 2012+b 2013 =12012+13 =1+= 2.
So the answer is: 2.
16. The sum of all integers greater than and less than is -4.
The test center estimates the size of irrational numbers.
Analyze the range of ﹣ sum, evaluate the integer solutions in the range, and finally add them.
Answer: ∵: 4 > ? > ﹣5,3<； & lt4,
? All integers greater than and less than are -4. 3,? 2,? 1,0,
? ﹣4﹣3﹣2﹣ 1+0+ 1+2+3=﹣4,
So the answer is: -4.
17. The point A is on the left side of the Y axis and on the upper side of the X axis, and the distance from each coordinate axis is 4 unit lengths, so the coordinate of the point A is (-4,4).
Coordinates of the test site.
According to the position of the point given in the question, the sign of the vertical and horizontal coordinates of the point can be determined, and its coordinates can be obtained by combining its distance from the coordinate axis.
Solution: according to the meaning of the question, point A is on the left side of the Y axis and on the upper side of the Y axis.
Then the abscissa of point A is negative and the ordinate is positive;
Each coordinate axis is 4 unit lengths apart,
Then the coordinates of point A are (-4,4).
So the answer is (-4,4).
18. as shown in the figure, AB∨CD,? B=40？ , CN is? The bisector of BCE, CM? CN，？ BCM is 20 degrees.
The nature of parallel lines in test sites; Definition of angular bisector.
According to the properties of parallel lines, the analysis first comes to the conclusion? The degree of BCE, and then according to the angle bisector? Degree BCN, finally press CM? CN, calculation? The level of BCM is enough.
Solution: ∫AB∨CD, B=40？ ,
BCE= 140？ ,
∵CN is? The bisector of BCE,
BCN=70？ .
∵CM？ CN，
BCM=20？ .
So the answer is: 20.
Iii. Answering questions (***90 points)
19. Calculation
( 1) + ﹣( )2+
(2) +| ﹣ 1|﹣( + 1)
The operation of real number in test center.
Analyze (1) the original formula, and define the calculation result with square root and cubic root.
(2) The original formula makes use of the property of quadratic root, which simplifies the algebraic meaning of absolute value and can get the result without bracket combination.
Solution: (1) Original formula = 5-2-3+2 = 2;
(2) The original formula = 2+- 1- 1 = 0.
20. given | 20 16 |+= a, find the value of a | 20 162.
The meaningful condition of the second root of the inspection center; absolute value
Find the range of a according to the number of roots greater than or equal to 0, and then remove the absolute number to get the solution.
Solution: from the meaning of the question, a-2017? 0,
What about a? 20 17,
If the absolute number is removed, a ~ a ~ 2016+= aa,
? =20 16,
Settle the two sides, a-2017 = 20162,
Therefore, a-20162 = 2017.
2 1. As shown in the figure, ADE=? b，？ 1=? 2、FG？ AB, Q: Is Q:CD perpendicular to AB? Try to explain why.
Determination and properties of parallel lines in the test site; vertical line
The reason why CD is perpendicular to AB is that two straight lines are parallel and the included angle is equal, and ED is parallel to BC according to the included angle in the question, and then the two straight lines are parallel and the included angle is equal. 1=? BCD, a pair of isosceles angles are equal and replaced by equivalence, GF and DC are parallel by two lines with equal isosceles angles, which can prove that one of the parallel lines is perpendicular to the other.
Solution: CD is perpendicular to AB for the following reasons:
∵? ADE=？ b，
? In ∨ BC,
1=? BCD，
∵? 1=? 2,
2=? BCD，
? CD∑FG，
CDB=？ FGB=90？ ,
? CD？ AB。
22. explain why
As shown in the figure, 1+? 2=230? , b∨c, then? 1、? 2、? 3、? How many degrees is four degrees?
Solution: ∵? 1=? 2 (equal vertex angles)
? 1+? 2=230?
1=? 2= 1 15? (Fill in the number)
∫b∑c
4=? 2= , 1 15? (Fill in the number)
(Two straight lines are parallel and the internal dislocation angles are equal)
? 2+? 3= 180? (The complementary angles of two parallel lines which are internal angles to each other)
3= 180? ﹣? 2= 65? (Fill in the number)
The nature of parallel lines in test sites.
Is the analysis based on equal vertex angle? 1 and? 2. According to the nature of parallel lines? 4=? 2,2+? 3= 180? Substitute in and find out.
Solution: ∵? 1=? 2 (equal to the vertex angle),? 1+? 2=230? ,
1=? 2= 1 15? ,
∫b∑c，
4=? 2= 1 15? (two straight lines are parallel and the internal dislocation angles are equal),
? 2+? 3= 180? (The complementary angles of two parallel lines that are internal angles to each other),
3= 180? ﹣? 2=65? ,
So the answer is: the vertex angles are equal, 1 15? , 1 15? Two straight lines are parallel, the internal dislocation angle is equal, two straight lines are parallel, and the internal angles are complementary, 65? .
23. Complete the following reasoning process:
As shown in the figure, it is known that DE∑BC, DF and BE are equally divided. Ade? ABC Can you give it a push? FDE=？ Debbie's reason is:
∫DE∨BC (known)
ADE=？ ABC (two lines are parallel and at the same angle)
∫DF and BE split equally? Ade? ABC，
ADF=？ Definition of angular bisector
? ABE=？ Definition of angular bisector
ADF=？ Abe
? DF∨BE (same angle, two straight lines are parallel)
FDE=？ Debenture corporate bonds (two parallel lines with equal internal angles)
Determination and properties of parallel lines in test site.
Is the analysis based on the properties of parallel lines? ADE=？ ABC, according to the definition of angular bisector? ADF=？ Ed. ABE=？ ABC, launch? ADF=？ ABE, as long as you get the judgment of DF∨BE based on parallel lines.
Solution: The reason is: ∫DE∨BC (known),
ADE=？ ABC (two straight lines are parallel and at the same angle),
∫DF and BE divide ADE and be equally. ABC，
ADF=？ ADE (definition of angular bisector),
? ABE=？ ABC (definition of angular bisector),
ADF=？ Abel,
? DF∨BE (same angle, two straight lines are parallel),
FDE=？ DEB (two straight lines are parallel and the internal dislocation angles are equal),
So the answer is:? ABC, two straight lines are parallel and the same angle is equal; ? ADE, the definition of angular bisector; ? ABC, the definition of angular bisector; DF, BE, same angle, two straight lines are parallel; Two straight lines are parallel and have equal internal angles.
24. As shown in the figure, AB∨CD, AE equally divided? No, CD and AE intersect at F. CFE=？ E. Verification: AD ∨ BC.
Determination of parallel lines of test points.
Firstly, the conditions about AD∑BC are satisfied by using the properties of parallel lines and angular bisectors. 2 and? E is equal, draw a conclusion.
The answer proves: ∫AE split equally? Not good,
1=? 2,
∵AB∨CD，？ CFE=？ e，
1=? CFE=？ e，
2=? e，
? AD ∨ BC.
25. As shown in the figure, write the coordinates of the three vertices of the triangle ABC and calculate the area of the triangle ABC.
Test center coordinates and graphic attributes; The area of a triangle.
For analysis? Digging and filling? Methods The area of triangle ABC was converted into S rectangle debf-s △ AEB-s △ BCF-s △ ADC, and then calculated according to the area formulas of rectangle and triangle.
Solution: As shown in the figure,
S△ABC=S rectangular debf-s △ AEB-s △ BCF-s △ ADC
= 12? 7﹣ ? 6? 7﹣ ? 12? 5﹣ ? 2? six
=27.
26. In the plane rectangular coordinate system, the positions of the three vertices of △ABC are shown in the figure (the side length of each small square is 1).
(1) Please draw △A after △ABC moves 3 unit lengths along the X axis and then 2 unit lengths along the Y axis. b？ c？ (where is a? 、B？ 、C？ They are the corresponding points of a, b and C.
2 write a directly? 、B？ 、C？ Coordinates of three points:
Answer? ( 0 , 5 );
b？ ( ﹣ 1 , 3 );
c？ ( 4 , 0 ).
Test site map-translation transformation.
Analysis (1) According to the grid structure, after translating the points A, B and C, find the corresponding point A? 、B？ 、C？ Position, and then connect in order;
(2) Write the coordinates of each point according to the plane rectangular coordinate system.
Solution: (1)△A? b？ c？ As shown in the figure;
(2) As can be seen from the figure, a? (0，5)，B？ (﹣ 1,3),C？ (4,0).
So, the answer is: 0, 5; ﹣ 1,3; 4,0.
27. As shown in the figure, it is known that straight lines l 1∑l2, l3 and l 1, L2 intersect at point A and point B respectively, and point P is on AB.
(1) Try to find out? 1、? 2、? 3. The relationship of giving reasons;
(2) If point P moves between point A and point B, excuse me? 1、? 2、? Has the relationship between 3 changed?
(3) If point P moves beyond points A and B, try to explore? 1、? 2、? 3 (point p does not coincide with a and b)
The nature of parallel lines in test sites.
Analyze the parallel lines whose (1) crossing point p is l 1, and solve the problem according to the properties of parallel lines. ② ③ It's the same.
Solution: (1)? 1+? 2=? 3;
Reason: the intersection p is a parallel line of l 1
∫l 1∑L2，
? l 1∨L2∨PQ，
1=? 4,? 2=? 5, (two straight lines are parallel, and the internal dislocation angle is equal)
∵? 4+? 5=? 3,
1+? 2=? 3;
(2) The same (1) can prove:? 1+? 2=? 3;
(3)? 1﹣? 2=? 3 or? 2﹣? 1=? three
Reason: When the point P is on the lower side, the parallel PQ passing through the point P is l 1.
∫l 1∑L2，
? l 1∨L2∨PQ，
2=? 4,? 1=? 3+? 4, (two straight lines are parallel and the internal dislocation angles are equal)
1﹣? 2=? 3;
When point p is on the upper side, you can also get:? 2﹣? 1=? 3.