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20 13 the second mathematical modeling test paper in Songjiang district, Shanghai.
24. Solution: (1)∫ The parabola passes through point A (0, 1) and point B (4, 3).

Therefore, ............................................. 1 min.

The solution is ................................................................. 1 min.

The analytical formula of parabola is .................................... 1.

(2) Point B is perpendicular to the axis, the vertical foot is H, Point A is AG⊥BO, and the vertical foot is G.

∫a(0, 1),B (4,3),∴ OA = 1,OB = 5 .............................................................................................................

* ∴ ∴ Joint-stock company = ...1point

∴∴ og = BG = ...........................................................1min.

∴ Tan ∠ ABO = .................................................1min.

(3)∵ Let the analytical formula of straight line AB be

Substitute a (0, 1) and b (4 4,3) to get the solution.

∴ The analytical formula of straight line AB is ................................................. 1 min.

Let m, n, Mn =................ 1 min.

∫ Quadrilateral MNCB is a parallelogram, ∴=3. ∴mn=bc=3.

The solution is ..................................................................... 1 min.

The parabola symmetry axis is a straight line, and the straight line MN is on the left side of the parabola symmetry axis.

..................... 1 point

∴∴ .............................................................................................................................+0 points.

25. Solution: (1) In Rt△ABC, ∠ BAC = 90, ∠ ABC = 60, AB = 4,

∴ ............................................1min.

From folding to ∠ Abd = 30, we get ... 0.

∴ CD = .................................................1min.

② From folding ∠ bed = ∠ bad = 90, ∴∠ced = 90°, ∴∠CED=∠CAB.

And ∫∠DCE =∠DCE, ∴△ CED ∽△ cab .................................................1min.

∴,∵,∴,∵

............................................... 1 min.

DE = AD = y, ..................................................... 1 min.

∴ ................................................... 2 points.

(3) the intersection point c is CH⊥BG and the vertical foot is H.

∵bg∥ac,∴∠acb=∠cbg,∵∠acb=∠cgb,∴∠cbg=∠cgb,

∴ CB = CG- 1。

∴BH=HG=AC=x, ∴BG=2x, ................................................ 1 min.

∵AE⊥BD,∴∠ADB+∠DAE=∠DAE+∠BAG=90,

∴∠ ADB = ∠ bag ............................................. 1 min.

∠∠BAC =∠ABG = 90,△ Abd ∽△ BGA。

∴ ............................................1min.

∴∴ ..................................................................................1min.

∵,

∴, solution (negative value has been abandoned)

That is AC = ..........................................................1min.