The Math Contest
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.
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