The happy time of summer vacation has passed more than half. Don't forget your summer homework when you play! The following are the math answers I provided for my seventh grade summer homework. Let's have a look!
Choose one carefully first (2 points for each question, 20 points for * *).
1, which cannot be folded into a cube in the following figure is ().
2. The cube as shown in the figure can be () as shown in the figure below after expansion.
*3. There are two points A and B on the number axis representing real numbers A and B respectively, so the length of line segment AB is ().
A.a-b b . a+b c│a-b│d│a+b│
4. Given the line segment AB, take a point C on the extension line of BA and make CA=3AB, then the ratio of line segment CA to line segment CB is ().
A.3︰4 b︰2︰3 c︰3︰5d︰ 1︰2
5. As shown in the figure, the straight line AB and CD intersect at O, EO⊥AB, so the relationship between ∠AOD and ∠AOC in the figure is ().
A. Opposite vertex angle B. Equal C. Complementary D. Complementary
6. As shown in the figure, the point on the straight line PQ is the bisector of the bisector sum, so the following statement is wrong ().
A. and mutual redundancy B. and mutual redundancy
C. Complementarity D. Complementarity
7. As shown in the figure, it cannot be judged that l 1∑L2 is () under the following conditions.
A.∠ 1 =∠3b .∠2 =∠3c .∠4 =∠5d .∠2+∠4 = 180
*8, as shown in the figure, is a fan-shaped statistical chart of the number of seventh-grade students participating in extracurricular activities in a middle school. If there are 42 students participating in dance, the number of students participating in ball games is ().
A. 145 people B. 147 people C. 149 people D. 15 1 person.
*9. A quadrilateral becomes () after cutting off an angle.
A. quadrilateral B. pentagon
C. triangle or quadrilateral or pentagon
* 10, the following statement is true ()
The congruent angles are equal. All right angles are equal. The complementary angle of an angle must be smaller than its complementary angle.
④ Among straight lines, rays and line segments, straight lines are the longest. ⑤ The length of the line segment between two points is the distance between these two points.
If two sides of one angle are parallel to two sides of another angle, then the two angles must be equal.
A.0 B. 1 C. 2 D.3
Second, fill in carefully (2 points for each question, 20 points for * * *)
1 1, as shown in the figure, where * * * has _ _ _ _ _ antipodal angle.
12, then its complementary angle is equal to _ _ _ _ _ _ _ _; The complementary angle of is, then = _ _ _ _ _.
13. As shown in the figure, if CB=4, DB=7 and D is the midpoint of AC, then AC = _ _ _ _ _ _
14, as shown in the figure, cd⊥ab ac⊥bc, the distance from point A to BC is the length of line segment _ _ _ _ _ _, and the distance from point B to CD is the length of line segment _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
15 As shown in the figure, straight lines AB and EF intersect at point D, and ∠ADC=90? If the ratio of ∠ 1 to ∠2 is 1: 4, the degrees of ∠CDF and ∠EDB are respectively.
* 16, as shown in the figure, it is known that ab∨CD, EF intersect with AB in M, CD intersect with F, MN⊥EF intersect with M, and MN intersect with CD in N. If ∠ BME = 1 10, then ∠.
* 17, as shown in the figure, if line A and line B intersect with line C and line D respectively, and ∠ 1+∠ 3 = 90, ∠ 2-∠ 3 = 90, ∠ 4 = 65438+.
18 and figure (1)(2) are broken-line statistical charts drawn according to the daily average temperature in a certain place in the first ten days of June in recent two years. By observing the chart, we can judge the year when the temperature was relatively stable in early June of these two years.
* 19. Use the game stick to build four equilateral triangles with the same size in the same plane, with at least _ _ _ _ _ roots; To build four equilateral triangles with the same size in space, at least _ _ _ _ _ sticks are needed.
**20. At 2: 30 on the clock, the angle formed by the hour hand and the minute hand is _ _ _ _.
Three, careful calculation (6 points per question, * * * 24 points)
2 1. As shown in the figure, CD is any two points on line AB, E is the midpoint of line AC, and F is the midpoint of line BD. If EF=a and CD=b, find the length of AB.
*22, as shown in the figure, AOB is a straight line, ∠ 1+∠2=90, ∠COD is a right angle.
(1) Please write the isometric in the drawing and explain the reasons;
(2) Please write the complementary angle and complementary angle. The angle in the picture.
*23. As shown in the figure, AD bisects ∠BAC, point F is on BD, FE∨AD intersects with AB at G, and the extension line of CA intersects with E. Please explain: ∠ Age = ∠ E.
*24. As shown in the figure, CD shares ∠ACB, DE shares ∨AC, EF shares ∨CD, verification: EF shares ∠BED.
Four, try to solve a solution (***36 points)
*25. Graphics composed of small cubes. The following three pictures are its front view, top view and left view respectively. Please observe how many cubes it is made of.
26. According to the population data of Beijing in 2000 and 2005 published by Beijing Municipal Bureau of Statistics, the following statistical charts are drawn:
Statistical table of education level of permanent residents in Beijing in 2000 and 2005 (unit: 10,000)
Number of people with junior college education (junior college and above), number of people with high school education (including technical secondary school), number of people with junior high school education, number of people with primary school education and others.
2000 233 320 475 234 120
2005 362 372 476 2 12 1 14
Please use the information provided in the above statistical chart to answer the following questions:
(1) From 2000 to 2005, how many tens of thousands of permanent residents in Beijing increased?
(2) Please combine the education level of permanent residents in Beijing in 2000 and 2005 to talk about your views.
27. The dice of a cube, 1 and 6, 2 and 5, 3 and 4 are points on opposite faces, respectively. There are 12 squares on the paper at present. As shown in the picture, if it can be folded into a dice, which six squares do you think should be cut out? Please put an "X" on the box to be cut with a pen, and don't write a reason.
**28. As shown in the figure, it is known that rays CB∥OA, ∠ C = ∠ OAB = 100, e and f are on CB, and it satisfies that ∠FOB=∠AOB and OE are equally divided into ∠COF.
(1) Find the degree of ∠EOB.
(2) If AB moves in parallel, does the value of ∠ OBC: ∠ OFC change accordingly? If it changes, find out the law of change; If it does not change, find this ratio.
(3) In the process of moving AB in parallel, is there any situation that ∠OEC =∠ Oba? If it exists, find out its degree; If it does not exist, explain why.
answer
1.C 2。 D 3。 C 4 explosive A 5。 D 6。 C 7。 B 8。 B 9。 D 10。 D
1 1 .4
12.39 43′,77 2 1′48″
13.22
14.AC、BD、ACB、ADC、CDB、ACD、B、BCD
15. 162 、 108
16.20
17.65
18.2005
19.9,6
20. 105 .
2 1. Because E is the midpoint of AC and F is the midpoint of BD, AE=EC and DF=FB. And because EF=a, CD = B.
So EC+DF=EF-CD=a-b, so AE+FB=EC+DF=a-b,
So AB = AE+EF+FB = (AE+FB)+EF = A-B+A = 2A-B, which means AB = 2A-B. 。
22.( 1)①∠AOC=∠ 1。 The reason is ∠ AOC+∠ 2 = 90 because ∠COD is a right angle. ∠ AOC+∠ COB = 180, and ∠AOC=∠ 1. According to the equivalence of complementary angles, ∠EOB=∠COB can be obtained.
(2) complementary angles: ∠ 1 and ∠2, ∠AOC and ∠2, complementary angles: ∠ 1 and ∠EOB, ∠AOC and ∠EOB,
∠AOC and ∠COB, ∠ 1 and ∠COB, ∠2 and ∠AOD.
23. because EF∨AD, so ∠AGE=∠BAD, ∠E=∠DAC. And because AD shares ∠BAC equally, ∠BAD=∠DAC, so ∠ age = ∠ E.
24. Because EF∥CD, ∠BEF=∠BCD, ∠FED=∠EDC. Because Germany ∨ACB, ∠EDC=∠DCA, ∠ Federal Reserve =∞.
25.2+1+3+1+0+2 =10. As shown:
26.( 1) 362+372+476+2 12+ 14-(233+320+475+ 120) = 1538.
(2) The proportion of people with university degrees is gradually increasing (the answer is not unique).
27. As shown in the figure:
28.( 1) Because CB∥OA, ∠ C = ∠ OAB = 100, ∠ COA = 180- 100 = 80.
(2) unchanged, because CB∥OA, so ∠CBO=∠BOA and ∠FOB=∠AOB, so ∠FOB=∠OBC, and ∠ FOB+∠ OBC.
(3) There is a situation that ∠OEC =∠ Oba = 60. The reasons are as follows: ∠ COE+∠ CEO+∠ C = 180. And because ∠FOB=∠AOB and OE share ∠ COF ∠ BOA = ∠ BOF = ∠ FOE = ∠ EOC = ∠ COA = 20, ∠OEC =∞.
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