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% Document Info
\author{amstoffel (amstoffel)}
\pdfinfo{
  /Title (a-level-physics-measurements-and-their-errors.pdf)
  /Creator (Cheatography)
  /Author (amstoffel (amstoffel))
  /Subject (A-Level Physics - Measurements and Their Errors Cheat Sheet)
}

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        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{A-Level Physics - Measurements and Their Errors Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{amstoffel (amstoffel)} via \textcolor{DarkBackground}{\uline{cheatography.com/197528/cs/41671/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}amstoffel (amstoffel) \\
  \uline{cheatography.com/amstoffel} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 3rd February, 2024.\\
   Updated 15th February, 2024.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
  www.readability-score.com
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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{3.08574 cm} x{1.89126 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{SI units}}  \tn
% Row 0
\SetRowColor{LightBackground}
mass (m) & kilograms (kg) \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
length (l) & metres (m) \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
time (t) & seconds (s) \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
amount of substance (n) & moles (mol) \tn 
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
temperature (t) & kelvin (K) \tn 
% Row Count 5 (+ 1)
% Row 5
\SetRowColor{white}
electric current (I) & amperes (A) \tn 
% Row Count 6 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Derivation of SI Units}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{A derived unit is comprised of a combination of SI units.} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{These can be derived by using the definition of the unit, or their equations eg. F=ma} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{eg. to find the SI units of force (F), multiply the units of mass and acceleration to give kgms\textasciicircum{}-2 (or N)} \tn 
% Row Count 7 (+ 3)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{This means that every unit can be broken down into its SI base units.} \tn 
% Row Count 9 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{3.08574 cm} p{1.89126 cm} }
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Prefixes}}  \tn
% Row 0
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Tera (T) & 10\textasciicircum{}12 \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Giga (G) & 10\textasciicircum{}9 \tn 
% Row Count 2 (+ 1)
% Row 2
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Mega (M) & 10\textasciicircum{}6 \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
Kilo (K) & 10\textasciicircum{}3 \tn 
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
Centi (c) & 10\textasciicircum{}-2 \tn 
% Row Count 5 (+ 1)
% Row 5
\SetRowColor{white}
Milli (m) & 10\textasciicircum{}-3 \tn 
% Row Count 6 (+ 1)
% Row 6
\SetRowColor{LightBackground}
Micro (µ) & 10\textasciicircum{}-6 \tn 
% Row Count 7 (+ 1)
% Row 7
\SetRowColor{white}
Nano (n) & 10\textasciicircum{}-9 \tn 
% Row Count 8 (+ 1)
% Row 8
\SetRowColor{LightBackground}
Pico (p) & 10\textasciicircum{}-12 \tn 
% Row Count 9 (+ 1)
% Row 9
\SetRowColor{white}
Femto (f) & 10\textasciicircum{}-15 \tn 
% Row Count 10 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{These prefixes could be added before any SI units}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Conversions between units}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{It is possible to convert between different units of the same quantity. Here are some examples listed below:} \tn 
% Row Count 3 (+ 3)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{1 eV =  1.6 × 10\textasciicircum{}–19 J} \tn 
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% Row 2
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\mymulticolumn{1}{x{5.377cm}}{1 kW h = 3 600 000 J or 3.6 MJ (×10\textasciicircum{}6)} \tn 
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\begin{tabularx}{5.377cm}{x{1.44333 cm} x{3.53367 cm} }
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Types of Errors}}  \tn
% Row 0
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Random error & Cause variations in both directions and are usually uncontrollable \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
Systematic error & Caused by faults in the experimental method or apparatus \tn 
% Row Count 5 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Zero error & A type of systematic error caused by uncalibrated equipment \tn 
% Row Count 8 (+ 3)
% Row 3
\SetRowColor{white}
Parallax error & A type of systematic error caused by the apparent position of an object due to the viewing angle \tn 
% Row Count 12 (+ 4)
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\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Reviewing measurements}}  \tn
% Row 0
\SetRowColor{LightBackground}
Precise & Consistent and fluctuate around a mean value \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Accuracy & A measurement that is close to the true value \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\seqsplit{Repeatability} & The original person can redo the experiement and get the same results \tn 
% Row Count 7 (+ 3)
% Row 3
\SetRowColor{white}
\seqsplit{Reproducibility} & A different person does an experiment differently and gets the same results \tn 
% Row Count 10 (+ 3)
% Row 4
\SetRowColor{LightBackground}
\seqsplit{Resolution} & The smallest change in the quantity being measured that gives a recognisable change in reading \tn 
% Row Count 14 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Uncertainty}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{The bounds in which the accurate value can be expected to lie} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{They should be given to the same number of significant figures as the data.} \tn 
% Row Count 4 (+ 2)
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{0.9954 cm} x{3.9816 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Types of Uncertainity}}  \tn
% Row 0
\SetRowColor{LightBackground}
\seqsplit{Absolute} & Uncertainty given as a fixed quantity \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\seqsplit{Fractional} & Uncertainty as a fraction of the measurement \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\seqsplit{Percentage} & Uncertainty as a percentage of the measurement \tn 
% Row Count 6 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Resolution and Uncertainity}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{{\emph{Readings}}}} are when one value is found} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{{\emph{Measurements}}}} are when the difference between 2 readings is found} \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{The uncertainty in a reading is +/- half the smallest division} \tn 
% Row Count 5 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{The uncertainty in a measurement is at least +/- 1 smallest division} \tn 
% Row Count 7 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{The {\bf{{\emph{resolution}}}} of an instrument will affect its uncertainty} \tn 
% Row Count 9 (+ 2)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Digital readings and given values will either have the uncertainty quoted, or assumed to be +/- the last significant digit} \tn 
% Row Count 12 (+ 3)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{For repeated data, the uncertainty is {\emph{half the range}}} \tn 
% Row Count 14 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Reducing Uncertainity}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{You can reduce uncertainty in the following ways:} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{• fixing one end of a ruler so there is only uncertainty in on reading} \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{• measuring multiple times} \tn 
% Row Count 4 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{• (for fractional and percentage) measure larger quantities} \tn 
% Row Count 6 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Combining Uncertainties}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Adding/subtracting data - ADD ABSOLUTE UNCERTAINTIES} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Multiplying/diving data - ADD PERCENTAGE UNCERTAINTIES} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Raising to a power - MULTIPLY PERCENTAGE UNCERTAINITY BY POWER} \tn 
% Row Count 6 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Uncertainties in graphs}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Uncertainties are shown as error bars on graphs} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{A line fo best fit on a graph should go through all error bars (excluding anomalies)} \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{The uncertainity in a gradient can be found by lines of best and worst fit} \tn 
% Row Count 5 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{This can be done using the gradients of the steepest and shallowest lines of best fits} \tn 
% Row Count 7 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{You can also use these two lines to find the uncertainty in the y-intercept} \tn 
% Row Count 9 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Graph}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/amstoffel_1702382017_4.-1.2.3-Worst-and-Best-Lines-of-Fit-3.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Estimation of physical quantities}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\emph{Orders of magnitude}} are powers of ten which describe the size of an object} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{These can be used to compare the sizes of objects} \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Estimation is a skill used to approximate the values of physical quantities, in order to make comparisons, or to check if a value calculated is reasonable.} \tn 
% Row Count 7 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.19448 cm} x{3.78252 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Variables}}  \tn
% Row 0
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\seqsplit{Dependant} & The variable that is being measured \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\seqsplit{Independent} & The variable that is being changed \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Control & Other variables that stay the same \tn 
% Row Count 6 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}