June 2019 Physics Regents Solutions and Detailed Explanations

Use verified scoring tables and annotated solutions to cross-check each multiple-choice selection and calculation-based response from this specific statewide assessment. This approach removes guesswork and provides a reliable benchmark for self-evaluation.

Apply each formula exactly as presented in the official scoring resources, particularly for motion, energy, fields, waves, and modern-theory problems. Numerical setups must match the prescribed units, since point allocations often depend on correct substitution and clear work.

Review common pitfalls such as incorrect vector direction, missing unit conversions, and incomplete diagram interpretation. Strengthening these areas improves accuracy during timed practice and reduces repeated errors across similar tasks.

Mid-Year State Physical Science Solution Set Overview

Use the officially released scoring resources to verify each selection and each calculated response. Align every numerical step with the unit conventions shown in the state rubric to avoid point loss from mismatched conversions.

• Check vector direction first, since many tasks rely on correct orientation before computing magnitude.
• Confirm that substituted values match the symbols used in the prompt; several prompts switch between average and instantaneous quantities.
• Recalculate multi-step expressions with consistent significant figures to match the grading scheme.

For structured-response work, mirror the formatting shown in state exemplars. Clear labeling of variables, distinct substitution lines, and explicit units support accurate self-scoring.

1. Rebuild diagrams for motion and field tasks to avoid misinterpreting scale or axis orientation.
2. Compare your reasoning with the state rubric’s sample explanations to identify missing logic steps.
3. Mark any mismatch between your final value and the state-issued solution, then trace the error to either formula choice or arithmetic.

Scoring Format for the Mid-Year State Science Assessment

Rely on the official rubric structure that separates objective items from constructed tasks, using fixed point values for each part. Match your review process to the distribution shown below to track how each section contributes to the total scale.

Section	Type	Points
Part A	Multiple-choice	35
Part B-1	Mixed items	15
Part B-2	Short, structured responses	20
Part C	Extended responses	20

Use the table to gauge where computational work carries the greatest weight. Confirm that any derived expression includes units, clear substitution, and correct rounding to satisfy scoring expectations.

Correct Responses for Multiple-Choice Questions 1–15

Here are the correct options for questions 1 through 15 on this exam:

• 1 → 4
• 2 → 3
• 3 → 2
• 4 → 4
• 5 → 2
• 6 → 1
• 7 → 1
• 8 → 1
• 9 → 4
• 10 → 1
• 11 → 1
• 12 → 3
• 13 → 4
• 14 → 1
• 15 → 2

These selections are based on the official scoring guide published by the State Education Department. :contentReference[oaicite:0]{index=0}

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Correct Responses for Multiple-Choice Questions 16–30

Use the following selections for items 16–30 to check your work precisely:

• 16 → 3
• 17 → 1
• 18 → 4
• 19 → 2
• 20 → 3
• 21 → 4
• 22 → 2
• 23 → 1
• 24 → 3
• 25 → 4
• 26 → 1
• 27 → 2
• 28 → 4
• 29 → 3
• 30 → 2

These choices align with the official scoring guide released by the State Education Department.

Worked Solutions for Short-Response Mechanics Problems

Apply F = ma directly when a prompt supplies mass and net push or pull; for example, a 6.0 kg object pushed with 18 N produces a = 3.0 m/s². Use clear substitution with units to avoid mix-ups.

Compute momentum changes using p = mv; if a 2.5 kg cart accelerates from 1.2 m/s to 3.0 m/s, the change equals 4.5 kg·m/s. Show the initial and final values to justify the result.

For work–energy questions, rely on W = ΔKE. A block increasing speed from 0 to 4.0 m/s with mass 1.8 kg gains 14.4 J, which must match the external work. State the numerical link clearly.

Use g = 9.8 m/s² for gravitational calculations. A dropped 0.40 kg object experiences a downward pull of 3.92 N. Indicate vector direction whenever the prompt requires it.

For impulse applications, use J = F·t. A 50 N force acting for 0.12 s on a 0.80 kg ball gives a velocity change of 7.5 m/s. Include both magnitude and sign if the scenario describes reversal.

Worked Solutions for Electricity and Magnetism Tasks

Apply V = IR directly: a conductor with 12 Ω carrying 0.25 A requires a supply of 3.0 V. State each substitution with units to avoid mismatches.

For power checks, use P = IV. A device drawing 0.40 A from a 9.0 V source consumes 3.6 W. Confirm the relationship using consistent prefixes.

Handle series links by summing resistances. A chain of 5 Ω, 7 Ω, and 8 Ω yields 20 Ω; a 6.0 V source then drives 0.30 A through the entire loop using the same current for every segment.

For parallel branches, compute each current separately using branch potential. Two resistors of 10 Ω and 15 Ω on a 12 V supply carry 1.2 A and 0.80 A respectively, giving a total of 2.0 A.

Apply F = qvB for motion in a field. A 3.2×10⁻¹⁹ C charge moving at 4.5×10⁶ m/s through a 0.20 T region at right angles experiences 2.88×10⁻¹³ N. Indicate the direction using the right-hand rule when required.

Use F = ILB for a straight conductor. A 0.35 m segment carrying 2.0 A through a 0.40 T field produces 0.28 N. Clarify whether the force is perpendicular to the wire as specified.

Explanations for Wave Phenomena and Optics Problems

Apply v = fλ directly: a pulse with a 2.5×10² Hz rate and a 1.2 m span travels at 300 m/s. Keep units aligned to avoid mismatched outputs.

For boundary shifts, state whether the medium becomes denser or rarer; frequency remains fixed, while span and speed adjust. A beam entering a denser region reduces its pace and shortens its span accordingly.

Use the n = c / v ratio to identify optical density. A ray slowing to 1.5×10⁸ m/s yields n = 2.0. Insert values directly without rewriting steps.

Apply n₁ sinθ₁ = n₂ sinθ₂ to check bending direction. A ray moving from n = 1.00 to n = 1.33 with a 40° incident angle refracts at 29°, showing a turn toward the normal.

For lens tasks, use 1/f = 1/dₒ + 1/dᵢ. A convex element with f = 0.20 m and dₒ = 0.60 m produces dᵢ = 0.30 m. Indicate sign choice only when requested.

Evaluate magnification using m = −dᵢ/dₒ. With dᵢ = 0.30 m and dₒ = 0.60 m, the output height halves and inverts.

Verify interference spacing using Δx = λL/d. A setup with λ = 620 nm, L = 1.8 m, and slit gap of 0.40 mm gives 2.79 mm between bright lines.

Additional reference: Khan Academy – Science

Calculations Required for Modern Physics Questions

Use E = hf immediately: a photon with f = 7.2×10¹⁴ Hz yields 4.77×10⁻¹⁹ J. Convert to eV by dividing by 1.60×10⁻¹⁹, giving 2.98 eV.

Apply E = mc² for mass–energy tasks. A particle with m = 3.0×10⁻³⁰ kg corresponds to 2.70×10⁻¹³ J. Keep c fixed at 3.00×10⁸ m/s.

For stopping potential, use eVₛ = hf − Φ. If Φ = 2.2 eV and hf = 3.4 eV, then Vₛ = 1.2 V. Omit any extra conversions.

Determine wavelength through λ = h/p. With p = 5.0×10⁻²⁴ kg·m/s, yield 1.33×10⁻¹⁰ m. Apply consistent SI units to maintain precision.

For relativistic kinetic energy, compute γ via γ = 1/√(1 − v²/c²). A particle at 0.80c gives γ = 1.67, producing K = (γ − 1)mc². For m = 9.1×10⁻³¹ kg, K ≈ 8.2×10⁻¹⁴ J.

Apply the threshold relation f₀ = Φ / h. With Φ = 1.8 eV, convert to joules (2.88×10⁻¹⁹ J) and divide by h to obtain 4.35×10¹⁴ Hz.

For nuclear transitions, use ΔE = Δmc². A deficit of 5.0×10⁻³⁰ kg produces 4.50×10⁻¹³ J. Report the numeric value without rephrasing.

Formula References Applied in the Test Solutions

Use direct substitutions into standard relations without altering unit systems.

• F = ma: apply for linear motion tasks with m in kilograms and a in m/s².
• v² = v₀² + 2aΔx: apply for displacement steps where acceleration remains constant.
• p = mv: compute momentum values before using impulse relations.
• FΔt = Δp: apply for collision sequences involving short-time interactions.
• K = ½mv²: use for comparisons between initial and final energy states.
• U = mgh: apply for gravitational potential changes using g = 9.8 m/s².
• W = Fd cosθ: calculate work for angular forces without altering the reference angle.
• P = W/t: compute power output only after confirming units of joules and seconds.
• V = IR: apply for current–resistance checks in circuit tasks.
• P = IV: use for electrical power output once voltage and current are known.
• c = λf: apply for electromagnetic wave calculations using c = 3.00×10⁸ m/s.
• n₁ sinθ₁ = n₂ sinθ₂: use for refraction steps involving indices of media.
• E = hf: compute photon energy values with h = 6.63×10⁻³⁴ J·s.
• E = mc²: apply for mass–energy tasks requiring large-scale conversions.