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Questions by David Farris and editors—round 1
1. They are bounded by Seifert (pron. SEE-fert) surfaces, and different projections of one
are related by Reidemeister (REE-de-my-ster) moves. Their invariants include the
fundamental group of their complements and the HOMFLY, Alexander and Jones
polynomials. FTP, name the mathematical object defined as an embedding of a circle in
three-space, such as the trefoil or figure eight.
Ans: knot (accept link before "embedding of a circle")
2. John Webb's research suggests it might have changed by 1 part in 100,000 over the
past 12 billion years. Its value can be calculated from the quantum Hall effect using the
von Klitzing resistance, or from the expansion of the gyromagnetic ratio in powers of this
quantity. The energy difference of two atoms with the same spin and angular momentum
quantum numbers is generally a multiple of its square. FTP, what is this coupling
constant of the electromagnetic force, equal to about .007297 or 1 divided by 137?
Ans: fine structure constant (accept dimensionless electromagnetic coupling
strength, prompt on alpha before "alpha is the coupling constant")
3. Synthesized from the carotenoid (pron. car-AH-te-noid) violaxanthin (pron. vie-oh-laZAN-thin), levels of this plant hormone increase when subjected to stresses such as
drought. A relatively fast-acting hormone, it acts in opposition to cytokines (pron. sighto-KINES), suppresses growth of lateral buds, and promotes growth of dormant winter
buds. FTP, name this plant hormone, best known for controlling the opening and closing
of stomata and for its ability to drop ripe fruits from plant stems.
Ans: abscisic acid
4. It assumes a secondary of zero tensile strength. For a single uniform density, it has a
value of about 2.45 primary radii. Planetary rings are always found inside, and satellites
are almost always found outside it. Sometimes called the tidal stability limit, FTP name
this distance from a planet inside which a satellite will be torn apart by tidal forces.
Ans: Roche limit
5. Discovered by Wilhelm Kattwinkel 1911 and first studied by Hans Reck, it consists of
four beds from a dried up lake whose shores were exposed by an earthquake in the upper
Pleistocene (PLIGH-stow-seen). From 1931, tools were found there, and later,
Australopithecus (ah-stral-oh-PITH-eh-cus) boisei (BOY-see-ie) and Homo habilis were.
For 10 points, name this site on the Serengeti Plains in northern Tanzania, famously
excavated by Mary and Louis Leakey.
Ans: Olduvai Gorge
6. DME, tetrahydrofuran (pron. the-tra-high-droe-FURE-an), and dioxane are often used
as solvents when miscibility (MISS-ih-bility) with water is required; otherwise, diethyl
ether is the most common solvent. Lesser-known reactions are the opening of epoxides
and the addition of a carbonyl group to an alkyl halide. From ketones they produce
tertiary alcohols, aldehydes, secondary alcohols: except in one case in which
formaldehyde forms primary alcohols. FTP, name this class of organomagnesium
reagents named after the 1912 Nobel Prize winner in Chemistry.
Ans: Grignard reagents
7. It is often written with a numerical constant equal to one over two pi times the first
zero of the first-order Bessel function. It also names a statement that specific angular
momentum must increase outwards for stable Couette (pron. coo-ET) flow between
concentric rotating cylinders. In optics, it is satisfied when the center of the Airy disk of
one image is superimposed on the first minimum of the other. FTP, what is this condition
for resolution of two images?
Ans: Rayleigh criterion
8. The first computer that used this design was the Burroughs 5000, and it survives today
in the Java Virtual Machine. Its proponents argued that it leads to smaller code size
because the operands of arithmetic instructions are always implicit, but it has mostly been
replaced by general-purpose machines. FTP name this architecture that naturally
corresponds to expressions written in postfix form, and is named after a last-in-first-out
data structure.
Ans: stack machine or stack architecture
9. It is the only structure whose phi and psi values fall within the fully allowed regions of
the Ramachandran diagram. Methionine and alanine are the two most abundant types of
amino acids in this motif, while asparagine and glutamine often flank these motifs in a
cap structure. Often one side may contain polar side chains while the other contains
nonpolar side chains, but its stability is gained from hydrogen bonding of its backbone.
FTP, identify this secondary structure of proteins which has a pitch of 5.4 angstroms and
3.6 residues per turn.
Ans: alpha helix
10. This equation can also be applied to solids without modification. If the gas is an ideal
gas, this equation states that the derivative of the pressure with respect to temperature
equals the heat absorbed divided by the temperature times the change in volume. FTP,
name this equation that relates the vapor pressure of a liquid to the heat of vaporization
and temperature, named for two scientists.
Ans: Clausius-Clapeyron equation
11. Their focal mechanism beach ball diagrams always have 2 compressional and 2
extensional regions. Hypotheses for the formation of large continental ones include
highly oblique subduction, plate boundary jumps, or ridge subduction. They can be rightlateral or left-lateral and are associated with transform boundaries. The most famous
example may be the San Andreas Fault. FTP name this type of fault which shows
horizontal motion.
Ans: strike-slip faults
12. In a dielectric, the bound analog is given by the negative divergence of the
polarization. The continuity equation states that its partial time derivative equals the
negative divergence of the volume current density. Poisson's equation states that it is
proportional to the Laplacian of the potential, and Gauss's Law relates the electric field
flux through a surface to its volume integral. It must be zero throughout the interior of a
conductor since there is no net charge anywhere. FTP name this quantity, the charge per
unit volume.
Ans: volume electric charge density
13. Hyyrö and Makowski proved a weaker version of it. It's been known that the
exponents in a counter example either satisfy a certain class number condition or are
double Wieferich prime pairs, but in May 2002, Preda Mihailescu announced a proof of
the full conjecture. For 10 points—name the statement that 8 and 9, being 2 cubed and 3
squared, are the only nontrivial pair of consecutive powers, named for a Belgian
mathematician.
Ans: Catalan conjecture (after Eugene Catalan)
14. Part of the Zoomastigina (pron. zoh-oh-mast-ih-JEE-na) phylum, this disease evades
the host immune system by an elaborate genetic mechanism which repeatedly changes
epitopes on its glycoprotein coat. The prevalence of the disease prevents all animal
husbandry in central Africa. Symptoms include deep swollen lymph nodes called
Winterbottom’s sign, a canker sore at the site of the bite, and high fever. FTP, name this
disease spread by the tse-tse fly whose most common symptom is extreme fatigue.
Ans: African sleeping sickness or trypanosomiasis
15. An 1864 bill restricting the rights of street musicians is nicknamed for him, and that
subject earns an entire chapter in his 1864 Passages from the Life of a Philosopher. This
Lucasian professor, who also invented the locomotive cowcatcher, could not get funding
for the second in a series of three inventions, having run out of money to finish the
25,000 part Difference Engine. For 10 points, name this English designer of a mechanical
computer.
Ans: Charles Babbage
16. In its strictest thermodynamic sense, this law is a statement of the proportionality
between average kinetic energy of a gas molecule and its temperature. Because of the
ideal gas law, the average kinetic energy of any gas is the same, and thus, a
rearrangement of the equation leaves the square root of the ratio of the masses equal to
the inverse ratio of the volumes. This is the derivation, FTP, of what gas law that states
that the rate of effusion of a gas is inversely proportional to the square root of the
molecular weight?
Ans: Graham's law of effusion
17. Hypothesized by Baade and Zwicky, they cool at first by URCA processes. Their
radius is roughly proportional to one over the cube root of their mass, and their cores
superconduct at 100 million Kelvin. Their theoretical upper mass limit is three solar
masses, and inverse beta decay produces their main constituent. Born in supernovae, they
usually have a mass close to the Chandrasekhar limit. FTP, name this end state of stars
intermediate in mass between white dwarves and black holes.
Ans: neutron stars
18. This law is illustrated by the conjecture that three boxes of gases are in thermal
contact with one another, such that A is in contact with B, and B is in contact with C.
They reach thermal equilibrium; then B is removed, and A is put in direct contact with C.
This law states that the temperatures of A and C will not change. FTP, name this
thermodynamic law which states that if two systems are both in thermal equilibrium with
a third system, then they are in thermal equilibrium with each other.
Ans: zeroth law of thermodynamics
19. Like the kidney it is home to Malphighian (pron. mal-PIG-ee-an) bodies. In seals and
horses, this organ also functions as a location of red blood cell sequestration that
decreases the viscosity of blood and thus, heart workload. Home to the majority of
memory B cells, mononucleosis causes macrophages in this organ to overload and trap a
higher number of white blood cells, causing it to burst. FTP, name this lymphoid organ
responsible for recycling old red blood cells.
Ans: spleen
20. In continuum mechanics this man’s coordinate system is fixed in space. He proved
that the displacement of a rigid body with one point fixed is a rotation about some axis.
He developed the equations of rigid body motion in terms of the principal moments of
inertia, torque, and angular velocity, and his angles relate the principal axes of a rigid
body in motion to the axes of a fixed inertial frame. FTP, name this most prolific
mathematician whose formula states that e to the i pi is minus one.
Ans: Leonhard Euler
1. Name these reactive intermediates from simple organic chemistry FTPE.
10) This is the intermediate in which the reaction center has 7 electrons. They are sp 2
hybridized and planar. The odd electron is located perpendicular to the plane.
Ans: free radicals
10) Often called the carbonium ion, this intermediate has a positive charge, has 6
electrons on its reaction center, is sp2 hybridized, and reacts strongly with nucleophiles.
Ans: carbocations
10) These intermediates are uncharged and contain a divalent reaction center. They add to
double bonds to form cyclopropane rings.
Ans: carbenes
2. Name these algebraic objects for 10 points each.
10) A set with a possibly noncommutative multiplication and a commutative addition that
distribute over each other with additive but not necessarily multiplicative inverses.
Ans: ring
10) An additive subgroup of a ring which is closed under multiplication by elements in
the ring, such as all multiples of some integer.
Ans: ideal
10) The set of all prime ideals of a ring, which serves as the set of "points" in modern
algebraic geometry.
Ans: Spec or spectrum
3. Identify the following theorems from statistical mechanics F15PE.
15) The density of representative points in phase space corresponding to the motion of a
system of particles remans constant during the motion.
Ans: Liouville’s theorem
15) One consequence of this theorem is that in a self-gravitating system of particles, the
average total kinetic energy is minus one half times the gravitational potential energy.
Ans: virial theorem
4. Soil terms FTPE.
10) This is the term for partly decomposed organic matter in soil.
Ans: humus
10) This uppermost horizon forms the topsoil with the A horizon. The lower portion is
made up of humus.
Ans: O horizon
10) This is the depletion of soluble materials from the upper soil by water percolating
downwards.
Ans: leaching
5. Answer these questions related to evolution FTPE.
10) This is the type of genetic drift that refers to random changes in allelic (pron. uhLEE-lick) frequencies that arise out of the establishment of a new population by a small
number of individuals.
Ans: founder effect or principle
10) This is the evolution of several divergent forms from a primitive and unspecialized
ancestor that usually occurs when the ancestor spreads to several new environments.
Ans: adaptive radiation
10) As contrasted to sympatric speciation, where the new species arises out of a
subpopulation that is not isolated, this type of speciation occurs where new species arise
out of geographically isolated populations.
Ans: allopatric speciation
6. Name these pieces of software that have won the ACM Software System Award for 10
points each.
10) In 1985, Daniel Bricklin won Robert Frankston for designing this groundbreaking
spreadsheet program, whose descendants include Lotus 1-2-3 and Excel.
Ans: Visicalc
10) In 1989, the award honored this stack based programming language that allows for
platform independent descriptions of images.
Ans: postscript
10) The 1999 award went to this widely used free, open-source webserver software.
Ans: Apache
7. Pencil and paper may be required. 27 grams of solid hydrogen cyanide with molecular
weight of 27 grams per mole is added to water so that the final volume is 500mL. Give
the following values FTPE.
10) The solution’s molarity
Ans: 2 molar
10) The solution’s molality, assuming that the solute has no effect on weight
Ans: 2 molal
10) The solution’s normality
Ans: 4 normal
8. Name these structures present during plant germination FTPE.
10) These are the first immature leaves, one or two which may be present depending on
whether the species is a monocot or dicot.
Ans: cotyledons
10) The immature root below the cotyledons is called this; the lower end becomes the
radicle which gives rise to the primary root.
Ans: hypocotyl
10) The radicle tip contains one of these, a clump of cells which rapidly divides and
elongates the root.
Ans: root apical meristem
9. Identify these electromagnetic phenomena, FTPE.
10) From the German for "braking radiation" this is the radiation which results from the
fast deceleration of a charged particle over a short distance.
Ans: bremsstrahlung
10) The loss of energy per volume per cycle of this effect is given by the Steinmetz
equation. It arrises when the magnetization of a ferromagnetic substance due to a varying
magnetic field lags behind the field.
Ans: hysteresis effect
10) This is a weak repulsion in a magnetic field generated by the current of the orbiting
electron.
Ans: diamagnetism
10. Choose two large primes p and q as a key, and given a message M, consider its square
mod pq. FTPE:
10) Name the Israeli computer scientist for whom this encryption scheme, as well as a
widely used probabilistic primality test, is named.
Ans: Michael Rabin
10) Given the key, you can find M squared, hence M mod p and M mod q, and use this
theorem to reconstruct M mod pq. By appropriate choice of M, you can unambiguously
reconstruct the message.
Ans: Chinese remainder theorem
10) Rabin's scheme is provably as hard to break as factoring. The same has not been
proven true of which more frequently used algorithm, that instead considers p-1 times q1, a number relatively prime to it, and its inverse mod pq?
Ans: RSA
11. Given the organ or system, name the embryonic germ layer out of which it arises
FTPE.
10) Central nervous system
Ans: ectoderm
10) Liver
Ans: endoderm
10) Heart
Ans: mesoderm
12. Answer these questions related to reaction spontaneity FTPE.
10) Given by the equation delta G equals delta H – T delta S, this describes the
spontaneity of a chemical reaction given the enthalpy, temperature, and entropy.
Ans: Gibbs free energy
10) If delta H is equal to 1000, temperature is equal to 500 degrees Kelvin, and delta S is
equal to 1, what is delta G?
Ans: 500 joules
10) If the signs of delta H and delta S are both negative, is the reaction spontaneous,
nonspontaneous, or indeterminate?
Ans: indeterminate
13. Name these famous experiments named for the pairs of physicists who conducted
them FTPE.
10) This 1922 experiment, designed to measure the magnetic moment of individual silver
atoms, gave the first indication of the quantization of angular momentum.
Ans: (Otto) Stern - (Walter) Gerlach
10) Lise Meitner and Otto Frisch gave a theoretical explanation for this 1939 experiment
which discovered fission in uranium.
Ans: (Otto) Hahn - (Fritz) Strassman
10) This 1964 experiment showed a small CP violation in neutral kaon decay.
Ans: (Val) Cronin - (James) Fitch
14. Name the following related to really old stars, FTPE.
10) This type of star cluster found in the halo of the Galaxy usually contains about a
million stars. Stars in these clusters are among the oldest known objects in our galaxy.
Ans: globular clusters
10) Stars in globular clusters typically belong to this group of stars which are relatively
poor in heavy elements. They represent an early generation of stars.
Ans: Population II
10) These old horizontal-branch stars pulsate with shorter periods than the Cepheid
variables found in open clusters, and are used to determine distances to globular clusters.
Ans: RR Lyrae
15. Name these theorems of topology for 15 points each.
15) If a manifold M of dimension at least 6 has two boundary components W and W
prime whose inclusion is a homotopy equivalence, M is diffeomorphic to W times a
closed interval. This result of Stephen Smale is often called the most important theorem
in all of topology; the high-dimensional Poincare Conjecture is among its consequences.
Ans: h-Cobordism Theorem
15) The kth stable homotopy group of the unitary, orthogonal, and symplectic groups is
equal to the k plus 8th such group. It's been called the greatest result not recognized by a
Fields Medal.
Ans: Bott Periodicity theorem
16. Identify the following methods of microscopy, FTPE.
10) This type of microscopy reveals the surface structures of 3D objects by bouncing
electrons off their surfaces.
Ans: scanning electron microscopy
10) This type of light microscopy passes light directly through the cells. There is little
contrast and details are not distinguished.
Ans: bright-field microscopy
10) This type of light microscopy uses fluorescent materials and adds a system of
focusing both the stimulating and emitted light to give a sharper view of a plane through
the cell.
Ans: confocal microscopy
17. Answer these questions related to a bonding phenomenon FTSNOP.
10) This is the representation of a compound by two or more structures in which the
valence electrons are rearranged to give structures of similar probability.
Ans: resonance
10) In a resonance-stabilized molecule, the electrons are spread out, so that any charges
are also spread out among the atoms of the molecule. FTP, describe this stabilized state,
which serves to reduce the overall energy of the molecule.
Ans: delocalization (accept equivalents)
10) Not all resonance structures are created equal. More stable resonance forms are closer
representations of the real molecule than less stable ones. F5PE, name the term that
describes the more stable resonance form, and the term that describes the less stable
resonance form or forms of a molecule.
Ans: major contributor and minor contributor
18. Axes of rotation and spinning stuff, FTSNOP.
5;5;5) FFPE, what are the three axes of rotation of an airplane called?
Ans: roll, pitch, yaw
5;15) 5 for one, 15 for both, what are the two motions that a spinning top may undergo in
the presence of an external torque?
Ans: precession and nutation
19. Identify the following components of the peripheral nervous system FTPE.
10) These 12 pairs of nerves are concerned with sensory and motor systems associated
with the head. The only exception is nerve 10, the vagus nerve, which extends to the
heart and liver.
Ans: cranial nerves
10) These 31 pairs of nerves bring information into the namesake columns via the dorsal
root and leaves for the motor pathway via the ventral root.
Ans: spinal nerves
10) This collection of autonomic ganglia are composed of the junctions of pre- and postganglionic cells that innervate smooth muscles in organs and in the walls of blood
vessels, preparing the body for action by raising blood pressure, widening the pupils, and
quickening the heart.
Ans: sympathetic chain
20. Name the following about ocean waves for 10 points each.
10) If a wave is in sufficiently deep water, what is the ideal path of a particle on the
water's surface?
Ans: circle
10) "Sufficiently" in the previous part refers to the depth past which a wave is not
affected by the bottom of the water and its distance. What is this depth?
Ans: half the wavelength
10) Given that the wavelengths of seiches, tsunamis, and the tides are much more than
twice the depth of any ocean, what is the only type of wave that exists as a deep water
wave?
Ans: wind wave