Force,Density & Pressure

Physics Practical Guide: Question 1

Cambridge International AS & A Level (9702/31)

This guide is based on the official mark scheme for Paper 31. Follow these steps meticulously to maximize your marks in Question 1 of the Physics Practical exam.

1(a) Measuring the Initial Angle (θ₀)

Marking Criteria: Value(s) of raw θ₀ to the nearest degree and final θ₀ value in the range 75° < θ₀ < 85°.

What to do:

You will measure an initial angle, θ₀.

To score the mark:

Record your raw value(s) to the nearest degree.
Your final value for θ₀ must be between 75° and 85°.

Tip: Take multiple readings and calculate a mean to ensure accuracy and get a value within the required range.

1(b) Measuring the Mass (m)

Marking Criteria: Value of m in range 3.0 g < m < 6.0 g with unit and to at least 0.1 g.

What to do:

Measure a small mass, m.

To score the mark:

The value must be between 3.0 g and 6.0 g.
Record it to at least one decimal place (e.g., 4.5 g, 5.0 g).
You must include the unit (g).

1(c) Calculating Extension (e)

Marking Criteria: Correct calculation of e with correct unit.

What to do:

You will calculate an extension, e, likely from length measurements.

To score the mark:

Your calculation must be correct.
You must state the correct unit (e.g., cm, m, mm).

1(d) The Main Table of Results

This is where many marks are won or lost. Be systematic and precise.

Marking Criteria	How to Score Full Marks
Number of Readings & Trend (4 marks)	Take at least 6 sets of readings for M (total mass) and the corresponding angle θ. Trend: As M increases, θ must decrease. Your data must show this clearly.
Range of M (1 mark)	Ensure your maximum M - minimum M > 30 g. Plan your experiment to cover a wide range.
Column Headings (1 mark)	Each column must have a quantity and a unit in the correct scientific format. Correct Examples: M / g, θ / °, sin θ, e / cm Incorrect Examples: M(g), sin theta, e (cm)
Consistency (1 mark)	All raw measurements for length L must be recorded to the nearest millimetre (mm). Be consistent.
Significant Figures for sin θ (1 mark)	When you calculate sin θ, the number of significant figures must be the same as, or one more than, the s.f. in your raw θ values. Example: If your θ is 75° (2 s.f.), sin θ can be 0.97 or 0.966 (2 or 3 s.f.).
Correct Values of sin θ (1 mark)	Your calculated values of sin θ must be mathematically correct. Double-check them.

Example Table Structure:

M / g	θ / °	sin θ	e / cm
50.0	65	0.91	12.5
70.0	58	0.85	15.2
90.0	52	0.79	18.1

1(e) The Graph

This is another critical section. Use a sharp pencil and a good ruler.

(i) Drawing the Graph

Aspect	Requirements
Axes (1 mark)	Label both axes with the correct quantities (e.g., sin θ on the x-axis, e / cm on the y-axis). Choose a scale so that your plotted points cover more than half of the graph grid in both directions. Use a clear and simple scale (e.g., 1 large square = 0.1 units, not 0.3 or 0.4).
Plotting (1 mark)	Plot all the points from your table. Points must be small and precise (a fine dot with a circle, or a small x). They must be accurate to within half a small square.
Quality (1 mark)	The trend of your points must be negative. The points must be in a straight line and the scatter must be small. There should be a clear, single straight line that passes close to all points.

(ii) Line of Best Fit (1 mark)

Draw a single, straight line that best represents all your points.
There should be a roughly equal number of points on either side of the line along its entire length.
The line should be thin and sharp.
Anomalous Points: If one point clearly doesn't fit the trend, you may circle it and ignore it when drawing your line. You must have at least 5 points left to use.

(iii) Gradient and Y-Intercept

Component	Requirements
Gradient (1 mark)	Use a large triangle to calculate the gradient. The hypotenuse should be greater than half the length of your line of best fit. Show your working clearly on the graph: Gradient = Δy / Δx. Read off the values accurately to half a small square.
Y-Intercept (1 mark)	Method 1: Read the value directly from the y-axis where your line of best fit crosses it (at x = 0). Method 2: Choose a point on your line (not one of your plotted points), read its (x, y) values, and substitute them into y = mx + c to solve for c.

1(f) Stating P and Q

Marking Criteria: P = candidate's gradient value and Q = candidate's intercept value. Values must not be written as fractions, roots or given to only one significant figure. Correct and consistent units for P and Q.

What to do:

You will be asked to state P (which is your gradient) and Q (which is your y-intercept).

To score the marks:

Values (1 mark): State the values clearly. Do not give them as fractions, roots, or to only one significant figure.
Units (1 mark): Give the correct units for P and Q. These will be the same as the units for your y-axis (e.g., if e was in cm, then P and Q are in cm). Be consistent.

Summary: Key Takeaways for Success

Precision is Key

Record raw data to the specified precision (nearest degree, nearest mm).

Range Matters

Ensure your mass range is wide enough (>30 g difference).

Table Formatting

Use the correct "/ unit" format for headings. It's an easy mark.

Graph Excellence

Label axes, use a good scale, plot points accurately, and draw a thoughtful line of best fit.

Gradient Calculation

Use a large triangle and show your working.

Units, Units, Units

Never forget them in your final answers, your table, or your graph.

Good luck! By following this guide, you are well-prepared to tackle the practical methodically and score highly.

Pendulum Practical — Complete Mark Scheme & Worked Example

Cambridge 9702/34 Q1 — using S = √L₁ + √L₂ (lengths in cm). All values and worked steps included for teacher distribution.

Summary of the model & units

The linearised relation used in this practical is
T = a S + b where S = (√L₁ + √L₂) (units: cm^1/2), T in seconds. The gradient a therefore has units s cm^-1/2, and intercept b has units s.

From the theory (T = 2π√(L/g)), converting L (cm → m) and rearranging gives:
g = (2π / (10 a))²
(the factor 10 appears because √(cm)/10 = √(m) ).

Question-by-question mark scheme & worked example

1(a)(i) — Measure L₁ and L₂ (1 mark)

Requirement: record L₁ and L₂ to nearest mm, include units.

Worked example: L₁ = 53.0 cm, L₂ = 17.0 cm.

1(a)(ii) — Determine period T (2 marks)

Requirement: measure nT where n ≥ 5 (n = 5 used here) and compute T = nT / n; include unit (s).

Worked example (first row): n = 5, nT = 11.450 s ⇒ T = 11.450 / 5 = 2.290 s.

1(b) — Repeat for six sets & table (8 marks)

Requirements & marking points:

Six sets of L₁ (different), L₂ and T (up to 3 marks for full six sets).
At least one L₂ ≤ 6.0 cm (1 mark).
Column headings must include quantity & correct units (1 mark).
Consistent precision: L₁ and L₂ to nearest mm (1 mark).
S = (√L₁ + √L₂) to 3 s.f. (1 mark).
T calculated from nT correctly (1 mark).

Worked data (sample):

L₁ (cm)	L₂ (cm)	S = (√L₁ + √L₂) (cm^1/2)	n	nT (s)	T (s)
53.0	17.0	11.403 → 11.4	5	11.450	2.290
48.0	14.5	10.736 → 10.7	5	10.760	2.152
43.0	12.0	10.022 → 10.0	5	10.060	2.012
38.0	9.5	9.247 → 9.25	5	9.265	1.853
33.0	7.0	8.390 → 8.39	5	8.425	1.685
28.0	4.5	7.413 → 7.41	5	7.425	1.485

1(c)(i) — Plot T (y) vs S (x) (3 marks)

Requirement: label axes (units), use sensible scales, plot points accurately to ±½ small square, points should occupy ≥ half grid and show positive trend.

^1/2) 7.41 8.39 9.25 10.0 10.7 11.40 1.48 1.68 1.85 2.01 2.15 2.29 (11.4, 2.29) (10.7, 2.15) (10.0, 2.01) (9.25, 1.85) (8.39, 1.69) (7.41, 1.49) Δx ≈ 3.99 Δy ≈ 0.803 slope (a) ≈ 0.201 s·cm^-1/2 intercept (b) ≈ -0.004 s

1(c)(ii) — Line of best fit (1 mark)

Draw a thin straight line, balanced about plotted points. If a point is anomalous (clear outlier) mark and ignore it when drawing the best-fit.

1(c)(iii) — Gradient & intercept (2 marks)

Requirement: gradient found using a large triangle (hypotenuse ≥ ½ the drawn line) and intercept read at x = 0 (±½ small square) or calculated via y = ax + b.

Worked (regression / large-triangle): a = 0.201 s·cm^-1/2, b = -0.004 s.

1(d) — Values of a and b with units (2 marks)

Report: a = 0.201 s·cm^-1/2, b = -0.004 s.

1(e) — Calculate g (1 mark)

Formula: g = (2π / (10 a))²

Worked substitution:

a = 0.201 s·cm^-1/2
g = (2π / (10 × 0.201))² ≈ (6.2832 / 2.01)² ≈ (3.126)² ≈ 9.77 m·s^-2 (rounded)

Full marks breakdown (20 marks)

1(a)(i)	1
1(a)(ii)	2
1(b)	8
1(c)(i)	3
1(c)(ii)	1
1(c)(iii)	2
1(d)	2
1(e)	1
Total	20

Teacher notes & common pitfalls

Use S = (√L₁ + √L₂) on the x-axis and label the unit cm^1/2 — students lose marks if S is omitted or in wrong units.
Avoid readings where the bob rises above the lower rod — geometry changes and the model is invalid.
Time ≥5 oscillations (prefer 10 if time allows) and repeat for consistency.
Keep amplitudes small (≤ 10°) to keep SHM approximation valid.
Use a large triangle (≥ half-line) to reduce gradient reading error.

If you would like, I can now:

Provide the same content as a printable PDF (teacher mark scheme) with the SVG graph embedded.
Create a student worksheet PDF (blank table + blank graph grid).
Provide a downloadable PNG version of the graph.

— Sunshine, would you like the PDF versions or the downloadable graph next?