Why are the wings of some modern gliders tadpole shaped, rather than teardrop shaped? An example is the Schleicher ASG 29. Or did they just add a flat plate at the trailing edge for the flaps and ailerons?
The flaps and ailerons are "reflexed" on this glider. They have been raised to a setting above the normal zero position, above the airfoil's normal chord line. A number of flapped gliders have this feature.
Two main benefits are a reduction in pitching moment as the pressure distribution on the wing is moved forward, so less downforce work for the tail, reducing trim drag, and lower induced drag because with the trailing edge partially unloaded it has an effect like reducing wing area and moves the best L/D speed up a bit. So overall, best glide angle is a bit better, and the speed it's achieved is a bit higher.
You use reflex for "penetration", going as flat as possible as fast as possible, for whatever reason, like getting through an area of sink in a hurry.
You can position the flaps/ailerons on the ASG 29 not only downwards but also upwards. The flap/aileron is triangle shaped as you can (barely) see on this photo of an ASG 29 wing joint:
Basically you can reduce the lift (and therefore drag) of the wing by moving the flaps/ailerons upwards, extracting better speed from the wing.
Flapped airfoils will have a suction peak once the flap is deflected away from its zero deflection position. This means more load on the boundary layer and earlier flow separation at the same lift coefficient. In order to avoid this suction peak over a range of flap angles, the airfoil contour is optimized on the top side for a small positive deflection and on the lower side for a small negative deflection. Now you get that "tadpole" shape between those two flap deflections, but also more flap effectivity and lower drag.
This effect is increased on the upper side for negative flap deflections. They are standard on gliders in order to shift the laminar bucket of the airfoil to the actual lift coefficient. I bet the lower side contour of the wing in the photo is smooth across the flap hinge line.
Effectively the raised flap lowers the angle of attack by virtue of the variation of the chord line.
Less drag, higher speeds for, as has been said, penetration.