AP Calculus Class, Take Your Seats by David Pleacher, 1991 VCTM Mathematics Teacher
Can you fill in the first
initial of each student in this math teacher’s seating chart using only the
clues below?
CLUES:
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. Wallis
is seated on the line which is normal to the curve f(x) = x2 – 2x
+ 4 at its minimum point.
3. Newton
is seated at a point of inflection of f(x) = 4x2 + 
.
4. Euler
sits at the point on the curve 2y = (x – 2)2 which is nearest
to Boole.
5. MacLaurin
is located at the relative maximum point of the function f(x) = x3
– 3x2 – 9x – 4.
6. Saccheri
is seated at the absolute maximum point of the function f(x) = -x2
+ 4x – 1.
7. Riemann’s
seat is one of the critical points of the curve f(x) = 
- x3 + x2
– 1.
8. The
function f(x) = x2 + 
has a point of
inflection at x = 1. Zeno sits
at this point.
9. Boole
is seated at the absolute maximum point on the curve (x – 2)2 + y2
= 1.
10. Archimedes
is located at one of the vertices of the rectangle with the largest area that
can be drawn with its upper vertices on the line y = 1 and its lower
vertices on the parabola y = x2 – 2.
11. Thales
sits at a point on the curve f(x) = 2x3 – 6x2 + 43
where the slope is 48.
12. Leibniz
sits at a point on the curve y = cos(x) where the 99th
derivative of that curve is 0.
13. Kronecker
sits on the line which is tangent to the curve y = 4x2 – 22x + 35
at the point (3, 5).
14. Fermat
is seated at the point of inflection of the curve y = x3 – 6x2
+ 33x – 51.
15. Descartes
is located at one of the critical points of the curve y = -3x4 +
6x2.
16. Cantor
is located on the line tangent to the curve y = -x2 + 10x – 25
at its maximum point.
17. Gauss
sits at the absolute maximum point on the curve 4y = -2x3 + 3x2
+ 7 over the interval
[-1,
2].
18. Viete’s seat is collinear with those of Gauss and Kronecker.
19. Heron is located at the point of inflection of the curve f(x)
= x3 – 3x2 + 3x + 1.
20. Pascal lies on the line tangent to the curve 12y = 16 – 6x2
– x3 at its point of inflection.
CLUE Worksheet
For each problem, write down
all possible answers from the given domain and range.
|
NAME |
CLUE |
Possible Ordered Pairs
for the Seat |
||||
|
|
1 |
none |
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Wallis |
2 |
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Newton |
3 |
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Euler |
4 |
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MacLaurin |
5 |
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Saccheri |
6 |
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Riemann |
7 |
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Zeno |
8 |
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Boole |
9 |
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Archimedes |
10 |
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Thales |
11 |
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Leibniz |
12 |
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Kronecker |
13 |
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Fermat |
14 |
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Descartes |
15 |
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Cantor |
16 |
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Gauss |
17 |
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Viete |
18 |
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Heron |
19 |
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Pascal |
20 |
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