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Problems, Questions, and Puzzles to spark discussion and argument in the maths classroom.

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Is it possible to find a positive integer value of  n so that this quotient is an integer?




.: [ALG2], [UVM], [Find the Pattern].

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You don't need a calculator for this one either. Why not?


.: [PRE-CALC], [UVM], [Puzzle].

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\(log_7{\frac{1}{8}} * (log_8{25} + log_2{5}) * log_5{49} \)

Why don't we need a calculator for this problem?


.: [PRE-CALC], [UVM], [Notice, Wonder].

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Why don't we need a calculator for this?


.: [ALG2], [UVM], [Epiphany].

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There are 40 students in the Travel Club. They discovered that 17 members have visited Mexico, 28 have visited Canada, 10 have been to England, 12 have visited both Mexico and Canada, 3 have been only to England and 4 have been only to Mexico. Some club members have not been to any of the three foreign countries and an equal number have been to all three countries. How many students have been to all three countries?


.: [LOGIC], [UVM], [Puzzle].

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Two circles, radius 1 (each does not pass through the others center). All seven regions are of equal area.

What is the area of the pentagon?



.: [GEOM], [UVM], [Notice, Wonder].

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What is

\(log_2 3 * log_3 4 * log_4 5 *log_5 6 * log_6 7 * log_7 8 \) ?


.: [PRE-CALC], [UVM], [Epiphany].

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Express the value of \(S\) as a rational number in lowest terms where

\(sin^2(10^{\circ}) + sin^2(20^{\circ}) + sin^2(30^{\circ}) +\\ sin^2(40^{\circ}) + sin^2(50^{\circ}) + sin^2(60^{\circ}) +\\ sin^2(70^{\circ}) + sin^2(80^{\circ}) + sin^2(90^{\circ}) \\ = S\)

And NO Calculator allowed.


.: [PRE-CALC], [UVM], [Raw Pure Math].
that's it.