IB Physics HL Topic 6.1: Experimental skills | Notes & Flashcards

IB Physics HL — Experimental skills

Topic 6.1 of IB Physics covers Experimental skills, which is part of Unit 6: Experimental skills. Students explore key concepts including Measurement technique & choosing instruments, Uncertainties & error propagation, Graphing: plotting, best-fit lines & gradients, and more. A strong understanding of experimental skills is essential for IB Physics HL exams and builds the foundation for connected topics across the syllabus.

Higher Level students should use this topic hub as a map: start with the shared sub-topics, then follow the HL-only extensions and exam-skill links where this topic asks for deeper analysis.

Key concepts in Experimental skills

Key Idea: This topic is the experimental-skills toolkit — how you take a measurement, attach an uncertainty to it, push that uncertainty through a calculation, and turn a table of readings into a straight-line graph you can read a physics quantity off. These skills are examined as a whole paper of their own — Paper 1B (data analysis) — built around one experiment. Expect: pick the right instrument and justify it; quote and combine uncertainties; draw a best-fit line and read its gradient (with the steepest/shallowest lines for the gradient's uncertainty); linearize a law and decide whether the data support it; and evaluate the method (random vs systematic error, repeats, anomalies). The same habits — units, significant figures, ± uncertainties — also score easy marks all through Paper 2.

📋 Key rules & formulas

The multiply/divide and power propagation rules carry the data-booklet badge (look for it). The add/subtract rule, the gradient and the gradient-uncertainty are not printed — you reproduce those from the definitions.

\frac{\Delta x}{x}\quad\text{and}\quad \frac{\Delta x}{x}\times 100\%

The three forms of an uncertainty carry the SAME information: absolute Δx (a ± in the unit), fractional = absolute ÷ value, percentage = fractional × 100%.

$\Delta x$: the absolute uncertainty — a ± value in the SAME unit as x
$x$: the measured value
$\tfrac{\Delta x}{x}$: the fractional uncertainty — a plain number, no unit
$\tfrac{\Delta x}{x}\times 100\%$: the percentage uncertainty

\text{if } y = a \pm b \;\Rightarrow\; \Delta y = \Delta a + \Delta b

Add or subtract → add the ABSOLUTE uncertainties. (Not in the booklet, but you must use it.)

$y$: a result found by adding or subtracting measurements
$a, b$: the measured quantities added or subtracted
$\Delta a, \Delta b$: their absolute uncertainties (same unit as the quantity)
$\Delta y$: the absolute uncertainty in the result (same unit)

y = \frac{ab}{c} \;\Rightarrow\; \frac{\Delta y}{y} = \frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c}

Multiply or divide → add the FRACTIONAL (or percentage) uncertainties. Given in the data booklet (Uncertainties page).

$y$: the calculated result (e.g. a density = m ÷ V)
$a, b, c$: the measured quantities multiplied or divided to get y
$\tfrac{\Delta a}{a}$: the fractional uncertainty in a (no unit)
$\tfrac{\Delta y}{y}$: the fractional uncertainty in the result y

y = a^{n} \;\Rightarrow\; \frac{\Delta y}{y} = \left| n \right|\frac{\Delta a}{a}

Power → multiply the fractional uncertainty by the SIZE of the power |n| (½ for a square root, 2 for a square, 3 for a cube). Given in the data booklet.

$y = a^{n}$: the result is a raised to a power n (e.g. area = πr², so r²)
$n$: the power (2 for a square, 3 for a cube, ½ for a square root)
$\tfrac{\Delta a}{a}$: the fractional uncertainty in a (no unit)
$\tfrac{\Delta y}{y}$: the fractional uncertainty in the result (no unit)

m = \frac{\Delta y}{\Delta x}

Gradient of a best-fit line = rise ÷ run, read off TWO well-separated points ON THE LINE (never the raw data points).

$m$: gradient (slope) of the best-fit line — usually a physics quantity
$\Delta y$: rise — change in the y-value between two points ON THE LINE
$\Delta x$: run — change in the x-value over the same interval

\Delta m = \frac{m_{max} - m_{min}}{2}

Uncertainty in the gradient = half the spread between the steepest and shallowest lines that still pass through all the error bars.

$\Delta m$: uncertainty in the gradient
$m_{max}$: gradient of the STEEPEST line that still passes through all the error bars
$m_{min}$: gradient of the SHALLOWEST such line

Y = mX + c

Straight-line form. Rearrange the law so your two plotted quantities match Y and X; the gradient m and intercept c are then physics quantities. c = 0 means 'directly proportional'.

$Y$: the quantity plotted UP the vertical axis (chosen so the graph is straight)
$X$: the quantity plotted ACROSS the horizontal axis
$m$: the gradient — equals a physics constant you are trying to find
$c$: the vertical intercept — 0 for a 'directly proportional' law

📐 Choosing the instrument (resolution)

Instrument	Resolution (smallest division)	Use it to measure
Metre rule	1 mm	lengths from a few cm up to about 1 m
Vernier caliper	0.1 mm	the diameter of a marble or the width of a block
Micrometer screw gauge	0.01 mm	the thickness of a wire or a single sheet of paper
Measuring cylinder	≈ 1 mL	the volume of a liquid
Stopwatch	0.01 s	a time interval (time several swings, then divide)

Choose the instrument whose smallest division is small compared with what you are measuring. A 0.5 mm wire on a mm ruler is hopeless (±0.5 mm is the whole thing) but easy on a micrometer (±0.005 mm). Reading uncertainty from a single instrument = ± half its smallest division.

⚖️ The three propagation rules side by side

Operation	What you do with the uncertainties	Booklet?
Add or subtract (+ , −)	Add the ABSOLUTE uncertainties: Δy = Δa + Δb	No — derived
Multiply or divide (× , ÷)	Add the FRACTIONAL (or %) uncertainties: Δy/y = Δa/a + Δb/b + …	Given (6.1)
Power (aⁿ)	Multiply the fractional uncertainty by \|n\|: Δy/y = \|n\|·Δa/a	Given (6.1)

🎯 Random vs systematic error

	Random error	Systematic error
What it does	Scatters readings either side of the true value	Shifts EVERY reading the same way (a zero error, a wrong calibration)
Affects	Precision (the spread)	Accuracy (how close to the true value)
Repeat & average?	Yes — the scatter partly cancels, shrinking it	No — averaging does nothing; you must fix the instrument or method
On a graph	Points scatter about the best-fit line	A non-zero intercept, or every point shifted

A straight line alone only means the law is linear (Y = mX + c). It is directly proportional only if the line also passes through the origin (c = 0). Equivalently, the ratio Y/X is constant across every row of the table.

✏️ Worked exam-style questions

IB-style questionDetermine[4 marks]

A student measures the thickness of one sheet of paper. A micrometer (resolution 0.01 mm, so ±0.005 mm) on a single sheet would give a fractional uncertainty of nearly 7%. Instead they measure a stack of 80 sheets and get 8.40 mm with the same ±0.005 mm. (a) Find the thickness of one sheet. (b) Find the absolute and percentage uncertainty in the thickness of one sheet, and say why this method is better.

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IB-style questionDetermine[4 marks]

A small cube has side L = 2.00 ± 0.01 cm and mass m = 64.0 ± 0.5 g. The density is ρ = m ÷ V, where V = L³. (a) Find the density. (b) Find its percentage uncertainty. (c) Quote ρ with its absolute uncertainty.

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IB-style questionDetermine[4 marks]

On a force-versus-extension graph the best-fit line passes through (0, 0). Two points read off THE LINE are (0.020 m, 2.4 N) and (0.080 m, 9.6 N). The steepest and shallowest lines through the error bars have gradients 124 N m⁻¹ and 116 N m⁻¹. (a) Find the spring constant from the best-fit gradient. (b) Find the uncertainty in the gradient and quote k properly.

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IB-style questionShow that[4 marks]

Theory predicts the depth d a marker sinks is d = k√P, where P is the water pressure. (a) State what to plot on each axis to get a straight line through the origin, and what the gradient represents. (b) A classmate instead claims d is directly proportional to P. Using the rows (P = 4.0 kPa, d = 3.1 cm) and (P = 9.0 kPa, d = 4.6 cm), show that this claim is wrong.

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🧠 Quick self-check

Tap each card to reveal the answer.

Which instrument for a 0.5 mm wire diameter, and why? A micrometer (resolution 0.01 mm). Its smallest division is tiny compared with 0.5 mm, so the percentage uncertainty is small. A mm ruler (±0.5 mm) would be useless here.

What are the three ways to quote an uncertainty? Absolute (a ± value in the unit), fractional (absolute ÷ value), and percentage (fractional × 100%). They all carry the same information.

How do uncertainties combine for × and ÷, and for a power aⁿ? For × / ÷ add the fractional uncertainties (Δy/y = Δa/a + Δb/b + …). For a power multiply the fractional uncertainty by |n|. Both are GIVEN in the data booklet.

Which points do you use to read a gradient, and how do you get its uncertainty? Two well-separated points on the best-fit line (not the raw data). The uncertainty is Δm = (mₘₐₓ − mₘᵢₙ) ÷ 2 from the steepest and shallowest lines through the error bars.

A graph is a straight line but does NOT pass through the origin — proportional? No. That is linear but not directly proportional. 'Directly proportional' needs the line to pass through the origin (c = 0), i.e. a constant ratio Y/X.

Will repeating and averaging fix a systematic error? No. Averaging only cuts random error (the scatter). A systematic error shifts every reading the same way — you must fix the instrument or method (e.g. correct a zero error).

🎯 Exam tips

Exam Tips

Match the instrument's RESOLUTION to the quantity, and reading uncertainty = ± half the smallest division. To shrink it, measure a MULTIPLE (a stack of sheets, 10 swings) and divide by the exact count.
Pick the right propagation rule by the operation: + or − → add ABSOLUTE uncertainties; × or ÷ → add FRACTIONAL/percentage uncertainties; a power aⁿ → multiply the fractional uncertainty by |n|. The last two are in the data booklet.
In a quotient with a power (like ρ = m ÷ L³), the side's fractional uncertainty counts |n| times — here three times — so that term usually dominates. Measure the powered quantity most carefully.
Round the absolute uncertainty to 1 significant figure, then match the value to the same decimal place: ρ = 8.0 ± 0.2 g cm⁻³, never 8.00 ± 0.23.
Read a gradient off TWO well-separated points ON the best-fit line, not the data points. State what the gradient represents and give its units — it is always a physics quantity.
For the gradient's uncertainty, draw the steepest and shallowest lines that still pass through all the error bars, then Δm = (mₘₐₓ − mₘᵢₙ) ÷ 2.
Linearize by rearranging the law to Y = mX + c, then plot Y against X. 'Directly proportional' demands a straight line THROUGH THE ORIGIN (or a constant ratio across rows) — a straight line alone is only 'linear'.
Random error scatters readings → cut it by repeating and averaging. Systematic error shifts them all the same way → averaging won't help; fix the instrument or method. Always discard a clear anomaly before averaging.
Dimensional analysis: balance the fundamental SI units (kg, m, s, A) on both sides to find an unknown exponent, or to state the units of a constant read off a gradient (y-axis units ÷ x-axis units).

IB Physics HL — Experimental skills

Higher Level students should use this topic hub as a map: start with the shared sub-topics, then follow the HL-only extensions and exam-skill links where this topic asks for deeper analysis.

Key concepts in Experimental skills

Key Idea: This topic is the experimental-skills toolkit — how you take a measurement, attach an uncertainty to it, push that uncertainty through a calculation, and turn a table of readings into a straight-line graph you can read a physics quantity off. These skills are examined as a whole paper of their own — Paper 1B (data analysis) — built around one experiment. Expect: pick the right instrument and justify it; quote and combine uncertainties; draw a best-fit line and read its gradient (with the steepest/shallowest lines for the gradient's uncertainty); linearize a law and decide whether the data support it; and evaluate the method (random vs systematic error, repeats, anomalies). The same habits — units, significant figures, ± uncertainties — also score easy marks all through Paper 2.

📋 Key rules & formulas

\frac{\Delta x}{x}\quad\text{and}\quad \frac{\Delta x}{x}\times 100\%

The three forms of an uncertainty carry the SAME information: absolute Δx (a ± in the unit), fractional = absolute ÷ value, percentage = fractional × 100%.

$\Delta x$: the absolute uncertainty — a ± value in the SAME unit as x
$x$: the measured value
$\tfrac{\Delta x}{x}$: the fractional uncertainty — a plain number, no unit
$\tfrac{\Delta x}{x}\times 100\%$: the percentage uncertainty

\text{if } y = a \pm b \;\Rightarrow\; \Delta y = \Delta a + \Delta b

Add or subtract → add the ABSOLUTE uncertainties. (Not in the booklet, but you must use it.)

$y$: a result found by adding or subtracting measurements
$a, b$: the measured quantities added or subtracted
$\Delta a, \Delta b$: their absolute uncertainties (same unit as the quantity)
$\Delta y$: the absolute uncertainty in the result (same unit)

y = \frac{ab}{c} \;\Rightarrow\; \frac{\Delta y}{y} = \frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c}

Multiply or divide → add the FRACTIONAL (or percentage) uncertainties. Given in the data booklet (Uncertainties page).

$y$: the calculated result (e.g. a density = m ÷ V)
$a, b, c$: the measured quantities multiplied or divided to get y
$\tfrac{\Delta a}{a}$: the fractional uncertainty in a (no unit)
$\tfrac{\Delta y}{y}$: the fractional uncertainty in the result y

y = a^{n} \;\Rightarrow\; \frac{\Delta y}{y} = \left| n \right|\frac{\Delta a}{a}

Power → multiply the fractional uncertainty by the SIZE of the power |n| (½ for a square root, 2 for a square, 3 for a cube). Given in the data booklet.

$y = a^{n}$: the result is a raised to a power n (e.g. area = πr², so r²)
$n$: the power (2 for a square, 3 for a cube, ½ for a square root)
$\tfrac{\Delta a}{a}$: the fractional uncertainty in a (no unit)
$\tfrac{\Delta y}{y}$: the fractional uncertainty in the result (no unit)

m = \frac{\Delta y}{\Delta x}

Gradient of a best-fit line = rise ÷ run, read off TWO well-separated points ON THE LINE (never the raw data points).

$m$: gradient (slope) of the best-fit line — usually a physics quantity
$\Delta y$: rise — change in the y-value between two points ON THE LINE
$\Delta x$: run — change in the x-value over the same interval

\Delta m = \frac{m_{max} - m_{min}}{2}

Uncertainty in the gradient = half the spread between the steepest and shallowest lines that still pass through all the error bars.

$\Delta m$: uncertainty in the gradient
$m_{max}$: gradient of the STEEPEST line that still passes through all the error bars
$m_{min}$: gradient of the SHALLOWEST such line

Y = mX + c

Straight-line form. Rearrange the law so your two plotted quantities match Y and X; the gradient m and intercept c are then physics quantities. c = 0 means 'directly proportional'.

$Y$: the quantity plotted UP the vertical axis (chosen so the graph is straight)
$X$: the quantity plotted ACROSS the horizontal axis
$m$: the gradient — equals a physics constant you are trying to find
$c$: the vertical intercept — 0 for a 'directly proportional' law

📐 Choosing the instrument (resolution)

Instrument	Resolution (smallest division)	Use it to measure
Metre rule	1 mm	lengths from a few cm up to about 1 m
Vernier caliper	0.1 mm	the diameter of a marble or the width of a block
Micrometer screw gauge	0.01 mm	the thickness of a wire or a single sheet of paper
Measuring cylinder	≈ 1 mL	the volume of a liquid
Stopwatch	0.01 s	a time interval (time several swings, then divide)

Choose the instrument whose smallest division is small compared with what you are measuring. A 0.5 mm wire on a mm ruler is hopeless (±0.5 mm is the whole thing) but easy on a micrometer (±0.005 mm). Reading uncertainty from a single instrument = ± half its smallest division.

⚖️ The three propagation rules side by side

Operation	What you do with the uncertainties	Booklet?
Add or subtract (+ , −)	Add the ABSOLUTE uncertainties: Δy = Δa + Δb	No — derived
Multiply or divide (× , ÷)	Add the FRACTIONAL (or %) uncertainties: Δy/y = Δa/a + Δb/b + …	Given (6.1)
Power (aⁿ)	Multiply the fractional uncertainty by \|n\|: Δy/y = \|n\|·Δa/a	Given (6.1)

🎯 Random vs systematic error

	Random error	Systematic error
What it does	Scatters readings either side of the true value	Shifts EVERY reading the same way (a zero error, a wrong calibration)
Affects	Precision (the spread)	Accuracy (how close to the true value)
Repeat & average?	Yes — the scatter partly cancels, shrinking it	No — averaging does nothing; you must fix the instrument or method
On a graph	Points scatter about the best-fit line	A non-zero intercept, or every point shifted

A straight line alone only means the law is linear (Y = mX + c). It is directly proportional only if the line also passes through the origin (c = 0). Equivalently, the ratio Y/X is constant across every row of the table.

✏️ Worked exam-style questions

IB-style questionDetermine[4 marks]

🔒 Model answer plan

See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.

Unlock free for 7 days →

IB-style questionDetermine[4 marks]

🔒 Model answer plan

See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.

Unlock free for 7 days →

IB-style questionDetermine[4 marks]

🔒 Model answer plan

See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.

Unlock free for 7 days →

IB-style questionShow that[4 marks]

🔒 Model answer plan

See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.

Unlock free for 7 days →

🧠 Quick self-check

Tap each card to reveal the answer.

🎯 Exam tips

Exam Tips

Match the instrument's RESOLUTION to the quantity, and reading uncertainty = ± half the smallest division. To shrink it, measure a MULTIPLE (a stack of sheets, 10 swings) and divide by the exact count.
Pick the right propagation rule by the operation: + or − → add ABSOLUTE uncertainties; × or ÷ → add FRACTIONAL/percentage uncertainties; a power aⁿ → multiply the fractional uncertainty by |n|. The last two are in the data booklet.
In a quotient with a power (like ρ = m ÷ L³), the side's fractional uncertainty counts |n| times — here three times — so that term usually dominates. Measure the powered quantity most carefully.
Round the absolute uncertainty to 1 significant figure, then match the value to the same decimal place: ρ = 8.0 ± 0.2 g cm⁻³, never 8.00 ± 0.23.
Read a gradient off TWO well-separated points ON the best-fit line, not the data points. State what the gradient represents and give its units — it is always a physics quantity.
For the gradient's uncertainty, draw the steepest and shallowest lines that still pass through all the error bars, then Δm = (mₘₐₓ − mₘᵢₙ) ÷ 2.
Linearize by rearranging the law to Y = mX + c, then plot Y against X. 'Directly proportional' demands a straight line THROUGH THE ORIGIN (or a constant ratio across rows) — a straight line alone is only 'linear'.
Random error scatters readings → cut it by repeating and averaging. Systematic error shifts them all the same way → averaging won't help; fix the instrument or method. Always discard a clear anomaly before averaging.
Dimensional analysis: balance the fundamental SI units (kg, m, s, A) on both sides to find an unknown exponent, or to state the units of a constant read off a gradient (y-axis units ÷ x-axis units).

IB Physics HL — Experimental skills

Key concepts in Experimental skills

📋 Key rules & formulas

📐 Choosing the instrument (resolution)

⚖️ The three propagation rules side by side

🎯 Random vs systematic error

✏️ Worked exam-style questions

🧠 Quick self-check

🎯 Exam tips

Exam Tips

What you'll learn in Topic 6.1

Study resources — 6.1 Experimental skills

Measurement technique & choosing instruments

Uncertainties & error propagation

Graphing: plotting, best-fit lines & gradients

Linearizing relationships & testing a law

Evaluating method & dimensional analysis

Ready to study Experimental skills?

Ready to practice?

IB Physics HL — Experimental skills

Key concepts in Experimental skills

📋 Key rules & formulas

📐 Choosing the instrument (resolution)

⚖️ The three propagation rules side by side

🎯 Random vs systematic error

✏️ Worked exam-style questions

🧠 Quick self-check

🎯 Exam tips

Exam Tips

What you'll learn in Topic 6.1

Study resources — 6.1 Experimental skills

Measurement technique & choosing instruments

Uncertainties & error propagation

Graphing: plotting, best-fit lines & gradients

Linearizing relationships & testing a law

Evaluating method & dimensional analysis

Ready to study Experimental skills?

Ready to practice?