Q1 Planning — Mark Breakdown (always fixed)

Section	Marks	What earns marks
Defining the problem	2	Name IV and DV explicitly. State every remaining symbol in the equation as controlled.
Methods of data collection	6	Labelled diagram. How to measure each variable. Correct instrument connections.
Method of analysis	3	Which graph to plot. What gradient equals. What y-intercept equals. Validity statement.
Additional detail + safety	6	Any 6 from ~10 listed points covering safety, measurement, precision, validity.

Control variables ruleList every symbol in the equation. Remove IV, DV, and universal constants (g, π, c). Everything left must be stated as "kept constant". One missing = 0/1 for that mark.

Q2 Analysis — Sub-Part Structure

Structure varies between papers(a)→(b)→(c)(i–iv) are always identical. After (c)(iv) the labelling varies: some papers end at (e), others have (f). Always read the paper carefully. The 6 graphing marks in (c) are always the same.

Part	Marks	What earns marks
(a)	1	Gradient and y-intercept in terms of constants. If equation has no intercept term, only gradient is asked.
(b)	2	Calculated column(s) + absolute uncertainties. Sometimes two new columns (e.g. s25: lg λ and lg μ).
(c)(i)	2	6 points plotted + all error bars (symmetrical, correct length).
(c)(ii)	2	Best-fit line (balanced) + worst acceptable line. Both clearly labelled.
(c)(iii)	2	Gradient of best-fit + uncertainty. Points > ½ line length apart.
(c)(iv)	2	y-intercept via y = mx + c substitution + uncertainty. False origin method not credited.
(d) onwards	3–4	Physical constants with SI units + uncertainties. Final substitution calculation.

Q1 Linearisation — All Types Seen

y = Axⁿ Plot lg y vs lg xgradient = n · intercept = lg A → A = 10^c

y = Ae^kx Plot ln y vs xgradient = k · intercept = ln A → A = e^c

y = Ae^−kx Plot ln y vs xgradient = −k (negative). Check sign.

Already linear Plot y vs x directlyx may be a function: e.g. sin(4θ). Do NOT take logs of a linear equation.

Trig equations (s25 type — new)If the equation is already y = mx + c but x involves sin/cos/tan, plot y vs trig(x). The mark scheme explicitly rejects logarithms in this case.

Validity statement"Relationship valid IF a straight line is produced passing through [expected intercept]." Never "through origin" unless intercept = 0.

Q2 Uncertainty Propagation

y = 1/xδy = δx/x² · fractional: δy/y = δx/x

y = ln xδy = δx/x

y = lg xδy = 0.434 × δx/x

y = √xδy/y = ½ · (δx/x)

y = xⁿδy/y = |n| · (δx/x)

y = A·B or A/Bδy/y = δA/A + δB/B

From graph

Δgradient = |m_best − m_worst|

% unc(constant) = (Δm/m + Δc/c) × 100

Log scale special case

If constant = 10^(y-intercept):
Δk = 10^(c_best) − 10^(c_worst)

Why different?k = 10^c is non-linear. The fractional formula only applies to products/quotients. Must compute 10^c at best and worst intercept and subtract.

Q1 Additional Detail — Full Category List

Safety — name hazard + specific precaution (e.g. "cushion if load falls", "goggles from sharp wire", "gloves from hot coil")
Repeat + average — for DV at each IV value
Measure secondary quantity — diameter → micrometer; mass → balance; B → Hall probe; angle → protractor or trig
Multiple measurements of same quantity — different positions/orientations; average (e.g. diameter along length and around rod)
Derived quantity formula — e.g. A = πd²/4, ρ = m/AL, v = √(2gh), k = mg/extension
Ruler alignment — clamped parallel/perpendicular to motion; set square to verify vertical
Fiducial mark — pin or marker at equilibrium/reference position
Control method in practice — specific action to keep variable constant (e.g. remark ball contact point as θ changes)
Increase data range — use large IV values; drop from greater height for larger d values
Video/slow-motion — camera + slow playback + ruler in view for fast/small displacements or peak EMF
Oscilloscope reading — T = timebase × divisions, f = 1/T; V = y-gain × divisions
Hall probe detail — adjust probe until maximum reading; or measure ± directions and average
Validity statement — straight line confirms relationship; specify expected intercept value

Q2 Graph Drawing — Exact Rules

Points

Within ½ small square of correct position
Point diameter < ½ small square
Line thickness < ½ small square (penalised from s25 onwards)

Error bars

ALL 6 bars plotted — missing any one can cost the WAL mark
Symmetrical about the point
Total length accurate to < ½ small square

Best-fit line

Points balanced on either side — do NOT connect end points

Worst acceptable line (WAL)

Steepest OR shallowest line through ALL error bars
Both lines clearly labelled
All error bars must be plotted or WAL mark cannot be awarded

Gradient

Two points ON the line, > ½ line length apart
Show substitution with values written out
Check units: y-axis units / x-axis units

False origin trapIf y-axis ≠ 0 at origin, do NOT read intercept from graph. Substitute a line point into y = mx + c. ECF explicitly not given for false origin method.

! Most Common Mark-Losing Mistakes

Q1: Only one control variable stated when equation has two or more
Fix: scan every symbol, remove IV/DV/universal constants, state the rest
Q1: Diagram labels missing or instrument wrongly connected
Q1: Safety answer too vague — "be careful" scores nothing
Fix: name the hazard AND the action (e.g. "cushion below spring in case load falls")
Q1: "Straight line through origin" when intercept ≠ 0
Q1: Taking logarithms of a linear equation (trig type)
Q2: Uncertainty in transformed column propagated incorrectly
1/I: δ(1/I) = δI/I² · lg x: δ(lg x) = 0.434×δx/x · √x: δ(√x) = δx/(2√x)
Q2: WAL does not pass through every single error bar
Q2: Gradient points too close together (< ½ line length)
Q2: y-intercept read from graph with false origin
Q2: Missing units or wrong power of ten on physical constants
Q2: % uncertainty uses gradient only — forgetting to add y-intercept fraction
Q2: When k = 10^(intercept), using fractional formula instead of 10^c_best − 10^c_worst

Q1 Diagram Checklist + Q2(a) Rearrangement

Diagram must-haves

Workable arrangement (not a list of equipment)
At least 2 components labelled by name
Voltmeter in parallel · Ammeter in series · Oscilloscope at output
Ruler clamped parallel to what is measured
For B fields: pair of magnets/coils shown with correct orientation
Hall probe shown if B is measured; set square if verifying perpendicular

Q2(a) rearrangement examples

E = 3IR + 4IZ → 1/I = (3/E)R + 4Z/E
Plot 1/I vs R · grad = 3/E · intercept = 4Z/E

I = (E/R)e^(−t/RC) → ln I = −t/(RC) + ln(E/R)
Plot ln I vs t · grad = −1/RC · intercept = ln(E/R)

F = kλ^n → lg F = n·lg λ + lg k
Plot lg F vs lg λ · grad = n · intercept = lg k

R = 4ρL/πYZd² → 1/R = (πYZd²/4ρ)·(1/L)
Plot 1/R vs 1/L · grad only (no intercept term)

No-intercept case (w22)If rearrangement gives y = mx with no constant term, part (a) only asks for gradient. Do not invent an intercept.

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