1. Fill in the blanks or choose: (4 points for each small question, ***40 points)
1. As shown in figure 1, in the right-angled trapezoid ABCD, ∠ b = 90, DC∨AB, the moving point P starts from point B and moves along the dotted line B→C→D→A, the distance of the moving point P is, and the area of ABP is. If the image of the function y of x is shown in fig. 2,
2. As shown in the figure, two squares with side lengths of sum, one of which is on the same horizontal line, and the small square passes through the big square at a constant speed from left to right along the horizontal line. Let the elapsed time be, and the area of the big square except the small square is (shaded part), then the approximate image of sum should be ().
3. As shown in the figure, point A is a point on the correlation function image. When point a moves along the image,
When the abscissa increases by 5, the corresponding ordinate ()
A. decrease1.b. decrease by 3.
C. Add1.d. Add 3.
4. As shown in the figure, A, B, C and D are the four dividing points of the circle O, and the moving point P starts from the center of the circle O and moves at a constant speed along the O-C-D-O route. Let the movement time be x (seconds), ∠ APB = y (degrees), and the figure on the right is the functional relationship between y and x, then the abscissa of point M should be ().
2nd century BC+2nd century BC
5. As shown in the figure, c is the moving point on the diameter AB of ⊙O, and the straight line passing through point C intersects with points D and E ⊙O, and ∠ ACD = 45, DF⊥AB is at point F, and EG ⊥ AB is at point G. When point C moves on AB, let AF=, D E.
6. This figure is a schematic cross-sectional view of a reservoir divided into deep pools and shallow pools. If the reservoir is filled with water at a fixed flow rate, the following figure can roughly show the relationship between the maximum depth h of water and time t ().
7. As shown in the figure, c is the moving point on the diameter AB of ⊙O, and the straight line passing through point C intersects with points D and E ⊙O, and ∠ ACD = 45, DF⊥AB is at point F, and EG ⊥ AB is at point G. When point C moves on AB, let AF=, D E.
], 8. In △ABC, AB = 6, AC = 8, BC = 10, P is a fixed point on the edge BC, PE⊥AB is in E, PF⊥AC is in F, and M is the midpoint of EF, so the minimum value of AM is.
9. As shown in the figure, it is known that the coordinate of point F is (3,0), point A and point B are the intersections of a function image with X axis and Y axis respectively, and point P is the moving point on this image. Let the abscissa of point P be X, the length of PF be D, and the relationship between D and X satisfy: D = 5-X (0 ≤ X ≤ 5), then the conclusion is: ① AF =
10. Use four identical rectangles, length 3 and width 1, to make a big rectangle with a circumference of _ _ _ _ _.
Second, solve the problem (each small question 10, ***60)
1. As shown in figure 1, in the plane rectangular coordinate system, the known point is on the positive semi-axis, and the moving point moves from one point to another point at the speed of one unit per second on the line segment, and the moving time is set to seconds. Take two points on the axis as equal sides. (1) Find the analytical formula of the straight line; (2) Find the length of the equilateral (expressed by algebraic expression), and find the value when the equilateral vertex moves to coincide with the origin; (3) If we take the midpoint as the edge and make a rectangle as shown in Figure 2 in it, let the area of the overlapping part of the equilateral and rectangle be the point on the line segment, and find the functional relationship of the sum when the second is 0, and find the maximum value.
[Source: Xue. Part. Net]
2.(20 10 Henan senior high school entrance examination simulation question 3) In △ABC, ∠ A = 90, AB = 4, AC=3, M is the moving point on AB (not coincident with A and B), the intersection point M is MN∨BC, AC is at N, and MN is the diameter. (2) In the process of moving point M, remember that the overlapping area of △MNP and trapezoidal BCNM is y, try to find the functional relationship between y and x, and find out what the value of x is and what the maximum value of y is.
3.(20 10 Henan senior high school entrance examination simulation question 4) As shown in the figure, in the plane rectangular coordinate system, the quadrilateral OABC is rectangular, and the coordinate of point B is (4,3). The straight line M parallel to the diagonal AC starts from the origin O and moves at the speed of 1 unit length per second along the positive direction of the X axis. Both sides of the straight line M intersect with the right-angle OABC at points M and N respectively.
(1) The coordinates of point A are _ _ _ _ _ _ _, and the coordinates of point C are _ _ _ _ _ _ _ _ _;
(2) Let the area of △OMN be S, and find the functional relationship between S and T;
(3) Does the function s obtained in (2) have a maximum value? If yes, find the maximum value; If not, explain why.
As shown in the figure, in the plane rectangular coordinate system, points A (0 0,6) and B (8 8,0) are known, and the moving point P moves from point A to point O at a speed of 1 unit length per second on the line segment AO, while the moving point Q moves from point B to point A at a speed of 2 unit lengths per second on the line segment BA.
(1) Find the analytical formula of straight line AB; (2) When t is what value, is △APQ similar to △AOB?
(3) When t is what value, is the area of △APQ a square unit?
[Source: Xue. Part. Net]
5. It is known that parabola Y = AX2+BX+C intersects with X axis at points A and B, and intersects with Y axis at point C, where point B is on the positive semi-axis of X axis and point C is on the positive semi-axis of Y axis, and the lengths of line segments OB and OC (OB
[Source: Subject Network]
6. (A model of Heilongjiang) As shown in the figure, ∠ABM is a right angle, point C is the midpoint of line segment BA, point D is the moving point on ray BM (not coincident with point B), even AD is ⊥ AD, the suspension foot is E, even CE, the point E is EF⊥CE, and the point F passes BD. (65438).
(3) In what range ∠ A, there is a point G on the line segment DE, which satisfies the condition DG= DA, and explain the reasons.
1, answer: solution: (1) The analytical formula of the straight line is:.
(2) Method 1,,,,
,, is an equilateral triangle,
, .
The second method, as shown in figure 1, is to make the axes in, in,
Available,
When the points coincide,
，_X_K]。 , .
(3) (1) when, as shown in figure 2. Set the intersection point,
The overlapping part is a right-angled trapezoid,
Write in ...
, , , ,
, ,
It increases with the increase of when and ② when, as shown in Figure 3. Suppose it intersects a point, intersects a point, intersects a point, and the overlapping part is a Pentagon. Method 1 is done in, and method 2 is derived from the meaning of the question.
Recalculate,
. There is a maximum when.
(3) When, that is, with coincidence,
Set intersection point, intersection point and overlapping part.
Divided into isosceles trapezoid, as shown in Figure 4.
[Source: Subject Network ZX to sum up: when,;
When,; When.
The maximum value of is.
2. Answer: (1) As shown in the figure, if the lines BC and ⊙O are tangent to point D and connect OA and OD, then OA=OD= MN.
At Rt⊿ABC, BC = = 5∫Mn∨BC, ∴∠AMN=∠B, ∠ ANM = ∠ C.
⊿AMN∽⊿ABC,∴, ∴MN= 10th, ∴OD= 10th.
If the intersection m is MQ⊥BC in Q, then MQ=OD= x,
In Rt⊿BMQ and Rt⊿BCA, ∠B is the male role ∴Rt⊿BMQ∽Rt⊿BCA,
∴ ,∴BM= = x，AB=BM+MA= x +x=4,∴x=
When x=, ⊙O is tangent to the straight line BC,
(3) With the movement of point M, when point P falls on BC and connects with AP, point O is the midpoint of AP.
∵mn∥bc,∴∠amn=∠b,∠aom=∠apc∴⊿amo∽⊿abp,∴=，AM=BM=2
Therefore, it is discussed in two cases as follows: when 0 < x ≤ 2, y=S⊿PMN= x2. ∴ When x=2, the maximum value of y = ×22=
(1) When 2 < x < 4, let PM and PN intersect BC in E, and F∶ quadrilateral AMPN is rectangular.
∴PN∥AM, PN=AM=x and ∵Mn∨BC, ∴ quadrilateral MBFN is a parallelogram.
∴ fn = BM = 4-x，∴ PF = x-(4-x) = 2x-4，∴( ⊿pef∽⊿acb)2 =
∴S⊿PEF= (x-2)2，y = s⊿pmn- s⊿pef= x-(x-2)2 =-x2+6x-6
When 2 < x < 4, y =-x2+6x-6 =-(x-) 2+2 ∴ when x=, 2 < x < 4 is satisfied, and the maximum y =2.
To sum up, when x=, the value of y is the largest, and the maximum value of y =2.
3. Answer: (1) (4,0) (0,3)
(2) when 0 < t ≤ 4, om = T. From △OMN ∽△OAC,
∴ ON=，s =× om× on =。 [Source: Subject Network] When 4 < t < 8,
As shown in the figure, od = t, ∴ AD = T-4. From △DAM∽△AOC, AM =. The height of △OND is 3.
The area of S=△OND -△OMD =× t× 3 -× t×.
(3) There is a maximum value. Method 1: When 0 < t ≤ 4, the opening of parabola S= is upward, and on the right side of symmetry axis t=0, S increases with the increase of T, and when t=4, S can reach the maximum value = 6;
When 4 < t < 8, the opening of ∵ parabola S= is downward, and its vertex is (4,6), ∴ s < 6.
To sum up, when t=4, the maximum value of S is 6.
Method 2:
∫S =
∴ When 0 < t < 8, draw the image of the functional relationship between s and t, as shown in the figure.
Obviously, when t=4, the maximum value of S is 6.
4. Answer: (1) Let the analytical formula of straight line AB be y = kx+b.
So the analytical formula of straight line AB is y =-x+6.
(2) AB = 10 is obtained from AO = 6 and BO = 8, so AP = T and AQ = 10-2t.
1) When ∠ apq = ∠ AOB, △ apq ∽△ AOB. So = t = (seconds).
2) When ∠ AQP = ∠ AOB, △ AQP ∽△ AOB. So = t = (seconds).