The final examination questions of the first volume of mathematics in the first day of junior high school of Jiangsu Education Edition.
1. Multiple choice question: This big question is ***8 small questions, each with 2 points, and * * * is 16 points. Of the four options given in each small question, exactly one meets the requirements of the topic. Please fill in the serial number of the correct option on the answer sheet.
The absolute value of 1 -2 is ()
A.﹣2 B.2 C.﹣ D
2. The following calculations are correct ()
A.6a+a=6a2 B.﹣2a+5b=3ab
c.4m2n﹣2mn2=2mn d.3ab2﹣5b2a=﹣2ab2
3. A survey agency conducted a survey on the audience's viewing choice of domestic variety shows on Friday. It is estimated that about 6.5 million people in China choose to watch Super Brain by Jiangsu Satellite TV, and the scientific notation for 6.5 million people should be ().
A.6.5？ 106 B.6.5？ 107 C.65？ 105 D.0.65？ 107
4. Among the following statements about monomials, the correct one is ().
A. the coefficient is ﹣, the degree is 3 b, the coefficient is ﹣ and the degree is 4.
C the coefficient is -5, the degree is 3 d, the coefficient is -5, and the degree is 4.
5. Among the following equations, the equation whose solution is x=2 is ().
A.﹣x+6=2x b.4﹣2(x﹣ 1)= 1 c.3x﹣2=3 d . x+ 1 = 0
6. In the following four plane figures, the one that cannot be folded into a rectangular box without a cover is ().
A.B. C. D。
7. The right-angled triangle rotates once around the right-angled edge, and the geometric figure obtained after rotation is ().
A. cylinder B. circle C. cone D. triangle
8. The following statement is true ()
A. the distance between two points is the line segment between them.
B two lines perpendicular to the same line are also perpendicular.
C On the same plane, there is one and only one straight line parallel to the known straight line.
D on the same plane, there is one and only one straight line perpendicular to the known straight line at one point.
Two. Fill-in-the-blank question: This big question is a small question of *** 10, with 3 points for each small question and 30 points for * * *. There is no need to write an answer process. Please write the correct answer directly in the corresponding position on the answer sheet.
9. Known: |x|=3, |y|=2, xy
10. Is it known that the degree of an angle is 18? 20? 32? Then the complementary angle of this angle is.
1 1. Given that the algebraic expression x2-2x+6 has a value of 9, the value of -2x2+4x+6 is.
12. Given that equation (a-4) x | a |-3+2 = 0 is a linear equation about x, then a=.
13. The meaning of the specified symbol is: A ※ B = AB-A+B+ 1, then (-2) ※ 5 =.
14. As shown in the figure, if the plane expansion diagram in the figure is folded into a cube according to the dotted line, and the sum of the two opposite numbers is 0, then x﹣2y=.
15. When the clock is at 3: 20, the acute angle formed by the hour hand and the minute hand is.
16. The monomial list is arranged according to the following rules: x, 3x2, 5x2, 7x, 9x2, 1 1x2, 13x,? , 20 16 should read.
17. The following four life and production phenomena:
(1) you can use two nails to fix the batten on the wall;
(2) When planting trees, as long as the positions of two trees are determined, the straight line where the same row is located can be determined;
(3) From A to B, when erecting wires, always try to erect them along the AB line;
(4) Straightening the curved road can shorten the journey. Which theorem can be used? Between two points, the line segment is the shortest? The phenomena that need to be explained are. (Fill in serial number)
18. Fold a rectangular piece of paper as shown in the figure, and use BD and BE as creases. What if? ABE=35？ then what DBC is a degree.
Three. Solution: This big question is ***9 small questions, with a score of 74 * *. Please answer in the designated area of the answer sheet, and write down the necessary calculation steps, proof process or text description when answering.
19. Calculation:
( 1) 17﹣8? (﹣2)+4? (﹣3)
(2)9+5? (﹣3)﹣(﹣2)2? 4.
20. Solve the equation:
( 1)3x=5x﹣ 14
(2) = 1﹣ .
2 1. Simplify the following formula first, and then evaluate it: 5 (3a2b-ab2)-4 (-ab2+3a2b), where a =-2 and b=3.
22. As shown in the figure, what is point P? A point on the edge OB of AOB.
(1) Draw the vertical line of OA through point P, and the vertical foot is H;
(2) Draw the vertical line of OB through point P and cross OA at point C;
(3) The line segment length PH is the distance from point P to a straight line and the distance from point C to straight line OB. The relationship between line segment PH and PC length is: PH PC (fill in.
23. It is known that the solution of equation 2x+5= 1 about x and a(x+3)= a+x is the same. Find the value of A2+ 1
24. A garment factory originally planned to complete the order of a batch of clothes in a few days. If it produces 20 sets of clothes every day, it will produce 100 sets less than the ordering task, and if it produces 23 sets of clothes every day, it will produce 20 sets more than the ordering task. How many days can it be completed? How many sets of clothes are ordered?
25. Assuming that the line segment AB=20cm, there is a point C on the straight line AB, BC=6cm, and M is the midpoint of the line segment AC, try to find the length of AM (hint: draw a picture first).
26.( 1) The geometric figure composed of small cubes with the same size is shown in figure 1. Please draw the top view and left view of this geometry in the grid of Figure 2.
(2) Build a geometry with a small cube, so that its top view and left view are consistent with what you draw in the grid, then such a geometry should have at least one small cube and at most one small cube.
27. As shown in the figure, the straight line AB and CD intersect at point O,? AOC=72？ Is Leo there? Inside BOD, DOE=2? BOE。
(1) Q? BOE and? AOE degree;
(2) If the light is perpendicular to OE, please write directly? Degree of freedom.
The final examination paper of the first volume of mathematics in the first day of junior high school of Jiangsu Education Edition refers to the answer.
1. Multiple choice question: This big question is ***8 small questions, each with 2 points, and * * * is 16 points. Of the four options given in each small question, exactly one meets the requirements of the topic. Please fill in the serial number of the correct option on the answer sheet.
The absolute value of 1 -2 is ()
A.﹣2 B.2 C.﹣ D
Absolute value of test center.
According to the definition of absolute value, the absolute value of -2 can be obtained directly.
Solution: | | = 2.
So choose B.
The key to the definition of absolute value is to use the nature of absolute value.
2. The following calculations are correct ()
A.6a+a=6a2 B.﹣2a+5b=3ab
c.4m2n﹣2mn2=2mn d.3ab2﹣5b2a=﹣2ab2
Test sites merge similar items.
Analysis can be judged according to the definition of similar items and the method of merging similar items.
Solution: a, 6a+a=7a? 6a2, so A is wrong;
B, -2A and 5b are not similar items and cannot be merged, so B is wrong;
C, 4m2n and 2mn2 are not the same item and cannot be merged, so C is wrong;
D, 3ab2-5ab2 =-2ab2, so d is correct.
Therefore, choose: d.
Comment on the knowledge points examined in this question: the definition of similar items: the same letters, the same index.
The method of merging similar items: the indexes of letters and letters remain unchanged, only the coefficients are added and subtracted. Similar projects may not be merged.
3. A survey agency conducted a survey on the audience's viewing choice of domestic variety shows on Friday. It is estimated that about 6.5 million people in China choose to watch Super Brain by Jiangsu Satellite TV, and the scientific notation for 6.5 million people should be ().
A.6.5？ 106 B.6.5？ 107 C.65？ 105 D.0.65？ 107
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: 6,500,000 is expressed by scientific notation as: 6.5? 106.
So choose: a.
Comment on this question to examine the representation of scientific notation. What is the representative of scientific notation? 10n, where 1? | a |< 10, where n is an integer, the key is to correctly determine the value of a and the value of n.
4. Among the following statements about monomials, the correct one is ().
A. the coefficient is ﹣, the degree is 3 b, the coefficient is ﹣ and the degree is 4.
C the coefficient is -5, the degree is 3 d, the coefficient is -5, and the degree is 4.
Test center singleton
According to the concepts of single coefficient and times, the analysis problem is solved.
Solution: The coefficient of single term-is-and the degree is 4.
So choose B.
This question examines the knowledge of similar projects. The numerical factor in the monomial is called the coefficient of the monomial, and the sum of the indexes of all the letters in the monomial is called the degree of the monomial.
5. Among the following equations, the equation whose solution is x=2 is ().
A.﹣x+6=2x b.4﹣2(x﹣ 1)= 1 c.3x﹣2=3 d . x+ 1 = 0
Solutions of one-dimensional linear equations.
Special calculation problems.
The solution of an analytical equation is an unknown number that can make the left and right sides of the equation equal. Substitute x=2 into each equation to test whether the left and right sides of the equation are equal.
Solution: Substitute x=2 into four options:
A, left =-x+6 =-2+6 = 4 = right =2x=2? 2=4, therefore, A is correct;
B, left = 4-2 (x- 1) = 2? Right = 1, so b is wrong;
C, left = 3x-2 = 6-2 = 4? Right =3, so c is wrong;
d，left = x+ 1 = 1+ 1 = 2？ Right =0, so d is wrong;
So choose a.
The review of this topic mainly examines the definition of the solution of the equation, so we should master this content skillfully.
6. In the following four plane figures, the one that cannot be folded into a rectangular box without a cover is ().
A.B. C. D。
Fold the expanded test site map into geometric figures.
Using the characteristics of cuboid and its surface expansion diagram to solve the problem.
Solution: Options B, C and D can all be folded into a rectangular box without a lid.
In option A, the lengths of the upper and lower bottoms are inconsistent with the side lengths, and cannot be folded into a rectangular box without a cover.
So choose a.
When commenting on solving such problems, we might as well do something to solve them.
7. The right-angled triangle rotates once around the right-angled edge, and the geometric figure obtained after rotation is ().
A. cylinder B. circle C. cone D. triangle
Test points, lines, surfaces and objects.
According to the surface moving body, a triangle can be rotated around a right angle to get a cone.
Solution: the axial section of the cone is a right triangle, so the cone can be regarded as a right triangle that rotates once on a straight line with right-angled sides.
Therefore, a right triangle can form a cone by rotating once around its right side.
So choose: C.
The comment on this topic mainly examines the knowledge of line moving surface, and students should pay attention to the cultivation of spatial imagination. The key to solve this problem is to master the characteristics of various surface moving objects.
8. The following statement is true ()
A. the distance between two points is the line segment between them.
B two lines perpendicular to the same line are also perpendicular.
C On the same plane, there is one and only one straight line parallel to the known straight line.
D on the same plane, there is one and only one straight line perpendicular to the known straight line at one point.
Parallel axiom and test center reasoning; The nature of line segment: the shortest line segment between two points; vertical line
Analysis is based on the related concepts and properties of line segments, vertical lines and parallel lines.
Solution: a, the distance between two points refers to the length of the line segment between two points, not the line segment itself, wrong;
B, in the same plane, two straight lines perpendicular to the same straight line are parallel and wrong;
C, in the same plane, one and only one straight line is parallel to the known straight line, which point should be emphasized? Out of line? , error;
D, this is the nature of the vertical line, correct. So choose D.
This review mainly examines the definition of axioms, and mastering axioms and definitions is the key to learning mathematics well.
Two. Fill-in-the-blank question: This big question is a small question of *** 10, with 3 points for each small question and 30 points for * * *. There is no need to write an answer process. Please write the correct answer directly in the corresponding position on the answer sheet.
9. Known: |x|=3, |y|=2, xy
Test site rational number multiplication; Absolute value; Addition of rational numbers.
Analysis If |x|=3 and |y|=2, then x=? 3，y=？ 2; With xy<0, xy is different; So x+y=? 1.
Solution: | x | = 3, |y|=2,
? x=？ 3，y=？ 2,
∵xy & lt； 0,
? The xy sign is opposite,
(1) when x = 3 and y =-2, x+y =1;
② When x =-3 and y=2, x+y =- 1.
Comment on the simplification of absolute value, the absolute value of positive number is itself, the absolute value of negative number is its opposite number, and the absolute value of 0 is 0.
10. Is it known that the degree of an angle is 18? 20? 32? The complementary angle of this angle is 73? 4 1? 28? .
Supplementary angle and supplementary angle of the test center; Conversion of degrees, minutes and seconds.
Is the analysis basis sum 90? When the two angles are complementary, a conclusion can be drawn.
Solution: 90? ﹣ 18? 20? 32? =73? 4 1? 28? ,
So the answer is: 73? 4 1? 28? .
The comments on this topic mainly examine the knowledge points of complementary angles and complementary angles. The sum of the two angles is 90? The two angles are complementary, and this problem is relatively simple.
1 1. Given that the value of algebraic expression x2-2x+6 is 9, the value of -2x2+4x+6 is 0.
Algebraic evaluation of test points.
If the equation x2-2x+6 = 9 is listed according to the meaning of the question, x2-2x = 3 is obtained, so the whole equation is substituted into the required algebraic expression for evaluation.
Answer: according to the meaning of the question, you must
X2 2x+6 = 9, then X2 2x = 3.
So -2x2+4x+6 =-2 (x2-2x)+6 =-2? 3﹣6=0.
So the answer is: 0.
Comments on this topic examine algebraic evaluation. Pay attention to the whole substitution method.
12. It is known that the equation (a﹣4)x|a|﹣3+2=0 is a linear equation about x, so a= ﹣4.
Definition of one-dimensional linear equation of test center.
Analysis According to the definition of linear equation of one variable, it is concluded that | a |-3 = 1, pay attention to a |-4? 0, and then get the answer.
Solution: From the meaning of the question: | a |-3 = 1, a |-4? 0,
Solution: A =-4.
So the answer is: -4.
This paper mainly investigates the definition of linear equation with one variable, and correctly grasping the definition is the key to solving the problem.
13. The meaning of the specified symbol is: A ※ B = AB-A+B+ 1, then (-2) ※ 5 =-2.
Mixed operation of rational numbers in test sites.
A new definition of topic.
According to the new definition in the analysis, the formula is simplified and the result can be obtained by calculation.
Answer: According to the meaning of the question: (-2) ※ 5 =-2? 5﹣(﹣2)+5+ 1=﹣ 10+2+5+ 1=﹣2.
So the answer is: -2.
This topic reviews the mixed operation of rational numbers, and it is the key to solve this problem to clarify the new definition in the topic.
14. As shown in the figure, if the plane expansion diagram in the figure is folded into a cube according to the dotted line, and the sum of the two opposite numbers is 0, then x-2y = 6.
Test center topic: text on both sides of the cube.
Based on the characteristics of a cube and its surface expansion diagram, according to the fact that the sum of the two opposite numbers is 0, that is, the two numbers are opposite, the values of X and Y are obtained, and thus the value of x-2y is obtained.
Solution: Solution: Do you know that the plane expansion diagram in the title map is marked with numbers after it is folded into cubes according to the dotted line? 2? The face of and the face marked with X are opposite faces, marked with numbers? 4? The face of and the face marked with y are opposite faces.
∫ The sum of the two opposite numbers is 0,
? x=﹣2,y=﹣4，
? x﹣2y=﹣2﹣2？ (﹣4)=﹣2+8=6.
So the answer is: 6.
This question examines the unfolding figure of the cube, and pays attention to analyzing and answering questions from the opposite side.
15. When the clock is at 3: 20, the acute angle formed by the hour hand and the minute hand is 20? .
Clock face angle of test center.
Special application problems.
This analysis is solved by the characteristics of the clock plate. The clock dial * * has 12 numbers, and the included angle between each number is 30? There are 60 squares on the dial, and the degree between each square is 6? From this, it can be inferred that the angle between the minute hand and the hour hand of the clock is 3: 20.
Answer: At 3: 20, the hour hand points between the numbers 3 and 4. How far is it from 4? (60-20), the minute hand points to 4,
The clock has 12 digits, and the angle between every two adjacent digits is 30? ,
? What is the angle between the minute hand and the hour hand at 3: 20 sharp? (60﹣20)? 6? =20 degrees.
So the answer is: 20? .
This topic investigates the angle calculation of clock minute hand. In the clock problem, the degree relationship between the rotation of the hour hand and the minute hand is often used: each rotation of the minute hand 1? Turn clockwise ()? The angle diagram is established by using the position relationship between the hour hand and the minute hand at the starting time.
16. The monomial list is arranged according to the following rules: x, 3x2, 5x2, 7x, 9x2, 1 1x2, 13x,? , then the single item of 20 16 should be 4032x2.
Test center singleton
General types of topics.
According to the single law analysis, the coefficient of n terms is (2n- 1), and the law of times is that every three terms are grouped, which are 1 time, 2 times and 2 times respectively, and the answer can be obtained.
Solution: 20 16? 3=672
? 20 16 item should be (2? 20 16)x2，
So the answer is: 4032x2.
The key to solving this problem is to examine the monomial, observe the formula and find the law.
17. The following four life and production phenomena:
(1) you can use two nails to fix the batten on the wall;
(2) When planting trees, as long as the positions of two trees are determined, the straight line where the same row is located can be determined;
(3) From A to B, when erecting wires, always try to erect them along the AB line;
(4) Straightening the curved road can shorten the journey. Which theorem can be used? Between two points, the line segment is the shortest? The phenomena to be explained are ③ ④. (Fill in serial number)
The nature of the test center line segment: the line segment between two points is the shortest.
Analyze the meaning of the question, carefully analyze the stem of the question, and make a judgment directly by using the nature of the line segment.
Solution: ① ② The phenomenon can be explained by two points that can determine a straight line;
③ ④ This phenomenon can be explained by the shortest line segment between two points.
So the answer is: ③ ④.
The comment on this topic mainly examines the nature of the shortest line segment between two points and the fact that two points set a straight line, which should be understood and distinguished.
18. Fold a rectangular piece of paper as shown in the figure, and use BD and BE as creases. What if? ABE=35？ then what Is DBC 55 years old? Degree.
Test center folding transformation (folding problem); Definition of angular bisector; Calculation of angle; Opposite vertex angle and adjacent complementary angle.
Special calculation problems.
According to the analysis of the nature of folding, we can know? ABE=？ Answer? Is it? DBC=？ DBC？ , again? ABE+？ Answer? BE+？ DBC+？ DBC？ = 180? ,? ABE=35？ And then you can get the answer.
Solution: According to the nature of folding, we can know? ABE=？ Answer? Is it? DBC=？ DBC？ ,
Again? ABE+？ Answer? BE+？ DBC+？ DBC？ = 180? ,
ABE+？ DBC=90？ ,
Again? ABE=35？ ,
DBC=55？ .
So the answer is: 55.
Comment on this question to examine the essence of folding transformation. The shape of the triangle after folding is the same as the original one, and the corresponding angles are equal. What is the conclusion? ABE=？ Answer? Is it? DBC=？ DBC？ It is the key to solving the problem, and the difficulty is average.
Three. Solution: This big question is ***9 small questions, with a score of 74 * *. Please answer in the designated area of the answer sheet, and write down the necessary calculation steps, proof process or text description when answering.
19. Calculation:
( 1) 17﹣8? (﹣2)+4? (﹣3)
(2)9+5? (﹣3)﹣(﹣2)2? 4.
Mixed operation of rational numbers in test sites.
Analysis (1) calculates multiplication and division before addition and subtraction;
(2) Calculate the power first, then multiply and divide, and finally add and subtract.
Solution: (1) Original formula = 17+4- 12.
=9;
(2) The original formula = 9- 15-4? four
=9﹣ 15﹣ 1
=﹣7.
This question examines the mixed operation of rational numbers, and understanding the law of mixed operation of rational numbers is the key to solve this question.
20. Solve the equation:
( 1)3x=5x﹣ 14
(2) = 1﹣ .
Try to solve the one-dimensional linear equation.
Thematic calculation problems; Linear equation (group) and its application.
By analyzing the shift term combination of (1) equation, the x coefficient is transformed 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: The sum of (1) shift terms is 2x= 14.
Solution: x = 7；;
(2) Denominator: 3 (x- 1) = 6-2 (x+2),
Without brackets: 3x-3 = 6-2x-4,
Merge moved items: 5x=5,
Solution: x= 1.
The key to solving this problem is to understand the linear equation of one yuan and master the algorithm skillfully.
2 1. Simplify the following formula first, and then evaluate it: 5 (3a2b-ab2)-4 (-ab2+3a2b), where a =-2 and b=3.
Addition and subtraction of algebraic expressions? Simplify the assessment.
To analyze this problem, we should remove the brackets from the equation, merge similar terms, simplify the algebraic expression to the simplest form, and then substitute the values of A and B. Note that when removing the brackets, if there is a negative sign before the brackets, every item in the brackets will change sign; When merging similar items, only the coefficients are added and subtracted, and the letter index remains unchanged.
Solution: 5 (32B-AB2)-4 (-AB2+32B),
= 15a2b﹣5ab2+4ab2﹣ 12a2b
=3a2b﹣ab2，
When a =-2 and b=3,
Original formula =3? (﹣2)2? 3﹣(﹣2)? 32
=36+ 18
=54.
This topic examines the simplification of algebraic expressions. The addition and subtraction of algebraic expressions is actually to remove brackets and merge similar items, which is a common test site in the 20 16 senior high school entrance examination.
22. As shown in the figure, what is point P? A point on the edge OB of AOB.
(1) Draw the vertical line of OA through point P, and the vertical foot is H;
(2) Draw the vertical line of OB through point P and cross OA at point C;
(3) The line segment length PH is the distance from point P to line AO, CP is the distance from point C to line OB, and the relationship between line segment pH and PC length is pH.
Test site mapping? Basic mapping; The vertical segment is the shortest; The distance from a point to a straight line.
Analysis (1) uses a right-angled triangle, one right-angled side coincides with AO, translates along AO, and makes the other right-angled side intersect with P, then draws a straight line, and the intersection point with AO is recorded as H;
(2) Use a right-angled side of a right-angled triangle to coincide with BO, translate along BO, make the other right-angled side pass through P, and then draw a straight line, and the intersection point with AO is marked as C;
(3) According to the distance from the point to the straight line: the length from a point outside the straight line to the vertical section of the straight line is called the distance from the point to the straight line; The shortest answer is the vertical line segment.
Solution: (1)(2) As shown in the figure:
(3) The length of straight line PH is the distance from point P to straight line AO,
CP is the distance from point c to straight line OB,
The relationship between pH of line segment and PC length is: ph.