Alternative to Practical Skills

General rule. A reading should be quoted to a precision equal to half the smallest division on the scale.

• Metre ruler ($\text{mm}$ divisions): read to nearest $0.5\,\text{mm}$.
• Stopwatch ($0.01\,\text{s}$): record to the displayed precision but acknowledge $\pm 0.2\,\text{s}$ reaction error.
• Vernier callipers: read to $0.1\,\text{mm}$ (or $0.05$).
• Micrometer: read to $0.01\,\text{mm}$.
• Voltmeter / ammeter: read to half the finest scale division.

Avoiding parallax. Read with your eye DIRECTLY in front of the scale at the level of the indicator (mercury column, needle, etc.). Looking at an angle introduces a systematic offset.

Worked. A meniscus reading is between $50.0\,\text{cm}^{3}$ and $50.2\,\text{cm}^{3}$, closer to the lower mark. Record as $50.1\,\text{cm}^{3}$ (estimating to half the smallest division, which is $0.2\,\text{cm}^{3}$).

Tip. Always read from the BOTTOM of the meniscus (curved liquid surface) for transparent liquids in glass.

Tables.

• One column per quantity.
• Heading and unit on top of each column (e.g. "Time / s").
• Use consistent decimal places (matching instrument precision).
• Calculated columns (e.g. averages) ALSO consistent.

Plotting graphs.

1. Choose scales so the plotted points fill at least half of each axis. Use multiples of $1, 2, 5, 10$ (NOT $3$ or $7$).
2. Label axes with quantity AND unit (e.g. "Force / N").
3. Plot ALL data points with a small cross or dot, marking each clearly.
4. Draw best-fit line. Straight line through the cloud, with similar numbers of points above and below. NOT dot-to-dot.
5. Anomalies. Circle clearly anomalous points and IGNORE them when drawing the line.

Gradient. Use the steepest reasonable triangle on your line — base of triangle should be at least $50\%$ of the $x$-axis span. Gradient = $\Delta y / \Delta x$, with units.

Worked. Best-fit line passes through $(0, 2)$ and $(10, 22)$.

• Gradient $= (22 - 2)/(10 - 0) = 2.0\,\text{units of } y \text{ per unit of } x$.

Intercepts. Read directly off the graph or extrapolate using the gradient.

Random errors. Different each time you measure. Examples:

• Reaction-time variations when using a stopwatch.
• Parallax in reading scales.
• Slight environmental variations.

Reducing random error.

• REPEAT measurements and average.
• Time MANY oscillations (then divide by N).
• Increase the size of the measurement (e.g. measure 10 dominoes rather than 1).

Systematic errors. Always in the same direction. Examples:

• Zero error on an ammeter (needle doesn't read 0 when no current flows).
• Miscalibrated thermometer.
• A ruler with a worn end.

Reducing systematic error.

• ZERO the instrument before use.
• Use a different instrument and compare.
• Calibration check.

Precautions Cambridge wants to see in answers:

• Read scale at eye level (avoid parallax).
• Repeat the measurement and average.
• Wait for needle to settle before reading.
• Insulate from drafts (cooling experiments).
• Keep angles small (pendulum).

Worked. A student measures the period of a pendulum five times, getting values $1.20, 1.22, 1.18, 1.21, 1.19\,\text{s}$.

• Mean: $1.20\,\text{s}$.
• Range: $1.22 - 1.18 = 0.04\,\text{s}$ — uncertainty $\sim \pm 0.02\,\text{s}$.
• Reasonable for a stopwatch with $\sim 0.2\,\text{s}$ reaction time, by averaging the random error decreased.

Paper 6 often asks you to PLAN an investigation rather than just analyse data. A good plan has four parts.

1. Identify the variables.

• Independent variable — the one you deliberately CHANGE.
• Dependent variable — the one you MEASURE because it changes in response.
• Controlled variables — everything else, kept CONSTANT.

For example, investigating how the current through a wire depends on the voltage: independent = voltage; dependent = current; controlled = the wire (its length, thickness, material) and its temperature.

2. Describe HOW and explain WHY you control variables. Don't just list them.

• HOW: state the practical step ('use the same wire throughout', 'keep the room temperature steady').
• WHY: explain that if a controlled variable changed too, you could not tell which variable caused the change in the result — it would not be a fair test.

3. Choose a number and range of values for the independent variable. Pick ENOUGH values, spread over a WIDE enough range, to reveal the trend clearly — usually at least five or six values, evenly spaced. Too few values, or values bunched together, give an unreliable graph.

4. Make a reasoned prediction. Where asked, predict the expected result and JUSTIFY it with known physics — e.g. 'I predict extension is proportional to load because the spring obeys Hooke's law'. A prediction must be reasoned, not a guess.

The $\pm 10\%$ accuracy convention. When you compare two results (for example, a value calculated from two parts of a graph, or a measured value against a predicted one), they count as equal within the limits of experimental accuracy if they agree to within $\pm 10\%$ — the standard tolerance at this level of study. If the percentage difference is below $10\%$, state that the results agree; if it is well above, the difference is significant and should be explained.

Cambridge tip. When a question says 'describe how you would investigate...', work through the four planning steps in order — variables, control, values, prediction. Examiners credit each step separately.

Five common Paper 6 question types.

1. Reading instruments and recording in a table. Match the table's precision to the instrument's. Don't add false decimal places.

2. Plotting a graph. Big-scale, labelled, points + best-fit line. ~50% of available marks come from neat plotting.

3. Calculating a gradient or intercept. Big triangle, show the coordinates used, units in the gradient.

4. Calculations from the gradient. Often the gradient links to a physical quantity (e.g. acceleration from $v$-$t$ slope, spring constant from $F$-$x$ slope).

5. Evaluating the experiment. Identify systematic error, suggest improvement, suggest a precaution. Cambridge asks for SPECIFIC suggestions, not generic ones.

Common Cambridge improvements (memorise).

• Use a "fiducial mark" (a fixed reference) for timing oscillations.
• Use a light gate / data logger for fast events.
• Eliminate parallax by reading at eye level / using a mirror behind the scale.
• Average more trials.
• Use a more precise instrument (vernier instead of ruler).

Cambridge tip. When the question says "describe how you would improve the experiment", give SPECIFIC technical answers (light gate, fiducial mark, more trials), not vague ones ("be more careful").