HS Sample Set 5, Round 10 from NSB
What is the minimum possible value of $$2^x + 2^y$$ if $$x + y = 2$$?
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What is the value of the infinite sum $$\displaystyle 1/2! \;-\; 1/3! \;+\; 1/4! \;-\; 1/5! \;+\cdots?$$
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Which of the following is a laboratory technique used to generate many copies of a gene? W) Polymerase chain reaction X) Gel electrophoresis Y) Southern blot Z) Titration
W: W) Polymerase chain reaction
X: X) Gel electrophoresis
Y: Y) Southern blot
Z: Z) Titration
Answer: W) W) Polymerase chain reaction
By name or number, identify all of the following four organisms that are endangered pinnipeds: 1) Bearded seal; 2) Hawaiian monk seal; 3) Ringed seal; 4) Spotted seal.
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Biodiesel generally outperforms regular petro diesel in all of the following categories, EXCEPT: W) Cetane rating X) Flash point Y) Calorific value Z) Sulfur content
W: W) Cetane rating
X: X) Flash point
Y: Y) Calorific value
Z: Z) Sulfur content
Answer: Y) Y) Calorific value
The backup controls for a solar cell operate on a 4-volt lithium-ion battery with 20 Ω internal resistance and an initial capacity of 3000 mAh. In watt‐hours, what is the electrical energy required to recharge the battery?
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A 4-kg ball is tossed at 5 m/s. How fast, in meters per second, must a 1-kg ball be thrown to have the same kinetic energy?
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A jogger moves at 4 m/s, then accelerates at 1 m/s² for 4 s. How far has she traveled during the acceleration?
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What is the term for the pastelike substance, which is also the least soluble nitrogenous waste, excreted by birds, reptiles, and insects?
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What is the scientific name of the only member of the family Eschrichtiidae?
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Consider the polar equation $$r = \sin(2\theta)\,. $$ Its graph looks like a rose. How many petals does it have?
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Assuming $P(A)=0.3$, $P(B)=0.3$, and $P(A\cup B)=0.5$, what are $P(A\cap B)$ and $P\bigl((A\cup B)^c\bigr)$, to the nearest tenth?
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In which of the following compounds does nitrogen have an unpaired electron? W) Ammonia X) Nitrous oxide Y) Sodium nitrate Z) Nitric oxide
W: W) Ammonia
X: X) Nitrous oxide
Y: Y) Sodium nitrate
Z: Z) Nitric oxide
Answer: Z) Z) Nitric oxide
Write the balanced molecular equation (with states) for the titration of a saturated solution of Ca(OH)₂ with HCl.
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Which time of day BEST corresponds to a decrease in ionization of particles in the ionosphere? W) Morning X) Noon Y) Afternoon Z) Night
W: W) Morning
X: X) Noon
Y: Y) Afternoon
Z: Z) Night
Answer: Z) Z) Night
Earth has prograde rotation. Which two planets in our Solar System exhibit retrograde rotation?
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Which of the following is NOT a colligative property of a solution? W) Freezing point depression X) Osmotic pressure Y) Percent by mass Z) Boiling point elevation
W: W) Freezing point depression
X: X) Osmotic pressure
Y: Y) Percent by mass
Z: Z) Boiling point elevation
Answer: Y) Y) Percent by mass
How many liters of 2 M H₂SO₄ are required to titrate 3 L of 0.4 M HNO₃?
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Which of the following is NOT true about snowy plovers? W) When fighting, they may grab their enemy’s tail with their bills X) They nest on sandy beaches Y) They are endemic to New Zealand Z) Males nurture their chicks
W: W) When fighting, they may grab their enemy’s tail with their bills
X: X) They nest on sandy beaches
Y: Y) They are endemic to New Zealand
Z: Z) Males nurture their chicks
Answer: Y) Y) They are endemic to New Zealand
What protein, released by cells in the ileum and colon, appears to inhibit appetite in humans?
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When $$\mathrm{O_2 + C_6H_{14} \to CO_2 + H_2O}$$ is balanced with lowest whole‐number coefficients, what is the coefficient of $$\mathrm{O_2}$$?
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Given $$4\,\mathrm{PH_3(aq)}\to\mathrm{P_4(g)}+6\,\mathrm{H_2(g)},$$ if 0.0048 mol of PH₃ is consumed per second, what is the rate of formation of P₄, to the nearest ten‐thousandth?
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Evaluate $$\lim_{x\to \pi/3}\frac{\sin x-\tfrac{\sqrt3}{2}}{x-\tfrac{\pi}{3}}\,. $$
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If the volume of an oil spill is given by $$V=\tfrac{0.05\pi}{2}\,r^2$$ and there is an error of 0.5 m in measuring a spill of radius $r=100/\pi$ m, use differentials to estimate the error in $V$.
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In a hydraulic device, a 100 N force on a piston of area 0.01 m² produces what force on a piston of area 0.5 m²?
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What is the centripetal acceleration of a point on a bicycle tire of radius 0.81 m moving at 9 m/s?
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What is the general term for scientific research that looks for a useful application, process, or product in nature?
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What is the term in immunobiology describing a lack of reaction by the body’s defense mechanisms, consisting of peripheral lymphocyte tolerance?
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Which of the following species is NOT considered an electrolyte? W) Sodium hydroxide X) Hydrogen chloride Y) Aluminum nitrate Z) Diethyl ether
W: W) Sodium hydroxide
X: X) Hydrogen chloride
Y: Y) Aluminum nitrate
Z: Z) Diethyl ether
Answer: Z) Z) Diethyl ether
By name or number, identify all of the following four substances that would show a positive result in a Benedict’s test: 1) Simple sugars; 2) Starches; 3) Proteins; 4) Lipids.
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How many layers of doped silicon are needed to make a transistor?
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A 1 m copper rod of mass 0.05 kg is in a 0.10 T magnetic field. What minimum current will produce an upward magnetic force that cancels its weight? (Use $g=10\,$m/s².)
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About 3.9 billion years ago, the Earth and other terrestrial bodies were heavily bombarded by leftover fragments. What was this period called?
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By number, identify all of the following that are advantages of solar‐sail propulsion versus a conventional rocket: 1) No need to carry fuel; 2) Quicker acceleration; 3) Constant acceleration; 4) Constant velocity.
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On a game show, contestants spin a large wheel to determine their prize. How should one apply force to spin the wheel as rapidly as possible? W) Tangential to the rim X) At a 45° angle to the rim Y) Away from the center Z) Toward the center
W: W) Tangential to the rim
X: X) At a 45° angle to the rim
Y: Y) Away from the center
Z: Z) Toward the center
Answer: W) W) Tangential to the rim
Nitrogen molecules (mass $4.65\times10^{-26}$ kg) collide elastically at 300 m/s with one wall of area $6\times10^{-4}$ m² at a rate of $5.0\times10^{23}$ collisions/s. What pressure do they exert, to the nearest kPa?
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A 5 kg mass moving at 10 m/s compresses a horizontal spring with spring constant 500 N/m. What is the maximum compression?
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Which of the following is NOT an example of smart grid technology? W) Ground-source heat pumps X) Advanced metering infrastructure Y) Conservation voltage reduction Z) Substation automation
W: W) Ground-source heat pumps
X: X) Advanced metering infrastructure
Y: Y) Conservation voltage reduction
Z: Z) Substation automation
Answer: W) W) Ground-source heat pumps
The last two digits of a positive integer $n$ are 1 and 8. Which of the following statements about $n$ can be TRUE? W) $n$ is divisible by 7 X) $n$ is divisible by 5 Y) $n$ is divisible by 4 Z) $n$ is a perfect square
W: W) $n$ is divisible by 7
X: X) $n$ is divisible by 5
Y: Y) $n$ is divisible by 4
Z: Z) $n$ is a perfect square
Answer: W) W) $n$ is divisible by 7
In simplest radical form, what is the radius of the circle tangent to the sides of an equilateral triangle of side length 2?
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Which happens to liquid water descending on the leeward side of a mountain range? W) It condenses X) It precipitates Y) It freezes Z) It evaporates
W: W) It condenses
X: X) It precipitates
Y: Y) It freezes
Z: Z) It evaporates
Answer: Z) Z) It evaporates
By number, identify all of the following four factors that contribute to global wind patterns: 1) Solar radiation; 2) Friction; 3) Pressure gradient; 4) Coriolis force.
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If $g_E$ and $g_M$ are surface gravities on Earth and the Moon, Millikan’s oil-drop experiment on each would measure the same electronic charge. The ratio $e_M/e_E$ equals: W) $g_E/g_M$ X) 1 Y) $g_M/g_E$ Z) $(g_M/g_E)^2$
W: W) $g_E/g_M$
X: X) 1
Y: Y) $g_M/g_E$
Z: Z) $(g_M/g_E)^2$
Answer: X) X) 1
How much energy (in J), in scientific notation with two significant digits, is required to heat a 4.8 kg clay pizza stone (specific heat 860 J/kg·K) from 25 °C to 235 °C?
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Which U.S. coastline would change the least as sea level rises? W) West coast X) Gulf coast Y) Northeast coast Z) Florida coast
W: W) West coast
X: X) Gulf coast
Y: Y) Northeast coast
Z: Z) Florida coast
Answer: W) W) West coast
By number, identify all of the following statements that represent a significance of an unconformity in the rock record: 1) It represents missing time; 2) Extra time; 3) Periods of erosion and/or non-deposition; 4) Periods of faster or increased deposition.
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Which hydroelectric dam has the greatest power capacity in the world?
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Two men lifted a 95 kg sack to the second floor, then the rope broke. Just before hitting the ground the sack had 3500 J of kinetic energy. Using $g=9.8\,$m/s², what was the height of the second floor (nearest m)?
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Of the seven species of sea turtles, six are found in U.S. waters. Which is NOT found in U.S. waters? W) Flatback X) Green Y) Kemp’s ridley Z) Leatherback
W: W) Flatback
X: X) Green
Y: Y) Kemp’s ridley
Z: Z) Leatherback
Answer: W) W) Flatback
By name or number, identify all of the following four types of fishing gear that inadvertently catch large numbers of sea turtles: 1) Gillnets; 2) Longlines; 3) Pound nets; 4) Trawls.
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