Beijing normal university eighth grade mathematics volume ii final exam questions 1. Choose one carefully (this big question * * 10 small question, 3 points for each question, 30 points for * *). I believe you will definitely choose the right one!
The value of 1. quadratic form is-().
A.-2014b.2014c.2014 or -20 14 D.20 142
2. The root of equation (-2)=0 is ()
A.0 B.2 C.0 or 2 D. No solution.
3. Master Liu wants to check whether a part is a parallelogram, but what can't be checked by the following methods is ().
A.AB∑CD，AB = CD
B.？ A =？ c，？ B =？ D
C.AB = CD，BC = AD
D.AB∨CD，AD = BC
4. In the figure below, it is both an axisymmetric figure and a centrally symmetric figure ().
5. Prove the proposition by reducing to absurdity? When an angle in a triangle is less than or equal to 60, it should be assumed that there is-in this triangle.
A. is there an internal angle less than 60? B. Each internal angle is less than 60?
C. Is there an internal angle greater than 60? D. Each internal angle is greater than 60?
6. A shoe store sells 1 1 pairs of sports shoes a day. The sales of shoes of various sizes are as follows:
Size (cm) 23.5 24 24.5 25.5
Sales volume (double) 1 2 2 5 1
Then in a set of data consisting of 1 1 the size of the pair of shoes, the mode and the median are-() respectively.
A.25，25 B. 24.5，25 C. 25，24.5 D. 24.5，24.5
7. Xiao Cong does this when making the middle vertical line of line segment AB: draw an arc with A and B as the center and the length greater than AB as the radius, and the two arcs intersect at C and D, then the straight line CD is the demand. According to his painting, the quadrilateral ADBC must be-.
A. rectangle b, diamond c, square d, parallelogram
8 .. If the hyperbolic image passes through the second and fourth quadrants, the value range of k is-().
A.k & GTB.k & LTC.k = D. does not exist.
9. If x 1 and x2 are two roots of quadratic equation 2x2-7x+4 = 0, then x 1+x2 and x 1? The value of x2 is ()
A.﹣ ,﹣2 B.﹣，2 C，2d ,﹣2
10. As shown in the figure, in a square ABCD with a side length of 2, m is the midpoint of the side length AD, extend MD to point E, let ME=MC, make a square DEFG with a side length of de, and point G is on the side CD, then the length of DG is ().
A.B. C. D。
Second, fill in carefully (this big question is a total of 10 small questions, with 2 points for each small question and * * 20 points. Please fill in the results directly on the question line. As long as you understand the concept, calculate carefully and think positively, you can certainly do it! )
1 1. The value range of the independent variable x in the quadratic formula is _ _ _ _ _ _.
12. If there are three numbers-3,7, 1 1 on the number axis, the number that can be covered by ink as shown in the figure is _ _ _ _ _ _.
13. Known data x 1, x2, x3,? The average value of xn is 4, so the data 2x 1+3, 2x2+3, 2x3+3,? The average value of 2xn+3 is
.
14. As shown in the figure, in □ABCD,? The bisector of A intersects BC at point E. If AB= 10cm and AD= 14cm, then EC = _ _ _ _ _
15. As shown in the figure, in △ABC,? A=90？ D, E and F are the midpoint of AC, BC and AB respectively. If BC= 13 and AB=5, the sum of the perimeters of △FBE and △DEC is.
16. It is known that the sum of the internal angles of a polygon is 10800, and this polygon is a polygon.
17 ... If ∣b- 1∣+ =0, and the quadratic equation with one variable has real roots, then the range of k is.
18. In the diamond ABCD,? Bad = 120? The perimeter of a given △ABC is 15, and the perimeter of a diamond-shaped ABCD is.
19. As shown in the figure, it is known that the image of inverse proportional function and the image of linear function y2=ax+b intersect at point A (1 4) and point B (m, -2). If point C and point A are symmetrical about X, find the area of △ABC.
20. As shown in the figure, with the function y=, there are some P 1, P2, P3 on the image. , Pn, Pn+ 1, the abscissa of point P 1 is 2, and the difference between the abscissa of each point behind it and the abscissa of the adjacent point in front of it is 2, passing through point P 1, P2, P3? , Pn, Pn+ 1 are vertical line segments of X axis and Y axis respectively, forming several rectangles. As shown in the figure, the area of the shaded part in the figure is recorded as S 1, S2, S3? , Sn, then S 1+S2+S3? +S20 14=。
Third, seriously answer (this big question ***6 small questions, out of 50 points. As long as you think carefully and calculate carefully, you will definitely get it right! )
2 1. (The full score of this small question is 7) Calculation:
( 1) (2)
22. (The full mark of this little question is 7) Solve the following equation:
( 1) ; (2)
23. (The full score of this small question is 6) In order to choose one player from A and B to take part in the shooting competition, give them a test. Under the same conditions, two people each shot 10 times. In order to compare their achievements, the following statistics are made:
Figure 1 Statistics of shooting scores of Party A and Party B Figure 2 Line charts of shooting scores of Party A and Party B.
The number of times the average mean variance reaches 10 cycle.
A 7 7 0
B 7 5.4 1
(1) Please complete the above figure (please fill in the blanks directly in the statistical table to complete the line chart);
(2) If the prescribed score is relatively stable, who do you think should win? State your reasons.
24. As shown in the figure, in □ABCD, e and f are the midpoint of AB side and CD side, BD is diagonal, and the extension line from point A to point G..
(1) verification: de ∑ BF;
(2) What if? G=90？ Verify that the quadrilateral DEBF is a diamond.
25. (Full score for this small question 10) There are a number of graphic calculators, the original price of which is each 800 yuan, which are sold by two companies. Company A adopts the following methods to promote sales: the unit price is one for 780 yuan, two for each 760 yuan, and so on, that is, the unit price is reduced by 20 yuan for each one, but the minimum price cannot be lower than that for each 440 yuan; Company B promotes sales at 75% of the original selling price, and Company A needs to buy a batch of graphic calculators:
(1) If this company needs to buy six graphic calculators, it needs (yuan) to buy six graphic calculators in Company A and (yuan) to buy them in Company B, so it should be cheaper to choose to buy them in the company.
(2) If this company just spent 7500 yuan and bought a certain number of graphic calculators in the same company, which company did you buy it from and what was the quantity?
26. (The full score of this short question is 12)
Definition: What do we call two triangles separated by the middle line on one side? Friendship triangle? .
Property: If two triangles are? Friendship triangle? Then the areas of these two triangles are equal.
Understanding: As shown in Figure ①, in △ABC, CD is the midline on the side of AB, so what are △ACD and △BCD? Friendship triangle? And s delta ACD = s delta BCD.
Application: As shown in Figure ②, in the rectangular ABCD, AB=4, BC=6, E point is on AD, F point is on BC, AE=BF, AF and BE intersect at O point.
(1) Verification: What are △AOB and△ △AOE? Friendship triangle? ;
(2) Connect OD, if △AOE and △DOE are? Friendship triangle? Find the area of quadrilateral CDOF.
Query: in △ABC,? A=30？ , AB=4, point d is on the AB line, connect CD, what are △ACD and △BCD? Friendship triangle? Fold △ACD along the straight line where the CD is located to get △A? CD, if △A? If the overlapping area of CD and △ABC is equal to the area of △ABC, please directly write the area of △ABC as.
The eighth grade Beijing Normal University mathematics volume two final examination questions reference answer 1. Carefully choose one (this big question * * 10 small question, 3 points for each question, 30 points for * * *). I believe you will definitely choose the right one!
The title is 1 23455 6789 10.
Answer B C D C D A B B C B b b b
Second, fill in carefully (this big question is a total of 10 small questions, with 2 points for each small question and * * 20 points. Please fill in the results directly on the question line. As long as you understand the concept, calculate carefully and think positively, you can certainly do it! )
1 1.x？ -6
14. IV
15.30
16.8
17.k？ Four and k? 0
18.20
19. 12
24. (The full score for this short question is 8)
Solution: (1) In □ABCD, ABCD, AB=CD.
E and f are the midpoint of the AB side and the CD side, respectively.
? DF= DC，BE= AB
? DF∨BE，DF=BE？ 2 points
? Quadrilateral DEBF is a parallelogram? 1 point
? DE∨BF？ 1 point
(2) Proof: ∫AG∨BD
G=？ DBC=90？
? △DBC is a right triangle? 1 point
F is the midpoint of the edge CD.
? BF= CD=DF？ 2 points
Similarly, the quadrilateral DEBF is a parallelogram.
? The DEBF of the quadrilateral is a diamond? 1 point
25. (Full score for this small question 10)
Solution: (1) 4080? 1 point
3600 ? 1 point
b？ 2 points
(2) If the company buys X units, it will cost x(800-20x) yuan to buy in A company; 1 point
75% if you buy it at company B? 800x=600x yuan; ? 1 point
(1) If the company spent 7500 yuan on a graphic calculator,
So x(800-20x)=7500,? 1 point
X= 15，x=25。
When x= 15, the unit price is 800-20? 15 = 500 & gt； 440, in line with the meaning of the question; 1 point
When x=25, the unit price is 800-20? 25 = 300 & lt440, if it doesn't meet the meaning of the question, give it up. 1.
(2) If the unit is a graphic calculator purchased by Company B for 7500 yuan, there is 600x=7500.
The solution is x= 12.5, which does not meet the meaning of the question and is discarded.
Answer: Our company bought a graphic calculator from Company A and 15 sets. 1 min.
26. (The full score of this short question is 12)
(1) proves that ∵ quadrilateral ABCD is a rectangle,
? AD ∨ BC 1 year.
AE = BF，
? The quadrilateral ABFE is a parallelogram with two points.
? OE=OB，
? △AOE and△△ AOB are friendly triangles. Two points.
(2) Solution: ∵△AOE and △DOE are friendly triangles.
? S△AOE=S△DOE，AE = ED = AD = 3 1。
∫△AOB and△△△ AOE are friendly triangles.
? S△AOB=S△AOE。 1.
∫△AOE?△ FOB,
? AOE = fob price,
? S△AOD=S△ABF, 1 min.
? S quadrilateral CDOF=S rectangle ABCD ~ 2s △ ABF = 4? 6﹣2 4? 3= 12.
2 points