HS Sample Set 7, Round 8 from NSB
A positive three digit integer \(n\) is chosen at random, with each three digit number having an equal chance of being chosen. What is the probability that \(\log_{2} n\) is an integer? W) 3/899 X) 1/300 Y) 1/222 Z) 1/150
W: W) 3/899
X: X) 1/300
Y: Y) 1/222
Z: Z) 1/150
Answer: X) X) 1/300
A point moves on the curve \(6x^2 - 3y^2 = 18\) so that its y-coordinate increases at a constant rate of 12 meters per second. At what rate, in meters per second, is the x-coordinate changing when the point is at \((3,\,2\sqrt{3})\)?
Acceptable Answers:
“Synthons” are key precursors associated with retrosynthetic analysis, a logical framework pioneered by what chemist? W) Emil Fischer X) Robert Robinson Y) E. J. Corey Z) Georg Wittig
W: W) Emil Fischer
X: X) Robert Robinson
Y: Y) E. J. Corey
Z: Z) Georg Wittig
Answer: Y) Y) E. J. Corey
A buffer solution contains a 10 to 1 ratio of conjugate base to weak acid. The pKa of the weak acid is 5. What is the pH of the solution?
Acceptable Answers:
A 20 kilogram mass is suspended from the end of a spring with a spring constant of 5 newtons per meter. If the mass is displaced 10 centimeters from equilibrium, what is the maximum speed of the mass in meters per second? W) 0.05 X) 0.25 Y) 0.5 Z) 2
W: W) 0.05
X: X) 0.25
Y: Y) 0.5
Z: Z) 2
Answer: W) W) 0.05
A distant planet has a 3:2 spin-orbit resonance due to tidal influences from its nearby host star. If this planet’s sidereal day is 50 Earth days, how long, respectively, in Earth days, are its year and its solar day?
Acceptable Answers:
Which two spectral classes of main sequence stars have the smallest vertical velocity dispersion about the plane of the galaxy?
Acceptable Answers:
Which of the following two organisms that still exist today first appeared in the recovery period directly after the Permian-Triassic extinction? W) Marsupial wombats and wallabies X) Sea urchins and sea stars Y) Sharks and rays Z) Magnolias and grasses
W: W) Marsupial wombats and wallabies
X: X) Sea urchins and sea stars
Y: Y) Sharks and rays
Z: Z) Magnolias and grasses
Answer: X) X) Sea urchins and sea stars
What is the most common autosomal recessive lethal disease in the U.S. among Caucasians?
Acceptable Answers:
Name all of the following five organisms that lack vessel elements as conducting cells: 1) Norway spruce; 2) Dandelion; 3) Eastern white pine; 4) White fir; 5) Kousa dogwood.
Choices:
Correct Answers:
Air source heat pumps rely on an evaporative and condensing intermediate fluid. What is the general term for this fluid?
Acceptable Answers:
Which of the following terms does NOT uniquely apply to the description of magnet properties? W) Coercive force X) Anisotropy Y) Curie temperature Z) Remanance
W: W) Coercive force
X: X) Anisotropy
Y: Y) Curie temperature
Z: Z) Remanance
Answer: X) X) Anisotropy
If \(f(x) = 2 - x\), find \(f\bigl(f'(x)\bigr)\).
Acceptable Answers:
Express the following in terms of a single trigonometric function, given that all fractions are defined: \[ \frac{\sec x + \csc x}{1 + \tan x}. \]
Acceptable Answers:
An enzyme begins oxidation of a fourteen-carbon fatty acid. This metabolic step produces a twelve-carbon fatty acid and what other product?
Acceptable Answers:
What ring size would be obtained at the end of the following three-step reaction sequence: (1) Diels–Alder cyclization of 1,3-cyclohexadiene with methyl vinyl ketone; (2) ozone; (3) dimethyl sulfide?
Acceptable Answers:
Which of the following light movement directions is NOT able to produce total reflection from a surface perpendicular to a light beam? W) From water to air X) From air to water Y) From glass to air Z) From oil to air
W: W) From water to air
X: X) From air to water
Y: Y) From glass to air
Z: Z) From oil to air
Answer: X) X) From air to water
A 100 watt current of heat flows via conduction between two stable temperature reservoirs through a material of length 5 cm and cross-sectional area 0.5 m². If the length of material is extended to 1 m and the cross-sectional area increased to 1 m², what is the new heat current in watts? W) 5 X) 10 Y) 20 Z) 50
W: W) 5
X: X) 10
Y: Y) 20
Z: Z) 50
Answer: X) X) 10
Hurricanes are rated on the Saffir–Simpson Scale. Tornadoes are rated on the Enhanced Fujita Scale. How are these ratings determined? W) Saffir–Simpson is based on central pressure and Enhanced Fujita is based on damage X) Saffir–Simpson is based on wind speed and Enhanced Fujita is based on damage Y) Both are based on damage Z) Both are based on vorticity
W: W) Saffir–Simpson is based on central pressure and Enhanced Fujita is based on damage
X: X) Saffir–Simpson is based on wind speed and Enhanced Fujita is based on damage
Y: Y) Both are based on damage
Z: Z) Both are based on vorticity
Answer: X) X) Saffir–Simpson is based on wind speed and Enhanced Fujita is based on damage
What are the two most abundant components of Venus’s atmosphere?
Acceptable Answers:
What is the unit in which the lengths of gene-coding DNA sequences are measured?
Acceptable Answers:
While on holiday in Mexico, you note a local vendor selling arrow plant seed pods that jump due to the presence of an immature insect that is violently throwing itself from side to side in the seed pod. The insect responsible for this would be a member of what insect order? W) Lepidoptera X) Diptera Y) Coleoptera Z) Hymenoptera
W: W) Lepidoptera
X: X) Diptera
Y: Y) Coleoptera
Z: Z) Hymenoptera
Answer: W) W) Lepidoptera
What is the term for a rate structure where the cost of electricity is based on the time of day you use it?
Acceptable Answers:
Enhanced Geothermal Systems, developed by the DOE, increased the availability of geothermal generated electricity in the U.S. by what multiple? W) 3 X) 5 Y) 10 Z) 40
W: W) 3
X: X) 5
Y: Y) 10
Z: Z) 40
Answer: Z) Z) 40
Given \(f(x) = \sqrt{7x^2 - 3}\), which of the following are \(u(x)\) and \(g(u)\) such that \(f(x) = g\bigl(u(x)\bigr)\)? W) \(u(x) = 7x^2 - 3\) and \(g(u) = \sqrt{u}\) X) \(u(x) = \sqrt{x}\) and \(g(u) = 7u^2 - 3\) Y) \(u(x) = \sqrt{7x^2 - 3}\) and \(g(u) = \sqrt{u}\) Z) \(u(x) = \sqrt{7x - 3}\) and \(g(u) = u^2\)
W: W) \(u(x) = 7x^2 - 3\) and \(g(u) = \sqrt{u}\)
X: X) \(u(x) = \sqrt{x}\) and \(g(u) = 7u^2 - 3\)
Y: Y) \(u(x) = \sqrt{7x^2 - 3}\) and \(g(u) = \sqrt{u}\)
Z: Z) \(u(x) = \sqrt{7x - 3}\) and \(g(u) = u^2\)
Answer: W) W) \(u(x) = 7x^2 - 3\) and \(g(u) = \sqrt{u}\)
Mother Goose divided her estate among her four favorite friends according to the following specifications: • Humpty Dumpty shall receive half of the estate, less \$9000; • Simple Simon shall receive one third of the estate, less \$3000; • Little Jack Horner shall receive exactly one fourth of the estate; • Little Miss Muffet shall receive one sixth of the estate, plus \$3000. What was the total dollar value of Mother Goose’s estate?
Acceptable Answers:
The PH₃ molecule has what type of molecular geometry? W) Trigonal pyramidal X) Trigonal planar Y) Angular Z) Tetrahedral
W: W) Trigonal pyramidal
X: X) Trigonal planar
Y: Y) Angular
Z: Z) Tetrahedral
Answer: W) W) Trigonal pyramidal
What term describes a reaction that forms two stereoisomers in unequal amounts?
Acceptable Answers:
Three unequal forces act on an object. If the forces have magnitudes of 30 N, 50 N, and 70 N, what is the minimum net force in newtons that can act on this object? W) 0 X) 10 Y) 50 Z) 90
W: W) 0
X: X) 10
Y: Y) 50
Z: Z) 90
Answer: W) W) 0
If we could capture one second of the total energy output of the Sun, store it, and use it with just 20% efficiency, how long, in years (to two significant digits), would this energy last based upon current global energy consumption? Assume the current global energy consumed per year is about \(5\times10^{8}\) TJ and the current luminosity of the Sun is \(4\times10^{26}\) W.
Acceptable Answers:
If a climate report shows the difference in surface air pressure between the Azores and Iceland, what phenomenon is it measuring? W) El Niño Southern Oscillation X) Pacific Decadal Oscillation Y) North Atlantic Oscillation Z) Arctic Oscillation
W: W) El Niño Southern Oscillation
X: X) Pacific Decadal Oscillation
Y: Y) North Atlantic Oscillation
Z: Z) Arctic Oscillation
Answer: Y) Y) North Atlantic Oscillation
Detrital rocks are classified based on which of the following? W) Mineral composition X) Grain size only Y) The conditions in which they formed Z) Grain shape, grain size, and sorting
W: W) Mineral composition
X: X) Grain size only
Y: Y) The conditions in which they formed
Z: Z) Grain shape, grain size, and sorting
Answer: Z) Z) Grain shape, grain size, and sorting
Barbara McClintock studied variation in maize kernel coloration and discovered genetic elements that could move within the genome. What were these elements called?
Acceptable Answers:
Which of the following processes is NOT correctly matched with the role it plays in the global nitrogen cycle? W) Nitrogen fixation with the Haber-Bosch process X) Nitrogen-fixing bacteria with ammonia produced from nitrogen gas Y) Legume root nodules with nitrate produced from ammonia Z) Denitrification with nitrogen gas produced from nitrates
W: W) Nitrogen fixation with the Haber-Bosch process
X: X) Nitrogen-fixing bacteria with ammonia produced from nitrogen gas
Y: Y) Legume root nodules with nitrate produced from ammonia
Z: Z) Denitrification with nitrogen gas produced from nitrates
Answer: Y) Y) Legume root nodules with nitrate produced from ammonia
A 2 kg piece of clay is moving at 4 m/s to the north when it collides perfectly inelastically with another 2 kg piece of clay moving at 3 m/s to the east. Which of the following is nearest the angle (in degrees) that the combined clay’s velocity will make with the east after the collision? W) 30° X) 37° Y) 53° Z) 60°
W: W) 30°
X: X) 37°
Y: Y) 53°
Z: Z) 60°
Answer: Y) Y) 53°
Given Planck’s constant \(h = 6.6\times10^{-34}\) J·s, what is the energy of a photon (in joules) with wavelength 0.1 μm? Provide your answer in scientific notation to one significant figure.
Acceptable Answers:
If \(X\) and \(Y\) are bounded sets, then which of the following is true? W) Both the union and the intersection of \(X\) and \(Y\) are bounded X) Both the union and the intersection of \(X\) and \(Y\) are unbounded Y) The union of \(X\) and \(Y\) is bounded and the intersection is unbounded Z) The union of \(X\) and \(Y\) is unbounded and the intersection is bounded
W: W) Both the union and the intersection of \(X\) and \(Y\) are bounded
X: X) Both the union and the intersection of \(X\) and \(Y\) are unbounded
Y: Y) The union of \(X\) and \(Y\) is bounded and the intersection is unbounded
Z: Z) The union of \(X\) and \(Y\) is unbounded and the intersection is bounded
Answer: W) W) Both the union and the intersection of \(X\) and \(Y\) are bounded
If each interior angle of a polygon is 14 times the size of each exterior angle, what is the sum in degrees of the interior angles of this polygon?
Acceptable Answers:
The Michaelis–Menten assumptions are integral to understanding enzyme kinetics. Which of the following is NOT one of these assumptions? W) Substrate is present in slightly greater quantities than the enzyme X) In a steady state, the concentration of the intermediate is always constant Y) Rate is highest when enzyme catalytic sites are saturated with substrate Z) The reaction between the substrate and the enzyme is reversible
W: W) Substrate is present in slightly greater quantities than the enzyme
X: X) In a steady state, the concentration of the intermediate is always constant
Y: Y) Rate is highest when enzyme catalytic sites are saturated with substrate
Z: Z) The reaction between the substrate and the enzyme is reversible
Answer: W) W) Substrate is present in slightly greater quantities than the enzyme
Hydrazine (\(N_2H_4\)) is manufactured at extremely high pressures and temperatures using ammonia gas and producing hydrogen gas. If 22.4 L of ammonia gas are used to make hydrazine, how many liters of hydrazine gas are produced (STP)?
Acceptable Answers:
If the proper energy of 15 g of matter is \(1.35\times10^n\) joules, what is the value of \(n\)? W) 9 X) 12 Y) 15 Z) 18
W: W) 9
X: X) 12
Y: Y) 15
Z: Z) 18
Answer: Y) Y) 15
Given that the elementary charge is \(1.6\times10^{-19}\) C, how many excess electrons would be present in an object with a net negative charge of 2.5 C? Provide your answer in scientific notation to one significant figure.
Acceptable Answers:
What is the shape of the orbit of a long-period comet that has exactly as much kinetic energy as the absolute value of its gravitational potential energy? W) Circle X) Parabola Y) Hyperbola Z) Ellipse
W: W) Circle
X: X) Parabola
Y: Y) Hyperbola
Z: Z) Ellipse
Answer: X) X) Parabola
Order the following four index minerals according to increasing grade of metamorphism of shale: 1) Sillimanite; 2) Biotite; 3) Chlorite; 4) Garnet.
Choices:
Correct Order:
What is the name of the phenomenon whereby microorganisms detect and respond to the microbial population density in their immediate surroundings?
Acceptable Answers:
Which of the following is NOT true regarding juvenile hormone (JH) in the silkworm moth as it pertains to the hormonal control of insect metamorphosis? W) JH is produced by the prothoracic gland X) Levels of JH are higher in first instar larvae relative to levels in fifth instar larvae Y) Pupae have little to no JH Z) The interplay of ecdysone and JH is important to the molting process
W: W) JH is produced by the prothoracic gland
X: X) Levels of JH are higher in first instar larvae relative to levels in fifth instar larvae
Y: Y) Pupae have little to no JH
Z: Z) The interplay of ecdysone and JH is important to the molting process
Answer: W) W) JH is produced by the prothoracic gland
What is the name of the energy storage method where water is pumped from a lower elevation reservoir to a higher elevation during off-peak periods, then released through turbines to produce electric power during peak periods?
Acceptable Answers:
Rank the following four sources of U.S. primary energy production in 2011 from greatest to least: 1) coal; 2) solar; 3) natural gas; 4) crude oil.
Choices:
Correct Order:
Which of the following sea turtle species is phylogenetically distinct from the others and can maintain body temperature elevated above ambient levels? W) Kemp’s Ridley X) Leatherback Y) Green Z) Loggerhead
W: W) Kemp’s Ridley
X: X) Leatherback
Y: Y) Green
Z: Z) Loggerhead
Answer: X) X) Leatherback
Which of the following scenarios most closely resembles Hardy–Weinberg equilibrium? W) Lizards on a large, isolated island with scarce, scattered food resources X) Lizards on a large, isolated island with plentiful food resources Y) Birds on a small island that have highly selective mating behavior Z) Birds on a small island that fly frequently back and forth to the mainland
W: W) Lizards on a large, isolated island with scarce, scattered food resources
X: X) Lizards on a large, isolated island with plentiful food resources
Y: Y) Birds on a small island that have highly selective mating behavior
Z: Z) Birds on a small island that fly frequently back and forth to the mainland
Answer: X) X) Lizards on a large, isolated island with plentiful food resources