Measurements, uncertainties and graphs (AS) flashcards

Test yourself one card at a time: say the answer, flip, then mark it. Cards you know drop out; the rest come back until you know them. Your progress stays in this browser.

Resolution of an instrument
The smallest change in the quantity that the instrument can show, e.g. 1 mm for a millimetre scale, 0.01 V for a meter showing two decimal places.
Uncertainty of a measurement
The interval either side of the recorded value within which the true value is expected to lie.
Percentage uncertainty
(uncertainty ÷ measured value) × 100%. No unit.
Random error
Error that makes repeated readings scatter unpredictably either side of the true value; reduced by repeating and averaging.
Systematic error
Error that shifts every reading in the same direction by the same amount (or fraction); not reduced by repeating.
Zero error
An instrument reads a non-zero value when the true value is zero, e.g. a newtonmeter showing 0.15 N with nothing attached. A systematic error.
Anomalous reading
A reading that clearly does not fit the pattern of the others — far outside the spread of its repeats or well off the best-fit line.
Best-fit line
A single thin straight line (or smooth curve) with the points scattered evenly either side along its whole length.
Uncertainty of a single reading
± half the resolution of the instrument. (No — learn it)
Uncertainty from repeated readings
± half the range = (largest − smallest) ÷ 2, after removing any anomaly. (No — learn it)
Gradient and intercept of a straight line
gradient = Δy/Δx from a large triangle on the line; intercept c = y − mx using a point on the line. (No — learn it)
Straight-line form for testing a relationship
y = mx + c: m is the gradient, c the intercept on the y-axis. (No — learn it)
Linearise T = 2π√(l/g)
Plot T² against l: straight line through the origin, gradient 4π²/g.
Linearise v² = u² + 2as
Plot v² against s: gradient 2a, intercept u².
Linearise R = ρl/A for a wire
Plot R against l: gradient ρ/A, so ρ = gradient × A; any intercept is contact resistance.
Linearise V = ε − Ir
Plot V against I: gradient −r, intercept ε.
Effect of a constant systematic error on a straight-line graph
The line moves up or down (or sideways): the intercept changes, the gradient does not.
Choosing graph scales
Points cover more than half the grid in each direction; 1, 2 or 5 units (× 10ⁿ) per large square; axes labelled quantity / unit.
How many readings, over what range?
At least 6 different values, spread over the widest range the apparatus allows, roughly evenly spaced; repeat and average where readings can vary.
Why time 10 or 20 oscillations instead of one?
The reaction-time uncertainty is shared over all the cycles, so the percentage uncertainty in the period is 10 or 20 times smaller.
What do you do with an anomaly?
Repeat that reading if possible; otherwise exclude it from the mean or best-fit line, keep it in the table, ring it and say why.
Why is a hand timing's uncertainty not half the stopwatch resolution?
Reaction time varies by tenths of a second, far more than 0.01 s; use half the range of repeats.
Why is a value from a gradient often better than from one reading?
The gradient uses all the points and is unaffected by a constant systematic error such as a zero error.
Recording a results table
Quantity / unit in each heading, no units in the cells, every reading of one quantity to the same number of decimal places set by the resolution.
A thermometer with 1 °C divisions reads 23 °C. Uncertainty and percentage uncertainty?
± 0.5 °C; 0.5 ÷ 23 × 100 = 2.2%.
Repeats: 2.36, 2.41, 2.33, 2.38 s. Mean, uncertainty, percentage uncertainty?
Mean 2.37 s; half range (2.41 − 2.33) ÷ 2 = ± 0.04 s; 0.04 ÷ 2.37 × 100 = 1.7%.
Diameters 0.52, 0.53, 0.51, 0.62, 0.52 mm. Mean and uncertainty?
0.62 mm is anomalous — exclude it. Mean 0.52 mm; half range ± 0.01 mm.
A best-fit line passes through (0.100 m, 0.55 s²) and (0.700 m, 3.08 s²). Gradient?
(3.08 − 0.55) ÷ 0.600 = 4.22 s² m⁻¹.
A T² against l graph has gradient 4.05 s² m⁻¹. Find g.
g = 4π² ÷ 4.05 = 9.75 m s⁻².
Mass 52.7 g, volume 19.4 cm³. Density to an appropriate number of s.f.?
52.7 ÷ 19.4 = 2.716… → 2.72 g cm⁻³ (3 s.f., like the data).
An ammeter with a +0.03 A zero error reads 0.62 A at 4.50 V. Corrected resistance?
I = 0.62 − 0.03 = 0.59 A; R = 4.50 ÷ 0.59 = 7.6 Ω.
Drawing a gradient triangle
Make it cover more than half the line, read both corners from the line (not data points), and show the values.
How many s.f. in a calculated answer?
The same as the least precise data (or one more); keep extra figures in the working and round at the end.
Suggesting an improvement
Be specific and aim at the largest uncertainty: e.g. “light gates and a data logger to remove reaction time”, never just “better equipment”.
Combining percentage uncertainties at AS?
Not needed in Units 1–3: find the percentage uncertainty of single quantities only. Combining them is a Unit 6 skill.
Half the range smaller than half the resolution
Quote half the resolution — the uncertainty cannot be smaller than the instrument allows.

Practise this topicNotes Questions (28)Test builder