Physics & Environmental Science — Midterm exam worked answers
Student exam paperAn independent assessment of the core chapters listed below, followed by corrections and discussion.
18 questions · 42 points · suggested 60 minutes
Student instructions
- Suggested time: 60 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, 3 | 7 |
| Motion & Kinematics | 4, 5, 6 | 7 |
| Forces, Rotation & Equilibrium | 7, 8, 9 | 7 |
| Work, Energy & Momentum | 10, 11, 12 | 7 |
| Waves, Sound & Optics | 13, 14, 15 | 7 |
| Electricity, Magnetism & Circuits | 16, 17, 18 | 7 |
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 3.0 kJ to joules.
Worked answer
3000 J
kilo means 1000.
1 point for the correct objective answer; no written-method marks for this item.
Question 2 · 3 points
Convert 250 ms to seconds.
Worked answer
0.250 s
250 ms×(.001 s/ms).
Cancel milliseconds.
Marking criteria
- 1 point: identify the appropriate model or mechanism for this task.
- 1 point: show the calculation or evidence in the worked steps: 250 ms×(.001 s/ms).
- 1 point: reach a scientifically supported conclusion: 0.250 s
Question 3 · 3 points
Evaluate the evidence in this supplied classroom investigation: Vector Measurement and Closure. State a supported claim, cite two specific entries from the dataset, and identify one limitation plus an improvement.
Worked answer
The component result is 5 m at 53.1° north of east. The supplied measurements agree within drawing resolution. Order changes the path but not vector sum; a wrong scale or angle zero could bias every measurement.
Read the column labels and compare entries using their stated units.
Connect the observed pattern to the investigation mechanism, not just a repeated description.
Evaluate the supplied example data; do not claim they establish every real-world case.
Marking criteria
- 1 point: a claim consistent with the supplied dataset and scientific mechanism.
- 1 point: cite and correctly compare at least two specific data entries.
- 1 point: a relevant limitation and improvement addressing it.
Question 4 · 1 point
Which of the following is a vector quantity?
- displacement
- speed
- distance
- mass
Worked answer
displacement
Displacement has both magnitude and direction, making it a vector. Distance, speed, and mass are scalars.
1 point for the correct objective answer; no written-method marks for this item.
Question 5 · 3 points
A student walks 40 m east, then turns and walks 30 m north. Find (a) the total distance traveled and (b) the magnitude of the displacement.
Worked answer
(a) distance = 70 m; (b) displacement = 50 m (to the northeast)
Distance is the total path length: 40 + 30 = 70 m.
The two legs meet at a right angle, so combine them with the Pythagorean theorem: displacement = √(40² + 30²).
= √(1600 + 900) = √2500 = 50.
Marking criteria
- 1 point: identify the appropriate model or mechanism for this task.
- 1 point: show the calculation or evidence in the worked steps: Distance is the total path length: 40 + 30 = 70 m.
- 1 point: reach a scientifically supported conclusion: (a) distance = 70 m; (b) displacement = 50 m (to the northeast)
Question 6 · 3 points
Evaluate the evidence in this supplied classroom investigation: Motion Graphs from a Gentle Roll. State a supported claim, cite two specific entries from the dataset, and identify one limitation plus an improvement.
Worked answer
The ratio x/t² is 0.40 m/s², giving a=0.80 m/s² and v=1.60 m/s at 2 s if initial velocity is zero. Timing, inconsistent release, and changing friction can alter this pattern; repeated trials are needed.
Read the column labels and compare entries using their stated units.
Connect the observed pattern to the investigation mechanism, not just a repeated description.
Evaluate the supplied example data; do not claim they establish every real-world case.
Marking criteria
- 1 point: a claim consistent with the supplied dataset and scientific mechanism.
- 1 point: cite and correctly compare at least two specific data entries.
- 1 point: a relevant limitation and improvement addressing it.
Question 7 · 1 point
A book rests on a table. Earth pulls the book down with the force of gravity. According to Newton's third law, what is the reaction force to this pull?
- The book pulling up on the Earth
- The book's inertia
- The table pushing up on the book
- The book pushing down on the table
Worked answer
The book pulling up on the Earth
A third-law pair acts on two different objects. If Earth pulls the book down, the reaction is the book pulling Earth up. (The table's push is a separate force, not the reaction to gravity.)
1 point for the correct objective answer; no written-method marks for this item.
Question 8 · 3 points
A net force of 84 N acts on a 12 kg cart on a frictionless surface. Find its acceleration.
Worked answer
7 m/s²
Rearrange ΣF = ma to solve for acceleration: a = ΣF ÷ m.
a = 84 ÷ 12.
= 7.
Marking criteria
- 1 point: identify the appropriate model or mechanism for this task.
- 1 point: show the calculation or evidence in the worked steps: Rearrange ΣF = ma to solve for acceleration: a = ΣF ÷ m.
- 1 point: reach a scientifically supported conclusion: 7 m/s²
Question 9 · 3 points
Evaluate the evidence in this supplied classroom investigation: Spring Force and Torque Evidence. State a supported claim, cite two specific entries from the dataset, and identify one limitation plus an improvement.
Worked answer
The slope gives k=100 N/m and energy at 0.03 m is 0.045 J. A 2 N input balances the load torque; support must also balance vertical force. Curvature or permanent stretch challenges the elastic model.
Read the column labels and compare entries using their stated units.
Connect the observed pattern to the investigation mechanism, not just a repeated description.
Evaluate the supplied example data; do not claim they establish every real-world case.
Marking criteria
- 1 point: a claim consistent with the supplied dataset and scientific mechanism.
- 1 point: cite and correctly compare at least two specific data entries.
- 1 point: a relevant limitation and improvement addressing it.
Question 10 · 1 point
Two cranes lift identical loads to the same rooftop, but Crane A takes 4 s while Crane B takes 8 s. Which statement is correct?
- Crane B does more work on the load
- The cranes have equal power
- Crane A has greater power
- Crane A does more work on the load
Worked answer
Crane A has greater power
Both cranes do the same work (same load, same height). Since P = W/t, doing that work in less time means Crane A delivers greater power.
1 point for the correct objective answer; no written-method marks for this item.
Question 11 · 3 points
A worker pulls a wagon with a 50 N force directed 60° above the horizontal, moving it 4.0 m along level ground. How much work does the pulling force do?
Worked answer
100 J
Only the part of the force along the motion does work, so use W = Fd·cosθ.
W = 50 × 4.0 × cos 60°.
cos 60° = 0.5, so W = 200 × 0.5 = 100.
Marking criteria
- 1 point: identify the appropriate model or mechanism for this task.
- 1 point: show the calculation or evidence in the worked steps: Only the part of the force along the motion does work, so use W = Fd·cosθ.
- 1 point: reach a scientifically supported conclusion: 100 J
Question 12 · 3 points
Evaluate the evidence in this supplied classroom investigation: Impulse and Energy Accounting. State a supported claim, cite two specific entries from the dataset, and identify one limitation plus an improvement.
Worked answer
Both pulses give 2 N·s impulse, so the 1 kg object reaches 2 m/s and 2 J kinetic energy. Twice the duration compensates for half the force. Real peak forces and motion need more detailed time profiles.
Read the column labels and compare entries using their stated units.
Connect the observed pattern to the investigation mechanism, not just a repeated description.
Evaluate the supplied example data; do not claim they establish every real-world case.
Marking criteria
- 1 point: a claim consistent with the supplied dataset and scientific mechanism.
- 1 point: cite and correctly compare at least two specific data entries.
- 1 point: a relevant limitation and improvement addressing it.
Question 13 · 1 point
A wave travels at 12 m/s with a frequency of 4 Hz. Find its wavelength.
Worked answer
3 m
λ = v ÷ f = 12 ÷ 4 = 3 m.
1 point for the correct objective answer; no written-method marks for this item.
Question 14 · 3 points
A wave has a frequency of 25 Hz and a wavelength of 8 m. Find its speed.
Worked answer
200 m/s
Use the wave speed equation v = f × λ.
v = 25 × 8.
= 200.
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 the wave speed equation v = f × λ.
- 1 point: reach a scientifically supported conclusion: 200 m/s
Question 15 · 3 points
Evaluate the evidence in this supplied classroom investigation: Standing-Wave Patterns. State a supported claim, cite two specific entries from the dataset, and identify one limitation plus an improvement.
Worked answer
Every row gives 48 m/s. Mode 2 has nodes 0.60 m apart. Fixed boundaries determine the allowed patterns; damping limits amplitude, and changes in tension can change the speed.
Read the column labels and compare entries using their stated units.
Connect the observed pattern to the investigation mechanism, not just a repeated description.
Evaluate the supplied example data; do not claim they establish every real-world case.
Marking criteria
- 1 point: a claim consistent with the supplied dataset and scientific mechanism.
- 1 point: cite and correctly compare at least two specific data entries.
- 1 point: a relevant limitation and improvement addressing it.
Question 16 · 1 point
Find the force between a 2 μC charge and a 3 μC charge separated by 0.3 m. (k = 9 × 10⁹ N·m²/C²)
Worked answer
0.6 N
F = kq₁q₂/r² = (9 × 10⁹)(2 × 10⁻⁶)(3 × 10⁻⁶) ÷ (0.3)² = 0.054 ÷ 0.09 = 0.6 N.
1 point for the correct objective answer; no written-method marks for this item.
Question 17 · 3 points
Find the electrostatic force between a +3 μC charge and a +4 μC charge separated by 0.6 m. (Use k = 9 × 10⁹ N·m²/C² and 1 μC = 1 × 10⁻⁶ C.)
Worked answer
0.3 N (repulsive, since both charges are positive)
Write Coulomb's law: F = k·q₁·q₂ ÷ r².
Substitute: F = (9 × 10⁹)(3 × 10⁻⁶)(4 × 10⁻⁶) ÷ (0.6)².
The top is 9 × 10⁹ × 12 × 10⁻¹² = 0.108; divide by 0.36.
Marking criteria
- 1 point: identify the appropriate model or mechanism for this task.
- 1 point: show the calculation or evidence in the worked steps: Write Coulomb's law: F = k·q₁·q₂ ÷ r².
- 1 point: reach a scientifically supported conclusion: 0.3 N (repulsive, since both charges are positive)
Question 18 · 3 points
Evaluate the evidence in this supplied classroom investigation: Low-Voltage Circuit Reasoning. State a supported claim, cite two specific entries from the dataset, and identify one limitation plus an improvement.
Worked answer
Series current is 0.5 A with 3 V across each resistor. Parallel branches each have 6 V and 1 A, totaling 2 A. Internal resistance causes terminal voltage drop and heating. These paper ideals do not authorize unreviewed physical circuits.
Read the column labels and compare entries using their stated units.
Connect the observed pattern to the investigation mechanism, not just a repeated description.
Evaluate the supplied example data; do not claim they establish every real-world case.
Marking criteria
- 1 point: a claim consistent with the supplied dataset and scientific mechanism.
- 1 point: cite and correctly compare at least two specific data entries.
- 1 point: a relevant limitation and improvement addressing it.