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Supplied data and formulae

Syllabus
9702–2028–2029
Topic
—
Level
A2

Learning objectives

—D.1-Supplied constants and dataUse supplied constants such as g, c, e, u, particle masses, Avogadro constant, gas constant, Boltzmann constant, gravitational constant, permittivity of free space, Planck constant and Stefan-Boltzmann constant.—D.3-A Level formulae supplied in Paper 4Select and apply supplied A Level formulae for gravitational potential, ideal gases, simple harmonic motion, electric potential, capacitors, Hall voltage, alternating current, radioactive decay, acoustic impedance, Stefan-Boltzmann law and Doppler redshift.—D.4-Choosing formulae without losing physical reasoningDecide whether a supplied formula is appropriate, identify each variable, convert units, rearrange correctly and explain the physical meaning of the result rather than relying on substitution alone.

Identify each supplied constant by physical role, unit and scale

g=9.81ms−2nearEarthG=6.67×10−11Nm2kg−2u=1.66×10−27kgg=9.81 m s⁻² near Earth G=6.67×10⁻¹¹ N m² kg⁻² u=1.66×10⁻²⁷ kg

e=1.60×10−19Cme=9.11×10−31kgmp≈mn≈1.67×10−27kgNA=6.02×1023mol−1e=1.60×10⁻¹⁹ C mₑ=9.11×10⁻³¹ kg mₚ≈mₙ≈1.67×10⁻²⁷ kg N_A=6.02×10²³ mol⁻¹

R=8.31JK−1mol−1k=1.38×10−23JK−1R=NAkR=8.31 J K⁻¹ mol⁻¹ k=1.38×10⁻²³ J K⁻¹ R=N_A k

ε0=8.85×10−12Fm−1h=6.63×10−34Jsc=3.00×108ms−1σ=5.67×10−8Wm−2K−4ε₀=8.85×10⁻¹² F m⁻¹ h=6.63×10⁻³⁴ J s c=3.00×10⁸ m s⁻¹ σ=5.67×10⁻⁸ W m⁻² K⁻⁴

Use the value printed on the examination data page. Match the requested model first, copy the unit and exponent carefully, and keep the full supplied value until final rounding.

G is the universal gravitational constant; g is local gravitational field strength/acceleration. u is unified atomic mass, not the micro-prefix μ. e is the positive elementary-charge magnitude; an electron has charge −e.

Attach the missing condition to every supplied AS formula

v=u+at;s=(u+v)t/2s=ut+at2/2;v2=u2+2asOnlyforstraight−linemotionwithconstantacceleration;chooseonepositivedirection.v=u+at; s=(u+v)t/2 s=ut+at²/2; v²=u²+2as Only for straight-line motion with constant acceleration; choose one positive direction.

Δp=ρgΔhforastaticfluidofuniformdensityupthrust=ρfluidgVdisplacedΔp=ρgΔh for a static fluid of uniform density upthrust=ρ_fluid g V_displaced

For the supplied moving-source sound formula, decide whether source motion makes wavefronts closer or farther apart before choosing the sign: approaching raises observed frequency; receding lowers it.

I=AnvqforchargecarriersSeries:R=R1+R2+…Parallel:1/R=1/R1+1/R2+…I=Anvq for charge carriers Series: R=R₁+R₂+… Parallel: 1/R=1/R₁+1/R₂+…

State what each symbol means in this situation, convert to SI, and test the result: series resistance exceeds every component; parallel resistance is below the smallest branch; upthrust uses displaced volume, not automatically total object volume.

Being printed on the sheet does not make an equation universally applicable. Reject SUVAT for changing acceleration and hydrostatic Δp=ρgΔh when density is not adequately constant.

Preserve signs, temperature scales and rms conventions in A Level formulae

gravitationalpotentialφ=−GM/rpV=NkT=nRTwithTinKSHM:a=−ω2x;v2=ω2(x02−x2)gravitational potential φ=−GM/r pV=NkT=nRT with T in K SHM: a=−ω²x; v²=ω²(x₀²−x²)

point−chargepotentialV=Q/(4πε0r)capacitors:series1/C=Σ1/Ci;parallelC=ΣCiHallvoltageVH=BI/(ntq)forthestatedslabgeometrypoint-charge potential V=Q/(4πε₀r) capacitors: series 1/C=Σ1/Cᵢ; parallel C=ΣCᵢ Hall voltage V_H=BI/(ntq) for the stated slab geometry

sinusoidal:Vrms=V0/√2,Irms=I0/√2x=x0e−lambdat;λ=ln2/t1/2sinusoidal: V_rms=V₀/√2, I_rms=I₀/√2 x=x₀e⁻ˡᵃᵐᵇᵈᵃᵗ; λ=ln2/t₁/₂

acousticimpedanceZ=ρcStefanluminosityL=4πr2σT4forsmallredshift:Δλ/λ≈v/cacoustic impedance Z=ρc Stefan luminosity L=4πr²σT⁴ for small redshift: Δλ/λ≈v/c

Before substitution mark the convention: zero potential at infinity, absolute temperature, amplitude versus instantaneous displacement, peak versus rms, decay constant time unit, surface area and small-speed redshift limit.

Do not remove a negative potential because energy magnitude is positive, use °C in pV=NkT or Stefan's law, or mix peak voltage with rms current in average-power calculations.

Choose the model before touching the calculator

  1. Name the system/process. 2. List known and target quantities. 3. State assumptions/conditions. 4. Select a relation containing the target and usable knowns. 5. Rearrange symbolically. 6. convert SI and calculate. 7. check unit, sign, scale and interpretation.

When several models could give energy, identify the transfer mechanism: ΔEₖ=mv²/2 for speed change, ΔEₚ=mgΔh near Earth, W=Fs cosθ for a force through displacement, E=Pt for steady power. Compare like quantities only after calculating each under its conditions.

A formula given in the question may be unfamiliar. Treat it as a model: define each symbol from the stem, inspect powers/roots, rearrange for the requested quantity, and derive the unit from the expression.

Show the selected equation and numerical substitution so method marks remain visible. Keep more figures than the final answer and carry previous answers at full precision where possible.

Finish in physics language: direction from sign, larger/smaller from a ratio, valid/invalid from conditions, or agreement/disagreement within precision. A bare number is not an explanation.

Matching symbol letters is not model selection: the same letter can mean different quantities, and the right variables in a relation do not guarantee that its assumptions hold.