HS Sample Set 5, Round 8 from NSB
What is the inverse function of $\displaystyle f(x)=x^5+1$?
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For a function $f(x)$, suppose that $f$ is continuous on the closed interval $[-1,3]$, differentiable on the open interval $(-1,3)$, and that $f(-1)=-2$ and $f(3)=2$. Which of the following is the value of the derivative for at least one value, $c$, on the open interval $(-1,3)$? W) –1 X) 0 Y) 1 Z) 2
W: W) –1
X: X) 0
Y: Y) 1
Z: Z) 2
Answer: Y) Y) 1
A solution is prepared by mixing 1 g of ethanol with 100 g of water to give a final volume of 101 mL. Calculate to the nearest integer the mass percent of ethanol in the solution.
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What is the conjugate acid in the reaction of sulfuric acid and sodium hydroxide?
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There is an igneous rock where all crystals are visible and the same size. Knowing only these two facts, what can be said about the cooling history of this rock? W) It cooled in stages, at different levels within the crust X) It cooled rapidly near the surface Y) It cooled on the surface and was quenched Z) It cooled slowly, at one time, at depth
W: W) It cooled in stages, at different levels within the crust
X: X) It cooled rapidly near the surface
Y: Y) It cooled on the surface and was quenched
Z: Z) It cooled slowly, at one time, at depth
Answer: Z) Z) It cooled slowly, at one time, at depth
What type of fault occurs if the hanging wall moves downward relative to the footwall?
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Which of the following is a covalent bond formed by orbitals overlapping end to end? W) Alpha X) Beta Y) Sigma Z) Pi
W: W) Alpha
X: X) Beta
Y: Y) Sigma
Z: Z) Pi
Answer: Y) Y) Sigma
The radius of a gold atom is 144 pm and its density is 19.32 g/cm³. What kind of crystal structure does the unit cell of elemental gold have?
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What is the technical term, rarely used by the general public, by which scientists designate the sense used by moths to find mates?
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The fat body of insects is an important organ for metabolism. Which of the following is NOT a function of the fat body? W) Metabolize fat, sugar, and protein X) Store fat, sugar, and protein Y) Filter water from the hemolymph Z) Synthesize hemolymph proteins
W: W) Metabolize fat, sugar, and protein
X: X) Store fat, sugar, and protein
Y: Y) Filter water from the hemolymph
Z: Z) Synthesize hemolymph proteins
Answer: Y) Y) Filter water from the hemolymph
The convex meniscus of mercury in a capillary tube indicates which of the following? W) Mercury is highly attracted to glass X) Mercury is polar Y) Mercury’s cohesion is greater than its adhesion Z) Mercury is soluble in water
W: W) Mercury is highly attracted to glass
X: X) Mercury is polar
Y: Y) Mercury’s cohesion is greater than its adhesion
Z: Z) Mercury is soluble in water
Answer: Y) Y) Mercury’s cohesion is greater than its adhesion
What compound is the reducing agent in the reaction: $$\mathrm{CH_4 + 2\,O_2 \;\rightarrow\; CO_2 + 2\,H_2O}\;?$$
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If $$f(x)=\frac{x-2}{x^2-4}\;,$$ at which value or values of $x$ does the graph of $f(x)$ have a vertical asymptote?
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Given $u(4)=-2$ and $u'(4)=3$, if $$f(x)=x\,u(x)\;,$$ evaluate $f'(4)$.
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A $2\text{ m}\times2\text{ m}$ raft sinks $10\text{ cm}$ into the water. Which of the following approximates its weight in newtons? W) 5000 X) 3900 Y) 2500 Z) 1600
W: W) 5000
X: X) 3900
Y: Y) 2500
Z: Z) 1600
Answer: X) X) 3900
A bat emits sound waves at a frequency of 83 kHz while flying at 9.0 m/s as it chases a moth flying at 8.0 m/s. Given the speed of sound is 343 m/s, to the nearest integer what frequency in kHz does the moth detect?
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What is the common name for a mechanical and electrically conductive link between two abutting neurons?
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How many horizontal layers are classically identified in the neocortex?
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Which series of spectral line emissions of the hydrogen atom is in the visible spectrum? W) Paschen X) Balmer Y) Brackett Z) Lyman
W: W) Paschen
X: X) Balmer
Y: Y) Brackett
Z: Z) Lyman
Answer: X) X) Balmer
A student repeatedly fills a graduated cylinder to the 25 mL mark from a buret and records: 26.54, 26.51, 26.60, 26.49, 26.57 mL. What type of error do these results primarily demonstrate? W) Systematic X) Random Y) Conceptual Z) Observational
W: W) Systematic
X: X) Random
Y: Y) Conceptual
Z: Z) Observational
Answer: W) W) Systematic
What is the family name for composite particles made from quarks?
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A 1.0 kg block on a spring with $k=16\rm\ N/m$ is pulled 11 cm from equilibrium and released on a frictionless surface. What is the period of oscillation, to the nearest tenth of a second?
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Which of the following is NOT a discovery attributed to Edwin Hubble? W) The existence of galactic redshifts X) The redshift of distant galaxies is proportional to their distance Y) The Andromeda nebula is a separate galaxy Z) The existence of the asteroid 1373 Cincinnati
W: W) The existence of galactic redshifts
X: X) The redshift of distant galaxies is proportional to their distance
Y: Y) The Andromeda nebula is a separate galaxy
Z: Z) The existence of the asteroid 1373 Cincinnati
Answer: W) W) The existence of galactic redshifts
Which of the following is NOT consistent with the Cenozoic rock record? W) Flowering plants X) Foraminifera Y) Dominance of reptiles increases with time Z) Dominance of mammals increases with time
W: W) Flowering plants
X: X) Foraminifera
Y: Y) Dominance of reptiles increases with time
Z: Z) Dominance of mammals increases with time
Answer: Y) Y) Dominance of reptiles increases with time
The potential difference between two points is 100 V. If a particle with charge 2 C is moved between them, what is the work done in joules?
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Three particles A, B, and C form an equilateral triangle of side 140 cm. A at (0,0) has mass 1.1 kg; B on the $x$-axis has mass 2.5 kg; C in quadrant I has mass 3.4 kg. To the nearest centimeter, what is the $x$-coordinate of the center of mass?
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In the nuclear fission chain of U-235 used for electricity, the decay products eventually end with which stable element?
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Which vehicle engine technology improves fuel efficiency the most? W) Cylinder deactivation X) Direct fuel injection and a turbocharger Y) Integrated starter/generator Z) Variable valve timing and lift
W: W) Cylinder deactivation
X: X) Direct fuel injection and a turbocharger
Y: Y) Integrated starter/generator
Z: Z) Variable valve timing and lift
Answer: X) X) Direct fuel injection and a turbocharger
Suppose the average score on a national test is 500 with a standard deviation of 100. If each score is increased by 25, what are the new mean and standard deviation, respectively?
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On what set of real numbers is the function $$f(x)=\ln\!\bigl(\tfrac{x+2}{\,1+\sqrt{2-x}\,}\bigr)$$ well defined?
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Which of the following areas exhibits the highest total relief? W) Tibetan plateau X) Rocky Mountains Y) Great Plains Z) Hawaiian Islands and seamounts
W: W) Tibetan plateau
X: X) Rocky Mountains
Y: Y) Great Plains
Z: Z) Hawaiian Islands and seamounts
Answer: Z) Z) Hawaiian Islands and seamounts
Which of the following will cause adiabatic warming? W) Increasing pressure X) Decreasing pressure Y) Condensation releasing latent heat Z) Heat added to the volume of air
W: W) Increasing pressure
X: X) Decreasing pressure
Y: Y) Condensation releasing latent heat
Z: Z) Heat added to the volume of air
Answer: W) W) Increasing pressure
Which statement about the magnetic field inside and far from a long, current-carrying solenoid is TRUE? W) It is zero X) It is non-zero and nearly uniform Y) It varies as $1/r$ from the axis Z) It is independent of the current
W: W) It is zero
X: X) It is non-zero and nearly uniform
Y: Y) It varies as $1/r$ from the axis
Z: Z) It is independent of the current
Answer: X) X) It is non-zero and nearly uniform
Given these four statements, identify all that are TRUE for objects with nonzero mass: 1) Momentum is a form of energy. 2) If an object has momentum, then it must also have mechanical energy. 3) If an object does not have momentum, then it does not have mechanical energy either. 4) If two objects of different mass have the same momentum, then the less massive object will have the greater kinetic energy.
Choices:
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What is the name of the surface generated by the equation $z=x^2+y^2$?
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If $P(A)=0.25$, $P(B)=0.50$, and $P(A\cup B)=0.55$, what is $P(A\cap B)$? (Decimal to the nearest tenth.)
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What is the purpose of a fuel cell stack in a fuel cell vehicle? W) Store hydrogen gas under high pressure X) Govern the flow of electricity Y) Store energy from regenerative braking Z) Convert hydrogen and oxygen gas into electricity to power the electric motor
W: W) Store hydrogen gas under high pressure
X: X) Govern the flow of electricity
Y: Y) Store energy from regenerative braking
Z: Z) Convert hydrogen and oxygen gas into electricity to power the electric motor
Answer: Z) Z) Convert hydrogen and oxygen gas into electricity to power the electric motor
In an experiment, students find the relationship between the period of a stick vibrating at its natural frequency and its length $L$. Which best reflects their result? W) Proportional to $L$ X) Inversely proportional to $L$ Y) Proportional to $L^2$ Z) Inversely proportional to $L^2$
W: W) Proportional to $L$
X: X) Inversely proportional to $L$
Y: Y) Proportional to $L^2$
Z: Z) Inversely proportional to $L^2$
Answer: Y) Y) Proportional to $L^2$
What is the name of the main respiratory structure in arachnids?
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Book lungs evolved from book gills. What ancient arthropod group, still extant today, has book gills?
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Which of the following is a function for which $f(-x)=-f(x)$? W) $\sin(x)$ X) $x^2$ Y) $\cos(x)$ Z) $e^x$
W: W) $\sin(x)$
X: X) $x^2$
Y: Y) $\cos(x)$
Z: Z) $e^x$
Answer: W) W) $\sin(x)$
The four lateral faces of a square pyramid are equilateral triangles. If the area of the base is 49 cm², what is the total surface area in simplest radical form?
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How many copies of each chromosome does a male wasp have?
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Which of the following is NOT in the insect group Apterygota? W) Cockroach X) Firebrat Y) Bristletail Z) Silverfish
W: W) Cockroach
X: X) Firebrat
Y: Y) Bristletail
Z: Z) Silverfish
Answer: W) W) Cockroach
In an experiment, students burned samples of methanol, ethanol, vegetable oil, peanut oil, and kerosene. Which two were the cleanest burning?
Choices:
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What kind of compound consists of methane surrounded by a crystal cage of water molecules, forming a solid similar to ice?
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Given $g=9.8\rm\ m/s^2$, how much kinetic energy in joules is lost when a 100-g ball dropped from 2 m height rebounds to 1.5 m? W) 1.96 X) 1.47 Y) 0.98 Z) 0.49
W: W) 1.96
X: X) 1.47
Y: Y) 0.98
Z: Z) 0.49
Answer: Z) Z) 0.49
A 4 kg rock drops from a 40 m-high cliff and experiences an average air-resistance force of 20 N during descent. Given $g=10\rm\ m/s^2$, at what speed does the rock hit the ground?
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Cyclic photophosphorylation functions mainly for which purpose? W) Generating NADPH X) Generating PGAL Y) Recycling electrons resulting from light absorption in Photosystem I Z) Regenerating RuBP
W: W) Generating NADPH
X: X) Generating PGAL
Y: Y) Recycling electrons resulting from light absorption in Photosystem I
Z: Z) Regenerating RuBP
Answer: Y) Y) Recycling electrons resulting from light absorption in Photosystem I
Which compound acts as the activator protein for the lactose operon in *Escherichia coli*? W) AP-1 X) AP-2γ Y) CAP Z) SAP
W: W) AP-1
X: X) AP-2γ
Y: Y) CAP
Z: Z) SAP
Answer: Y) Y) CAP