At the end of the second volume of the seventh grade, the mathematics people's education edition title 1. Multiple choice questions (*** 10 small questions, 3 points for each small question, out of 30 points)
1. Which of the following numbers? 1 and? 2 stands for vertex angle, and ()
A.B. C. D。
2. Where is the estimated value between two integers ().
A.77 and 79 B.6 and 7 C.7 and 8 D.8 and 9
3. If m is an arbitrary real number, the point M(m2+2, -2) is in the () quadrant.
A. 1 B.2 C.3 D.4
4.AB line is translated from PQ line, and the point corresponding to point P (﹣ 1, 3) is a (4 4,7), so the coordinate of point B of point Q (﹣ 3, 1) is ().
A.(2.5)b.(﹣6,﹣ 1)c.(﹣8,﹣3)d.(﹣2,﹣2)
5. In the real number 0,? 、 、2+ 、3. 123 123 12? 、﹣ 、 、 1. 10 100 1000 1? In, the number of irrational numbers is ()
A.3 B.4 C.5 D.6
6. As shown in the figure, the condition for judging EC∨AB is ().
A.？ B=？ ACB Bay? A=？ ACE C？ B=？ Ace d? A=？ Electron capture detector
7. If the solution of the equation satisfies x+y=0, the value of a is ().
A.a =-1b.a =1c.a = 0d.a cannot be determined.
8. Among the following surveys, () is suitable for a comprehensive survey (census).
A. the air quality of the city on a certain day
B. A survey of the weight of 40 students in a class
C. Safety investigation of a certain type of fireworks and firecrackers
D. Investigation on the quality of zongzi in the market during the Dragon Boat Festival
9. The inequality 2x+a about x? The solution set of -3 is shown in the figure, so the value of a is ().
A.0 B.﹣ 1 C.﹣2 D.﹣3
10. In the plane rectangular coordinate system, points A (-2,2), B (3 3,5) and C(x, Y), if AC∑x axis, the minimum value of line segment BC and the coordinates of point C at this time are () respectively.
a.6,(﹣3,5)b. 10,(3,﹣5)c . 1，(3，4) D.3，(3，2)
Fill in the blanks (***6 small questions, 3 points for each small question, full score 18 points)
1 1. Known = 18.044, then? = .
12. Known A >；; 3. The solution set of inequality (3-a) x > a-3 is.
13. It is known that a sample size is 60, and in the frequency distribution histogram, the height ratio of each small rectangle is 2: 4: 1: 3, so the frequency of the second group is.
14. As shown in the figure, put the right vertex of the triangle on one side of the ruler, if? 1=70? And then what? The degree of 2 is.
15. In the following claims,
(1) The complementary angle of an acute angle is smaller than this angle;
(2) Two straight lines are cut by a third straight line, and the internal dislocation angles are equal;
(3)a, B and C are straight lines. If a? b，b？ C, then a? c；
(4) If a2+b2=0, then both A and B are 0.
There are false propositions. (Please fill in the serial number)
16. As shown in the figure, A 1 (1, 0), A5(2( 1, |1) and A3 (|1,|) are known. The coordinates of point A20 17 are.
Iii. Answer questions (* *17)
17. Calculation: (-1) 20 16+-3+? .
18. Solve the equation:
19. Solve the inequality group and find its integer solution.
Four. (** 16, 8 for 20 questions and 8 for 2 1 questions)
20. As shown in the figure, AB∑CD, EF intersect AB at G point, CD intersect at F point, FH intersect AB at H point. Age =70? ,? BHF= 125？ , FH split equally? EFD？ Please explain your reasons.
2 1. After an exam, the head teacher talked to Xiao Qiang:
Teacher: Xiao Qiang, your total score in this exam is 348. Do you have any plans to make the total score of the next exam reach 382?
Xiao Qiang: Teacher, I will try my best to keep Chinese 1.24, English 1.6 and Math 1.5% in the next exam, just reaching 382.
Excuse me, what are Xiao Qiang's English and math scores in this exam?
V * * * * 19, 22 8, 23 1 1.
22.23 April? World Book Day? , school development? Let books overflow the campus? Reading activities, in order to enhance teenagers' interest in reading, the math activity group of Class 9 (1) made statistics on the reading time of 600 students in this grade every day, and drew two incomplete statistical charts according to the obtained data (each group contains the minimum value but does not contain the maximum value). Students in Class 9 (1) who study less than 0.5 hours a day account for 8% of the class. According to the statistical chart, answer the following questions:
(1) Nine-year (1) class has students;
(2) completing the histogram;
(3) There are 165 students in other classes in Grade 9, and they read 1 ~ 1.5 hours every day, except for Class 9 (1). Please fill in the fan statistics table.
(4) How many students do you want to read at least 1 hour every day in this grade?
23. Xiao Ming, who is good at thinking, adopted one? Overall substitution? Solution:
Solution: Transform equation ②: 4x+ 10y+y=5, that is, 2(2x+5y)+y=5③.
Bring equation ① into ③ to get: 2? 3+y=5，？ y=﹣ 1
Substitute y =- 1 into ① to get x=4. The solution of the equation is.
Please solve the following problems:
(1) Imitate Xiao Ming's? Overall substitution? Solve the equation by normal method;
(2) It is known that x and y satisfy the equation.
① Find the value of x2+9y2;
② Find the value of x+3y [refer to formula (a+b)2=a2+2ab+b2].
Mathematics examination paper at the end of the seventh grade (next) in 20 15-20 16 school year in Nanling County, Wuhu City, Anhui Province.
Reference answers and analysis of test questions
Seventh grade final examination paper, Volume II, Reference Answer of Mathematics People's Education Edition 1. Multiple choice questions (*** 10 small questions, 3 points for each small question, out of 30 points)
1. Which of the following numbers? 1 and? 2 stands for vertex angle, and ()
A.B. C. D。
The test center is opposite to the vertex angle and the adjacent complementary angle.
The two sides of one angle are the relative extension lines of the other angle, and these two angles are diagonal. Can be judged according to the definition.
Solution: two mutually diagonal angles: two sides of one angle are opposite extension lines of the other angle. Only d meets the requirements.
So choose D.
2. Where is the estimated value between two integers ().
A.77 and 79 B.6 and 7 C.7 and 8 D.8 and 9
The test center estimates the size of irrational numbers.
The analysis first estimates and then determines which two adjacent integers are in between.
Solution: ∫; 3. the solution set of inequality (3-a) x > A-3 is X.
Try to solve the one-dimensional inequality.
The analysis first judges that 3 < a
Answer: ∫ A > 3,
? 3﹣a<； 0,
? The solution set of inequality (3 ~ a) x > A-3 is X.
So the answer is X.
13. It is known that a sample size is 60, and the height ratio of each small rectangle in the frequency distribution histogram is 2: 4: 1: 3, so the frequency of the second group is 24.
Histogram of frequency (rate) distribution of test sites; Population, individual, sample, sample size.
According to the analysis, the height ratio of each small rectangle is 2: 4: 1: 3 and the frequency ratio is 2: 4: 1: 3, which can solve the problem.
Solution: The sample size is 60, and the height ratio of each small rectangle is 2: 4: 1: 3.
? So the frequency of the second group is 60? =24,
So the answer is 24.
14. As shown in the figure, put the right vertex of the triangle on one side of the ruler, if? 1=70? And then what? The degree of 2 is 20? .
The nature of parallel lines in test sites.
According to analysis, two straight lines are parallel and have the same angle. 3=? 1, and then according to the angle, it is equal to 180? The solution can be obtained by column calculation.
Solution: ∵ The ruler is parallel to the opposite side.
3=? 1=70? ,
2= 180? ﹣70? ﹣90? =20? .
So the answer is: 20? .
15. In the following claims,
(1) The complementary angle of an acute angle is smaller than this angle;
(2) Two straight lines are cut by a third straight line, and the internal dislocation angles are equal;
(3)a, B and C are straight lines. If a? b，b？ C, then a? c；
(4) If a2+b2=0, then both A and B are 0.
There are (1)(3) false propositions. (Please fill in the serial number)
Propositions and theorems of test sites.
Analysis is conducive to the definition of acute angle, the nature of parallel lines and the definition of verticality, and then the correct options can be determined.
Solution: (1) The complementary angle of an acute angle is smaller than this angle, which is an error and a false proposition;
(2) It is a true proposition that two straight lines are cut by a third straight line and the internal dislocation angles are equal and correct;
(3)a, B and C are straight lines. If a? b，b？ C, then a∑c, so it is wrong and a false proposition;
(4) If a2+b2=0, then both A and B are 0, which is correct and valid.
So the answer is (1)(3).
16. As shown in the figure, A 1 (1, 0), A5(2( 1, |1) and A3 (|1,|) are known. The coordinates of point A20 17 are (-505, -505).
Regularity of test sites: coordinates of points.
Through analysis and observation, it can be found that the abscissa and ordinate of the points on the diagonal of the square in the first quadrant are increased by 1, and the abscissa and ordinate of the points in the second quadrant are increased by-1 and 1. The abscissa of the third quadrant plus-1, the ordinate plus-1, the abscissa of the fourth quadrant plus-1, the ordinate plus-1, and the absolute values of the abscissa and ordinate of the second, third and fourth quadrants are equal, then
Solution: It is easy to get points with integer multiples of 4, such as A4, A8, A 12, in the second quadrant.
∵20 17? 4=504? 1;
? The coordinates of A20 17 are in the third quadrant.
The abscissa is |? 4+ 1|=﹣505; The ordinate is -505,
? The coordinates of point A20 17 are (-505, -505).
So the answer is: (-505, -505).
Iii. Answer questions (* *17)
17. Calculation: (-1) 20 16+-3+? .
The operation of real number in test center.
In the analysis, the numbers are calculated respectively according to the power and root laws of numbers, and then calculated according to the mixed operation law of real numbers.
Solution: The original formula = 1+2-3+ 1.
=3﹣3+ 1
= 1.
18. Solve the equation:
Test points to solve binary linear equations.
Analytic equations can be solved by addition, subtraction and elimination.
Solution: ①+②? 3: 5x=40, that is, x=8,
Substitute x=8 into ② to get y=2.
Then the solution of the equation is.
19. Solve the inequality group and find its integer solution.
Integer solutions of linear inequalities with one variable in test sites; Solving linear inequalities.
The solution set of each inequality is obtained by analysis, and then its common solution set is obtained, and its integer solution is found in its common solution set.
Solution: from ①, x & gt-2, from 2, x? 2,
Therefore, the range of inequality group is-2 <; /x≤2, and its integer solution is:-1, 0, 1, 2. >
Four. (** 16, 8 for 20 questions and 8 for 2 1 questions)
20. As shown in the figure, AB∑CD, EF intersect AB at G point, CD intersect at F point, FH intersect AB at H point. Age =70? ,? BHF= 125？ , FH split equally? EFD？ Please explain your reasons.
The nature of parallel lines in test sites.
By analyzing the properties of parallel lines, we can find the equal angle and complementary angle. EFD=2？ DFH= 1 10？ , causing FH to split? The conclusion of EFD.
Solution: FH split equally? EFD, for the following reasons:
∫AB∨CD，
CFE=？ Age,? BHF+？ DFH= 180？ ,
∵? Age =70? ,? BHF= 125？ ,
CFE=70？ ,? DFH=55？ ,
∵? EFD= 180？ ﹣? CFE= 1 10？ ,
EFD=2？ DFH= 1 10？ .
? FH split? EFD。
2 1. After an exam, the head teacher talked to Xiao Qiang:
Teacher: Xiao Qiang, your total score in this exam is 348. Do you have any plans to make the total score of the next exam reach 382?
Xiao Qiang: Teacher, I will try my best to keep Chinese 1.24, English 1.6 and Math 1.5% in the next exam, just reaching 382.
Excuse me, what are Xiao Qiang's English and math scores in this exam?
Application of binary linear equations in test center.
The analysis assumes that Xiao Qiang's English score is X and his math score is Y, and the equivalence relationship is: Chinese score+math score+English score =348, Chinese score+English score+16+ math score? (1+ 15%)=382, list the equations and solve them.
Solution: Suppose Xiao Qiang's English score is X and his math score is Y.
Judging from the meaning of the question,
Solution:
Xiao Qiang scored 104 in English and 120 in math.
V * * * * 19, 22 8, 23 1 1.
22.23 April? World Book Day? , school development? Let books overflow the campus? Reading activities, in order to enhance teenagers' interest in reading, the math activity group of Class 9 (1) made statistics on the reading time of 600 students in this grade every day, and drew two incomplete statistical charts according to the obtained data (each group contains the minimum value but does not contain the maximum value). Students in Class 9 (1) who study less than 0.5 hours a day account for 8% of the class. According to the statistical chart, answer the following questions:
(1) Nine-year (1) class with 50 students;
(2) completing the histogram;
(3) There are 165 students in other classes in Grade 9, and they read 1 ~ 1.5 hours every day, except for Class 9 (1). Please fill in the fan statistics table.
(4) How many students do you want to read at least 1 hour every day in this grade?
Histogram of frequency (rate) distribution of test sites; Estimate the population with samples; Department statistical chart.
Analyze the number of people in (1)0 ~ 0.5 hours and their proportion in histogram and fan chart, and then get the class number;
(2) Use the class size to get the number of people from 0.5 to 1 hour, and then get the answer;
(3) Using the1~ 165 students who read1.5 hours every day in other classes of Grade 9, we can find out the ratio of 1 ~ 1.5 hours in the sector statistical chart, and then get 0.5 ~ 1 hour in the sector statistical chart.
(4) Get the number of people who read at least 1 hour every day in this grade by using the fan-shaped statistical chart, and then get the answer.
Solution: (1) can be obtained from the meaning of the question: 4? 8%=50 (person);
So the answer is: 50;
(2) from (1): 0.5 ~ 1 hour: 50 ~ 4 ~ 18 ~ 8 = 20 (person),
As shown in the figure:
;
(3)∵ Except for the nine-year class (1), there are 165 students in other classes in the ninth grade who study 1 ~ 1.5 hours a day.
? The proportion of 1 ~ 1.5 hours in the pie chart is: 165 100%=30%.
Therefore, the proportion of 0.5 ~ 1 hour in the departmental statistical chart is:1~ 30% ~10% ~12% = 48%.
As shown in the figure:
;
(4) The students who read at least 1 hour every day in this grade are: (30%+10%)+18+8 = 246 (people).
23. Xiao Ming, who is good at thinking, adopted one? Overall substitution? Solution:
Solution: Transform equation ②: 4x+ 10y+y=5, that is, 2(2x+5y)+y=5③.
Bring equation ① into ③ to get: 2? 3+y=5，？ y=﹣ 1
Substitute y =- 1 into ① to get x=4. The solution of the equation is.
Please solve the following problems:
(1) Imitate Xiao Ming's? Overall substitution? Solve the equation by normal method;
(2) It is known that x and y satisfy the equation.
① Find the value of x2+9y2;
② Find the value of x+3y [refer to formula (a+b)2=a2+2ab+b2].
Higher order equation of measuring point; Solutions of binary linear equations.
Analysis: (1) Convert ② into 6x-3y+y = 6, and substitute it as a whole to get Y first;
Solution: (1)
From ②: 6x-3y+y = 6,
3(2x﹣y)+y=6③，
Substitute ① into ③ to get: 3? 1+y=6，
Solution: y=3,
Substituting y=3 into ① gives 2x-3 = 1.
Solution: x=2,
So the solution of the original equation is:
(2)①
①? 2+②，7x2+63y2= 126，
Divide both sides of the equation by 7 to get x2+9y2= 18.
②.①? 3﹣②? 2，get-7xy =-2 1，
? xy=3，6xy= 18
∫x2+9 y2 = 18，
? x2+6xy+9y2= 18+ 18，
? (x+3y)2=36，
? x+3y=？ 6.