People's education printing plate eighth grade first volume mathematics final examination questions
A, multiple-choice questions * * * This question ***8 small questions, each small question 3 points, * * * each small question 24 points, each small question 4 options, one and only one answer is correct * * *
1. Among the following four Chinese characters, * * * * * can be regarded as an axisymmetric figure.
A. charm B. power C. yellow D. gang
2. The following calculations are correct * * * * *
a . 2 a2+a3 = 3 a5 b . * * * 3xy * * * 2÷* * * xy * * * = 3xy c . * * * 2 B2 * * * 3 = 8 b5 d . 2x？ 3x5=6x6
3. If one side of an isosceles triangle is 6cm long and 30cm in circumference, then the other two sides are * * * * * respectively.
A.6cm， 18cm B. 12cm， 12cm
C.6cm, 12cm D.6cm, 18cm or 12cm, 12cm.
4. In order to make the score meaningful, the value of x should satisfy * * * * *.
a.x=﹣2 b . x & lt； ﹣2 c . x & gt； ﹣2 D.x≠﹣2
5. Four pieces of wood with the length of 10, 7, 5 and 3, three of which are connected end to end in turn to form a triangle, and the selection method is * * * * *.
1。
6. Given A-B = 3, ab=2, the value of A2-AB+B2 is * * * *.
a . 9 b . 13 c . 1 1d . 8
7. If-= 5 is known, the value of the score is * * * * * *.
1。
8. As shown in the figure, in equilateral △ABC, BD bisects ∠ABC and intersects with AC at point D, and the intersection point D is DE⊥BC at point E, and CE= 1.5, then the length of AB is * * * *.
A.3 B.4.5 C.6 D.7.5
2. Fill in the blanks * * * This question has 8 small questions, each with 3 points and * * * 24 points.
9. Factorization 3x3+ 12x2+ 12x=.
10. Graphene is the thinnest and hardest nano-material in the world at present, and its theoretical thickness is only 0.0000000034 meters, which is expressed by scientific notation.
1 1 * * * 2m2n ~ 2 * * * 2? The result of 3m ~ 2n3 is.
12. If the value of the score is 0, then x=.
13. As shown in the figure, in △ABC, AB=AC, D is a point above BC, CD=AD, AB=BD, then the degree of ∠B is.
14. Calculate 2016× 512 ~ 2016× 492, and the result is as follows.
15. As shown in the figure, triangular paper ABC, AB= 10cm, BC=7cm, AC=6cm. Fold this triangle along a straight line passing through point B, so that the vertex C falls at point E on the side of AB, and the folding seam is BD, then the circumference of △AED is cm.
16. As shown in the figure, in △ABC, the bisector of the middle vertical line DP between BC and ∠BAC intersects at point D, and the vertical foot is point P. If ∠ BAC = 84, ∠BDC=.
Three. Answer the question * * * * 72 points * * *
17. Calculate the following questions:
*** 1******﹣2***3+ ×0﹣***﹣ ***﹣2.
***2***[***x2+y2***﹣***x﹣y***2﹣2y***x﹣y***]÷4y.
18. Solve the equation:.
19. Simplify first and then evaluate: * * * * * *, where x=3.
20. As shown in the figure, point E ∠A=∠D C is on ∠B=∠F, BE=CF, AB=DF, ∠ B = ∠ F Verification: ∠A=∠D.
2 1. As shown in the figure, the vertices of △ABC are A * * *-2, 3***, B * * *-4, 1 * *, C * *-1,2 * * respectively.
* * *1* * Draw the figure of △ABC's axis symmetry about X △ A1b1;
* * * 2 * * Write the coordinates of A 1, B 1 and C 1;
***3*** Find the area of △ABC.
22. Two construction teams, Party A and Party B, plan to participate in the construction of a project, and Team A will complete it in 30 days alone. At this time, team B will join in, and both teams need to work at the same time for 65,438+05 days to complete the project.
* * *1* * If Team B goes it alone, how many days will it take to complete the project?
* * * 2 * * If Team A participates in the construction of the project for less than 36 days, how many days will it take Team B to complete the project at least?
23. As shown in the figure, at Rt△ABC, ∠ ACB = 90, AC=BC, point D is on the hypotenuse of AB, AD=AC, and intersection point B is the intersection line CD of BE⊥CD at point E. 。
* * *1* * Find the degree of ∠BCD;
***2*** Verification: CD=2BE.
24. as shown in figure ①, CA=CB, CD=CE, ∠ACB=∠DCE=α, AD and BE intersect at point m, and the connecting line is CM.
*** 1*** verification: BE = AD
***2*** The number of times ∠AMB is expressed by a formula containing α;
* * * 3 * * When α = 90, take the midpoint of AD and BE as points P and Q respectively, and connect CP, CQ and PQ, as shown in Figure ②, and judge and prove the shape of △CPQ.
Reference answer
A, multiple-choice questions * * * This question ***8 small questions, each small question 3 points, * * * each small question 24 points, each small question 4 options, one and only one answer is correct * * *
1. Among the following four Chinese characters, * * * * * can be regarded as an axisymmetric figure.
A. charm B. power C. yellow D. gang
Axisymmetric figure of test point.
Analysis According to the concept of axisymmetric graphics, each option is analyzed and judged, and the solution can be obtained.
Solution: A, "Charm" is not an axisymmetric figure, so this option is wrong;
B, "force" is not an axisymmetric figure, so this option is wrong;
C, "yellow" is an axisymmetric figure, so this option is correct;
D, "Gang" is not an axisymmetric figure, so this option is wrong.
So choose C.
2. The following calculations are correct * * * * *
a . 2 a2+a3 = 3 a5 b . * * * 3xy * * * 2÷* * * xy * * * = 3xy c . * * * 2 B2 * * * 3 = 8 b5 d . 2x？ 3x5=6x6
Division of algebraic expression of test center; The power of power and the power of products; Multiply the monomial by the monomial.
Analyzing the power of the product is equivalent to multiplying each factor of the product by the power, and then multiplying it by the obtained power; The division rule of single item and the operation rule of single item multiplication are calculated and solved by exclusion method.
Solution: A, 2a2 and a3 are not similar items and cannot be merged, so this option is wrong;
B, it should be * * 3xy * * * 2 ÷ * * xy * * = 9X2y2 ÷ xy = 9xy, so this option is wrong;
C, it should be * * * 2b2 * * * 3 = 23 * * * B2 * * * 3 = 8b6, so this option is wrong;
d、2x？ 3x5=6x6, correct.
So choose D.
3. If one side of an isosceles triangle is 6cm long and 30cm in circumference, then the other two sides are * * * * * respectively.
A.6cm， 18cm B. 12cm， 12cm
C.6cm, 12cm D.6cm, 18cm or 12cm, 12cm.
Test the nature of the central isosceles triangle; The trilateral relationship of a triangle.
Analysis shows that the circumference of an isosceles triangle is 30cm, and one side of the triangle is 6cm long. The answer can be obtained by analyzing and solving the problem from 6cm as the base length and 6cm as the waist length.
Solution: The circumference of an isosceles triangle is 30cm, and the length of one side of the triangle is 6cm.
∴ If 6cm is the base length, then the waist length is: * * * 30 ~ 6 * * * ÷ 2 =12 * * cm * * *,
∵6cm, 12cm, 12cm can form a triangle.
∴ at this time, the other two sides are 12cm and12 cm respectively;
If 6cm is the waist length, then the bottom length is: 30-6-6 = 18 * * * cm * * *,
∵6+6 & lt； 18,
You can't form a triangle, so give up.
∴ The other two sides are 12cm and 12cm respectively.
So choose B.
4. In order to make the score meaningful, the value of x should satisfy * * * * *.
a.x=﹣2 b . x & lt； ﹣2 c . x & gt； ﹣2 D.x≠﹣2
Conditions for the meaningful part of the test point.
It is meaningful to analyze the scores with non-zero denominator and get the answer.
Solution: It is meaningful in terms of score, and it is obtained.
x+2≠0，
Solve x ≠ 2,
Therefore, choose: d.
5. Four pieces of wood with the length of 10, 7, 5 and 3, three of which are connected end to end to form a triangle, and the selection method is * * * * *.
1。
Test the trilateral relationship of the central triangle.
Analyze whether a triangle can be formed according to whether the sum of any two sides is greater than the third side.
Solution: Select three of them to form triangles, and the different selection methods are 3cm, 5cm, 7cm3cm, 5cm,10 cm; 5cm，7cm， 10cm； 3cm，7cm， 10cm；
Only 3cm, 5cm and 7cm can form a triangle; 5cm，7cm， 10cm；
***2 kinds.
So choose B.
6. Given A-B = 3, ab=2, the value of A2-AB+B2 is * * * *.
a . 9 b . 13 c . 1 1d . 8
Complete square formula of test center.
The analysis can find the answer according to the complete square formula.
Solution: ∫* * A-B * * * 2 = A2-2AB+B2
∴32=a2+b2﹣2×2
∴a2+b2=9+4= 13，
∴ Original formula = 13-2 = 1 1
So choose ***C***
7. If-= 5 is known, the value of the score is * * * * * *.
1。
The value of the test center score.
By analyzing the left common fraction of the known equation and using the subtraction rule of the same denominator fraction, the offspring are sorted out and the results can be obtained by calculation in the original formula.
Solution: It is known that the equation is arranged as =5, that is, x-y =-5xy.
Original formula = = 1,
So choose one
8. As shown in the figure, in equilateral △ABC, BD bisects ∠ABC and intersects with AC at point D, and the intersection point D is DE⊥BC at point E, and CE= 1.5, then the length of AB is * * * *.
A.3 B.4.5 C.6 D.7.5
Test the properties of the central equilateral triangle; Properties of angular bisector.
From the analysis of DE⊥BC in equilateral triangle ABC, we can get ∠ CDE = 30, then we can get the length of CD, and divide ∠ABC into D points from BD, then we can get the answer.
Solution: ∫△ABC is an equilateral triangle,
∴∠ABC=∠C=60，AB=BC=AC，
∵DE⊥BC，
∴∠CDE=30，
∫EC = 1.5，
∴CD=2EC=3，
∫BD bisects∠ ∠ABC intersects AC at point D,
∴AD=CD=3，
∴AB=AC=AD+CD=6.
So choose C.