Shanghai science edition, eighth grade, second volume, mathematics final exam 1. Multiple choice questions (***8 small questions, 3 points for each small question, ***24 points)
The square root of 1 9 is ()
A.3 B？ 3 C.8 1 D？ 8 1
2. The following figures are not centrosymmetric figures ().
A. equilateral triangle b parallelogram c rectangle d square
3. The coordinate of point P (- 1, 2) about the Y-axis symmetry point is ().
A.( 1，-2) B.(- 1，-2) C.(2，- 1) D.( 1，2)
4. If the sum of the inner angles of a polygon is twice the sum of its outer angles, then the number of sides of the polygon is ().
A.3 B. 4 C. 5 D. 6
5. In a shooting training, A and B each shot 10 times, and the average of their shooting scores 10 times was 9. 1 ring, and the variance was 0 respectively, so the description of A and B's stable performance in this shooting training is correct ().
A.A is more stable than B. B is more stable than A. C is as stable as B. The stability of D and B cannot be compared.
6. As shown in the figure, in the rectangle, the diagonal line intersects with the point. If is, the length is ().
A.B.
C.D.
7. If one root of the equation about x is 0, the value of m is ().
A.6 B.3 C.2 D. 1
8. As shown in figure 1, in the rectangular ABCD, diagonal lines AC and BD intersect at points O, E and F, which are the midpoint of BC and AD respectively, with AB=2 and BC=4. The moving point P starts from point B and moves along B-A-D-C on the side of the rectangle until it stops at point C, and point M is a certain point in the graph 1.
A.C, b, o, c, e, d and f.
Fill in the blanks (***6 small questions, 4 points for each small question, ***24 points)
9. As shown in the figure, in the parallelogram ABCD, e is the midpoint of the AB side.
F is the midpoint of diagonal BD, if EF=3, then BC.
10. If the equation about x has two equal real roots, then =.
1 1. Please write an analytical formula of a straight line that passes through the first, second and third quadrants and intersects with the Y axis at point (0,1) _ _ _.
12. If the quadratic equation of one variable is transformed into a form by matching method, then =, =.
13. As shown in the figure, in the diamond-shaped ABCD, CF? AD at point e,
And BC=CF, the diagonal AC connecting BF reaches point M, then? FMC= degrees.
14. As shown in the figure, in the plane rectangular coordinate system xOy, there is an edge with the length of 1.
Square OABC, point B is on the positive semi-axis of the X axis, if correct.
Make the second square OBB 1C 1 with the corner line OB as the edge, and then use the diagonal line.
OB 1 is the third square on the side. OB 1 B2C2，？ According to this rule.
Continue, then the coordinate of B2 is;
The coordinates of B20 14 are.
Iii. Answer questions (* * 13 small questions, ***72 points)
15.(5 points) Calculation:.
16.(5 points) As shown in the figure, C is the midpoint of line AB, CD∑BE, CD=BE,
Proof: AD=CE.
17.(5 points) Solve the equation:.
18.(5 points) As shown in the figure, in a square ABCD, e and f are points above the sides of AD and BC, respectively, while? 1=? 2.
It is proved that quadrilateral BFDE is a parallelogram.
19.(5 points) As shown in the figure, in the plane rectangular coordinate system xOy, the image of a linear function intersects the X axis at one point.
A (1, 0), which intersects with Y axis at point B (0, 2), finds the analytical expression of linear function and the length of line segment AB.
20.(6 points) The radar velocimeter of a certain road section measures the speed of cars passing in a period of time, and collates the monitored data to obtain the following incomplete chart:
Hourly frequency
30~40 10 0.05
40~50 36 0. 18
50~60 0.39
60~70
70~80 20 0. 10
Total 200 1
Note: 30 ~ 40 is the speed greater than or equal to 30 km and less than 40 km, and others are similar.
(1) Please fill in the data in the form completely;
(2) completing the frequency distribution histogram;
(3) If the speed of cars on this section reaches or exceeds 60 kilometers per hour, which is illegal, then how many cars are there?
2 1.(6 points) As shown in the figure, the middle vertical line of the side CD of the parallelogram ABCD intersects with the extension lines of the sides DA and BC at points E and F, and intersects with the side CD at point O, connecting CE and d F respectively.
(1) verification: DE = CF
Please judge the shape of the quadrangle ECFD and prove your conclusion.
22.(5 points) A village plans to build a rectangular vegetable greenhouse, as shown in the figure. The length of the greenhouse is four times the width, with an open space 3 meters wide on the left and a passage 1 meter wide on the other three sides. The rectangular vegetable planting area covers an area of 288 square meters. What is the length and width of the greenhouse?
23.(6 points) The univariate quadratic equation about X is known ().
(1) Prove that the equation always has two real roots;
(2) If m is a positive integer and both roots of the equation are integers, find the value of m. 。
24.(6 points) In the plane rectangular coordinate system xOy, the straight line intersects with the axis at point A, the straight line intersects with the point, and P is the point on the straight line.
(1) Find the values of m and n;
(2) When the line segment AP is the shortest, find the coordinates of point P. 。
25.(6 points) As shown in the figure, in the diamond ABCD, point A is AE? CD is at point e, diagonal BD is at point f, and the intersection point f is FG? AD is at the g point.
(1) Verification: BF = AE+FG;
(2) If AB=2, find the area of quadrilateral ABFG.
26.(6 points) Party A and Party B started from Shunyi Children's Palace and ran to Shunyi Park along the same route. After Party A ran a certain distance, Party B started to set out. When Party B exceeds Party A150m, Party B will stop here and wait for Party A. After the two meet, Party B and Party A will run to Shunyi Park at the original speed of Party A, as shown in the figure, the distance Y passed by Party A and Party B during the whole running.
(1) During the whole running, A * * * ran meters, and A's speed was meters per second;
(2) Find the running speed of B and the time for B to wait for A on the way;
How long did it take for Begun B to meet A for the first time?
27.(6 points) As shown in the figure, the right-angle OABC is placed in the plane right-angle coordinate system xOy, with point A on the X axis, point C on the Y axis, OA=3, OC=2, and P is a point on the side of BC, which does not coincide with B, connecting AP and intersection point P? CPD=？ APB, X axis is at point D, Y axis is at point E, passing through point E is EF//AP, and X axis is at point F. 。
(1) If △APD is an isosceles right triangle, find the coordinates of point P;
(2) If the quadrilateral with vertices A, P, E and F is a parallelogram, find the analytical formula of straight line PE.
Shanghai science edition, eighth grade, second volume, final examination paper of mathematics, reference answer 1. Multiple choice questions (*** 10 questions, 3 points for each question, ***30 points)
Title 1 2 3 4 5 6 7 8
Answer B A D D A C B B
Fill in the blanks (***6 small questions, 4 points for each small question, ***24 points)
9.6; 10.2 or-2; 1 1.； (The answer is not unique) 12. 1 5;
13. 105; 14.,. (give 2 points for each space)
Iii. Answer questions (*** 12 small questions, ***66 points)
16.(5 points)
Proof: ∫CD∨BE,
? . 1 point
∫C is the midpoint of line AB,
? AC=CB。 ? 2 points
Again? 3 points
? △ACD?△CBE。 ? 4 points
? AD=CE。 ? 5 points
18.(5 points)
Method 1: prove that the quadrilateral ABCD is a square,
? AD∨BC, DE∨BF, 2 points.
3=? 2,
Again? 1=? 2,
3=? 1, ? 3 points
? BE∑DF, 4 points
? The quadrilateral BFDE is a parallelogram. 5 points
Method 2: prove that the quadrilateral ABCD is a square,
? AB=CD=AD=BC，，？ 2 points
Again? 1=? 2,
? △ABE?△CDF，？ 3 points
? AE=CF, BE=DF, 4 points
? DE=BF，
? The quadrilateral BFDE is a parallelogram. 5 points
19.(5 points)
Solution: According to the meaning of the question, point A and point B are in a straight line.
? 1 point
3 points for the solution
? The analytical formula of a straight line is .4 points.
∫OA = 1，OB=2，，
? .5 points
20.(6 points)
Hourly frequency
30~40 10 0.05
40~50 36 0. 18
50~60 78 0.39
60~70 56 0.28
70~80 20 0. 10
Total 200 1
Solution: (1) See Table 3 (1).
(2) See the figure. 4 points
(3)56+20=76
A: There are 76 illegal vehicles. Six points.
2 1.(6 points)
(1) proves that ∵ quadrilateral ABCD is a parallelogram,
? AD ∨ BC,? 1 point
EDO=？ FCO？ DEO=？ Chief financial officer,
Divide the CD equally with ef,
? DO=CO，
? △EOD?△FOC，？ 2 points
? DE=CF？ 3 points
(2) Conclusion: The quadrangle ECFD is a diamond.
It is proved that ∫EF is the middle vertical line of CD,
? DE=EC, CF=DF, 4 points.
And DE = CF,
? DE=EC=CF=DF, 5 points.
? The quadrilateral ABCD is a diamond. 6 points
22.(5 points)
Solution: If the width of the greenhouse is x meters, then the length of the greenhouse is 4x meters. 1 point
Have to. ? 3 points
Tidy up, take,
Solution, (irrelevant) .4 points
Then 4x=40.
Answer: The greenhouse is 40m long and10m wide.
23.(6 points)
(1) Proof: 1 min
∵ ,
? This equation must have a real root. Three points
(2) Solution: ∵,
? , .？ 5 points
Both roots of the equation are integers, and m is a positive integer.
? M is 1 or 3. 6 points
24.(6 points)
Solution: (1)∵ Point is on a straight line,
? n= 1，，？ 2 points
Point on a straight line,
? M=-5。 3 points
(2) The vertical intersection point A is a straight line and the vertical foot is p,
At this time, the line segment AP is the shortest.
? ,
∫ the intersection of a straight line and an axis, the intersection of a straight line and an axis,
? AN=9，，
? AM=PM=, 4 points
? OM=, 5 points
? .6 points
25.(6 points)
(1) Proof: Connect AC at point O and BD.
The quadrilateral ABCD is a diamond,
? AB= AD，，？ 4=，，AC？ BD，
∵ ,
2=? 4= ,
∵AE？ CD at point e,
? ,
1=30? ,
1=? 4,? AOB=？ DEA=90？ ,
? △ABO?△DAE， 1。
? AE=BO。
FG again? At point g AD,
AOF=？ AGF=90？ ,
Again? 1=? 3，AF= AF，
? △ AOF△ AGF, 2 points
? FG=FO。
? BF= AE +FG.3 points
(2) Solution: ∵? 1=? 2=30? ,
? AF=DF。
FG again? At point g AD,
? ,
AB = 2，
? AD=2，AG= 1。
? DG= 1，AO= 1，FG=，BD=，
? The area of △ABD is, and the area of RT△DFG is 5 points (both areas are 1 min).
? What is the area of quadrilateral ABFG? 6 points
(Note: Please give points for other certificates. )
26.(6 points)
Solution: (1)900, 1.5. 2 points (65438+ 0 points for each space)
(2) pass b as it is? The x axis is on the e axis.
A runs for 500 seconds, which is 500? 1.5 = 750m，
How long does it take for A to run 600 meters (750- 150)? 1.5=400 seconds,
What is the running speed of B? (400- 100) = 2.5m/s，
3 points
The time for B to wait for A on the way is 500-400= 100 seconds.
4 points
(3)
∵ , , ,
? The function of OD is, and the function of AB is,
According to the meaning of the question
Solve? 5 points
? B meets A for the first time in 150 seconds. Six points.
(Note: All other solutions and statements are reasonable. )
27.(6 points) Solution:
(1)∫△APD is an isosceles right triangle,
? ,
? .
The quadrilateral ABCD is a rectangle,
? OA∨BC，，AB=OC，
? .
? AB=BP，？ 1 point
OA = 3，OC=2，
? BP=2，CP= 1，
? .2 points
(2)∵ Quadrilateral APFE is a parallelogram,
? PD=DE，OA∑BC，
∵? CPD=？ 1,
CPD=？ 4,? 1=? 3,
3=? 4,
? PD=PA，
More than p is PM? The x-axis is in m,
? DM=MA，
Again? PDM=？ Edo,
? △PDM?△EDO，？ 3 points
? OD=DM =MA= 1，EO=PM =2，
? 0.5 point (65438+ 0 point for each point)