10 of 10 Items .... Source: UVM

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

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

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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?

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Why don't we need a calculator for this?

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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?

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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?

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What is

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

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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.

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NEW

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The test is designed for 11th/12th, Precalculus or above. There's 41 questions. No calculators, tech, or references. Pencil & paper only.

and just TWO HOURS.

Average precalculus students can get 10/41 in the allotted time, really good ones about 20/41, exceptional ones 25-30.

Since there's no calculators, all the questions must be solvable with only pencil/paper (duh). That combined with "rational number in lowest terms" means there's a clever insight needed, a step that changes the imposing to manageable. That's what I like about them.

INSTRUCTIONS:
CALCULATORS, COMPUTERS AND/OR ANY OTHER ELECTRONIC DEVICES ARE NOT PERMITTED.

UNLESS OTHERWISE INDICATED, ALL ANSWERS MUST BE EXPRESSED IN SIMPLEST FORM.

A radical expression of index \(n\) is in simplest form if the radicand is not a fraction, denominators are rationalized and integer radicands do not have any factors that are \(n\)th powers of a prime. For example, \(\sqrt{\frac{5}{12}}\) simplifies to \(\frac{\sqrt{15}}{6} \)
Do NOT approximate the number π.
Do NOT approximate radicals.

Logarithms: The notation \(\log \) is logarithm to the base 10. The notation \(\log_a\) is logarithm to the base a. The notation LN is logarithm to the base e.

The symbol ! is the factorial symbol. For example, 3! = 3∙2∙1 = 6.
The symbol i is the complex unit \(\sqrt{-1}\)

All numbers are in base 10 unless otherwise indicated (e.g., \(1001_2\) is the base 2 representation of the decimal number 9).

Any answer which is a nonintegral rational number must be expressed in the form \(\frac{a}{b}\), where a and b are integers that have no common divisor other than 1.