Physics & Environmental Science — Sample exam worked answers

A rehearsal paper with separate worked solutions; use it before the final.

22 questions · 44 points · suggested 90 minutes

Student instructions

Suggested time: 90 minutes; allow breaks or accommodations and record them.
Work independently with a calculator, blank paper and the reference relationships printed in this paper. Grades 9, 11 and 12 may also use the course-linked NYSED reference tables. Use no lesson notes or answer key during an assessed attempt.
Show reasoning and units for written tasks. All supplied datasets are illustrative; do not present them as measurements you collected.
Objective items: 1 point each. Written items: 3 points each, one per criterion. A parent or teacher marks the written work; the app never grades an explanation automatically.
Sample exam: try the whole paper before opening the worked key, then revisit the linked chapters. The sample and final are different papers; this is a course assessment, not an official Regents examination.

Reference relationships

Relationship, constant or reference	Use / conditions
Components	Ax=Acosθ; Ay=Asinθ; θ from +x; use correct quadrant
Constant acceleration	v=v₀+at; x−x₀=v₀t+½at²; Constant a only
Force	ΣF=ma; weight=mg; Selected object and vector components
Circular acceleration	ac=v²/r; Inward; supplied by actual interactions
Torque	τ=rFsinθ; Specify pivot and angle
Mechanical energy	K=½mv²; Ug=mgh; Us=½kx²; Define height zero and valid spring range
Impulse	J=Δp=FavgΔt; Vector signs; negligible external impulse for total p conservation
Waves	v=fλ; T=1/f; Medium and mode conditions
Optics	n=c/v; n₁sinθ₁=n₂sinθ₂; Angles from normal
Electricity	I=Q/t; V=IR; P=VI; E=Pt; Ohmic R for V=IR; component values
Capacitor	Q=CV; U=½CV²; Linear capacitance model
Photon	E=hf=hc/λ; Kmax=hf−φ; Emission requires threshold energy
Relativity	γ=1/√(1−v²/c²); Inertial-frame definitions required
Population	dN/dt=rN(1−N/K); Instantaneous continuous-model rate
Diversity	D=1−Σpi²; State this index convention and sampling
Resource budget	Δstorage=inputs−outputs; Common boundary and interval
Capacity factor	Eactual/(Prated×time); Not conversion efficiency
NA=6.022×10²³ mol⁻¹	Avogadro constant, rounded for school calculations
h=6.626×10⁻³⁴ J·s	Planck constant, rounded
c=3.00×10⁸ m/s	Vacuum light speed, rounded
e=1.602×10⁻¹⁹ C	Elementary charge magnitude; 1 eV=1.602×10⁻¹⁹ J
g=9.8 m/s²	Typical near-surface Earth approximation; use a supplied local value if given
R=8.314 J/(mol·K)	Use SI pressure Pa and volume m³
R=0.0821 L·atm/(mol·K)	Use atmosphere pressure and liter volume
F≈96485 C/mol electrons	Faraday constant
1 u·c²≈931.5 MeV	Mass-energy conversion for consistent nuclear mass accounting
T(K)=T(°C)+273.15	Use 273 only when a question specifies that rounded convention
1 L=1000 mL; 1 mL=1 cm³	Volume conversions
1 kWh=3.60×10⁶ J	Energy conversion
cwater≈4.18 J/(g·°C)	Approximate liquid-water specific heat in ordinary conditions
Lf,water≈334 J/g; Lv,water≈2260 J/g	Water fusion and vaporization near ordinary-pressure transition conditions

Coverage and marks

Chapter	Questions	Points
Measurement & Vector Foundations	1, 2	4
Motion & Kinematics	3, 4	4
Forces, Rotation & Equilibrium	5, 6	4
Work, Energy & Momentum	7, 8	4
Waves, Sound & Optics	9, 10	4
Electricity, Magnetism & Circuits	11, 12	4
Modern Physics	13, 14	4
Ecology, Populations & Biodiversity	15, 16	4
Energy, Water & Material Resources	17, 18	4
Pollution, Carbon & Climate Evidence	19, 20	4
Conservation, Systems & Environmental Design	21, 22	4

Parent / teacher marking guide

Mark objective answers after submission. Written marks remain pending until a parent or teacher applies the three-point criteria.
Accept scientifically equivalent wording and valid alternative methods. Award stated method credit for a correct model or substitution even if later arithmetic fails.
A raw percentage describes this paper only; it is not a validated course grade or a certification. Review chapter-level evidence and the learner’s independent explanations.
Record support and accommodations, save corrections and reassess with different tasks. Do not count copied solutions as independent mastery.

Question 1 · 1 point

Convert 450 milliseconds to seconds.

Worked answer

0.45 s

450/1000=.450 s.

1 point for the correct objective answer; no written-method marks for this item.

Question 2 · 3 points

A 10N force is 30° above horizontal. Resolve it.

Worked answer

8.66N right,5.00N up

Fx=10cos 30≈8.66.

Fy=10sin 30=5.

Marking criteria

1 point: identify the appropriate model or mechanism for this task.
1 point: show the calculation or evidence in the worked steps: Fx=10cos 30≈8.66.
1 point: reach a scientifically supported conclusion: 8.66N right,5.00N up

Question 3 · 1 point

A jogger runs 8 km east then 5 km west along one road. What is the magnitude of the displacement?

Worked answer

3 km

Displacement combines opposite directions: 8 − 5 = 3 km east.

1 point for the correct objective answer; no written-method marks for this item.

Question 4 · 3 points

A rock is dropped from rest and falls 44.1 m to the ground. How long does it take — and would a rock launched horizontally from that same height take longer? (g = 9.8 m/s²)

Worked answer

3.0 s; no — the horizontally launched rock takes the same 3.0 s

Use 44.1 = ½(9.8)t² = 4.9t².

t² = 44.1 ÷ 4.9 = 9.0, so t = 3.0 s.

Because vertical motion is independent of horizontal motion, a horizontally launched rock falls in the same 3.0 s — its sideways speed doesn't change the timing.

Marking criteria

1 point: identify the appropriate model or mechanism for this task.
1 point: show the calculation or evidence in the worked steps: Use 44.1 = ½(9.8)t² = 4.9t².
1 point: reach a scientifically supported conclusion: 3.0 s; no — the horizontally launched rock takes the same 3.0 s

Question 5 · 1 point

A club strikes a 0.045 kg golf ball, giving it an acceleration of 2,000 m/s². What net force did the club apply?

Worked answer

90 N

ΣF = ma = 0.045 × 2,000 = 90 N.

1 point for the correct objective answer; no written-method marks for this item.

Question 6 · 3 points

A 6N load at .20 m balances an input at .60 m on the other side. Find input.

Worked answer

2N, neglecting lever mass.

Equal opposite torques:6(.20)=F(.60).

F=1.20/.60.

Marking criteria

1 point: identify the appropriate model or mechanism for this task.
1 point: show the calculation or evidence in the worked steps: Equal opposite torques:6(.20)=F(.60).
1 point: reach a scientifically supported conclusion: 2N, neglecting lever mass.

Question 7 · 1 point

A crane lifts a 150 kg steel beam 8.0 m upward at constant speed. How much work does it do against gravity? (g = 9.8 m/s²)

Worked answer

11760 J

The lifting force equals the weight, mg = 150 × 9.8 = 1,470 N. W = Fd = 1,470 × 8.0 = 11,760 J.

1 point for the correct objective answer; no written-method marks for this item.

Question 8 · 3 points

A 2N·s impulse acts over .010 s versus .100 s. Compare average forces.

Worked answer

A tenfold longer time gives one-tenth the average force.

Favg=J/Δt.

2/.010=200N and 2/.100=20N.

Marking criteria

1 point: identify the appropriate model or mechanism for this task.
1 point: show the calculation or evidence in the worked steps: Favg=J/Δt.
1 point: reach a scientifically supported conclusion: A tenfold longer time gives one-tenth the average force.

Question 9 · 1 point

A wave has a period of 0.004 s. Find its frequency.

Worked answer

250 Hz

f = 1 ÷ T = 1 ÷ 0.004 = 250 Hz.

1 point for the correct objective answer; no written-method marks for this item.

Question 10 · 3 points

Same source recedes.

Worked answer

566.7 Hz

fobs=600×340/(340+20).

204000/360.

Marking criteria

1 point: identify the appropriate model or mechanism for this task.
1 point: show the calculation or evidence in the worked steps: fobs=600×340/(340+20).
1 point: reach a scientifically supported conclusion: 566.7 Hz

Question 11 · 1 point

A charge of 2 μC (2 × 10⁻⁶ C) sits at a point where it feels an electric force of 0.1 N. Find the electric field strength there.

Worked answer

50000 N/C

E = F ÷ q = 0.1 ÷ (2 × 10⁻⁶) = 50,000 N/C.

1 point for the correct objective answer; no written-method marks for this item.

Question 12 · 3 points

A paper-model device uses 1.2 kW for 2h at supplied price .20 currency/kWh.

Worked answer

0.48 currency units, excluding other charges.

E=1.2×2=2.4 kWh.

Cost=2.4×.20.

Marking criteria

1 point: identify the appropriate model or mechanism for this task.
1 point: show the calculation or evidence in the worked steps: E=1.2×2=2.4 kWh.
1 point: reach a scientifically supported conclusion: 0.48 currency units, excluding other charges.

Question 13 · 1 point

Using hc=1240 eV·nm, find photon energy at 620 nm.

Worked answer

2 eV

1240/620=2.

1 point for the correct objective answer; no written-method marks for this item.

Question 14 · 3 points

A detector gives 120 counts in 60 s; background 30 in 60 s. Estimate net count rate.

Worked answer

1.5 counts/s; statistical and detector limits remain.

Subtract counts 120−30=90.

Divide by 60 s.

Marking criteria

1 point: identify the appropriate model or mechanism for this task.
1 point: show the calculation or evidence in the worked steps: Subtract counts 120−30=90.
1 point: reach a scientifically supported conclusion: 1.5 counts/s; statistical and detector limits remain.

Question 15 · 1 point

A wetland's producers have a GPP of 18,000 kcal/m²/yr and spend 7,000 kcal/m²/yr on respiration. What is the net primary productivity (NPP)?

Worked answer

11000 kcal/m²/yr

NPP = GPP - respiration = 18,000 - 7,000 = 11,000 kcal/m²/yr.

1 point for the correct objective answer; no written-method marks for this item.

Question 16 · 3 points

Counts across three 1 m² quadrats are 4,8,6. Find mean density.

Worked answer

6 individuals/m²; range 4–8.

Total 18 over 3 m².

18/3.

Marking criteria

1 point: identify the appropriate model or mechanism for this task.
1 point: show the calculation or evidence in the worked steps: Total 18 over 3 m².
1 point: reach a scientifically supported conclusion: 6 individuals/m²; range 4–8.

Question 17 · 1 point

Which fossil fuel typically releases the LEAST carbon dioxide per unit of energy when burned?

Coal
Oil (petroleum)
Natural gas
Peat

Worked answer

Natural gas

Natural gas emits roughly half the CO2 of coal per kilowatt-hour, which is why it is often called a 'cleaner' fossil fuel.

1 point for the correct objective answer; no written-method marks for this item.

Question 18 · 3 points

A2 kW source produces 12 kWh in 24h. Find capacity factor.

Worked answer

0.25 or 25%

Maximum 2×24=48 kWh.

12/48.

Marking criteria

1 point: identify the appropriate model or mechanism for this task.
1 point: show the calculation or evidence in the worked steps: Maximum 2×24=48 kWh.
1 point: reach a scientifically supported conclusion: 0.25 or 25%

Question 19 · 1 point

Biomagnification refers to the way that

decomposers break pollutants down into harmless molecules
a pollutant spreads evenly through the air until it is harmless
a factory's scrubber removes pollutants before they leave the smokestack
a persistent pollutant becomes more concentrated in organisms at each higher step of a food chain

Worked answer

a persistent pollutant becomes more concentrated in organisms at each higher step of a food chain

Because predators eat many contaminated prey and store rather than excrete the toxin, persistent pollutants grow more concentrated at each higher trophic level.

1 point for the correct objective answer; no written-method marks for this item.

Question 20 · 3 points

Change baseline from 14.0 to 14.2°C for absolute temperature 15.0°C.

Worked answer

Baseline alters offset, not the observation.

Original anomaly=1.0°C.

New anomaly=.8°C.

Underlying temperature is unchanged.

Marking criteria

1 point: identify the appropriate model or mechanism for this task.
1 point: show the calculation or evidence in the worked steps: Original anomaly=1.0°C.
1 point: reach a scientifically supported conclusion: Baseline alters offset, not the observation.

Question 21 · 1 point

An invasive species is best described as

a non-native species that spreads rapidly in a new area and harms native species
any large predator at the top of a food chain
a native species that has lived in an ecosystem for thousands of years
any species that is currently close to extinction

Worked answer

a non-native species that spreads rapidly in a new area and harms native species

Invasive species are non-natives that, lacking natural predators or competitors in the new range, spread out of control and damage native populations.

1 point for the correct objective answer; no written-method marks for this item.

Question 22 · 3 points

A10W reduction operates 2000h/year. Find saved energy.

Worked answer

20 kWh/year

10W=.010 kW.

.010×2000.

Marking criteria

1 point: identify the appropriate model or mechanism for this task.
1 point: show the calculation or evidence in the worked steps: 10W=.010 kW.
1 point: reach a scientifically supported conclusion: 20 kWh/year

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