People's Education Press eighth grade math final exam questions 1, multiple-choice questions (this question is a small question of * *10, with 3 points for each small question and 30 points for * * *).
The reciprocal of 1 | Yes ().
b.﹣2·d.﹣
2. The following calculation is correct ()
a . 3a+3b = 6ab b. 19a2b2﹣9ab= 10ab
C.﹣2x2﹣2x2=0 D.5y﹣3y=2y
3. Since the opening of Chengdu Metro, its development speed has been accelerating, and now it has become one of the main modes of travel for Chengdu citizens. On April 29th this year, Chengdu Metro safely transported about 1, 8 1, 000 passengers, setting a new passenger flow record. This is also the fourth time this year to refresh the passenger flow record. With scientific notation, 1, 8 1, 000 passengers are ().
A. 18. 1？ 105 B. 1.8 1？ 106 C. 1.8 1？ 107 D. 18 1？ 104
4. In the following equation, belongs to the linear equation is ().
a.4x﹣5=0 b.2x﹣y=3 c.3x2﹣ 14=2·﹣2=3
5. Cut the pentagonal prism with a plane. What is impossible in the obtained section is ().
A. octagon B. quadrilateral C. hexagon D. triangle
6. The following statement is wrong ()
A. Rational numbers can be divided into positive rational numbers, negative rational numbers and zero.
The reciprocal of B.0 is equal to itself.
C.0 is neither positive nor negative.
D. The absolute value of any rational number is positive.
7. Students in Class 7 (3) of a school have a safety knowledge test. After sorting out the test results, divide them into four groups and draw the frequency histogram as shown in the figure. Then the frequency of the second group is ().
A.0.4 B. 18 C.0.6 D.27
8. As shown in the figure, OC shares equally? AOB, OD split equally? AOC and COD=25? And then what? AOB equals ()
.50 caliber? B.75？ C. 100？ D.20？
9. Given a+b=4, c+d=2, the value of (B-C)-(D-A) is ().
B.﹣6
10. A shopping mall marked a backpack with a price increase of 50% according to the purchase price, and then sold it at a 20% discount, so that every backpack sold by the shopping mall can make a profit in 8 yuan. Let the purchase price of each backpack be X yuan, and make an equation with one yuan according to the meaning of the question. The correct one is ().
A.( 1+50%)x？ 80%﹣x=8 B.50%x？ 80%﹣x=8
C.( 1+50%)x？ 80%=8 D.( 1+50%)x﹣x=8
II. Fill in the blanks (5 small questions in this big question, 3 points for each small question, *** 15 points)
1 1. In order to investigate the service life of a batch of light bulbs, the method (optional sampling survey or general survey) is generally adopted.
12. In the operation flow as shown in the figure, if the input number X =-4, the output number y=.
13. It is known that the solution of equation 3a+x= about x is 2, then the value of a is.
14. Observe the following figure. They are arranged according to certain rules. According to this rule, the seventh number has one.
15. In a magic square, the sum of three numbers on each row, column and diagonal has the same value, as shown in the figure, three numbers in a magic square are known, and the value of x is.
Iii. Answer the following questions (***20 points, the answers are written on the answer sheet)
16.( 1) Calculation: -32+ 100? (﹣2)2﹣(﹣2)? (﹣ )
(2) Calculation: (1+-2.75)? (﹣24)+(﹣ 1)20 17﹣|﹣2|3.
17.( 1) Solve the equation: =1.
(2) Simplify first and then evaluate: (9ab2-3)+(7a2b-2)+2 (ab2+1)-2a2b, where a and b satisfy (A+2) 2+| B-3.
Four, solve the following problems (***22 points)
18.( 1) As shown in the figure, there are three views of the geometry:
(1) Write the name of this geometry;
(2) Drawing the surface development diagram of the geometric body;
③ If the height of a rectangle is 10cm and the side length of a regular triangle is 4cm, find the lateral area of this geometric figure.
(2) The solution of equation [(a) x+] = 1 is the same as that of equation | 1 =, so the value of a is found.
19.( 1) Polynomials A=2x2﹣xy+my﹣8, B=﹣nx2+xy+y+7 and A﹣2B do not contain x2 and y terms, so find the value of nm+mn.
(2) As shown in the figure, the line segment AB=20, C is a point on AB, D is a point on CB, E is the midpoint of DB, and DE=3.
① If CE=8, find the length of AC;
② If c is the midpoint of AB, find the length of CD.
Verb (abbreviation of verb) solves the following problems (20 questions with 6 points, 2 1 question with 7 points, *** 13 points).
20. In order to understand the air quality in our city, an environmental protection interest group randomly selected the air quality of several days from the environmental monitoring network as a sample for statistics, and drew a histogram and a fan chart as shown in the figure (some information is not given).
Please answer the following questions according to the information provided in the picture:
(1) Calculate the number of days to be extracted;
(2) Please complete the bar chart and find the representative in the fan chart. Excellent? The degree of the central angle of the sector;
Please estimate the achievements of this city this year? Excellent? And then what? Okay？ Total days.
2 1. A middle school held a math contest, and planned to use two copiers, A and B, to copy the test papers. If it takes 90 minutes to print on the A machine alone and 60 minutes to print on the B machine alone, for the sake of confidentiality, the school decided to copy the test paper at the same time before the exam.
(1) Two copiers copy at the same time. How many minutes does it take to finish printing?
(2) If two copiers copy for 30 minutes at the same time, machine B fails and cannot copy for the time being. At this time, there are still 13 minutes before the paper is issued. Please calculate, if the rest of the copying tasks are completed by machine A alone, will it affect the exam that will be handed out on time?
(3) In the problem of (2), machine B was repaired urgently and resumed normal use after 9 minutes. Please calculate again, can the school issue exams on time?
People's Education Press eighth grade math final exam papers reference answer 1, multiple-choice questions (this question *** 10 small questions, 3 points for each small question, 30 points for * *).
The reciprocal of 1 | Yes ().
b.﹣2·d.﹣
The test center is the reverse sign.
According to the analysis, only two numbers with different signs are called reciprocal solutions.
Answer: The inverse operation of ﹣ is.
So choose C.
2. The following calculation is correct ()
a . 3a+3b = 6ab b. 19a2b2﹣9ab= 10ab
C.﹣2x2﹣2x2=0 D.5y﹣3y=2y
Test sites merge similar items.
The analysis directly uses the rule of merging similar items to judge the answers respectively.
Solution: A, 3a+3b cannot be calculated, so the option is wrong;
B, 19A2B2-9AB cannot be calculated, so the option is wrong;
C, -2x2-2x2 =-4x2, so the option is wrong;
D, 5y-3y = 2y, correct.
Therefore, choose: d.
3. Since the opening of Chengdu Metro, its development speed has been accelerating, and now it has become one of the main modes of travel for Chengdu citizens. On April 29th this year, Chengdu Metro safely transported about 1, 8 1, 000 passengers, setting a new passenger flow record. This is also the fourth time this year to refresh the passenger flow record. With scientific notation, 1, 8 1, 000 passengers are ().
A. 18. 1？ 105 B. 1.8 1？ 106 C. 1.8 1？ 107 D. 18 1？ 104
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:1810000 =1810000 =1.81? 106,
Therefore, choose: B.
4. In the following equation, belongs to the linear equation is ().
a.4x﹣5=0 b.2x﹣y=3 c.3x2﹣ 14=2·﹣2=3
Definition of one-dimensional linear equation of test center.
The analysis can be obtained according to the definition of one-dimensional linear equation.
Solution: A is a linear equation with one variable, so this option is correct;
B is not a linear equation, so this option is wrong;
C is not a linear equation, so this option is wrong;
D is not a linear equation, so this option is wrong;
So choose a.
5. Cut the pentagonal prism with a plane. What is impossible in the obtained section is ().
A. octagon B. quadrilateral C. hexagon D. triangle
Cut a geometric figure in the test center.
The surface obtained by cutting a geometric figure with a plane is called the cross section of the geometric figure and can be solved.
Solution: Cut a pentagonal prism with a plane, and the section with the largest number of sides is a heptagon.
So choose a.
6. The following statement is wrong ()
A. Rational numbers can be divided into positive rational numbers, negative rational numbers and zero.
The reciprocal of B.0 is equal to itself.
C.0 is neither positive nor negative.
D. The absolute value of any rational number is positive.
Reasonable number of test sites; Countdown; absolute value
According to the meaning and classification method of rational number, the meaning and solution of absolute value and the meaning and solution of reciprocal, we can judge them one by one.
Solution: ∫ Rational numbers can be divided into positive rational numbers, negative rational numbers and zero.
? Option a is correct;
The reciprocal of 0 is equal to itself,
? Option b is correct;
∫0 is neither positive nor negative,
? Option c is correct;
The absolute value of any rational number is positive or 0,
? Option d is incorrect.
Therefore, choose: d.
7. Students in Class 7 (3) of a school have a safety knowledge test. After sorting out the test results, divide them into four groups and draw the frequency histogram as shown in the figure. Then the frequency of the second group is ().
A.0.4 B. 18 C.0.6 D.27
Histogram of frequency (rate) distribution of test sites.
The analysis can be solved according to the histogram of frequency distribution.
Solution: According to the histogram of frequency distribution, the second group frequency is 18.
So choose B.
8. As shown in the figure, OC shares equally? AOB, OD split equally? AOC and COD=25? And then what? AOB equals ()
.50 caliber? B.75？ C. 100？ D.20？
Definition of bisector of test center angle.
Is the analysis based on the definition of angular bisector? AOD=？ COD，？ AOB=2？ AOC=2？ Bank of China, did you find out? AOD？ The degree of AOC can be answered.
Solution: ∵OC is? What is the bisector of AOB? AOC bisector, COD=25? ,
AOD=？ COD=25？ ,? AOB=2？ AOC，
AOB=2？ AOC=2(？ AOD+？ COD)=2？ (25? +25? )= 100? ,
So choose: C.
9. Given a+b=4, c+d=2, the value of (B-C)-(D-A) is ().
B.﹣6
Addition and subtraction of algebraic expressions.
Firstly, (b﹣c)﹣(d﹣a) is transformed into (b+a)﹣(c+d), and then a+b=4 and c+d=2 are substituted for the solution.
Solution: ∫a+b = 4, c+d=2,
? (b﹣c)﹣(d﹣a)
=(b+a)﹣(c+d)
=4﹣2
=2.
So choose C.
10. A shopping mall marked a backpack with a price increase of 50% according to the purchase price, and then sold it at a 20% discount, so that every backpack sold by the shopping mall can make a profit in 8 yuan. Let the purchase price of each backpack be X yuan, and make an equation with one yuan according to the meaning of the question. The correct one is ().
A.( 1+50%)x？ 80%﹣x=8 B.50%x？ 80%﹣x=8
C.( 1+50%)x？ 80%=8 D.( 1+50%)x﹣x=8
The test center abstracts a linear equation from the actual problem.
The analysis first shows the price as (1+50%)x according to the meaning of the question, and then shows the price as (1+50%)x? 80%, and then use the price-purchase price = profit to get the equation.
Solution: Assuming that the purchase price of each backpack is X yuan, according to the meaning of the question:
( 1+50%)x？ 80%﹣x=8.
So choose: a.
II. Fill in the blanks (5 small questions in this big question, 3 points for each small question, *** 15 points)
1 1. In order to investigate the service life of a batch of light bulbs, sampling survey (optional sampling survey or general survey) is generally adopted.
Comprehensive survey and sampling survey of test sites.
The survey results obtained from the analysis and census are more accurate, but more manpower, material resources and time are needed, while the survey results obtained from the sampling survey are similar.
Solution: In order to investigate the service life of a batch of light bulbs, sampling survey is generally adopted.
So the answer is: sampling survey.
12. In the operation flow as shown in the figure, if the input number X =-4, the output number Y =-8.
Mixed operation of rational numbers in test sites.
Analyze the operation method based on rational number mixed operation. If the input number is x=﹣4, find out what the output number y is.
Solution: (-4) 2? (﹣2)
= 16? (﹣2)
=﹣8
? If the input number x =-4, the output number y =-8.
So the answer is: -8.
13. It is known that the solution of equation 3a+x= about x is 2, then the value of a is ﹣.
Solutions of one-dimensional linear equations.
Analysis: Substitute x=2 into equation 3a+x= to get 3a+2=, and then get the solution of the equation.
Solution: Substitute x=2 into equation 3a+x= to get: 3a+2=,
Solution: a =,
So the answer is:
14. Observe the following figure. They are arranged according to certain rules. According to this rule, the seventh number is 7 1.
Regularity of test sites: diversity of graphics.
The analysis shows that the number of small suns in the first row is a continuous natural number starting from 1, and the number of small suns in the second row is 1, 2,4,8,? , 2n ~ 1, and the answer can be obtained by calculation.
Solution: The number of small suns in the first row is 1, 2, 3, 4,? The fifth figure has five suns.
The number of small suns in the second row is 1, 2, 4, 8,? 2n ~ 1, and the fifth number is 24= 16 suns.
So the seventh figure * * * has 7+64=7 1 sun.
So the answer is: 7 1
15. In the Rubik's Cube, the sum of three numbers in each row, column and diagonal has the same value. As shown in the figure, three numbers in a Rubik's cube are known, and the value of X is 26.
The application of one-dimensional linear equation in examination center.
By analyzing the meaning of the question, we can first get that the number in the upper right corner is 28. Since the sum of three numbers in each row, column and diagonal is required to have the same value, the middle number is the average of the numbers in the upper right corner and the lower left corner, so we can get the value of X. 。
Solution: The number in the upper right corner is: 22+27+x-x-2 1 = 28.
The number of centers is: (22+28)? 2=25,
So x+27+22=22+25+28,
Solution: x=26.
So the answer is: 26.
Iii. Answer the following questions (***20 points, the answers are written on the answer sheet)
16.( 1) Calculation: -32+ 100? (﹣2)2﹣(﹣2)? (﹣ )
(2) Calculation: (1+-2.75)? (﹣24)+(﹣ 1)20 17﹣|﹣2|3.
Mixed operation of rational numbers in test sites.
Analyze (1) the original formula, first calculate the power operation, then calculate the multiplication and division operation, and finally calculate the addition and subtraction operation to get the result;
(2) Using the law of multiplication distribution, the meaning of power and the algebraic meaning of absolute value, the original formula can be obtained.
Solution: (1) Original formula =-9+25-5 =11;
(2) The original formula =-32-3+66- 1-8 = 22.
17.( 1) Solve the equation: =1.
(2) Simplify first and then evaluate: (9ab2-3)+(7a2b-2)+2 (ab2+1)-2a2b, where a and b satisfy (A+2) 2+| B-3.
The test site solves a linear equation of one variable; The nature of non-negative number: absolute value; The nature of non-negative number: even power; Addition and subtraction of algebraic expressions? Simplify the assessment.
Analysis (1) can first remove the denominator, then remove the brackets, move items, merge similar items, and convert the coefficient into1;
(2) It can be simplified by removing brackets and merging similar terms, and then the values of A and B can be obtained according to the properties of non-negative numbers, which can be obtained by substituting them into the simplified formula.
Solution: divide (1) by the denominator to get 5(x﹣ 1)= 15﹣3(3x+2).
Without brackets, you get 5x-5 =15-9x-6,
When the term is shifted, it is 5x+9x = 15-6+5.
Merge similar items to get 14x= 14.
X = 1 when the coefficient is converted into1;
(2) The original formula = 3ab2- 1+7ab2+2-2a2b.
= 10ab2﹣2a2b+ 1，
∵(a+2)2+|b﹣3|=0，
? a+2=0,b﹣3=0，
? a=﹣2,b=3.
So the original formula = 10? (﹣2)? 9﹣2? 4? 3+ 1=﹣ 180﹣24+ 1=﹣203.
Four, solve the following problems (***22 points)
18.( 1) As shown in the figure, there are three views of the geometry:
(1) Write the name of this geometry;
(2) Drawing the surface development diagram of the geometric body;
③ If the height of a rectangle is 10cm and the side length of a regular triangle is 4cm, find the lateral area of this geometric figure.
(2) The solution of equation [(a) x+] = 1 is the same as the solution of equation [1 =], so the value of a is found.
The test center judges geometry with three views; Homotopy equation; The expanded diagram of the geometric figure.
Analyze (1)① as shown in the figure, and answer according to the knowledge of three views; (2) According to the geometric figure, draw the surface development diagram of the geometric figure; ③ According to the method of finding the area of the graph, the result can be obtained;
(2) According to the meaning of the question, a conclusion can be drawn.
Solution: (1)① According to the top view of the triangle, the front view and the left view are both rectangular, so it can be concluded that this geometry is a triangular prism;
② As shown in the figure,
(3) Geometric lateral area =3? 10? 4 = 120 cm2；
(2) the solution [(a) x+] =1gives x = |,
Answer-1 = x=,
Equation [(a) x+] = 1 has the same solution as equation-1 =.
? ﹣ = ,
? a=。
19.( 1) Polynomials A=2x2﹣xy+my﹣8, B=﹣nx2+xy+y+7 and A﹣2B do not contain x2 and y terms, so find the value of nm+mn.
(2) As shown in the figure, the line segment AB=20, C is a point on AB, D is a point on CB, E is the midpoint of DB, and DE=3.
① If CE=8, find the length of AC;
② If c is the midpoint of AB, find the length of CD.
Distance between two points in the test center; Addition and subtraction of algebraic expressions.
Analysis (1) lists the relationship according to the meaning of the question. After removing the brackets, the result does not contain x2 and y items, and the values of m and n are obtained, and the conclusion can be drawn by substituting them into algebraic expressions;
(2)① If E is the midpoint of DB, BD=DE=3 can be obtained, and a conclusion can be drawn according to the sum and difference of line segments; ② If E is the midpoint of DB, BD = 2DE = 6；; If c is the midpoint of AB, BC = AB =10; And can draw a conclusion according to the sum and difference of line segments.
Solution: (1) According to the meaning of the question, a﹣2b = 2 x2﹣xy+ I ﹣ 8 ﹣ 2 (﹣ nx2+xy+y+7) = (2+2n) x2.
Sum does not contain x2, y,
? 2+2n=0,m﹣2=0，
Solution: m=2, n =- 1,
? nm+mn=﹣ 1；
(2)①∫E is the midpoint of DB,
? BD=DE=3，
CE = 8，
? BC=CE+BE= 1 1，
? ac=ab﹣bc=9；
②∫E is the midpoint of DB,
? BD=2DE=6，
∫C is the midpoint of AB,
? BC= AB= 10，
? CD=BC﹣BD= 10﹣6=4.
Verb (abbreviation of verb) solves the following problems (20 questions with 6 points, 2 1 question with 7 points, *** 13 points).
20. In order to understand the air quality in our city, an environmental protection interest group randomly selected the air quality of several days from the environmental monitoring network as a sample for statistics, and drew a histogram and a fan chart as shown in the figure (some information is not given).
Please answer the following questions according to the information provided in the picture:
(1) Calculate the number of days to be extracted;
(2) Please complete the bar chart and find the representative in the fan chart. Excellent? The degree of the central angle of the sector;
Please estimate the achievements of this city this year? Excellent? And then what? Okay？ Total days.
Bar chart of test center; Estimate the population with samples; Department statistical chart.
Analysis (1) According to the proportion of air in the pie chart is 20% and the number of days in the bar chart is 12, the total number of days extracted can be obtained.
(2) The number of light pollution days is 60-36- 12-3-2 = 5 days; Use 360? Multiplied by the best share, the degree of the central angle of the best sector is obtained;
(3) Multiply the proportion of excellent days in the sample by one year to get the total number of excellent days.
Solution: (1) The proportion of air in the pie chart is 20%, and the number of days of air in the bar chart is 12 days.
? Total days extracted are: 12? 20%=60 (days);
(2) The number of light pollution days is 60-36- 12-3-2 = 5 days;
What is the degree of excellent central angle? =72? ,
As shown in the figure:
;
(3) The excellent days in the sample were12,36,
What is the total number of days to be excellent and good in one year? 365=292 (days).
Therefore, it is estimated that the total number of days in a year in this city is 292 days.
2 1. A middle school held a math contest, and planned to use two copiers, A and B, to copy the test papers. If it takes 90 minutes to print on the A machine alone and 60 minutes to print on the B machine alone, for the sake of confidentiality, the school decided to copy the test paper at the same time before the exam.
(1) Two copiers copy at the same time. How many minutes does it take to finish printing?
(2) If two copiers copy for 30 minutes at the same time, machine B fails and cannot copy for the time being. At this time, there are still 13 minutes before the paper is issued. Please calculate, if the rest of the copying tasks are completed by machine A alone, will it affect the exam that will be handed out on time?
(3) In the problem of (2), machine B was repaired urgently and resumed normal use after 9 minutes. Please calculate again, can the school issue exams on time?
The application of one-dimensional linear equation in examination center.
Analysis (1) assumes that * * * printing takes x minutes. According to the meaning of the question, get (+)x= 1 and solve the equation.
(2) Assume that it takes Y minutes for Machine A to complete the remaining copying tasks alone. 30+ = 1, the solution can be compared with 13;
(3) When Machine B was put into use again, both machines copied the test paper for z minutes, and got (+) according to the meaning of the question? 30+ +(+)z= 1, add 9 after solving and compare with 13.
Solution: (1) Let * * take x minutes to print, (+)x= 1, and the solution is x=36.
A: Two copiers copy at the same time, and it takes 36 minutes to finish printing.
(2) Assuming that it takes Y minutes for Machine A to complete the remaining copying tasks alone,
( + )? 30+ = 1，y = 15 >； 13
Answer: it will affect the school to issue examination papers on time;
(3) When Machine B is restored to use, two machines copy the test paper for z minutes.
( + )? 30+ +( + )z= 1
The solution is z=2.4.
Then there is 9+2.4 = 1 1.4.
A: The school can give the exam on time.
?