Physics · Lesson 29

Practical 2: results tables, graphs, slopes and precautions

WAECNECO

What the syllabus asks

WAEC: recording observations (tables, units, significant figures), graph plotting, slope and intercept, deducing constants, precautions and sources of error. Applies to all practical topics in the syllabus.

NECO: recording observations (tables, units, significant figures), graph plotting, slope and intercept, deducing constants, precautions and sources of error. Applies to all practical topics in the syllabus.

What you will learn

Construct a results table that meets examiners’ criteria.
Write correct units for derived quantities such as T², 1/u and sin i.
Choose axes and scales and plot points accurately.
Draw a line of best fit and handle anomalous points.
Calculate slope and intercept with units.
Linearise standard formulae and deduce constants.
State creditable precautions and sources of error.
Answer short theory items linked to experiments.

Key points

Tables: headings with units, 5–6 readings, consistent precision.
First-named quantity goes on the y-axis.
Scale 1, 2 or 5 per square; cover over half the grid.
One thin best-fit line; balanced scatter; ring anomalies.
Slope from a large triangle on the line, with unit and sign.
Intercepts only from a true zero; else c = y − mx.
Rearrange formula to y = mx + c to deduce constants.
Check answers are sensible (g ≈ 9.8 m s⁻²).
Precautions: specific, past tense, really taken.
Part (b): precise definitions and three-line calculations.

Start here: Anatomy of a results table

In unit pp1 you learned to take readings well. Now you must present them so that an examiner can award marks quickly. In WAEC and NECO marking, the results table is not just a place to store numbers: it is marked for its own sake, and so is the graph drawn from it. In a 25-mark question, the table and graph together usually carry roughly half the marks.

A model results table has five features:

A heading for every column, including the columns of calculated values (T, T², 1/x, sin i).
Units in every heading, written in the form quantity / unit (for example l / cm, T / s, T² / s²) or quantity (unit). Units are then not written beside each number in the body of the table.
Enough readings, normally the number asked for (five or six sets), spread across the full allowed range.
Raw readings first, then derived values, from left to right in the order you obtain them: the quantity you set (independent variable), the quantity you measure, then each calculated column.
Consistent precision: every value in a column of readings to the same number of decimal places (the precision of the instrument); every calculated value in a column to the same number of significant figures (normally three).

Table 2.1 shows a model table from an experiment you will meet again in unit pp3: masses m are hung from a spiral spring, the spring is set oscillating, and the time t for 20 oscillations is measured for each mass.

Table 2.1 Model results table: loaded spring (k unknown)
m / kg	t (20 osc) / s	T / s	T² / s²
0.10	13.3	0.665	0.442
0.15	16.0	0.800	0.640
0.20	18.3	0.915	0.837
0.25	20.4	1.020	1.04
0.30	22.2	1.110	1.23
0.35	23.9	1.195	1.43

Look at what the examiner sees at a glance. Six readings, evenly spaced over 0.10 kg to 0.35 kg. Times to 0.1 s (stopwatch precision). T = t/20 to three significant figures. T² to three significant figures. Every heading has a unit. Nothing is crossed out in a way that hides the original reading; if you must correct a value, put a single line through it and write the new value beside it.

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Practice questions

1. Give the units of the slope of: (a) T² / s² against l / m (b) V / V against I / A (c) sin i against sin r.

Show worked answer

(a) s² m⁻¹ (b) V A⁻¹ = Ω (c) no unit.

2. A slope triangle on a line runs from (10, 0.25) to (90, 2.65). Find the slope.

Show worked answer

(2.65 − 0.25)/(90 − 10) = 2.40/80 = 0.0300.

3. A line has slope 0.50 and passes through (40, 26). Its x-axis starts at 30. Find the y-intercept.

Show worked answer

c = 26 − 0.50 × 40 = 6.0 (calculated, because the x-axis has a false origin).

4. Values of y range from 0 to 7.6 and you have 8 large squares on the y-axis. Choose a scale.

Show worked answer

7.6 ÷ 8 = 0.95 per square; round up to 1 unit per large square.

5. Rewrite T = 2π√(l/g) in the form y = mx + c and state what is plotted.

Show worked answer

T² = (4π²/g) l: plot T² (y) against l (x); slope = 4π²/g; intercept = 0.

Key words

Independent variable: Quantity the experimenter sets (plotted on x).
Dependent variable: Quantity measured in response (usually on y).
Slope: Δy/Δx of a straight line; carries units.
Intercept: Value of y where x = 0.
False origin: Axis starting at a non-zero value.
Line of best fit: Straight line balancing the scatter of points.
Anomalous point: Reading that does not fit the trend.
Linearise: Rearrange a formula so a graph is a straight line.
Significant figures: Digits that carry meaning in a value.
Precaution: Specific step taken to improve accuracy.
Source of error: Factor that could make a result inaccurate.
Effective mass: Part of the spring mass that moves with the load.

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