The final examination questions of the second volume of seventh grade mathematics 1. Choose carefully (this topic is entitled *** 10, with 3 points for each topic and 30 points for * * *).
1. The following calculation is correct ()
A.2a？ 3a=6a B.a2？ a2=0
C.a？ (a-2)=a2-2a D.a？ a- 1=a
2. If m+n =- 1, the value of (m+n) 2-4m-4n is ().
1 D.4
3. In order to make the score meaningful, the value of x should satisfy ()
A.x？ 2 B.x？ ﹣ 1 C.x=2 D.x=﹣ 1
4. It is known that x and y satisfy the relationships 2x+y=9 and x+2y=6, so the value of x+y is ().
b.﹣ 1 c 15d . 5
5.？ Dragon Boat Festival? After the holiday, Director Liu randomly selected 50 students' homework from 650 students in Grade 7, and found that 5 students' homework was unqualified. The following judgment is correct ().
A. Director Liu adopts the method of comprehensive investigation. B.an individual is every student.
C. The sample size is 650 D, and about 65 junior high school students failed their homework.
6. As shown in the figure, CD∨AB, point F is on AB, EF? GF and f are vertical feet,
What if? 1=48? And then what? The degree of 2 is ()
.42 caliber? B.45？
C.48？ D.50？
7. The following factorization is correct ()
a . 4a 2+6ab = a(4a+6b)b . x2-(-2)2 =(x+2)(x-2)
c . x2+2x- 1 =(x- 1)2d . x2-2x+3 =(x+3)(x- 1)
8. The following score is the simplest score ()
A.B. C. D。
9. As shown in the figure, the condition for judging EB∑AC is ().
A.？ C=？ Abe
B.？ A=？ Emotional and behavioral disorders
C.？ C=？ American Broadcasting Company Inc (ABC)
D.？ A=？ Abe
10. Create for positive response? Beautiful countryside? Whew, a school 1500 students participated in the health knowledge contest, and their scores were recorded as A, B, C and D. Some students' scores were randomly selected for statistics and drawn into two incomplete statistical charts as shown in the figure. According to the information provided by the statistical chart, the following statement is incorrect ().
A. the central angle of a sector with a sample size of 200 B.D is 15?
C. the percentage of c in the sample is 10%. D. It is estimated that the whole school student A will get about 900 points.
Second, fill it out carefully (this question is ***8 small questions, with 3 points for each small question and 24 points for * * *).
1 1. Calculation: (-2ab2)2? =
12. define operation: a? B=(a+b)(b-2)。 The following are four conclusions of this operation: 13? 4= 14; ②a？ b=b？ a； 3 if a? B=0, then a+b = 0; (4) If a+b=0, then A? B=0。 The serial number of the correct conclusion is _ _ _ _ _ _. (Fill in the serial numbers of all correct conclusions on the horizontal line)
13. Simplified score: = _ _ _ _ _ _ _ _ _.
14. As shown in the figure, you know? 1= 122? ,? 2= 122? ,? 3=73? ,
then what The degree of 4 is _ _ _ _ _ _.
15. If the equation about X-= 1 has no solution, then the value of a must be _ _ _ _ _ _ _ _.
16. All positive integer solutions of binary linear equation 2x+3y=20 are _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
17. As shown in the figure, in the rectangular ABCD, AB=5cm and AD=8cm. Now this
Translate the rectangle along BC direction to get rectangle a1b1c1d1.If
The area of the overlapping part A 1B 1CD is 35cm2, and then the rectangular ABCD.
The translation distance to the right is _ _ _ _ cm.
18. During the National Day holiday, Xiao Ming originally planned to finish reading a 480-page novel within the specified time. However, due to the wonderful story of this book, Xiao Ming read 20 pages more every day, so he also read 120-page novella at the appointed time. If Xiao Ming originally planned to read X pages every day, then the equation can be _ _ _ _ _ _ _.
Iii. Answering questions (this topic is ***8 small questions, 19 and 20 are 8 points each; 2 1, 22 6 points for each small question; 23, 24, 8 points for each small question; The 25th question is 10, and the 26th question is 12, ***66).
19.( 1) The known polynomial A=(x+2)2+( 1-x)(2+x)-3. If (x+ 1)2=2, find the value of a.
(2) Simplify before evaluating: 1-? , where x= 1 and y=-2.
20. Solve the following equation (group)
(1) 1+ = (2) (solved by substitution method)
2 1. Grade 7 in a middle school 12 classes, with 48 students in each class. After the mid-term exam in the spring semester of 20 15, the school wants to know the situation of the seventh grade math exam and make a sample analysis of the math scores in the mid-term exam.
(1) If you want to sample 48 students from the whole grade, what do you think are the following sampling methods: ① Randomly sample 48 students from a class; ② 48 students were randomly selected from the whole grade; ③ Four students were randomly selected from each class of the whole grade 12, and 48 students were randomly selected from the first six classes of the seventh grade, among which the more reasonable sampling method was _ _ _ _ _ _ _. (Fill in serial number).
(2) Divide the scores of 48 students into groups, and get the following frequency statistics and fan statistics:
Statistics on the frequency of mathematics scores in the mid-term examination of seventh-grade students; Fan-shaped statistical chart of mathematics scores of seventh grade students in mid-term exam.
Please answer the following questions according to the data in the chart:
① Find the frequency of class C and the degree of the central angle of class D;
(2) Estimate the number of students who have reached Class A and Class B in the whole grade.
22. Translate the triangle ABC in the grid paper 2 squares to the right to get the triangle DEF, and then translate the triangle DEF up 3 squares to get the triangle GPH.
(1) Hands-on operation: according to the above steps, make a triangle with two translations respectively;
(2) Fill in the blank: There are _ _ _ _ _ _ _ lines parallel to AC and _ _ _ _ _ _ _ parallelograms in the drawing?
(3) What is the relationship between the position and quantity of line segments AD and BF?
23. Observe the following layout:
① 1? 3-22=3-4=-2;
②2? 4-32=8-9=- 1;
③3? 5-42= 15- 16=- 1
④__________________________ ?
(1) Please write the fourth formula according to the above rules;
(2) To express this rule with a formula containing letters;
(3) Do you think the formula written in (2) is valid? And explain why.
24. As shown in the figure, fold the rectangular paper strip in half along CE (CE is the crease), so that point B coincides with point F, and EG divides it equally. AEF to 700 ad, HG? EG, the vertical foot is the G point. Please explain HG∨CE.
25. A sporting goods mall spent 32,000 yuan to buy a batch of sportswear during the provincial games, which was sold out soon after listing. The mall also bought the second batch of the same sportswear for 68,000 yuan, which was twice as much as the first batch, but the purchase price of each set was higher 10 yuan.
(1) How many sets of this kind of sportswear did you buy in the mall twice?
(2) If the price of each set of these two batches of sportswear is the same, and the total profit reaches 20% after they are all sold out, what should the price be? (Profit rate =)
26. A travel agency plans to launch during the summer vacation? A two-day tour? Activities, the cost is as follows:
Number of people m 0 200
Charging standard 180 170 150
Two schools, A and B, plan to organize their own students to participate in this activity voluntarily. It is known that the number of students enrolled in A school exceeds 120, and the number of students enrolled in B school is insufficient 120. According to the accounting, it costs 4 1600 yuan for a group organized by the two universities, and only 36,000 yuan for a group organized by the two universities.
(1) Does the total enrollment of the two schools exceed 200? Why?
(2) How many students from two schools signed up for the tour?
The reference answer to the final examination questions in the second volume of seventh grade mathematics 1. Choose carefully (this topic is entitled *** 10, with 3 points for each topic and 30 points for * * *).
The title is 1 23455 6789 10.
Answer C A A D D A B B D B
Second, fill it out carefully (this question is ***8 small questions, with 3 points for each small question and 24 points for * * *).
1 1.3a4b5 12.①④;
13.- ; 14. 107;
15.-2; 16., ,
17. 1; 18.= .
Iii. Answering questions (this topic is ***8 small questions, 19 and 20 are 8 points each; 2 1, 22 6 points for each small question; 23, 24, 8 points for each small question; The 25th question is 10, and the 26th question is 12, ***66).
19. solution: (1) a = (x+2) 2+(1-x) (2+x)-3.
=x2+4x+4+2+x-2x-x2-3
=3x+3
=3(x+ 1)
∫(x+ 1)2 = 2，
? X+ 1= or x+ 1=-,
? When x+ 1=, A=3? =3 ,
When x+ 1=-, A=3? (- )=-3 ,
So the value of a is. 3 .
(2) 1- ?
= 1- ?
= 1-
=
When x= 1 and y=-2, the original formula = =3.
20. Solution: (1) The original equation can be changed to: 1+ =,
Multiply two sides of the equation by 2(x-2) to get: 2(x-2)+2( 1-x)=x,
Without brackets, we get 2x-4+2-2x=x,
Move items and merge items of the same category: -x=2,
Solution: x=-2,
Test: When x =-2(x-2 (x-2)? 0,
? X=-2 is the solution of the original fractional equation,
So the solution of the original equation is x=-2.
(2) From ②: y=4x- 13③,
Let ③ be ①: 3x+2(4x- 13)=7,
Solving this equation leads to: x=3,
Substituting x=3 into ③ gives: y=4? 3- 13=- 1,
? The solution of the original equation is:
2 1. Solution: (1) ② ③;
(2)① = ,360 =30? ,
Answer: Class C frequency is 0, and Class D central angle is 30? ;
②48? 12? (50%+25%)=432 (person),
A: It is estimated that there are about 432 students who have reached Class A and Class B in the whole grade.
22. Solution: (1) as shown in the right figure;
(2) The lines parallel and equal to AC are DF and GH, and there are two parallelograms in the figure;
(3) The positional relationship between line segment AD and BF is parallel, and the quantitative relationship is AD= BF.
23. Solution: (1)4? 6-52=24-25=- 1;
(2) The answer is not unique, such as n (n+2)-(n+1) 2 =-1;
(3) Established for the following reasons:
∫n(n+2)-(n+ 1)2 = N2+2n-(N2+2n+ 1)= N2+2n-N2-2n- 1 =- 1，
? Must be established.
24. Solution: Cause: From the folding nature:? CEF=？ BEC=？ BEF，
∵EG split? AEF (known),
GEF=？ AEG=？ AEF (definition of angular bisector),
CEF+？ GEF=？ AEF+？ BEF=(？ AEF+？ BEF) (the nature of the equation),
∵? AEF+？ BEF= 180？ (definition of boxer)
CEF+？ GEF=？ 180? =90? ,
Namely. GEC=90？ ,
∵HG？ EG (known),
EGH=90？ (Vertical definition)
GEC+？ EGH= 180？ (the nature of the equation),
? HG∨CE (complementary to the internal angle on the same side, two straight lines parallel).
25. Solution: (1) For every x sets of sportswear bought in the mall, buy 2x sets the second time.
From the meaning of the title, it means: -= 10,
Solve this equation and get: x=200,
It is verified that x=200 is the solution of the original equation.
2x+x=2？ 200+200=600 (sets),
A: The mall bought 600 sets of this kind of sportswear twice.
(2) Assume that the price of each set of sportswear is Y yuan.
=20%,
Solving this equation leads to: y=200,
A: The price of each sportswear should be set in 200 yuan.
26. solution: (1) let the sum of the number of students in school a and school b be a,
If a & gt200, then a=36000? 150=240 (person),
If 120
? The total enrollment of the two schools is equal to more than 240,200;
(2) There are X students registered in one school and Y students registered in one school, then:
① When 120
Solution:
② When x >; 200 hours, judging from the meaning of the question,
Solution: This solution is irrelevant and should be discarded.