People's education printing plate seventh grade second volume mathematics final examination questions
First, multiple-choice questions * * * This big question * * 10 small questions, 4 points for each small question, ***40 points. There are four options for each small question, only one of which is correct * * *
1. In the following figures, the irrational number is
A. 03 BC
2. In the following four figures, ∠ 1 and ∠2 are opposite.
A.B. C. D。
3. In the plane rectangular coordinate system, the point is
A. first quadrant B. second quadrant C. third quadrant D. fourth quadrant
4. Among the following surveys, those suitable for comprehensive survey are
A. Understand the eyesight of middle school students in China.
B. investigate the service life of a batch of fluorescent lamps.
C. Investigate the quality of mineral water in the market
D. Investigate whether passengers flying at the airport are carrying prohibited items.
5. The following statement is wrong.
The square root of A. 1 is 1 B. 0 is 0.
C. The arithmetic square root of1is1d. The cube root of1is-1.
6. if a
A.a+3 b-2
C. 12a & lt； 12b D. -2a >-2b
7. As shown in figure 1, whether AD∨BC is.
A.∠C=∠CBE B. ∠C+∠ABC= 180
C.∠FDC=∠C D
8. Which of the following propositions is true?
A. If yes, then > B. If >, then
C. If, then D. If, then
9. There is a question in Sun Tzu's Calculations, the original text is: "There are trees today, and I don't know the length. The rope is four feet and five inches; Bend the rope less than a foot. How long is the wood? " It means: measure a long piece of wood with a rope, and there are 4.5 feet left in the rope; Fold the rope in half and measure this long piece of wood. There is 1 foot left in Changlin. How long is the wood? Let the length of wood be x feet and the length of rope be y feet, then the following equation satisfying the meaning of the problem is
A.B. C. D。
10. There are only two integer solutions to the inequality group about X, so the value range of A is
A.B. C. D。
Second, fill in the blanks * * * There are 6 small questions in this big question, each with 4 points and * * * 24 points.
1 1. Calculation:.
12. Xiaoming's family of three went out with the tour group. The cost of this trip is shown in Figure 2.
If they spend 4000 yuan, they spend 2000 yuan on shopping.
13. The PE teacher selected 40 students from Grade 7 to participate in the school aerobics competition.
The maximum height of these students is 175, and the minimum height is 155.
If the group distance is 3, you can group.
14. As shown in Figure 3, it is known that, = 1: 3,
Then =
15. It is known that if it is an integer, then =.
16. It is known that points A***2, 2***, B * * 1, 0***, point C is on the coordinate axis, and the area of triangle ABC is 2. Please write down the coordinates of all points C that meet the conditions:
Three. Answer * * * There are 1 1 small questions in this big question, ***86 points * * *
17.*** The full mark of this question is 7 * * *
solve an equation
18.*** The full mark of this question is 7 * * *
Solve the inequality group and express the solution set on the number axis.
19.*** The full mark of this question is 7 * * *
The physical education committee of * *1* * * class in a school counted the times of skipping rope for 60 seconds, and drew the following frequency distribution table and frequency distribution histogram:
Multiply by 80 ≤ x
Frequency a 4 12 16 8 3
Use the chart to complete the following questions:
* * * 1 * * * a =；
* * * 2 * * Complete frequency distribution histogram.
***3*** If students who skip rope at least 140 get excellent grades,
What percentage of the total number of outstanding students in the class?
20.*** The full mark of this question is 7 * * *
It is called the solution of binary linear equation.
*** 1*** = ;
***2*** Complete the table below and draw a diagram on the given rectangular coordinate system.
The points of these solutions are ***x, y***.
0 1 3
y 6 2 0
2 1.*** The full mark of this question is 7 * * *
Complete the following proofs * * * Fill in the corresponding conclusions or reasoning basis in the brackets below * * *:
As shown in figure 4, ∠ bed = ∠ b+∠ d.
Proof: AB∨CD.
It is proved that if we cross point E, we can make EF∨AB *** parallel axiom * * *.
∵EF∨AB *** has done * * *,
∴∠BEF=∠B*** ***。
∵∠BED=∠B+∠D*** Known * * *,
And ? bed = ∠ BEF+∠ FED,
∴∠ Fed = * * * * * * Equivalent substitution * * * *.
∴EF∥CD*** ***。
∴AB∥CD*** ***。
22.*** The full mark of this question is 7 * * *
Xiamen is a famous tourist city in China, and "Xiamen Blue" has become a beautiful city card for Xiamen. Last year, Xiamen's air quality ranked second among 74 major cities in China, with 202 days of excellent grade and above. If the number of excellent days this year exceeds 60% of the annual number of days ***366 days, then this year,
23.*** The full mark of this question is 7 * * *
As shown in figure 5, it is divided into A***, 2***, B***-3, 1***, C***-2 and * *. Triangle ABC.
The translation of any point P***x0 and y0*** corresponds to P 1 * * x0+4, y0-1* *,
Do the same translation for triangle ABC to get triangle A1b1c1;
* * *1* * Write the coordinates of A 1;
* * * 2 * * Draw a triangle A 1B 1C 1.
24.*** The full mark of this question is 7 * * *
"Six? During the International Children's Day, a stationery store held a promotion activity, and all goods were given the same discount. Before the promotion, 28 yuan used to buy 6 pens and 2 notebooks, and 20 yuan used to buy 5 pens and 1 notebook. After the promotion, I bought five signature pens and five notebooks with 32 yuan. How much discount did the mall give to the goods in this promotion?
25.*** The full mark of this question is 7 * * *
It is known that they are all solutions of binary linear equations about x and y, and the value of.
26.*** The full mark of this question is11* *.
As shown in figure 6, ∠ABC, which is divided equally, intersects with AD at point E,
BD shares ∠EBC.
* * *1* * If ∠ DBC = 30, find the degree of ∠A;
* * * 2 * * If point F is on the AE line, 7 ∠ DBC-2 ∠ ABF = 180, is there an angle in Figure 6 equal to ∠DFB? If yes, please write down this angle and explain the reasons; If it does not exist, please explain why.
27.*** The full mark of this question is 12 * * *
As shown in Figure 7, in the plane rectangular coordinate system, the origin is O, which is divided into A***0, 3***, B***2, 3***, C***2, -3**, D * * 0,-3 * *. Points p and q are on the sides of the rectangle ABCD. At the same time, point Q also starts from point O and moves at a constant speed along the route of O→D→C→M at a speed of 2 unit lengths per second. When point Q moves to point M, both moving points stop moving. Let the moving time be t seconds and the area of the quadrilateral OPMQ be S.
* * *1* * When t =2, find the value of s;
***2*** If s
Reference answer
A, multiple-choice questions * * * every empty 4 points * * *
1 2 3 4 5 6 7 8 9 10
This is a good example.
II. Fill in the blanks * * * 4 points for each blank * * *
1 1. 12. 1000 13.7 14.35.5
15.- 1, 2, -2 * * Write-1 to get 2 points, 2 to get 1 minute * *.
16. * * * 3,0 * * *, * *-1,0 * * *, * * 0,2 * * *, * * 0,-6 * * *. * * Write the coordinates correctly.
Third, answer questions.
17. Solution:
①+②，get
3x = 3, 2 points.
∴ x =1..................................... 4 points.
Substitute x= 1 into ① to get 1-y = 1, ...
∴ y = 0 .......................................... 6 points.
So the solution of the original equation is
18.
In order to solve inequality (1), you get .................................................................................... 2 points.
If you solve inequality ②, you will get ................................................................... 4 points.
Correctly express the ................................. score of the solution set on the number axis.
Therefore, the solution set of the original inequality group is
19. Solution: * *1* * * A = 2; ................................., two points.
***2*** ........................................................................... scored 4 points for correctly completing the histogram of full frequency distribution.
***3*** Class size = 2+4+12+16+8+3 = 45 people. ...................................................................... scored 5 points.
Number of outstanding students =16+8+3 = 27 ... 6 points.
A: The number of outstanding students accounts for 60% of the total number of students in the class. ................................ scored 7 points.
20. Solution: * *1* * * = 4; .........................., two points.
Draw ......................... correctly in the plane rectangular coordinate system 7 points.
Remarks: 1. Write 1 coordinate correctly, and draw this point correctly for 1 minute;
2. Write two coordinates correctly and give 1 minute;
3. Draw two points correctly and give 1 point.
2 1. Prove that the passing point E is EF∨AB.
∫EF∨AB，
∴∠BEF=∠B*** Two straight lines are parallel, and the inner angle is equal to * * * ...........................................................................................................................
∠∠BED =∠b+∠D，
And ? bed = ∠ BEF+∠ FED,
∴∠ Federal Reserve Bank = * * ∠ D * * * ..............................................................................................................................................
∴ ef ∥ CD * * Internal dislocation angles are equal, and two straight lines are parallel * * * ...................................................................................................................................
∴AB∥CD*** If two straight lines are parallel to the third straight line, then the two straight lines are parallel to each other ***...7 points. Pay attention to the last basis, and the transitivity of writing parallel lines is not deducted.
22. Solution: Suppose that the number of days with good air quality this year is X days more than last year, depending on the meaning of the question.
202+x & gt； 366 60% ........................................... 3 points.
Solution, x >17.6 ................................ 5 points.
X should be a positive integer, so
X ≥18 ............................ 6 points.
A: The number of days with good air quality this year is at least 18 ... 7 points more than last year.
Remarks are solved by arithmetic, which can be clearly stated and graded according to the corresponding steps.
23. solution: A 1 * * * 4,1* * …………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
Draw the correct triangle A1B1C1......................... 7 points.
Note that the three vertices of the triangle A1* * 4,1* *, B 1 * * 1 * *, C1* * 2 and -3 * * * are tracked in the coordinate system.
24. solution: before the discount, each pen is x yuan and each notebook is y yuan, depending on the meaning of the problem.
............................., 3 points.
The solution is 5 o'clock.
∴ .................................... 6 points.
∴
In this promotion, the goods in the mall will be 20% off. .........................................................................................................................................................
25. Solution: ∵ is all the solutions of binary linear equations about X and Y,
∴ ................................................ 2 points.
................................................, 4 points.
It's also VIII
Five points.
Short for ... 6 points.
∴ ………………………………………………………………………………………………………………………………………………………………………………………………… 7 points.
26. Solution: * *1* * ∫ BD bisects ∠ EBC, ∠ DBC = 30.
∴∠ EBC = 2 ∠ DBC = 60 ............................1min.
∫∠ ∠ABC,
∴∠ ABC = 2
∫ AD ∨ BC,
∴∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠ = 180 .....................................
∴∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠.
* * * 2 * * exists ∠ DFB = ∠ DBF ................................ 5 points.
Let ∠ DBC = X, then ∠ ABC = 2 ∠ Abbe = * * * 4x * * ..................................................... scored 6 points.
∫7∠DBC-2∠ABF = 180
∴7x-2∠ABF= 180。
∴∠ ABF = .......................................... 7 points.
∴∠cbf=∠abc-∠abf=； ..........................., eight.
∠ DBF = ∠ ABC -∠ ABF-∠ DBC = 9 points.
∫ AD ∨ BC,
∴∠ DFB+∠ CBF =180 ............................................10.
∴∠DFB =…… 1 1。
∴∠DFB=∠DBF。
27. Solution: Let the area of triangle OPM be S 1 and the area of triangle OQM be S2.
Then S=S 1 +S2.
* * *1* * when t =2, it is divided into P***0, 2***, Q*** 1, -3 * * * .............................................................................................
The crossing point q is QE ⊥ the x axis is at point e.
∴ s1= ..................... 3 points.
S2 = 4 points.
∴ s = s1+S2 = 5 ......................, 5 points.
Remarks Step 1: If the positions of point P and point Q can be correctly marked on the map, give 2 points * * * The following similar steps are the same as * * *.
* * * 2 * * If the distance of point P is t, the distance of point Q is 2t.
(1) When point P is on line segment OA and point Q is on line segment OD,
At this time, the quadrilateral OPMQ does not exist, which is not suitable for the topic and is discarded.
② When point P is on line OA and point Q is on line DC.
S =……6 ... 6 points.
∵ ,
∴, solution.
At this moment, ............................ scored 7 points.
③ At this time, point P is on line segment OA and point Q is on line segment CM.
S = 8 points.
∵ ,
I see.
At this point, there is no ............................................................ 9 for t.
(4) When the time is right, point P is on line segment AB and point Q is on line segment CM.
S = 10.
∵ ,
Get a solution
At this time 1 1 min.
(4) When point P is the midpoint of line AB, point Q and point M coincide, both moving points stop moving.
At this time, the quadrilateral OPMQ does not exist, which is not suitable for the topic and is discarded.
To sum up, when, or ..................... 12 points.
Note * * * 2 * * The first two cases (① and ④) are clearly stated, and the score is1; To sum up, there is no penalty for not writing.