People's education printing plate eighth grade mathematics volume I final exam 1. Multiple choice questions (this big question * * 10 small questions, 3 points for each small question, 30 points for * * *, and only one correct answer for each small question).
1. Among the following propositions, the pseudo-proposition is ()
The arithmetic square root of A.9 is 3 B, what is the square root? 2
What is the cube root of C.27? 3 d. The real number whose cube root is equal to-1 is-1.
2. Among the following propositions, the false proposition is ()
A. Two lines perpendicular to the same line are parallel.
B. given a straight line a, b, c, if a? B, a∑c, what about B? c
C. complementary angles are adjacent complementary angles.
D. Adjacent complementary angles are complementary angles.
3. The length of the following line segments, can form a right triangle group is ().
A.，B.6，7，8 C. 12，25，27 D.2，2，4
4. The following calculation is correct ()
A.B. C.(2﹣ )(2+ )= 1 D
5. The coordinate of point P is (2-A, 3a+6), and the distance to the two coordinate axes is equal, so the coordinate of point P is ().
A. (3,3 3) B. (3 3,3 3) C. (6 6,6 6) D. (3 3,3) or (6,6)
6. The known proportional function y=kx(k? The function value y of 0) increases with the increase of x, so the image of linear function y=kx+k is roughly ().
A.B. C. D。
7. If the solution of the equations is, then the two covered numbers are () respectively.
C.2,﹣ 1 D.﹣ 1,9
8. It is known that the average of three numbers A, B and C is 4, and the average of four numbers A, B, C and D is 5, so the value of D is ().
A.4 B.8 C. 12 D.20
9. As shown in the figure, B=? What about c? ADC and? The size relationship of AEB is ()
A.？ ADC & gt？ AEB bay? ADC=？ Acute erythrocytopenia
C.？ ADC & lt？ Aeb D. the size relationship cannot be determined
10. As shown in the figure, there is a height higher than 8cm and a base diameter equal to 4cm (? =3), there is an ant at point A on the bottom surface of the cylinder. It wants to eat food at point B on the upper bottom opposite to point A, and the shortest distance it needs to crawl is about ().
A.10cm B.12cm C.19cm D.20cm.
Fill in the blanks (this topic is entitled ***8 small questions, with 3 points for each small question ***24 points)
1 1. In a comprehensive practice class, the number of six students doing manual work (unit: pieces) is 5, 7, 3, 6, 6 and 4 respectively; Then the median of this set of data is 1.
12. If point A (m, 5) and point B (2, n) are symmetrical about the origin, the value of 3m+2n is.
13. There are four real numbers, 32 and -23 respectively. Please calculate the difference between the sum of rational numbers and the product of irrational numbers. The result is.
14. As shown in the figure, it is known that AD = 4m and CD = 3m. ADC=90？ , AB = 13m, BC = 12m, and the area of this land is.
15. The right vertex C of isosceles right triangle ABC is on the Y axis, AB is on the X axis, A is on the left side of B, and AC=, then the coordinate of point A is.
16. If+(x+2y-5) 2 = 0, then x+y=.
17. As shown in the figure, point D is on the extension line of BC next to △ABC, DE? AB in e, AC in f, B=50？ ,? CFD=60？ And then what? ACB=。
18. It is known that A is 3 kilometers south of B, and both of them are driving at a constant speed from A and B to the north. The functional relationship between their distance s(km) from land A and their travel time t(h) is shown in the figure. When they travel for three hours, the distance between them is kilometers.
Three. (This big title is * * 7 small questions, 19 8 points, 6 points on the 20th, 2 1, 22, 23, 24 small questions, 8 points on 25 small questions, * * * 44 points).
19.( 1) Calculation: 3+-4
(2) Solve the equation:
20. As shown in the figure, after the flag-raising rope of a flagpole falls vertically, there is still 1 meter left. If the rope is straightened, the distance (BC) between the end of the rope and the bottom of the flagpole is 5m. Find the height of the flagpole.
2 1. Known: as shown in the figure, AB∨CD, AD∨BC,? 1=50? ,? 2=80? . Beg? The degree of C.
22. Two students, A and B, participated in the 100 meter sprint training organized by the school, and the coach recorded the training results of 10 day with a line chart.
(1) Please use the information provided by the known line chart to complete the following table:
The average variance is 10 days.
Number of times less than 15 second
One piece 15 2.6 5
second
(2) The school wants to choose one of the two to participate in the city middle school sports meeting 100 meter competition. Please help the school make a choice and briefly explain your reasons.
23. Before Class 3, Grade 8 held the final summary commendation meeting, the class teacher arranged for Li Xiaobo, the monitor, to go to the store to buy prizes. The following is a conversation between Li Xiaobo and the shop assistant:
Li Xiaobo: Hello, Aunt!
Shop assistant: Hello, classmate. what can I do for you?
Li Xiaobo: I only have 100 yuan. Please arrange for me to buy 10 and 15 notebooks.
Shop assistant: OK, each pen is more expensive than each notebook. 2 yuan, here is your money, 5 yuan. Please count. Goodbye.
According to this conversation, can you work out the unit price of a pen and a notebook?
24. Xiaoying and Liang Xiao went up the hill to play. Xiaoying takes the cable car and Liang Xiao walks. They meet at the end of the cable car at the top of the mountain. The distance from Liang Xiao to the end of the cable car is twice that from the cable car to the top of the mountain. Xiaoying boarded the cable car 50 minutes after leaving Liang Xiao, and the average speed of the cable car was 180m/min. Let Liang Xiao go. The dotted line in the figure indicates that Liang Xiao is in the whole.
(1) Xiao Liang walked a total of m and rested for min on the way.
(2) At the age of 50? x？ 80, find the functional relationship between y and x;
(3) How long does it take Xiaoying to reach her destination by cable car? How far did Liang Xiao go when Xiaoying reached the end of the cable car?
25. It is known that △ABC,
(1) As shown in figure 1, if point D is any point in △ABC, then verify:? D=？ A+？ ABD+？ ACD。
(2) If point D is a point outside △ABC, the position is shown in Figure 2. Guess what? D, is it? A: ABD? What does ACD have to do with it? Please write a satisfactory relationship directly. (No proof required)
(3) If point D is a point outside △ABC, the position is shown in Figure 3. D, is it? A: ABD? What does ACDs have to do with proving your conclusion?
People's education printing plate eighth grade mathematics volume I final examination paper reference answer 1. Multiple choice questions (this big question * * 10 small questions, 3 points for each small question, 30 points for * * *, and only one correct answer for each small question)
1. Among the following propositions, the pseudo-proposition is ()
The arithmetic square root of A.9 is 3 B, what is the square root? 2
What is the cube root of C.27? 3 d. The real number whose cube root is equal to-1 is-1.
Test site cube root; Arithmetic square root; Propositions and theorems.
Each option is analyzed and judged separately, and it is found that the wrong proposition is false.
Solution: the arithmetic square root of a and 9 is 3, so option a is a true proposition;
B =4, what is the square root of 4? 2, so option b is a true proposition;
The cube root of c and 27 is 3, so the c option is a false proposition;
The cube roots of d and ﹣ 1 are ﹣ 1, so the d option is a true proposition.
So choose C.
This topic examines the definitions of cube root and arithmetic square root, which are basic and relatively simple.
2. Among the following propositions, the false proposition is ()
A. Two lines perpendicular to the same line are parallel.
B. given a straight line a, b, c, if a? B, a∑c, what about B? c
C. complementary angles are adjacent complementary angles.
D. Adjacent complementary angles are complementary angles.
Propositions and theorems of test sites.
Analysis According to the nature of adjacent complementary angles and common knowledge points, each proposition is analyzed and the correct answer is obtained.
Solution: a, two straight lines perpendicular to the same straight line are parallel, which is a true proposition and does not conform to the meaning of the question;
B. given a straight line a, b, c, if a? B, a∑c, what about B? C, true proposition, does not meet the meaning of the question;
C, complementary angle is not necessarily an adjacent complementary angle, but a false proposition, which conforms to the meaning of the question;
D, the adjacent complementary angles are complementary angles, which are true propositions and do not conform to the meaning of the question.
So choose: C.
This review mainly examines propositions and theorems, and mastering relevant theorems is the key to solving problems.
3. The length of the following line segments, can form a right triangle group is ().
A.，B.6，7，8 C. 12，25，27 D.2，2，4
The Inverse Theorem of Pythagorean Theorem in Test Sites.
According to the inverse theorem of Pythagorean theorem, if the sum of squares of two sides of a triangle is equal to the square of the third side, then it is a right triangle. If there is such a relationship, it is a right triangle; if there is no such relationship, it is not a right triangle.
Solution: A, () 2+( )2? () 2, so it is not a right triangle, this option is wrong;
62+72？ 82, so it is not a right triangle, this option is wrong;
c、 122+252？ 272, so it is not a right triangle, this option is wrong;
D, (2 )2+(2 )2=(4 )2, so it is a right triangle. This option is correct.
Therefore, choose: d.
This topic examines the inverse theorem of Pythagorean theorem. When applying the inverse theorem of Pythagorean theorem, we should first carefully analyze the size relationship of a given side to determine the largest side, then verify the relationship between the sum of squares of two smaller sides and the square of the largest side, and then make a judgment.
4. The following calculation is correct ()
A.B. C.(2﹣ )(2+ )= 1 D
Addition and subtraction of secondary roots of test sites; Properties and simplification of quadratic roots: multiplication and division of quadratic roots.
Analyze according to the algorithm of quadratic root, calculate one by one, and then choose.
Solution: A, the original formula = 2-=, so it is correct;
B, the original type = =, so it is wrong;
C, the original formula = 4-5 =- 1, so it is wrong;
D, the original formula = = 3- 1, so it is wrong.
So choose a.
Comment on the addition and subtraction of the root sign, and note that items that are not of the same category cannot be combined. When calculating the quadratic root, pay attention to simplify it to the simplest quadratic root before calculating it.
5. The coordinate of point P is (2-A, 3a+6), and the distance to the two coordinate axes is equal, so the coordinate of point P is ().
A. (3,3 3) B. (3 3,3 3) C. (6 6,6 6) D. (3 3,3) or (6,6)
Coordinates of the test site.
According to the analysis, the distance from point P to two coordinate axes is equal, and we can get | 2-a | = | 3a+6 |, then we can get the value of a, and then we can get the coordinates of point P.
Solution: ∫ The coordinate of point P is (2a, 3a+6), and the distance to the two coordinate axes is equal.
? |2﹣a|=|3a+6|，
? 2﹣a=？ (3a+6)
The solution is a =- 1 or a =-4,
That is, the coordinates of point P are (3,3) or (6,6).
So choose D.
Comment on this topic, and investigate the feature that the distance between a point and two coordinate axes is equal, that is, the absolute value of the abscissa and ordinate of a point is equal.
6. The known proportional function y=kx(k? The function value y of 0) increases with the increase of x, so the image of linear function y=kx+k is roughly ().
A.B. C. D。
The image of the linear function of the test center; Properties of proportional function.
Firstly, the sign of k is judged according to the function value y of the proportional function y=kx which increases with the increase of x, and then a conclusion can be drawn according to the properties of linear functions.
Solution: ∫ The function value y of the proportional function y=kx increases with the increase of x,
? k & gt0,
∫b = k & gt； 0,
? The image with linear function y=kx+k passes through the first, second and third quadrants.
So choose a.
Comment on this topic, the relationship between the image of a linear function and the coefficient is investigated, that is, the linear function y=kx+b(k? 0), when k>0, the image of b> function at 0 is located in the first, second and third quadrants.
7. If the solution of the equations is, then the two covered numbers are () respectively.
C.2,﹣ 1 D.﹣ 1,9
Solution of binary linear equations in test sites.
Special calculation problems.
Analysis: Substitute x=2 into the second equation of the equations to find the value of y, determine the solution of the equations, and substitute into the first equation to find the covered number.
Solution: substitute x=2 into x+y=3 to get: y= 1,
Substitute x=2 and y= 1 to get 2x+y=4+ 1=5.
Then the two mask numbers are 5 1 respectively,
So choose B.
This topic reviews the solutions of binary linear equations, and the solutions of the equations are the values of unknown quantities that can make two equations in the equations hold.
8. It is known that the average of three numbers A, B and C is 4, and the average of four numbers A, B, C and D is 5, so the value of D is ().
A.4 B.8 C. 12 D.20
Arithmetic average of test sites.
As long as the average formula is used in the analysis, the equation about d can be listed and solved.
Solution: ∫ The average of the three numbers A, B and C is 4.
? a+b+c= 12
a+b+c+d=20
So d=8.
So choose B.
The solution of the average value of the sample is reviewed and investigated. Reciting formulas is the key to solve this problem.
9. As shown in the figure, B=? What about c? ADC and? The size relationship of AEB is ()
A.？ ADC & gt？ AEB bay? ADC=？ Acute erythrocytopenia
C.？ ADC & lt？ Aeb D. the size relationship cannot be determined
Test the exterior angle property of the center triangle.
The analysis is calculated by using the sum of the internal angles of the triangle as 180 degrees.
Solution: Is it in the △ADC? A+？ C+？ ADC= 180？ ,
Does Delta △AEB have it? AEB+？ A+？ B= 180？ ,
∵? B=？ c，
? After equivalent replacement? ADC=？ AEB。
So choose B.
Comment on this topic, the sum of the internal angles of the triangle is 180 degrees.
10. As shown in the figure, there is a height higher than 8cm and a base diameter equal to 4cm (? =3), there is an ant at point A on the bottom surface of the cylinder. It wants to eat food at point B on the upper bottom opposite to point A, and the shortest distance it needs to crawl is about ().
A.10cm B.12cm C.19cm D.20cm.
Test center plane expansion-shortest path problem.
According to analysis, between two points, the line segment is the shortest. Firstly, A and B are expanded into a plane, that is, half of the cylinder, and a rectangle is obtained. Then, according to Pythagorean theorem, the shortest distance for ants to crawl, that is, the length of the diagonal of the unfolded rectangle, is obtained.
Solution: expand half of the cylinder to get a rectangle: the length of the rectangle is half of the circumference of the cylinder bottom, that is, 2? =6, the width of the rectangle is the height of the cylinder, which is 8.
According to Pythagorean theorem, the shortest distance for ants to crawl is the diagonal length of the unfolded rectangle, that is, 10.
So choose a.
The commentary on this topic examines the extended application of Pythagorean theorem. Turn a surface into a plane? Is it a solution? How to climb recently? The key to this kind of problem. This problem only needs to expand half the side of the cylinder.
Fill in the blanks (this topic is entitled ***8 small questions, with 3 points for each small question ***24 points)
1 1. In a comprehensive practice class, the number of six students doing manual work (unit: pieces) is 5, 7, 3, 6, 6 and 4 respectively; Then the median of this set of data is 5.5 blocks.
Median testing center.
Special application problems.
Analysis is based on the definition of median. The data are arranged by size, and the average of the third and fourth numbers is the median.
Solution: The order from small to large is: 3, 4, 5, 6, 6, 7.