Errors and uncertainties

Quantity $X$ carries a fractional uncertainty of $x$, while quantity $Y$ carries a fractional uncertainty of $y$. What fractional uncertainty applies to $\frac{X}{Y^2}$?

Feb/March 2016

A student wants to determine a distance of about $10\,\text{cm}$ with a precision of $0.01\,\text{cm}$. Which measuring instrument ought to be used?

Feb/March 2017

Using the measurements shown, a person determines the potential difference across a wire. Which measured quantity makes the largest contribution to the percentage uncertainty in the calculated potential difference?

Feb/March 2018

Four students measure a time interval whose true value is $1.734\,\text{s}$. Each student's reading is given below. Which reading is the most accurate?

Feb/March 2019

A micrometer is being used to measure the diameters of two cylinders. Diameter of first cylinder $= (12.78 \pm 0.02)\,\text{mm}$. Diameter of second cylinder $= (16.24 \pm 0.03)\,\text{mm}$. The difference between the two diameters is then found. What is the uncertainty in this difference?

Feb/March 2020

Length, mass and temperature are all SI base quantities. State two other SI base quantities.

Feb/March 2020

A micrometer screw gauge is used to find the diameter of a copper wire. The reading with the wire in place is shown in diagram 1. The wire is then taken out and the micrometer jaws are closed. The updated reading is shown in diagram 2. What is the diameter of the wire?

Feb/March 2021

A student records the current and the potential difference across a resistor in a circuit. current $= (50.00 \pm 0.01)\,\text{mA}$ potential difference $= (500.0 \pm 0.1)\,\text{mV}$ These readings are then used to find the resistance of the resistor. Determine the percentage uncertainty in the resistance value calculated.

Feb/March 2021

A man whose mass is $75.2\ \text{kg}$ measures his mass three times using a set of weighing scales. The readings he gets are: reading 1 = $80.2\ \text{kg}$, reading 2 = $80.1\ \text{kg}$, reading 3 = $80.2\ \text{kg}$. Which statement best describes the precision and accuracy of the weighing scales?

Feb/March 2022

A student measures quantities in order to work out the density of a liquid in a beaker. The liquid has a height of $0.20\,\text{m} \pm 2\%$ in the beaker. The beaker’s internal diameter is $0.05\,\text{m} \pm 3\%$. The liquid’s mass is $0.36\,\text{kg} \pm 10\%$. Determine the percentage uncertainty in the calculated density of the liquid.

Feb/March 2025

How does a systematic error affect the measurement of a physical quantity?

Feb/March 2025

Explain what the accuracy of a measured value means.

Feb/March 2025

A student determines the density of a liquid by measuring its mass and its volume. His measurements are listed below: mass of empty beaker = $(20 \pm 1)\,\text{g}$; mass of beaker + liquid = $(70 \pm 1)\,\text{g}$; volume of liquid = $(10.0 \pm 0.6)\,\text{cm}^3$. He works out the density of the liquid correctly as $5.0\,\text{g cm}^{-3}$. What is the uncertainty in this value?

May/June 2010

A micrometer screw gauge is used to determine the diameter of a copper wire. Diagram 1 shows the reading when the wire is in place. The wire is then taken out and the jaws of the micrometer are closed. Diagram 2 shows the new reading. What is the diameter of the wire?

May/June 2010

A micrometer screw gauge is being used to find the diameter of a copper wire. With the wire inserted, the reading is shown in diagram 1. The wire is then taken out and the jaws of the micrometer are closed. The new reading is shown in diagram 2. State the diameter of the wire.

May/June 2010

A student determines the density of a liquid by finding its mass and its volume. The measurements are summarised below. mass of empty beaker $= (20 \pm 1)\,\text{g}$ mass of beaker + liquid $= (70 \pm 1)\,\text{g}$ volume of liquid $= (10.0 \pm 0.6)\,\text{cm}^3$ He works out the density of the liquid correctly as $5.0\,\text{g cm}^{-3}$. What is the uncertainty in this value?

May/June 2010

A student determines the density of a liquid by recording its mass and volume. The measurements are summarised below: mass of empty beaker $= (20 \pm 1)\,\text{g}$ mass of beaker + liquid $= (70 \pm 1)\,\text{g}$ volume of liquid $= (10.0 \pm 0.6)\,\text{cm}^3$ He works out the density of the liquid correctly as $5.0\,\text{g cm}^{-3}$. What uncertainty should be assigned to this value?

May/June 2010

A micrometer screw gauge is used to determine the diameter of a copper wire. The measurement taken with the wire in place is shown in diagram 1. The wire is then taken out and the jaws of the micrometer are closed. The updated reading is shown in diagram 2. Determine the diameter of the wire.

May/June 2010

The wire is made of metal and its cross-section has a diameter of about $0.8\,\text{mm}$.

May/June 2010

A three-digit digital voltmeter is used to measure the potential difference across a resistor. The meter’s manufacturer states that its accuracy is $1\%$ and $1$ digit. The voltmeter shows $2.05\,\text{V}$.

May/June 2010

The diagram illustrates an experiment for finding the speed of a small ball as it falls through a clear liquid inside a glass tube at constant speed. Two marks are shown on the tube. The upper mark is located at $115 \pm 1\,\text{mm}$ on the nearby rule, while the lower mark is at $385 \pm 1\,\text{mm}$. The ball reaches the upper mark at $1.50 \pm 0.02\,\text{s}$ and reaches the lower mark at $3.50 \pm 0.02\,\text{s}$. The ball's constant speed is found using $\frac{385 - 115}{3.50 - 1.50} = \frac{270}{2.00} = 135\,\text{mm s}^{-1}$. Which expression gives the fractional uncertainty in the speed value?

May/June 2011

When making reasonable estimates of physical quantities, which statement is incorrect?

May/June 2011

How much uncertainty there is in the momentum of a trolley moving between points X and Y depends on which measuring devices are chosen. Readings for the same trolley taken with different instruments are given below. 1 distance between X and Y measured with a metre rule with cm divisions $= 0.55\,\text{m}$ 2 distance between X and Y measured with a metre rule with mm divisions $= 0.547\,\text{m}$ 3 timings taken with a wristwatch reading to the nearest $0.5\,\text{s}$ at X $= 0.0\,\text{s}$ and at Y $= 4.5\,\text{s}$ 4 timings taken with light gates reading to the nearest $0.1\,\text{s}$ at X $= 0.0\,\text{s}$ and at Y $= 4.3\,\text{s}$ 5 mass of trolley measured with a balance reading to the nearest g $= 6.4 \times 10^{-2}\,\text{kg}$ 6 mass of trolley measured with a balance reading to the nearest $10\,\text{g} = 6 \times 10^{-2}\,\text{kg}$ Which measurements, one for each quantity measured, produce the smallest uncertainty in the trolley's momentum value?

May/June 2011

The diagram illustrates an experiment for measuring the speed of a small ball as it falls through a clear liquid inside a glass tube at constant speed. Two marks are drawn on the tube. The upper mark is at $115 \pm 1\,\text{mm}$ on the nearby rule, while the lower mark is at $385 \pm 1\,\text{mm}$. The ball crosses the upper mark at $1.50 \pm 0.02\,\text{s}$ and crosses the lower mark at $3.50 \pm 0.02\,\text{s}$. The constant speed of the ball is found using $\dfrac{385 - 115}{3.50 - 1.50} = \dfrac{270}{2.00} = 135\,\text{mm s}^{-1}$. Which expression is used to calculate the fractional uncertainty in this speed value?

May/June 2011

The readings for a sample of metal wire are given in Fig. 1.1. They are: length $1750\,\text{mm}$ with uncertainty $\pm 3\,\text{mm}$, diameter $0.38\,\text{mm}$ with uncertainty $\pm 0.01\,\text{mm}$, and resistance $7.5\,\Omega$ with uncertainty $\pm 0.2\,\Omega$.

May/June 2011

For each item below, tick one box to show whether the experimental technique would reduce random error, systematic error or neither. The first row has already been done as an example.

May/June 2011

During an experiment, a radio-controlled car requires $2.50 \pm 0.05\,\text{s}$ to cover $40.0 \pm 0.1\,\text{m}$. What are the car’s average speed and the uncertainty in this value?

May/June 2012

In an experiment carried out to determine the acceleration of free fall using a falling body, what would cause the value obtained to be too large?

May/June 2012

A micrometer screw gauge is used to measure the diameter of a cylindrical metal rod. The diagram gives an enlarged view of the micrometer screw gauge scale when the measurement is being taken. What is the cross-sectional area of the rod?

May/June 2012

A mass is released from rest and travels a distance of $2.0\,\text{m}$ in a vacuum. An observer measures the time for the mass to move through this distance with a stopwatch operated by hand, then repeats the timing twice more. The mean of the three recorded times is used to find a value for the acceleration of free fall, which is calculated as $9.8\,\text{m s}^{-2}$. The measured times are $0.60\,\text{s}$, $0.73\,\text{s}$ and $0.59\,\text{s}$, giving an average of $0.64\,\text{s}$. Which statement is most appropriate for this experiment?

May/June 2012

During an experiment, a radio-controlled car needs $2.50 \pm 0.05\,\text{s}$ to cover $40.0 \pm 0.1\,\text{m}$. What is the car’s average speed and the uncertainty in this value?

May/June 2012

In an experiment to find the acceleration of free fall using a falling body, what would cause the calculated value to be too large?

May/June 2012

The liquid volume $V$ that passes in time $t$ through a pipe of radius $r$ is described by $\frac{V}{t} = \frac{\pi P r^4}{8 C l}$, where $P$ is the pressure difference across the two ends of a pipe of length $l$, and $C$ is determined by the liquid’s frictional effects. An experiment is carried out in order to find $C$. The readings obtained are shown in Fig. 1.1.

May/June 2012

In an experiment used to find the acceleration of free fall $g$, the period of oscillation $T$ and the length $l$ of a simple pendulum were recorded. The estimated uncertainty in the measurement of $l$ is $4\%$, while the estimated uncertainty in the measurement of $T$ is $1\%$. The value of $g$ is found from $g = \frac{4\pi^2 l}{T^2}$. What uncertainty is there in the calculated value of $g$?

May/June 2013

A student carried out an experiment in which an electric current was known to fall with time. The readings obtained, from first to last, were $3.62\,\text{mA}$, $2.81\,\text{mA}$, $1.13\,\text{mA}$, $1.76\,\text{mA}$ and $0.90\,\text{mA}$. Which statement would be unable to account for the anomalous $1.13\,\text{mA}$ reading?

May/June 2013

Which statement is wrong by a factor of $100$ or more?

May/June 2013

The diagram shows the stem of a Celsius thermometer, with markings indicating the initial and final temperature readings. What is the temperature change, written to an appropriate number of significant figures?

May/June 2013

The Young modulus of a wire’s material is to be determined. The Young modulus $E$ is given by the equation $E = \dfrac{4Fl}{\pi d^2 x}$. A known force is used to stretch the wire, and these measurements are recorded. Which measurement contributes the greatest uncertainty to the calculated value of the Young modulus?

May/June 2014

A value $y$ is to be found using the equation below. $y = \frac{px}{q^2}$ The percentage uncertainties for $p$, $x$ and $q$ are given. What is the percentage uncertainty in $y$?

May/June 2014

A thermometer may be read with an accuracy of $\pm 0.5^{\circ}\text{C}$. It is used to measure a temperature increase from $40^{\circ}\text{C}$ to $100^{\circ}\text{C}$. What is the percentage uncertainty in the measurement of the temperature increase?

May/June 2014

The resistance of a lamp is found using the value of the potential difference (p.d.) across it and the value of the current flowing through it. Which statement gives the correct way to combine the uncertainties in the p.d. and in the current?

May/June 2014

A digital caliper is being used to measure the $28.50\,\text{mm}$ width of a plastic ruler. The digital caliper shows readings to the nearest $0.01\,\text{mm}$. How should this reading be recorded correctly?

May/June 2014

The strain energy $W$ stored in a spring depends on its spring constant $k$ and its extension $x$. This spring follows Hooke’s law, and $W$ is found by using the equation below. $W = \frac{1}{2}kx^2$ The spring constant is $100 \pm 2\,\text{N m}^{-1}$ and the extension is $0.050 \pm 0.002\,\text{m}$. What percentage uncertainty is there in the calculated value of $W$?

May/June 2015

An analogue ammeter uses a pointer that travels across a scale. After being used for a long time, the pointer no longer returns completely to zero when the current is switched off, and the meter has become less sensitive at larger currents than it is at smaller currents. Which diagram best shows the calibration graph required to give an accurate current reading?

May/June 2015

One sheet of aluminium foil is folded two times so that a pile of four sheets is formed. The measured total thickness of this pile is $(0.80 \pm 0.02)\,\text{mm}$. A digital calliper with a zero error of $(-0.20 \pm 0.02)\,\text{mm}$ is used for the measurement. What is the percentage uncertainty in the calculated thickness of one sheet?

May/June 2015

In an experiment designed to find the acceleration of free fall $g$, a ball bearing is supported by an electromagnet. Once the current to the electromagnet is turned off, a clock begins and the ball bearing drops. After it has fallen a distance $h$, the ball bearing hits a switch that stops the clock, which records the time $t$ for the fall. If systematic errors make $t$ and $h$ be measured wrongly, which error would have to make $g$ seem larger than $9.81\,\text{m s}^{-2}$?

May/June 2015

A student is provided with a reel of wire with a diameter smaller than $0.2\,\text{mm}$ and must determine the density of the metal. Which pair of instruments would be most appropriate for measuring the volume of the wire?

May/June 2015

A ruler is used by four different students to measure the length of a $15.0\,\text{cm}$ pencil. The measurements are shown on four separate charts. Which chart displays measurements that are precise but not accurate?

May/June 2015

In a basic electrical circuit, the current through a resistor is measured as $(2.50 \pm 0.05)\,\text{mA}$. The resistor is labelled with a value of $4.7\,\Omega \pm 2\%$. If these measurements were applied to determine the power dissipated in the resistor, what percentage uncertainty would the result have?

May/June 2015

When carrying out an experiment, a student should reduce the uncertainty in every measurement as much as possible. In which situation is the student lowering the systematic error in a measurement?

May/June 2016

A student works out the density $\rho$ of steel from measurements made on a steel wire. mass $m = 6.2 \pm 0.1\ \text{g}$ length $l = 25.0 \pm 0.1\ \text{cm}$ diameter $d = 2.00 \pm 0.01\ \text{mm}$ He uses the equation $\rho = \frac{4m}{\pi d^2 l}$. Calculate the percentage uncertainty in his calculated value of density?

May/June 2016

The diagram shows a metre rule resting horizontally on two pivots. The vertical displacement $y$ at the centre of the rule is related by $y = \dfrac{kML^3}{wt^3}$ where $k$ is a constant, $L$ is the separation between the pivots, $M$ is the mass of the rule, $t$ is the thickness of the rule and $w$ is the width of the rule. In an experiment, these values are measured: $L = (80.0 \pm 0.2)\,\text{cm}$ $M = (60 \pm 1)\,\text{g}$ $t = (6.0 \pm 0.1)\,\text{mm}$ $w = (23.0 \pm 0.5)\,\text{mm}$ Which measurement makes the largest contribution to the uncertainty in the calculated value of $y$?

May/June 2016

Estimate the mass, in kg, of a wooden metre rule.

May/June 2016

Describe, separately in each case, what systematic errors and random errors do to readings when a micrometer screw gauge is used to measure the diameter of a wire.

May/June 2016

A student is trying to determine the density $\rho$ of aluminium by measuring a rectangular sheet. mass $m = 51.6 \pm 0.1\,\text{g}$ length $l = 100.0 \pm 0.1\,\text{cm}$ width $w = 10.0 \pm 0.1\,\text{cm}$ thickness $t = 0.20 \pm 0.01\,\text{mm}$ He applies the equation $\rho = \frac{m}{wlt}$ to calculate the density. What is the density value obtained, together with its uncertainty?

May/June 2017

A voltage is measured precisely using a reliable instrument and the result is $2.321\,\text{V}$. Two students, working by two different methods, state that the voltage is $2.33\,\text{V}$ and $2.344\,\text{V}$ respectively. Which statement is correct?

May/June 2017

A caliper is used to measure the edges of a cube. Each edge is found to have a length of $(30.0 \pm 0.1)\,\text{mm}$. These measurements are then applied to determine the volume of the cube. What is the percentage uncertainty in the calculated value of the volume?

May/June 2018

A student records the current through a resistor and the potential difference (p.d.) across it. The current reading has an uncertainty of $4\%$ and the p.d. reading has an uncertainty of $1\%$. The student then determines the resistance of the resistor. What is the percentage uncertainty in the calculated resistance?

May/June 2018

A student places a potential difference $V$ of $(4.0 \pm 0.1)\,\text{V}$ across a resistor with resistance $R$ of $(10.0 \pm 0.3)\,\Omega$ for a duration $t$ of $(50 \pm 1)\,\text{s}$. The student then finds the energy $E$ dissipated by using the equation shown below: $$E = \frac{V^2 t}{R} = \frac{4.0^2 \times 50}{10.0} = 80\,\text{J}.$$ What is the absolute uncertainty in the energy value calculated?

May/June 2018

What can be done to reduce systematic errors during a measurement?

May/June 2018

An analogue voltmeter is used to measure a steady potential difference across a resistor.

May/June 2018

A car’s speedometer display is proportional to the tyre rotation rate. If the tyre diameter changes as the tyre wears, the speed reading on the speedometer becomes inaccurate. A car is fitted with new tyres that each have a diameter of $600\,\text{mm}$. The speedometer has been correctly set for this diameter. As the tyres wear, $6\,\text{mm}$ of material is removed from the outer surface, as shown. Determine the error in the speed indicated by the speedometer after this wear occurs.

May/June 2019

A student wants to find the density $\rho$ of lead. She records the mass and diameter of a small lead sphere: mass $= (0.506 \pm 0.005)\,\text{g}$ diameter $= (2.20 \pm 0.02)\,\text{mm}$. What is the most suitable estimate of the percentage uncertainty in her calculated value of $\rho$?

May/June 2019

The two quantities $p$ and $q$ are directly proportional. Experimental readings are collected and then plotted on a graph of $q$ against $p$. Which graph indicates that the measurements of $p$ and $q$ included random errors?

May/June 2019

A man with a mass of $75.2\,\text{kg}$ uses a set of weighing scales to find his mass three times. The results are: reading 1: $80.2\,\text{kg}$ reading 2: $80.1\,\text{kg}$ reading 3: $80.2\,\text{kg}$. Which statement most suitably describes the precision and accuracy of the weighing scales?

May/June 2019

A micrometer screw gauge is used to determine the diameter of a small uniform steel sphere. The micrometer reading is $5.00\,\text{mm} \pm 0.01\,\text{mm}$. What is the percentage uncertainty in a calculation of the volume of the sphere from these values?

May/June 2019

A cylinder has diameter $d = 0.0125\,\text{m} \pm 1.6\%$. Find the absolute uncertainty for this measurement.

May/June 2019

A reading is made properly, but using a ruler that is at a much higher temperature than the one at which it was calibrated. Because of this increased temperature, the ruler expands. What effect does the higher temperature have on the reading, and how can the reading be made more accurate?

May/June 2020

Two liquid-in-glass thermometers in a liquid that is well mixed are each separately read by $10$ different students. Every student records that one thermometer shows $21\,^{\circ}\text{C}$ and the other shows $23\,^{\circ}\text{C}$. What might account for the discrepancy?

May/June 2020

A micrometer screw gauge is employed to find the diameter of a wire. When the jaws are shut, the micrometer gives a reading of $(-0.05 \pm 0.02)\,\text{mm}$. With the wire placed between the two jaws, the reading becomes $(+1.03 \pm 0.02)\,\text{mm}$. Determine the diameter of the wire.

May/June 2021

Students record the volume of a liquid by using three different measuring instruments X, Y and Z. The actual value of the liquid’s volume is $V$. The students’ outcomes are shown. How many of the instruments are precise and how many are accurate?

May/June 2021

The diagram presents two micrometer readings. What is the difference between these two readings?

May/June 2021

A circular disc has a measured diameter of $(7.0 \pm 0.1)\,\text{mm}$. Determine its area and the absolute uncertainty in the area.

May/June 2021

The acceleration of free fall on Earth is stated as $(10 \pm 2)\,\text{m s}^{-2}$. Which statement is correct?

May/June 2022

Which statement concerning systematic errors is incorrect?

May/June 2022

A micrometer screw gauge is used to determine the diameter of a small, uniform steel sphere. The diameter is measured as $5.00\,\text{mm} \pm 0.01\,\text{mm}$. Using these values, what percentage uncertainty is there in the calculated volume of the sphere?

May/June 2022

From the units listed below, underline every one that is an SI base unit: ampere, degree Celsius, kilogram, newton.

May/June 2022

The actual diameter of a copper pipe is $42.03\ \text{mm}$. A builder measures the pipe’s diameter five times using digital calipers. The readings are given below: $48.01\ \text{mm}$ $47.99\ \text{mm}$ $48.01\ \text{mm}$ $48.00\ \text{mm}$ $47.99\ \text{mm}$ Which statement best describes the builder’s measurements?

May/June 2023

The following two measurements are given for a solid sphere. mass $= (32.5 \pm 0.1)\,\text{g}$ diameter $= (1.87 \pm 0.04)\,\text{cm}$ These measurements are then used to work out the sphere’s density. What is the percentage uncertainty in the density?

May/June 2023

The actual width of a desk is $50.0\,\text{cm}$. Two learners, X and Y, are measuring the desk's width. Learner X uses a tape measure and obtains a width of $(49.5 \pm 0.5)\,\text{cm}$. Learner Y uses a metre rule and obtains a width of $(51.4 \pm 0.1)\,\text{cm}$. Which statement about learner X's measurement is correct?

May/June 2023

A well is 36\,\text{m} deep from ground level to the water surface, as shown in Fig. 1.1. A student wants to determine the depth of the well. To do this, the student intends to let a stone fall down the well and measure the time from the moment the stone is released until the splash is heard when it enters the water.

May/June 2023

A thermometer may be read with an accuracy of $\pm 0.5^\circ\text{C}$. It is used to measure a rise in temperature from $40^\circ\text{C}$ to $100^\circ\text{C}$. What is the percentage uncertainty in the measurement of the temperature rise?

May/June 2024

Quantity $X$ has a percentage uncertainty of $2\%$. Quantity $Y$ has a percentage uncertainty of $4\%$. A quantity $W$ is found using the values of $X$ and $Y$. The percentage uncertainty in $W$ is $8\%$. What relationship could link $W$, $X$ and $Y$?

May/June 2024

When a physical quantity is measured, the result can be affected by random errors as well as systematic errors. Which statement is correct?

May/June 2024

The items listed below include some SI quantities. Underline the one that is not an SI base quantity: charge, current, length, time.

May/June 2024

Four students, A, B, C and D, have finished an experiment aimed at finding the acceleration of free fall, $g$. Each student carried out the experiment three times. The measured values of $g$ are listed in the table. Which set of results shows high precision but low accuracy?

May/June 2025

A ball’s diameter is measured to be $(5.26 \pm 0.02)\,\text{cm}$. Calculate the absolute uncertainty in the ball’s volume.

May/June 2025

Which of the following statements about measurement errors is correct?

May/June 2025

Calipers are used to find the wall thickness of a glass tube. These measurements are taken. internal diameter of the tube = $(10.0 \pm 0.1)\,\text{mm}$ external diameter of the tube = $(12.0 \pm 0.1)\,\text{mm}$ What is the wall thickness of the tube?

May/June 2025

In an experiment with experimental uncertainty, a constant quantity $x_0$ is measured repeatedly. A graph is drawn to display the number $n$ of occasions on which a given value $x$ is recorded. Which graph might be obtained if the measurement of $x_0$ contains a large systematic error but only a small random error?

Oct/Nov 2010

To determine the length of a piece of wire, a metre rule is used. The measured length is $70\,\text{cm}$ correct to the nearest millimetre. How ought this result to be shown in a table of results?

Oct/Nov 2010

The value of $x$ is to be found using the equation $x = P - Q$. $P$ is recorded as $1.27 \pm 0.02\,\text{m}$. $Q$ is recorded as $0.83 \pm 0.01\,\text{m}$. Calculate the percentage uncertainty in $x$ to one significant figure.

Oct/Nov 2010

An experiment with experimental uncertainty is used to measure a fixed quantity $x_0$ repeatedly. A graph is drawn to show how many times, $n$, each measured value $x$ occurs. Which graph would be seen if the measurement of $x_0$ contains a large systematic error but only a small random error?

Oct/Nov 2010

Which statement is incorrect?

Oct/Nov 2011

A micrometer is employed to measure the diameters of two cylinders. Diameter of first cylinder $= 12.78 \pm 0.02\ \text{mm}$ Diameter of second cylinder $= 16.24 \pm 0.03\ \text{mm}$ The difference between the two diameters is then worked out. What is the uncertainty in this difference?

Oct/Nov 2011

A car’s speedometer has a rotating pointer. The pointer is placed a few millimetres away from a calibrated scale. What might produce a random error in the driver’s reading of the car’s speed?

Oct/Nov 2011

Which statement is incorrect?

Oct/Nov 2011

The density of the material in a coil made of thin wire is to be determined. Which collection of instruments would be used to carry this out most accurately?

Oct/Nov 2012

A quantity $X$ depends on temperature $\theta$ as shown. $\theta$ is found from the matching values of $X$ by using this graph. $X$ is measured with a percentage uncertainty of $\pm 1\%$ of its value at all temperatures. Which statement about the uncertainty in $\theta$ is correct?

Oct/Nov 2012

A measurement of a physical quantity can be affected by random errors and by systematic errors. Which statement is correct?

Oct/Nov 2012