Jiangsu education edition eighth grade first volume mathematics final examination questions
A, multiple-choice questions (this big titled ***6 small questions, each small question 2 points, *** 12 points. Of the four options given in each small question, just one meets the requirements of the topic. Please fill in the corresponding answer column on page 3.
1. Of the four Chinese characters shown in the figure, () can be regarded as an axisymmetric figure.
A.B. C. D。
2. if a>0, b <-2, the point (a, b+2) is in ().
A. first quadrant B. second quadrant C. third quadrant D. fourth quadrant
3. The value of x that makes the score meaningless is ()
A.x=﹣ B.x= C.x？ -Dacres?
4. As shown in the figure, known? 1=? 2. The condition that △ Abd△ ACD may not be done is ().
A.AB=AC B.BD=CD C？ B=？ C D？ BDA=？ Command data interception (abbreviation for Command and Data Acquisition)
5. The image of linear function y = mx+| m ~ 1 | passes through point (0,2). If y increases with the increase of x, the value of m is ().
A.-1b.1c.3d.-1or 3
6. Party A and Party B advance at a constant speed from place A to place B along the same route. The distance between A and B is 20km, their forward distance is s (unit: km), and the time after Party A leaves is t (unit: hour). The function image of distance and time between Party A and Party B is shown in the figure. According to the image information, the following statement is true ().
The speed of A.a is 4km/h B. B is10 km/h.
C.a arrives at B 3 hours later than B, and B leaves 1 hour later than A..
2. Fill in the blanks (this big question is a small question of *** 10, with 2 points for each small question and 20 points for * * *. Please fill in the answer in the corresponding answer column on page 3, the answer in the first volume is invalid)
7. Suppose the function y=(n﹣2)x+n2﹣4 is a proportional function, then n is.
8. The distance from point C to the X axis is 1, and the distance to the Y axis is 3, which is in the third quadrant, so the coordinates of point C are.
9. Simplify: =.
10. If known, the value of the algebraic expression is.
1 1. In isosceles delta △ABC, AB=AC, and its circumference is 20cm, then the value range of AB side is cm.
12. As shown in the figure, in isosceles △ABC, AB=AC,? DBC= 15？ The perpendicular line MN of AB intersects with AC at point D, then? The degree of a is.
13. As shown in the figure, △ABC is an equilateral triangle, point D is a point on the side of AC, and BD is an equilateral △BDE, connecting CE. If CD= 1 and CE=3, then BC=.
14. As shown in the figure, it is known that the images of functions y=3x+b and y = ax | 3 intersect at point p (| 2, | 5), then the inequality 3x+b > can be obtained from the images. The solution set of AX-3 is.
15. In △ABC, AB= 13cm, AC=20cm, and the height on the side of BC is 12cm, so the area of △ABC is cm2.
16. When x is ﹣, ﹣? 、﹣ 、﹣2、﹣ 1、0、 1、2、? , 20 15, 20 16, 20 17, calculate the values of the scores, and then add up the results, and the sum is equal to.
Third, answer the question (this big question * * * has 9 small questions, ***68 points. When answering the question, write the necessary text description, proof process or calculation steps in the corresponding position of the test paper. )
17. Calculation: +| 1+ |.
18. Solve the equation: = 1+.
19. As shown in the figure, the side length of each small square in the square grid is 1.
(1) Given the line segments AB and CD in the figure 1, draw the line segment EF to form an axisymmetric figure with AB and CD (only one is needed);
(2) Draw a line segment with the grid point as the endpoint in Figure 2.
20. As we all know, y-3 is directly proportional to x, and when x =-2, the value of y is 7.
(1) Find the functional relationship between y and x;
(2) If point (-2, m) and point (4, n) are two points on the function image, try to compare the sizes of m and n and explain the reasons.
2 1. In Rt△ABC,? ACB=90？ , AC=BC, D is the midpoint of BC, CE? The extension line of AD at e, BF∑AC and CE is at F.
(1) Verification: △ ACD △ CBF;
(2) Verification: AB bisects DF vertically.
22. Simplify first and then evaluate: (-)? , where x=.
23. as shown in the figure, Zhao Shuang's string diagram? It consists of four congruent right-angled triangles, which are located at Rt△ABC,? ACB=90？ , AC=b, BC=a, please use this diagram to solve the following problems:
(1) Prove Pythagorean Theorem;
(2) Explain a2+b2? Conditions of 2ab and its equal sign.
24. it is known that the straight line l 1: y = | intersects with the straight line l2: y = kX | at the same point a on the x axis, and the straight line l 1 intersects with the y axis at point b, and the intersection of the straight line l2 and the y axis is C. 。
(1) Find the value of k and make a straight line l2 image;
(2) If point P is a point on the AB line and the area of △ACP is 15, find the coordinates of point P;
(3) If points M and N are moving points on the X axis and line segment AC respectively (point M and point O are not coincident), do points M and N make △ anm △ AOC? If it exists, request the coordinates of n points; If it does not exist, please explain why.
25. In △ABC,? BAC=90？ , AB=AC, outside of △ABC? ACM，make？ ACM=？ ABC, point D is the moving point on the straight line BC, the intersection point D is the vertical line of the straight line CM, the vertical foot E, and the intersection line AC is in F. 。
(1) As shown in figure 1, when point D coincides with point B, the intersection point n of BA and CM is prolonged, which proves that DF = 2EC.
(2) When point D moves on the straight line BC, do DF and EC always keep the above quantitative relationship? Please draw the graph when point D moves to a point on the CB extension line in Figure 2 to prove the quantitative relationship between DF and EC at this time.
Jiangsu Education Edition Grade 8 Volume I Mathematics Final Examination Paper Reference Answer
A, multiple-choice questions (this big titled ***6 small questions, each small question 2 points, *** 12 points. Of the four options given in each small question, just one meets the requirements of the topic. Please fill in the corresponding answer column on page 3.
1. Of the four Chinese characters shown in the figure, () can be regarded as an axisymmetric figure.
A.B. C. D。
Axisymmetric figure of test point.
The analysis is based on the concept of axisymmetric graphics.
Solution: A, it is an axisymmetric figure, so it is correct;
B, it is not an axisymmetric figure, so the error is large;
C, not axisymmetric graphics, so the error is large;
D is not an axisymmetric figure, so it is wrong.
So choose a.
This topic examines the concept of axisymmetric graphics: the key to axisymmetric graphics is to find the axis of symmetry, and the two parts of the graphics can overlap after being folded along the axis of symmetry.
2. if a>0, b <-2, the point (a, b+2) is in ().
A. first quadrant B. second quadrant C. third quadrant D. fourth quadrant
Coordinates of the test site.
Theme finale.
Analysis should first judge the symbols of the abscissa and ordinate of the point, and then judge the quadrant where the point is located.
Answer: ∫ A > 0，b & lt﹣2,
? b+2 & lt； 0,
? Point (a, b+2) is in the fourth quadrant, and choose D.
The key to solve this problem is to remember the symbols of each quadrant point in the plane rectangular coordinate system. The symbolic features of the four quadrants are: the first quadrant (+,+); The second quadrant (-,+); The third quadrant (-,-); The fourth quadrant (+,|).
3. The value of x that makes the score meaningless is ()
A.x=﹣ B.x= C.x？ -Dacres?
Conditions for the meaningful part of the test point.
It is meaningless to find the value range of x according to the fraction with denominator of 0.
Solution: According to the meaning of problem 2x- 1 = 0,
The solution is x=
Therefore, choose: B.
The comment on this topic mainly examines the condition that the score is meaningless is that the denominator is 0.
4. As shown in the figure, known? 1=? 2. The condition that △ Abd△ ACD may not be done is ().
A.AB=AC B.BD=CD C？ B=？ C D？ BDA=？ Command data interception (abbreviation for Command and Data Acquisition)
Congruent triangles's judgment of the test center.
Theme finale.
Congruent triangles's decision theorems ASA, SAS and AAS are used to analyze each option one by one to get the answer.
Solution: a, ∵? 1=? 2. AD is the public side, and if AB=AC, then △ Abd △ ACD (SAS); Therefore, a does not meet the meaning of the question;
b、∵？ 1=? 2. AD is a common * * * edge. If BD=CD, it does not conform to congruent triangles's judgment theorem, and it is impossible to judge △ Abd △ ACD; So b meets the meaning of the question;
c、∵？ 1=? 2, AD is the public party, if? B=？ C, then △ Abd△ ACD (AAS); So c does not meet the meaning of the question;
d、∫？ 1=? 2, AD is the public party, if? BDA=？ CDA, then △ Abd△ ACD (ASA); So d doesn't fit the question.
Therefore, choose: B.
This topic mainly examines students' understanding and mastery of congruent triangles's judgment theorem. It's not difficult, it belongs to the basic topic.
5. The image of linear function y = mx+| m ~ 1 | passes through point (0,2). If y increases with the increase of x, the value of m is ().
A.-1b.1c.3d.-1or 3
Properties of linear functions of test points.
The equation about m is obtained by substituting x=0 and y=2 into the resolution function from (0,2) on the linear function image, and the value of m can be obtained by solving the equation.
Solution: ∵ Image passing point (0,2) of linear function y = MX+| m1|.
? Substitute x=0 and y=2 into y = MX+| m |1| to get | m |1| = 2.
Solution: m=3 or-1,
∵y increases with the increase of x,
So m>0,
So m=3,
Therefore, choose c;
In order to solve this problem, we studied how to find the analytic expression of linear function by using the undetermined coefficient method. This method generally has four steps: setting, substituting, seeking and answering, that is, setting the corresponding analytical formula according to the type of the function, substituting the known point coordinates, determining the set coefficient, and substituting the calculated coefficient into the set analytical formula to obtain the analytical formula of the function.
6. Party A and Party B advance at a constant speed from place A to place B along the same route. The distance between A and B is 20km, their forward distance is s (unit: km), and the time after Party A leaves is t (unit: hour). The function image of distance and time between Party A and Party B is shown in the figure. According to the image information, the following statement is true ().
The speed of A.a is 4km/h B. B is10 km/h.
C.a arrives at B 3 hours later than B, and B leaves 1 hour later than A..
Image of test center function.
According to the image analysis, the distance between A and B is 20 kilometers. A started earlier than B 1 hour, but arrived 2 hours late. It takes 4 hours for A to go from A to B, and B needs 1 hour, so that the speed of A and B can be obtained and the information can be answered in turn.
Solution: a, the speed of a: 20? 4=5km/h, error;
B, b's speed: 20? (2 ~ 1) = 20km/h, error;
C, the time when A arrives at B later than B: 4-2 = 2h, wrong;
The departure time of D and B after A is 1h, which is correct;
So choose D.
This review mainly examines the function of images, focusing on students' ability to read images to obtain information, and what aspects should be paid attention to? The key point? And be good at analyzing the changing trend of each image.
2. Fill in the blanks (this big question is a small question of *** 10, with 2 points for each small question and 20 points for * * *. Please fill in the answer in the corresponding answer column on page 3, the answer in the first volume is invalid)
7. Assuming that the function y=(n﹣2)x+n2﹣4 is a proportional function, then n is ﹣2.
Definition of proportional function of test center.
Analysis is based on proportional function: the definition condition of proportional function y=kx is: k is constant, k? 0, the answer is available.
Solution: y=(n﹣2)x+n2﹣4 is a proportional function, so.
,
The solution is n =-2, n=2 (if it doesn't meet the meaning of the question, it will be discarded).
So the answer is: -2.
The key to solving the problem is to master the definition conditions of proportional function: the definition conditions of proportional function y=kx are: k is a constant, k? 0, the number of independent variables is 1.
8. The distance from point C to the X axis is 1, and the distance to the Y axis is 3, and in the third quadrant, the coordinate of point C is (-3,-1).
Coordinates of the test site.
According to the analysis, the distance to the X axis is equal to the length of the ordinate, the distance to the Y axis is equal to the length of the abscissa, and both the abscissa and the ordinate of the point in the third quadrant are negative solutions.
Solution: The distance from point ∵C to X axis is 1, and the distance to Y axis is 3, and it is in the third quadrant.
? The abscissa of point C is -3 and the ordinate is-1.
? The coordinates of point C are (-3,-1).
So the answer is: (-3,-1).
This topic comments on the coordinates of the inspection point and remembers the symbolic characteristics of the four quadrants: the first quadrant (+,+); The second quadrant (-,+); The third quadrant (-,-); The fourth quadrant (+,﹣) is the key to solving problems.
9. Simplify: =.
Addition and subtraction of quadratic roots in test sites.
Firstly, each radical is transformed into the simplest quadratic radical, and then it is calculated according to the subtraction of quadratic radical.
Solution: Original formula = 2.
= .
So the answer is:
Comment on this topic to examine the addition and subtraction of quadratic roots. Knowing the addition and subtraction of quadratic roots, first turn each quadratic root into the simplest quadratic root, and then merge the quadratic roots with the same number of roots. The method of merging is coefficient addition and subtraction, and the root is the key to solve this problem.
10. If known, the value of the algebraic expression is 7.
Complete square formula of test center.
Theme finale.
According to the complete square formula, the analysis can be solved by squaring both sides of the known condition.
Solution: ∫x+= 3,
? (x+ )2=9，
Namely x2+2+ =9,
? x2+ =9﹣2=7.
This topic mainly examines the complete square formula. According to the characteristics of the topic, using the product binomial without letters is the key to solving the problem.
1 1. In isosceles delta △ABC, AB=AC, and its circumference is 20cm, then the value range of AB side is 5.