Physics & Environmental Science — Final exam

Parent / teacher answer key

An independent assessment of the core chapters listed below, followed by corrections and discussion.

44 questions · 88 points · suggested 180 minutes

Student instructions

  1. Suggested time: 120 minutes; allow breaks or accommodations and record them.
  2. 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.
  3. Show reasoning and units for written tasks. All supplied datasets are illustrative; do not present them as measurements you collected.
  4. 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.
  5. 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 referenceUse / conditions
ComponentsAx=Acosθ; Ay=Asinθ; θ from +x; use correct quadrant
Constant accelerationv=v₀+at; x−x₀=v₀t+½at²; Constant a only
ForceΣF=ma; weight=mg; Selected object and vector components
Circular accelerationac=v²/r; Inward; supplied by actual interactions
Torqueτ=rFsinθ; Specify pivot and angle
Mechanical energyK=½mv²; Ug=mgh; Us=½kx²; Define height zero and valid spring range
ImpulseJ=Δp=FavgΔt; Vector signs; negligible external impulse for total p conservation
Wavesv=fλ; T=1/f; Medium and mode conditions
Opticsn=c/v; n₁sinθ₁=n₂sinθ₂; Angles from normal
ElectricityI=Q/t; V=IR; P=VI; E=Pt; Ohmic R for V=IR; component values
CapacitorQ=CV; U=½CV²; Linear capacitance model
PhotonE=hf=hc/λ; Kmax=hf−φ; Emission requires threshold energy
Relativityγ=1/√(1−v²/c²); Inertial-frame definitions required
PopulationdN/dt=rN(1−N/K); Instantaneous continuous-model rate
DiversityD=1−Σpi²; State this index convention and sampling
Resource budgetΔstorage=inputs−outputs; Common boundary and interval
Capacity factorEactual/(Prated×time); Not conversion efficiency
NA=6.022×10²³ mol⁻¹Avogadro constant, rounded for school calculations
h=6.626×10⁻³⁴ J·sPlanck constant, rounded
c=3.00×10⁸ m/sVacuum light speed, rounded
e=1.602×10⁻¹⁹ CElementary charge magnitude; 1 eV=1.602×10⁻¹⁹ J
g=9.8 m/s²Typical 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 electronsFaraday constant
1 u·c²≈931.5 MeVMass-energy conversion for consistent nuclear mass accounting
T(K)=T(°C)+273.15Use 273 only when a question specifies that rounded convention
1 L=1000 mL; 1 mL=1 cm³Volume conversions
1 kWh=3.60×10⁶ JEnergy conversion
cwater≈4.18 J/(g·°C)Approximate liquid-water specific heat in ordinary conditions
Lf,water≈334 J/g; Lv,water≈2260 J/gWater fusion and vaporization near ordinary-pressure transition conditions

Coverage and marks

ChapterQuestionsPoints
Measurement & Vector Foundations1, 2, 3, 48
Motion & Kinematics5, 6, 7, 88
Forces, Rotation & Equilibrium9, 10, 11, 128
Work, Energy & Momentum13, 14, 15, 168
Waves, Sound & Optics17, 18, 19, 208
Electricity, Magnetism & Circuits21, 22, 23, 248
Modern Physics25, 26, 27, 288
Ecology, Populations & Biodiversity29, 30, 31, 328
Energy, Water & Material Resources33, 34, 35, 368
Pollution, Carbon & Climate Evidence37, 38, 39, 408
Conservation, Systems & Environmental Design41, 42, 43, 448

Name: ____________________   Date: ____________________

Question 1 · 1 point

Trials are 1.8,2.0,2.2 s. Find mean.

Question 2 · 1 point

Which pair are both vector quantities?

  1. Speed and distance
  2. Velocity and force
  3. Mass and time
  4. Energy and temperature

Question 3 · 3 points

Find resultant magnitude for 6 m east and 8 m north. Describe a measurement check.

Question 4 · 3 points

Velocity rises from 2 to 14 m/s over 4 s. Find slope and interpret it.

Question 5 · 1 point

A jogger runs 8 km east, then turns around and runs 5 km west along the same road. What total distance did she cover?

Question 6 · 1 point

A car rounds a bend at constant speed. It is

  1. not accelerating
  2. accelerating, because its direction changes
  3. decelerating
  4. in equilibrium

Question 7 · 3 points

An object starts at rest and accelerates at 2 m/s² for 5 s. Find velocity and displacement.

Question 8 · 3 points

A horizontal projectile has vx=6 m/s and falls for 2 s. Find range and drop with g=9.8.

Question 9 · 1 point

A net force of 36 N acts on a 4 kg block on a frictionless surface. Find its acceleration.

Question 10 · 1 point

An object moves at constant velocity. The net force on it is

  1. zero
  2. constant and non-zero
  3. increasing
  4. equal to its weight

Question 11 · 3 points

A 5 kg object has 30 N right and 10 N left. Find acceleration.

Question 12 · 3 points

A 4 N perpendicular force acts 0.30 m from a pivot. Find torque and state static-equilibrium conditions.

Question 13 · 1 point

A 30 N force pushes a box 3.0 m in the direction of the force. How much work is done?

Question 14 · 1 point

Doubling an object's speed changes its kinetic energy by a factor of

  1. 2
  2. 3
  3. 4
  4. 8

Question 15 · 3 points

A 2 kg object is 4 m above a chosen zero; g=9.8. Find potential energy and ideal speed after falling from rest.

Question 16 · 3 points

A 0.5 kg ball changes velocity +4 to −2 m/s in 0.10 s. Find impulse and average force.

Question 17 · 1 point

A wave has a frequency of 10 Hz and a wavelength of 3 m. Find its speed.

Question 18 · 1 point

For a wave of fixed speed, increasing the frequency

  1. increases the wavelength
  2. decreases the wavelength
  3. leaves the wavelength unchanged
  4. increases the amplitude

Question 19 · 3 points

A string fixed at both ends has L=1 m and v=40 m/s. Find first two harmonics.

Question 20 · 3 points

Light goes from index 1.5 toward index 1.0. State total-internal-reflection conditions and find critical angle.

Question 21 · 1 point

Two small spheres both carry a positive charge. The electric force between them is:

  1. attractive
  2. repulsive
  3. zero
  4. always gravitational

Question 22 · 1 point

Two identical resistors in series compared with one alone give a total resistance that is

  1. halved
  2. unchanged
  3. doubled
  4. zero

Question 23 · 3 points

Two 12 Ω resistors are parallel on 6 V. Find total current and power.

Question 24 · 3 points

Find energy stored in a 100 μF capacitor at 10 V.

Question 25 · 1 point

Photon 5 eV, work function 2 eV. Find Kmax.

Question 26 · 1 point

Higher-frequency electromagnetic radiation carries

  1. less energy per photon
  2. more energy per photon
  3. the same energy per photon
  4. no energy

Question 27 · 3 points

A 4 eV photon hits a surface with work function 2.5 eV. Find maximum electron energy and stopping potential.

Question 28 · 3 points

A proper interval is 8 s at γ=1.25. Find other-frame interval. Separately, find nuclear energy for 0.010 u mass loss at 931.5 MeV/u.

Question 29 · 1 point

In an energy pyramid, which trophic level has the LEAST energy available to it?

  1. Primary consumers
  2. Secondary consumers
  3. Top predators
  4. Producers

Question 30 · 1 point

A population levels off at its carrying capacity because

  1. reproduction stops
  2. density-dependent factors increasingly limit growth
  3. predators vanish
  4. the habitat grows

Question 31 · 3 points

Two ecological species have fractions 0.25 and 0.75. Find D=1−Σpi².

Question 32 · 3 points

N=1000, r=0.2/year, K=2000. Find instantaneous logistic rate. Is it the exact next-year increase?

Question 33 · 1 point

Which of the following is a fossil fuel?

  1. Wind
  2. Coal
  3. Uranium
  4. Sunlight

Question 34 · 1 point

The main limitation of 'reserves divided by current use' as a lifetime estimate is that it assumes

  1. prices are fixed
  2. use stays constant and no new reserves are found
  3. the resource is renewable
  4. extraction is free

Question 35 · 3 points

A 2 kW generator delivers 18 kWh in 24 h. Find capacity factor and distinguish efficiency.

Question 36 · 3 points

A reservoir starts at 1000 units with annual input 120 and output 150. Find storage change and final amount.

Question 37 · 1 point

Which of the following is an example of nonpoint-source pollution?

  1. A pipe discharging waste from a single factory into a river
  2. Smoke pouring from one power plant's smokestack
  3. Fertilizer and motor oil washing off lawns and roads across a whole watershed
  4. Untreated sewage released from one broken outfall pipe

Question 38 · 1 point

A single unusually hot year is weak evidence of a climate trend because

  1. thermometers are unreliable
  2. year-to-year variation is large and a trend is a change in the long-run average
  3. heat is not measurable
  4. one year is too cold

Question 39 · 3 points

Modeled pH falls from 8.2 to 8.1. Find the hydrogen-ion factor and explain acidification while remaining basic.

Question 40 · 3 points

Anomaly rises from 0.3 to 0.9°C in 30 years. Find trend per decade and one attribution limitation.

Question 41 · 1 point

Which listed activity directly removes habitat and separates remaining habitat patches?

  1. Scientists collecting a few specimens for study
  2. Natural predators hunting their usual prey
  3. Zoos keeping some animals in captivity
  4. Habitat loss and fragmentation from clearing and dividing land

Question 42 · 1 point

Comparing two environmental options by cost per tonne of carbon saved is incomplete because it ignores

  1. the arithmetic
  2. who bears the cost, reliability and side effects
  3. the units
  4. the total emissions

Question 43 · 3 points

Habitat area falls from 8000 to 2000 ha. Find percent loss and propose a monitored conservation measure.

Question 44 · 3 points

An upgrade costs 400 currency units and saves 50 kWh/year at 0.20/kWh. Find simple payback and a design limitation.

Revisit the covered chapters

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