1. All students are located at integral coordinates in the xy-plane. The x-coordinates belong to the set {-2, -1, 0, 1, 2}, and the y-coordinates belong to the set {-1, 0, 1, 2, 3}.
2. Alvin is seated on the line which is normal to the curve f(x) = x^2 - 2x + 4 at the point (1, 3).
3. The curve y = ax^2 + bx + c passes through the point (2, 4) and is tangent to the line y = x + 1 at (0, 1). Determine values for a, b, and c. Gavin sits at the point (-b - c, 4a).
4. Handy sits at one of the points on the curve y = 2x^3 - 3x^2 - 12x + 20 where the tangent is parallel to the x-axis.
5. Kamille is located on the tangent line to y = 3x^2 - x at x = 1.
6. Mandel sits at the point on the curve y = (x + 2)^2 where the normal to that curve is parallel to the y-axis.
7. Determine the values of a, b, and c where the curves y = x^2 + ax + b and y = cx + x^2 have a common tangent line at (1, 0). Pauline sits at the point (b, a + c).
8. Romeo sits on the line normal to the curve y = x^2 - 3x + 2 at x = 1.
9. The line tangent to a curve at a point (x1, y1) is y = 2x - 2. The normal to that curve at the same point passes through (11, -5). Trixia sits at the point (x1, y1).
10. Vina's seat is collinear with those of Brahmagupta and Zeno.
11. Wilo is seated on the line tangent to y = 4 - 3x - x^2 at the point (2, -6).