Jiangsu education printing plate seventh grade first volume mathematics final examination questions.
First, multiple-choice questions (this big question * * *, there are 10 small questions. 2 points for each small question, 20 points * * *)
1. The following operation is correct ()
A.﹣a2b+2a2b=a2b B.2a﹣a=2
C.3a2+2a2=5a4 D.2a+b=2ab
2. The proven combustible ice reserves in a certain sea area of the South China Sea are about 654.38+094 billion cubic meters. 65.438+09.4 billion is expressed as () by scientific notation.
A. 1.94？ 10 10 B.0. 194？ 10 10 C. 19.4？ 109 D. 1.94？ 109
3. Given that (1-m) 2+| n+2 | = 0, the value of m+n is ().
A.-1B.-3 C. 3 D. Not sure.
4. Among the following statements about monomials, the correct one is ().
A. The coefficient is 3 and the degree is 2 b. The coefficient is 2 and the degree is 2.
C. the coefficient is, the degree is 3 d, the coefficient is, and the degree is 3.
5. The geometric figure consisting of a cylinder and a cuboid is shown in the figure, and the left view of this geometric figure is ().
A.B. C. D。
6. as shown in the figure, three straight lines intersect at point o, if CO? AB，？ 1=56? And then what? 2 equals ()
.30 caliber? B.34？ C.45？ D.56？
7. As shown in the figure, point E is a point on the AD extension line. In the following conditions, it cannot be determined that the straight line BC∨AD is ().
A.？ 3=? 4 B？ C=？ CDE C？ 1=? 2 D？ C+？ ADC= 180？
8. The solution of equation 4x-3m = 2 about x is x=m, so the value of m is ().
A.﹣2 B.2 C.﹣ D
9. The following statement:
① Of all the connecting lines between two points, the line segment is the shortest;
(2) Equal angle is the opposite angle;
③ There is one and only one straight line parallel to the known straight line at a point outside the straight line;
The distance between two points is the line segment between them.
The correct number is ()
1。
10. As shown in the figure, there are six rays OA, OB, OC, OD, OE and OF with common endpoints in the plane. Write the numbers 1, 2, 3, 4, 5, 6, 7 from ray OA. What about this number? 20 16? At ()
A. on the ray.
Fill in the blanks (there are 10 small questions in this big question, with 3 points for each small question and 30 points for * * *).
1 1. Comparative size: -0.4.
12. Calculation: =.
13.If =34？ 36? The complementary angle of is.
14. If ﹣2x2m+ 1y6 and 3x3m﹣ 1y 10+4n are similar projects, then m+n=.
15. If the position of rational number on the number axis is as shown in the figure, simplify | a+c |+a | b | | c+b | =.
16. If the value of algebraic expression x+y is 1, then the value of algebraic expression (x+y) 2-x-y+ 1 is.
17. If 2(2x﹣ 1)=3x+ 1 equation is the same as m=x﹣ 1 equation, then the value of m is.
18. Given that the line segment AB=20cm, there is a point C on the straight line AB, and BC=6cm, and M is the midpoint of the line segment AC, then AM= cm.
19. The price of a commodity is 330 yuan, and if it is sold at 20% of the price, it can still make a profit 10%, so the purchase price of each commodity is RMB.
20. Cut a square with a side length of 10cm, cut four small squares with a side length of cm along the thick black solid line, and make a big square as the bottom surface of the regular quadrangular prism; The rest are folded into straight quadrangular prisms without cover according to the dotted line; Finally, the two parts are put together to form a complete right-angled quadrangular prism with a surface area equal to that of the original square.
Third, answer the question (this big question has 8 small questions, ***50 points)
2 1. Calculation: | 14 | (1 |)? 3? |3﹣(﹣3)2|.
22. Solve the equation:
( 1)4﹣x=3(2﹣x)；
(2) ﹣ = 1.
23. Simplify before evaluating: 5 (32B-AB2)-4 (-AB2+32B), where a =- 1 and b =-2.
24. It is known that the value of the algebraic expression 6x2+bx-y+5-2ax2+x+5y- 1 has nothing to do with the value of the letter X.
(1) Find the values of a and b;
(2) Find the value of A2 ~ 2AB+B2.
25. As shown in the figure, what is point P? A point on the edge OB of AOB.
(1) Draw the vertical line of OB through point P, and cross OA at point C,
(2) Draw the vertical line of OA through point P, and the vertical foot is H,
(3) The length PH of the line segment is the distance from point P, and the line segment is the distance from point C to straight line OB.
(4) Because the vertical line segment is the shortest among all the straight lines connected from one point outside the straight line to all points on the straight line, the size relationship of PC, PH and OC of the three line segments is (and? & lt？ Digital connection)
26. How many rooms are there in the hotel? There are triple rooms and double rooms. The daily rates of various rooms are as follows:
Ordinary (yuan/room) luxury (yuan/room)
Triple room 160 400
Double room 140 300
A 50-person tour group went to the hotel and chose some ordinary rooms for three people and deluxe rooms for two people, which just happened to be full. It is understood that the accommodation fee for the tour group on that day is RMB 4020. How many ordinary rooms for three people and deluxe rooms for two people did the tour group stay in?
27. known? AOC=？ BOD=？ (0? & lt？ & lt 180? )
(1) as shown in figure 1, if? =90?
(1) Write a set of equal angles (except right angles) in the diagram, because
Try to guess? Cod and? Whether AOB is equal, complementary or complementary in quantity, and explain the reasons;
② As shown in Figure 2,? COD+？ AOB and? The equivalence relation that AOC satisfies is: When? = ? ,? Cod and? AOB mutual redundancy
28. As shown in the figure, there are two points AB on the straight line L, AB= 12cm, point O is a point on the line segment AB, and OA = 2OB.
( 1)OA = cm OB = cm；
(2) If point C is a point on the AB line and satisfies AC=CO+CB, find the length of CO;
(3) If moving points P and Q start from A and B at the same time and move to the right, the speed of point P is 2cm/s, the speed of point Q is 1 cm/s, and the moving time is ts. When point P coincides with point Q, the two points P and Q stop moving.
① When t is what value, 2op-OQ = 4；;
② When point P passes through point O, move point M from point O and move to the right at a speed of 3 cm/s. When point M catches up with point Q, return immediately, move to point P at a speed of 3cm/s, return immediately after meeting point P, and move to point Q at a speed of 3 cm/s, and so on, until point P and point Q stop, and point M also stops moving. In this process, point m runs.
Jiangsu education printing plate seventh grade first volume mathematics final examination paper reference answer
First, multiple-choice questions (this big question * * *, there are 10 small questions. 2 points for each small question, 20 points * * *)
1. The following operation is correct ()
A.﹣a2b+2a2b=a2b B.2a﹣a=2
C.3a2+2a2=5a4 D.2a+b=2ab
Test sites merge similar items.
Special calculation problems.
According to the merging rules of similar items, the addition and subtraction coefficient and the letter index remain unchanged.
Solution: A, correct;
b、2a﹣a=a；
c、3 a2+2 a2 = 5a 2；
D, no further calculation.
So choose: a.
The commentary on this question examines two definitions of similar terms? Same? ：
(1) contains the same letters;
(2) The same letters have the same index, which is a confusing point. Note that similar items have nothing to do with alphabetical order.
The rules of merging similar items are also investigated, and attention should be paid to accurate application.
2. The proven combustible ice reserves in a certain sea area of the South China Sea are about 654.38+094 billion cubic meters. 65.438+09.4 billion is expressed as () by scientific notation.
A. 1.94？ 10 10 B.0. 194？ 10 10 C. 19.4？ 109 D. 1.94？ 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:19.4 billion =194000000, expressed in scientific notation: 1.94? 10 10.
So choose: a.
The comment on this question examines the appearance 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.
3. Given that (1-m) 2+| n+2 | = 0, the value of m+n is ().
A.-1B.-3 C. 3 D. Not sure.
The nature of non-negative test sites: even power; The nature of non-negative number: absolute value.
By analyzing this problem, we can get the values of m and n according to the properties of non-negative numbers, and then substitute them into the original formula to solve it.
Solution: According to the meaning of the problem:
1﹣m=0,n+2=0，
The solution is m= 1, n =-2,
? m+n= 1﹣2=﹣ 1.
So choose a.
Comments on this topic examine the nature of non-negative numbers. There are three types of non-negative numbers in junior high schools:
(1) absolute value;
(2) even power;
(3) Quadratic root (arithmetic square root).
When the sum of non-negative numbers is 0, each term must be equal to 0. According to this conclusion, this kind of problem can be solved.
4. Among the following statements about monomials, the correct one is ().
A. The coefficient is 3 and the degree is 2 b. The coefficient is 2 and the degree is 2.
C. the coefficient is, the degree is 3 d, the coefficient is, and the degree is 3.
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: According to the definition of single coefficient and times, the single coefficient is 3.
So choose D.
When determining the coefficient and degree of a single item, it is the key to decompose the single item into the product of a number factor and a letter factor.
5. The geometric figure consisting of a cylinder and a cuboid is shown in the figure, and the left view of this geometric figure is ().
A.B. C. D。
The test center judges geometry with three views; Three views of simple assembly.
Analyze and find the chart you get from the left.
Solution: You can see a rectangle from the left with a small rectangle in the middle.
Therefore, choose: d.
This topic examines the knowledge of three views, and the left view is the view seen from the left side of the object.
6. as shown in the figure, three straight lines intersect at point o, if CO? AB，？ 1=56? And then what? 2 equals ()
.30 caliber? B.34？ C.45？ D.56？
Test center vertical line.
Is the analysis based on the definition of vertical line? 3, and then use the solution of equal vertex angle.
Solution: ∵CO? AB，？ 1=56? ,
3=90? ﹣? 1=90? ﹣56? =34? ,
2=? 3=34? .
Therefore, choose: B.
This topic examines the definition of vertical line and the nature of equal vertex angle, which is a basic topic.
7. As shown in the figure, point E is a point on the AD extension line. In the following conditions, it cannot be determined that the straight line BC∨AD is ().
A.？ 3=? 4 B？ C=？ CDE C？ 1=? 2 D？ C+？ ADC= 180？
Determination of parallel lines of test points.
The analysis uses two parallel lines with the same internal angle to get the answer.
Solution: a, ∵? 3+? 4,
? BC∨AD, this option is irrelevant;
b、∵？ C=？ CDE，
? BC∨AD, this option is irrelevant;
c、∵？ 1=? 2,
? AB∨CD, this option is in line with the meaning of the question;
d、∫？ C+？ ADC= 180？ ,
? In A.D. ∨ B.C., this option does not meet the meaning of the question.
So choose: C.
The comment on this question examines the determination of parallel lines. The judgment methods of parallel lines are: the same angle is equal, and two straight lines are parallel; Internal dislocation angles are equal and two straight lines are parallel; The key to solve this problem is to master the judgment of parallel lines.
8. The solution of equation 4x-3m = 2 about x is x=m, so the value of m is ().
A.﹣2 B.2 C.﹣ D
Solutions of one-dimensional linear equations.
Thematic calculation problems; Application problem.
Analyzing the unknowns that make the two sides of the equation equal is called the solution of the equation.
Solution: substitute x=m into the equation.
4m﹣3m=2，
m=2，
So choose B.
This topic examines the solution of a linear equation with one variable. The key to solving the problem is to understand the meaning of the solution of the equation.
9. The following statement:
① Of all the connecting lines between two points, the line segment is the shortest;
(2) Equal angle is the opposite angle;
③ There is one and only one straight line parallel to the known straight line at a point outside the straight line;
The distance between two points is the line segment between them.
The correct number is ()
1。
The nature of the test site line segment: the line segment between two points is the shortest; The distance between two points; Opposite vertex angle and adjacent complementary angle; Parallel axioms and inferences.
According to the analysis, all the connecting lines of two points can have countless connecting ways, such as broken lines, curves, line segments and so on. Of all these lines, the shortest line segment can be obtained. According to the equal vertex angle, we can get ② error; According to the parallel axiom: after passing a point outside the straight line, there is one and only one straight line parallel to this straight line, so this statement is correct; According to the length of the line segment connecting two points, the distance between two points can be called error.
Solution: ① Among all the connecting lines between two points, the line segment is the shortest and the expression is correct;
② Equiangular is diagonal, which is wrong;
(3) it is correct that there is only one straight line parallel to the known straight line at a point outside the straight line;
The distance between two points is a line segment between two points, which is wrong.
There are two kinds of statements that are correct.
Therefore, choose: B.
The comment on this topic mainly examines the nature of line segments, parallel axioms, the distance between two points and right angles. The key is to master the basic knowledge of textbooks skillfully.
10. As shown in the figure, there are six rays OA, OB, OC, OD, OE and OF with common endpoints in the plane. Write the numbers 1, 2, 3, 4, 5, 6, 7 from ray OA. What about this number? 20 16? At ()
A. on the ray.
Regularity of test sites: diversity of numbers.
By analyzing the graph, we can get the characteristics of points on each ray, and then we can solve the problem by seeing which ray 20 16 conforms to.
Solution: According to the diagram, the point on OA is 6n, the point on OB is 6n+ 1, the point on OC is 6n+2, the point on OD is 6n+3, the point on OE is 6n+4, and the point on OF is 6n+5, (n? n)
∵20 16? 6=336,
? 20 16 is on ray OA.
So choose a.
Comment on the number transformation of this problem, the key to solving the problem is to get the characteristics of the number on each ray according to the figure.
Fill in the blanks (there are 10 small questions in this big question, with 3 points for each small question and 30 points for * * *).
1 1. Comparison size: >-0.4.
Comparison of rational numbers of test sites.
Fill in the blanks with thematic reasoning; Real number.
The rules for analyzing the comparison of rational numbers are as follows: ① All positive numbers are greater than 0; ② Negative numbers are all less than 0; ③ Positive numbers are greater than all negative numbers; ④ For two negative numbers, the larger absolute value is smaller, which can be judged accordingly.
Solution: || =, | | 0.4 | = 0.4,
∵& lt； 0.4,
? ﹣& gt； ﹣0.4.
So the answer is: >.
This review mainly examines the method of rational number comparison, which needs to be mastered skillfully. The key to solve this problem is to be clear: ① positive number is greater than 0; ② Negative numbers are all less than 0; ③ Positive numbers are greater than all negative numbers; ④ Of the two negative numbers, the larger one has the smaller absolute value.
12. Calculation: =.
Power of rational number of test center.
Analysis directly uses the meaning and calculation method of power to calculate the answer.
Solution: () 2 =.
So the answer is:
It is the key to solve the problem to investigate the power of rational numbers and master the meaning and calculation method of power.
13.If =34？ 36? The complementary angle is 55? 24? .
Supplementary angle and supplementary angle of the test center; Conversion of degrees, minutes and seconds.
According to analysis, if the sum of two angles is equal to 90? (right angle), that is, these two angles are complementary to each other, that is, one of them is complementary to the other.
The complementary angle of the solution is: 90? ﹣34? 36? =89? 60? ﹣34? 36? =55? 24? ,
So the answer is: 55? 24? .
This review mainly examines the complementary angle, and the key is to master the definition of complementary angle.
14. If ﹣2x2m+ 1y6 and 3x3m﹣ 1y 10+4n are similar projects, then m+n= 1.
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 = 3m- 1, 10+4n=6 are listed, the values of n and m are calculated, and then they are substituted into algebraic expressions.
Solution: ∵ 2x2m+ 1y6 and 3x3m 1y 10+4n are similar items.
? 2m+ 1=3m﹣ 1, 10+4n=6，
? n=﹣ 1,m=2，
? m+n=2﹣ 1= 1.
So the answer is 1.
This topic examines the definition of similar terms, the idea of equations and the significance of negative integer exponent. This is a basic question and easy to answer.
15. If the position of rational number on the number axis is as shown in the figure, simplify | a+c |+a | b | | c+b | = 0.
Real number and axis of test center.
Special calculation problems.
Firstly, the symbols of a, b and c and the sizes of |a|, |b| and |c| are determined according to the positions of points on the number axis, then the symbols of a+c, a-b and c+b are determined, and the absolute value can be simplified to solve.
Solution: as can be seen from the above picture, C.