path: root/0625/speedrun.tex

\documentclass[aspectratio=169]{beamer}

\title{IGCSE Physics Speed Run}
\subtitle{\alert{UNFINISHED/INCOMPLETE}}
\author{Runxi~Yu}
\institute{YKPS Y10}
\date{Updated \today}

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\begin{document}
\section{Preamble}
\maketitle

\begin{frame}{Information}
	This document, based on the IGCSE Physics Syllabus, was written to aid revision of IGCSE Physics concepts to students who just need to pass the IGCSE Physics examination. Some memory of ZK Physics is expected. This document does not, however, attempt to systematically cover the subject, and some of the concepts are deliberately oversimplified in order to match IGCSE exam strategy.
\end{frame}

\begin{frame}{How to use this revision packet}
	This is the main revision resource that should have been sent to you as part of a larger revision packet. The packet contains a handout document, containing sample questions, reference sheets, and additional explanations.
	
	This document is best viewed interactively and contains hyperlinks to aid navigation. ``IGCSE Physics / \textit{Section name}'' is displayed in the bottom right along with the page number. Click ``IGCSE Physics'' to return to the main contents page; click ``\textit{Section name}'' to return to the section's contents page. All items of the contents pages are clickable. A PDF navigation outline is also available, if your PDF viewer supports it.

	The Git repository that includes all resources used in this speed run:
	\url{https://git.andrewyu.org/andrew/school/igcse-physics-speedrun.git/}
\end{frame}

\begin{frame}{Note to self}
	Remember to re-check the learner guide's syllabus section for highlighted/missing items.
\end{frame}

\begin{frame}[label=Preamble]{Contents}
	\listofunits
\end{frame}

\definecolor{MainColor}{RGB}{78,174,71}
\definecolor{SubColor}{rgb}{0.9591020408163266, 0.9826122448979591, 0.9573877551020409}
\csection{General physics}

\begin{frame}{Measurement}
	Use common sense, and:
	\begin{itemize}
		\item Read perpendicular to the ruler / measuring cylinder to avoid \textbf{parallax error}
		\item Eyes parallel to the \textbf{meniscus} (lowest\footnote{EXCEPT mercury, where the meniscus is the highest point} point of curved liquid surface)
		\item State the unit
		\item Use the correct significant digits
		\item Measure very small intervals by stacking and dividing to obtain average\\[1ex]
			E.g. $\displaystyle\text{thickness of 1 sheet of paper}=\frac{\text{thickness of 20 sheets}}{20}$
	\end{itemize}

	\textbf{Complete question~0(a).}
\end{frame}


\begin{frame}{Vector and scalar quantities}
	\begin{tabular}{|L{12em}|L{20em}|}
		\hline
		{}\hfill\bfseries Scalar quantity\hfill\mbox{} & {}\hfill\bfseries Vector quantity\hfill\mbox{} \\\hline
		Magnitude only & Magnitude and direction \\\hline
		Distance, speed, time, mass, energy, temperature &
		Force, weight, velocity, acceleration, momentum, electric field strength, gravitational field strength \\\hline
	\end{tabular}
\end{frame}


\begin{frame}{Motion basics}
	\begin{align*}
		\text{speed } v &= \frac{\text{distance } s}{\text{time } t}
	\end{align*}
		
	\begin{itemize}
		\item \textbf{Velocity} = speed in a given direction
		\item \textbf{Displacement} = distance in a given direction
		\item $\displaystyle\qty{3.6}{\kilo\metre\per\hour} = \qty{1}{\metre\per\second}$
		\item $\displaystyle \frac{s}{t} = \frac{\left(u+v\right)}{2}$ or $\displaystyle s = \frac{\left(u+v\right)}{2}t$
	\end{itemize}
\end{frame}

\begin{frame}{Acceleration}
	\begin{align*}
		\text{acceleration } a &= \frac{\text{velocity } v}{\text{time } t}
	\end{align*}
	
	\begin{itemize}
		\item $\displaystyle \text{new velocity } v = \text{old velocity } u + at$
 		\item $\displaystyle s = ut + \frac{1}{2} at^2$
		\item $\displaystyle v^2 = u^2 + 2as$ (see method~2 of question~2(a))
		\item (Ignoring air resistance) always \qty{9.8}{\metre\per\second\squared} near Earth surface
		\item $\text{Deceleration} = - \text{acceleration}$
	\end{itemize}
\end{frame}


\begin{frame}{Velocity-time graphs}
	\begin{figure}
		\begin{subfigure}{0.4\textwidth}
			\includegraphics[width=1\textwidth]{vt-1.pdf}
			\caption{Acceleration, constant speed and deceleration}
		\end{subfigure}
		\begin{subfigure}{0.4\textwidth}
			\includegraphics[width=1\textwidth]{vt-variable-acceleration.pdf}
			\caption{Variable acceleration}
		\end{subfigure}
	\end{figure}
	\begin{itemize}
		\item Area under the curve (shaded) is the distance travelled
		\item Find acceleration by drawing tangent and calculating gradient
	\end{itemize}
\end{frame}

\begin{frame}{Distance-time graphs}
	\begin{figure}
		\begin{subfigure}{0.4\textwidth}
			\includegraphics[width=1\textwidth]{st-1.pdf}
			\caption{Constant speed}
		\end{subfigure}
		\begin{subfigure}{0.4\textwidth}
			\includegraphics[width=1\textwidth]{st-2.pdf}
			\caption{Non-constant speed}
		\end{subfigure}
	\end{figure}
	\begin{itemize}
		\item Calculate velocity from gradient of tangent: $\displaystyle\frac{y_A-y_C}{x_A-x_C}$ for point $T$ in fig~(b)
	\end{itemize}
\end{frame}


\begin{frame}{Resultant forces on lines}
	Calculate the resultant of \qty{6}{\newton} to the left and \qty{4}{\newton} to the right.
	\begin{figure}
		\includegraphics{resultant-on-line.pdf}\hfill\mbox{}
	\end{figure}
	
	$\qty{6}{\newton} - \qty{4}{\newton} = \qty{4}{\newton} \text{ to the left}$
\end{frame}


\begin{frame}{Calculating vector resultants}
	Calculate the resultant of two perpendicular forces of \qty{3.0}{\newton} and \qty{4.0}{\newton}.
	
	\begingroup
	\renewcommand{\arraystretch}{1.5}
	\begin{tabular}{|l|l|}
		\hline
		Resultant magnitude & $\displaystyle\sqrt{3.0^2 + 4.0^2} = \qty{5.0}{\newton}$\\\hline
		Resultant angle & $\displaystyle\arctan{\left(\frac{4.0}{3.0}\right)} = \ang{53}$ from the \qty{3.0}{\newton} force\\\hline
	\end{tabular}
	\endgroup
	
	The syllabus doesn't technically require calculations for angles other than \ang{90}, but just use normal trigonometry if it ever occurs on papers.
	
	\textbf{You also need to be able to use scale diagrams to add vectors.\\Complete question~1.}
\end{frame}


\begin{frame}{Effects of forces}{Newton's laws}
	\begin{enumerate}
		\item An object has constant velocity unless acted on by a resultant force.
		\item \alert{$\text{force }F = \text{mass }m\times\text{acceleration }a$ (must be in the same direction)}\\
			i.e. $\unit{\newton} = \unit{\kilo\gram\metre\per\second\squared}$
		\item Every action force has an equal and opposite reaction force.
	\end{enumerate}
\end{frame}

\begin{frame}{Friction}
	\begin{itemize}
		\item Force between two surfaces
		\item Impedes motion (because friction is opposite to motion)
		\item Produces heat — loses energy
		\item \textbf{Friction increases, as speed increases}
		\item E.g. air resistance
	\end{itemize}
\end{frame}

\begin{frame}{Falling bodies}
	\begin{enumerate}
		\item Initially, there is no air resistance and the only force acting on it is weight.
		\item As it falls, it accelerates which increases its speed and therefore increases the air resistance (a type of friction).
		\item This causes the resultant force downwards to decrease.
		\item Therefore the acceleration decreases, so it is not speeding up as quickly.
		\item Eventually they are equal and opposite so there is no resultant force.
		\item So there is no acceleration and the \textbf{terminal velocity} is reached.
	\end{enumerate}
	\textbf{Complete question~3.}
\end{frame}

\begin{frame}{Gravity}
	\begin{itemize}
		\item Objects near to the surface of the Earth approximately accelerates at $\qty{9.8}{\metre\per\second\squared}$.
		\item Weight ($W$, not $G$) is a force by the gravitational field on an object that has mass. $g = \frac{W}{m}$ and $W = mg$. 
		\item Gravitational field strength $g \approx \qty{9.8}{\newton\per\kilo\gram}$.
	\end{itemize}
\end{frame}




\begin{frame}{Elasticity}
	Besides changing the state of movement of an object, forces may produce changes in the size and shape of an object.
	\begin{itemize}
		\item Springs obey Hooke's Law: Below its elastic limit, the extension of the spring is directly proportional to the force pulling on it. The spring constant $k$ follows $k = \frac{F}{x}$ where $F$ is the force and $x$ is the extension.
		\item Elastic bands do not obey Hooke's Law.  The slope of extension-over-force is quite steep at the start and at the end, and beyond the limit it will break.  The breaking point is the elastic limit.
		\item Both springs and elastic bands wouldn't be able to return to its original length when the force is removed, should it go beyond its elastic limit.
		\end{itemize}
\end{frame}
%
%
\begin{frame}{Circular motion}
	A resultant force \emph{not} on the line that the object is moving, changes the direction of the object's movement.
	
	\begin{equation*}
		F = \frac{mv^2}{r}
	\end{equation*}
	
	Properties of motion in a circular path due to \textbf{a force perpendicular to the motion}:
	\begin{itemize}
		\item Speed increases if force increases, with mass and radius constant.
		\item Radius decreases if force increases, with mass and speed constant.
		\item An increased mass requires an increased force to keep speed and radius constant.
	\end{itemize}
\end{frame}
%
\begin{frame}{Momentum}
	\begin{equation*}
		\text{momentum} = \text{mass}\times\text{velocity}
	\end{equation*}
	
	Momentum ($p$), a measure of how easily an object may be brought to rest, is a vector quantity, which has its magnitude measured in \unit{\kilo\gram\metre\per\second}
\end{frame}

\begin{frame}{Collisions}
	When two bodies collide,
	\begin{align*}
		& \text{total momentum of the two bodies before collision}\\ {=\;}& \text{total momentum of the two bodies after collision}
	\end{align*}
	
	Therefore,
	\begin{align*}
		m_1 v_1 + m_2 v_2 \text{ (before)} = m_1 v_1 + m_2 v_2 \text{ (after)}
	\end{align*}
	
	In exams you might be asked to consider a situation where two objects, $A$ and $B$, collide. You know their mass and velocity, and thus momentum, before the collision. You also know the velocity of $A$ after the collision. You are asked to calculate the velocity of $B$. Do you see how?
	
	TODO: Add a PPQ
\end{frame}
%
\begin{frame}{Impulse}
	\begin{itemize}
		\item $\text{Impulse} = F\Delta t = \Delta (mv) = \Delta p$
		\item $\text{Impulse} = \text{change in momentum} = \text{force for a set period of time}$
		\item Units: $\unit{\kilo\gram\metre\per\second} = \unit{\newton\second}$
		\item $\displaystyle F = \frac{\Delta p}{\Delta t}$
	\end{itemize}
\end{frame}

\begin{frame}{Moments}
	We've learned this in ZK Physics, but in summary:
	\begin{equation*}
		\text{moment} = \text{force}\times\text{perpendicular distance from pivot to force}
	\end{equation*}
	
	Note: $\unit{\newton\metre} \ne \unit{joule}$ here because the directions are perpendicular in moments, while the directions are the same in joules.
	
	Conditions for equilibrium:
	\begin{itemize}
		\item Clockwise moment = anti-clockwise moment;
		\item \textbf{AND} no resultant force.
	\end{itemize}
\end{frame}

\begin{frame}{Energy}
	\begin{itemize}
		\item Energy may be stored as kinetic, gravitational potential, chemical, elastic (strain), nuclear, electrostatic and internal (thermal).
		\item Energy is transferred between stores during events and processes, including examples of transfer by forces (mechanical work done), electrical currents (electrical work done), heating, and by electromagnetic, sound and other waves.
		\item Energy is conserved in an isolated system; energy is never created or destroyed, only transferred.
		\item Common ways to ``lose'' energy include producing heat, sound energy, etc.
	\end{itemize}
\end{frame}

\begin{frame}{Energy equations}
	\begin{itemize}
		\item Kinetic energy $= \displaystyle E_k = \frac{1}{2}mv^2$
		\item Gravitational potential energy $= \displaystyle \Delta E_p = mg\Delta h$
		\item Work $= \displaystyle W = Fd = \Delta E$ where $d$ is distance in the same direction as $F$
		\item Power $= \displaystyle p = \frac{\Delta E}{p} = \frac{W}{p}$
	\end{itemize}
	
	\textbf{Complete question~2.}
\end{frame}

\begin{frame}{Density}
	\begin{align*}
		\text{density }\rho &= \frac{\text{mass }m}{\text{volume }V}
	\end{align*}
	
	Measurement of volume for density calculation:
	\begin{itemize}
		\item For regular solids: rulers
		\item For irregular solids: displace water in measuring cylinder
	\end{itemize}
\end{frame}

\begin{frame}{Floating objects}
	\begin{tabular}{|l|l|}
		\hline
		{}\hfill\bfseries Density\hfill\mbox{} & {}\hfill\bfseries Floating condition\hfill\mbox{} \\\hline
		$\text{Object} < \text{fluid}$ & Floats to top \\\hline
		$\text{Object} = \text{fluid}$ & Floats at equilibrium \\\hline
		$\text{Object} > \text{fluid}$ & Sinks\\\hline
	\end{tabular}
	\begin{itemize}
		\item When two liquids don’t mix, the denser one goes below, i.e. water below oil
		\item $\text{``fluid''} \in {\text{liquid}, {gas}}$
		\item Density of air decreases when higher up; so helium balloons ultimately reach equilibrium
	\end{itemize}
\end{frame}

\begin{frame}{Pressure}
	\begin{align*}
		\text{pressure }p &= \frac{\text{force }F}{\text{area } A} & \text{(solids)}\\
		&= \text{density }\rho \times g \times \text{height to liquid surface} & \text{(liquids)}\\\\
		F &= p \times A & \text{(all)}\\
		\\
		\text{Unit} &= \unit{\newton\per\metre\squared}
	\end{align*}
	
	($g$ is the gravitational field strength, which on Earth would be $\qty{9.8}{\meter\per\second\squared}$)
\end{frame}

\definecolor{MainColor}{RGB}{0,80,147}
\definecolor{SubColor}{rgb}{0.94, 0.9726530612244898, 1.0}
\csection{Thermal physics}

\begin{frame}{Conduction}
	Thermal energy is transferred \textbf{through} a material, \textbf{without movement} of the material, from places of higher temperature to places of lower temperature.
	
	Example: Handle of metal spoon in boiling water.
	
	\begin{tabular}{|l|l|l|l|}
		\hline Material & Conductivity & Type & Mechanism\tabularnewline
		\hline Metals  & Good  & Thermal conductor & Delocalized electrons\tabularnewline
		\hline Most other solids  & Bad & \multirow{3}{*}{Thermal insulator} & \multirow{3}{*}{Lattice vibrations}\tabularnewline
		\cline{1-2} \cline{2-2} Liquids  & Bad & &\tabularnewline
		\cline{1-2} \cline{2-2} Gases  & Very bad & &\tabularnewline
		\hline 
	\end{tabular}
	
	\begin{itemize}
		\item Metals ``feel'' colder because it transfer's your hand's heat faster away
		% TODO: SEMICONDUCTORS?
	\end{itemize}
\end{frame}

\begin{frame}{Conductivity experiment}
	Task: Design an experiment to show different thermal conductivity in different materials.
	
	\centering
	\includegraphics{conductivity-materials-experiment.pdf}
\end{frame}

\begin{frame}{Convection}
	Thermal energy is transferred owing to \textbf{movement of the liquid or gas medium} itself.
	
	The liquid or gas expands on heating, so its density falls. They rise to the cooler region, transferring thermal energy in the process. Therefore, convection naturally goes \textbf{up}. The air that moves is called the convection current.
	
	Example: The air conditioners in your dorms.
\end{frame}

\begin{frame}{Radiation}
	Thermal energy is transferred by infrared radiation. All objects emit this radiation.

	Infrared is an electromagnetic wave, so it travels in vacuum. Radiation does not require a medium.
	
	\begin{tabular}{|l|l|}
		\hline Black dull surfaces  & Good absorber and emitter\tabularnewline
		\hline White shiny surface  & Bad absorber and emitter\tabularnewline\hline
	\end{tabular}
	
	Radiation is emitted by all bodies above absolute zero and consists mostly of infrared radiation, but light and ultraviolet are also present if the body is very hot.
\end{frame}

\begin{frame}{Radiation experiment}
Task: Design an experiment to compare absorption in different colors.

\begin{columns}
		\column{0.55\textwidth}
		\includegraphics{radiation-absorption.pdf}
		\column{0.45\textwidth}
		The inside surface of one lid is shiny and of the other dull black. The coins are stuck on the outside of each lid with candle wax. If the heater is midway between the lids, they each receive the same amount of radiation. After a few minutes the wax on the black lid melts and the coin falls off. The shiny lid stays cool and the wax unmelted.
	\end{columns}
\end{frame}

%\begin{frame}{Radiation}{Experiment to demonstrate radiation emission by color}
%	\begin{columns}
%		\column{0.4\textwidth}
%		\includegraphics{radiation-emission.pdf}
%		\column{0.45\textwidth}
%		Some surfaces also emit radiation better than others when they are hot. If you hold the backs of your hands on either side of a hot copper sheet that has one side polished and the other side blackened, it will be found that your hands feel warmer near the dull black surface. The dull black surface is a better emitter of radiation than the shiny one.
%	\end{columns}
%\end{frame}

\begin{frame}{Transfer rate and temperature}
	How does temperature affect thermal transfer?

	\begin{tabular}{|l|l|l|}
		\hline Equal in \& out & Maintain constant temperature\tabularnewline
		\hline More out than in  & Temperature falls\tabularnewline
		\hline More in than out & Temperature rises\tabularnewline
		\hline
	\end{tabular}
		
	But
	
	\begin{tabular}{|l|l|}
		\hline Higher temperature & Faster thermal transfer\tabularnewline
		\hline Lower temperature & Slower thermal transfer\tabularnewline
		\hline
	\end{tabular}
	
	Which means that things will try to reach an equilibrium---of the same temperature.
\end{frame}

\begin{frame}{Practical applications}{E.g. hot water bottles}
	\begin{columns}
		\column{0.3\textwidth}
		\mbox{}\hfill
		\includegraphics{hot-water-bottle.pdf}
		\column{0.45\textwidth}
		Transfer of thermal energy by conduction and convection is minimized by making the flask a double-walled glass vessel with a vacuum between the walls. Radiation is reduced by silvering both walls on the vacuum side.
	\end{columns}
	
	\textbf{Complete question~5.}
\end{frame}

\definecolor{MainColor}{RGB}{111,104,160}
\definecolor{SubColor}{rgb}{0.9648780487804878, 0.963170731707317, 0.9768292682926829}
\csection{Waves}

\begin{frame}{Waves basics}
	Waves transfer energy without transferring matter.
	\begin{itemize}
		\item TODO
		\item \textbf{Mechanical waves}: disturbance in a \textbf{material medium} and are \textbf{transmitted by the particles of the medium vibrating about a fixed position}\\
			Water, sound, seismic, etc.
		\item \textbf{Electromagnetic waves}: carried by photons\\
			See: \hyperlink{Electromagnetic spectrum}{\protect\usebeamercolor[fg]{structure}{Electromagnetic spectrum}}
			\end{itemize}
\end{frame}

\begin{frame}{Longitudinal waves}
	\centering
	\includegraphics{longitudinal.pdf}
	
	\raggedright
	The particles of the transmitting medium vibrate back and forth along the same line as (parallel to) that in which the wave is traveling.
	Examples: Sound waves, seismic P-waves.
\end{frame}

\begin{frame}{Transverse waves}
	\centering
	\includegraphics{transverse.pdf}
	
	\raggedright
	The direction of the disturbance is at right angles to the direction of propagation of the wave.
	Examples: water waves, electromagnetic waves, seismic S-waves.
\end{frame}

\begin{frame}{Transverse wave graphs}
	\centering
	\includegraphics{displacement-time-generic.pdf}
	
	\raggedright
	This is a \textbf{displacement--distance graph}. It shows, at a certain instant of time, the \textbf{displacement (sideways from their equilibrium)} by the parts of the medium vibrating at different distances from the cause of the wave. It therefore shows \textbf{wavelength}, \textbf{amplitude}, \textbf{crests and troughs}, etc. It does \textbf{not} take into account of \textbf{velocity}, \textbf{time}, or \textbf{frequency}.
\end{frame}

\begin{frame}{Transverse wave properties 1}
	\centering
	\includegraphics{displacement-time-generic.pdf}
	
	\raggedright
	\begin{itemize}
		\item \textbf{Wavelength} $\lambda$ is the \textbf{distance between successive crests}. It's basically the ``period'' when we learned about $\sin(x)$ in math, except that period in physics means \textbf{time} between successive crests. People suck at naming.
		\item \textbf{Amplitude} $a$ is the height of a crest or the depth of a trough measured from the equilibrium.
		\item A is \textbf{in phase} with C; B is in phase with D. They have the same speed and same direction, only they're on different parts of the whole wave.
	\end{itemize}
\end{frame}

\begin{frame}{Transverse wave properties 2}
	\begin{itemize}
		\item \textbf{Frequency} $f$ is the number of complete waves/phases each second. It is measured in Hertz (Hz), which means ``times per second''. It is also the number of crests passing a certain fixed point in space per second.
		\item \textbf{Wave speed} $v$ is the distance moved in the direction of travel of the wave by a crest or any point on the wave in 1 second.
	\end{itemize}
\end{frame}

\begin{frame}{The wave-speed equation}
	\begin{columns}
		\column{0.45\textwidth}
		\begin{align*}
			\text{wave speed} &= \text{frequency} \times \text{wavelength}\\
			v &= f\lambda
		\end{align*}
		\column{0.5\textwidth}
		\includegraphics{wave-speed.pdf}
	\end{columns}
\end{frame}

\begin{frame}{Wavefronts and rays}
	\begin{itemize}
		\item A \textbf{wavefront} shows \textbf{similar points in phase} of a progressive transverse wave when extended from 2D to 3D by a flat projection, such as a wave in water.
		\item A \textbf{ray} of a progressive transverse wave shows its \textbf{direction of travel}.
	\end{itemize}
\end{frame}

\begin{frame}{Reflection}
	\centering
	\includegraphics{wave-reflection.pdf}
	
	\raggedright
	\begin{itemize}
		\item Straight water waves are falling on a metal strip placed in a ripple tank.
		\item The \textbf{normal} is the line perpendicular to the surface where the incident wavefront strikes.
		\item The \textbf{angle of incidence} $i$ is equal to the \textbf{angle of reflection} $r$.
	\end{itemize}
\end{frame}

\begin{frame}\plainframetitle{Reflection example}
	TODO: REPLACE
	\includegraphics[width=\textwidth]{reflection-drawing-1.pdf}
	\includegraphics[width=\textwidth]{reflection-drawing-2.pdf}
\end{frame}

\begin{frame}{Refraction}
	\centering
	\includegraphics{wave-refraction.pdf}
	
	\raggedright
	\begin{itemize}
		\item In shallower water, the speed of the wave decreases.
		\item The frequency of the wave stays the same. (You don't need to know why.)
		\item Therefore, the wavelength increases by $v = f\lambda$.
	\end{itemize}
\end{frame}

\begin{frame}\plainframetitle{Refraction example}
	TODO: REPLACE
	\includegraphics[width=\textwidth]{refraction-drawing.pdf}
\end{frame}

\begin{frame}{Diffraction: narrow gap}
	\begin{columns}
		\column{0.47\textwidth}
		\includegraphics[scale=0.6]{diffraction-narrow.pdf}
		\column{0.5\textwidth}
		\begin{itemize}
			\item Diffraction of waves in a ripple tank by a gap that is narrower than the wavelength.
			\item Speed, wavelength and frequency are unchanged. Direction is diffracted.
		\end{itemize}
	\end{columns}
\end{frame}

\begin{frame}{Diffraction: edge or gap}
	\begin{columns}
		\column{0.47\textwidth}
		\includegraphics[scale=0.6]{diffraction-gap.pdf}
		\column{0.5\textwidth}
		\begin{itemize}
			\item Diffraction of waves in a ripple tank by a gap that is larger than the wavelength.
			\item Speed, wavelength and frequency are unchanged. Part of the original wave is preserved.
		\end{itemize}
	\end{columns}
\end{frame}

\begin{frame}{Diffraction, gap size, and $\gamma$}
	\begin{itemize}
		\item Reducing the wavelength with the same gap reduces diffraction.
		\item Increasing the wavelength with the same gap increases diffraction.
		\item Diffraction past an edge increases if the wavelength increases.
	\end{itemize}
\end{frame}

\begin{frame}{Image characteristics}
\end{frame}

\begin{frame}{Reflection of light}
\end{frame}

\begin{frame}{Refraction of light}
\end{frame}

\begin{frame}{Total internal reflection}
\end{frame}

\begin{frame}{Optical fibres}
\end{frame}

\begin{frame}{Thin lenses 1}
\end{frame}

\begin{frame}{Thin lenses 2}
\end{frame}

\begin{frame}{Dispersion of light}
\end{frame}

\begin{frame}[label={Electromagnetic spectrum}]{Electromagnetic spectrum}
\end{frame}

\begin{frame}{Sound}
\end{frame}

\begin{frame}{Echos}
\end{frame}

\begin{frame}{Sound waves}
\end{frame}

\definecolor{MainColor}{RGB}{162,37,124}
\definecolor{SubColor}{rgb}{0.9888442211055276, 0.9511557788944723, 0.9773869346733668}
\csection{Electricity and magnetism}

\begin{frame}{Magnetic materials}
	\begin{itemize}
		\item Magnetic/ferrous/ferromagnetic materials e.g. \ce{Fe}/steel/\ce{Ni}
			\begin{itemize}
				\item Attracted to magnets
				\item May be magnetized temporarily/permanently
			\end{itemize}
		\item Non-magnetic materials e.g. \ce{Al}/wood 
	\end{itemize}
\end{frame}

\begin{frame}{Magnetic poles}
	\begin{itemize}
		\item Magnetic materials that are \textbf{magnetized} (either temporarily or permanently) are magnets
		\item All magnets have have N and S poles
		\item Like poles repel, opposite poles attract
	\end{itemize}
\end{frame}

\begin{frame}{Induced magnetism}
	\begin{columns}
	\column{0.4\textwidth}
	\includegraphics{induced-magnetism.pdf}
	\column{0.5\textwidth}
	Unmagnetized magnetic material can be magnetized by being close to / touching a magnetized magnetic material.
	\end{columns}
	
	\begin{tabular}{|l|l|L{18em}|}
		\hline
		Type & Example & Properties \\\hline
		Soft magnetic material & Iron & Magnetized easily, loses magnetism easily, makes temporary magnets \\\hline
		Hard magnetic material & Steel & Hard to magnetize, but makes permanent magnets \\\hline
	\end{tabular}
\end{frame}

\begin{frame}{Magnetic fields}
	\begin{itemize}
		\item A region in which a magnetic pole experiences a force
		\item Field lines N \textrightarrow{} S
		\item Direction of field at a point = the direction of the force on the N pole of a magnet at that point
		\item Magnetic forces \textleftarrow{} interactions between magnetic fields
		\item Relatively stronger when field lines are closer
	\end{itemize}
	\vfill
	\begin{columns}
		{}\hfill
		\column{0.3\textwidth}
		\includegraphics[width=\linewidth]{single-magnet-field.pdf}
		\hfill\column{0.3\textwidth}
		\includegraphics[width=\linewidth]{double-magnet-field-1.pdf}
		\hfill\column{0.3\textwidth}
		\includegraphics[width=\linewidth]{double-magnet-field-2.pdf}
		\hfill\mbox{}
	\end{columns}
\end{frame}

\begin{frame}{Plotting with a compass}
	(New to the 2023 syllabus, no past paper questions as of Oct/Nov 2023)
	
	\vfill
	
	\begin{columns}
		\column{0.3\textwidth}
		\includegraphics{compass-plot.pdf}
		\column{0.65\textwidth}
		\begin{enumerate}
			\item Start from one pole
			\item Mark the head ($C$) and end ($B$) of the compass
			\item Move the compass's tail to the previous head (move the tail to $C$)
			\item Continue until you reach the other pole (it'll curve there eventually)
		\end{enumerate}
	\end{columns}
The compass's arrow is an N pole.

	\vfill
\end{frame}

\begin{frame}{Plotting with iron filings}
	(New to the 2023 syllabus, no past paper questions as of Oct/Nov 2023)

	\vfill

	\begin{enumerate}
		\item Place a sheet of paper on \textbf{top} of a bar magnet
		\item Sprinkle iron filings thinly and evenly onto the paper from a ``pepper pot''
		\item Tap the paper gently
	\end{enumerate}
	
	\vfill
	
	\begin{itemize}
		\item Quick
		\item \textbf{Not} for weak magnetic fields
	\end{itemize}
	
	\vfill
\end{frame}

\begin{frame}{Field direction from a compass}
	\begin{itemize}	
		\item The arrow of compasses are north poles\\
			So they point in the direction of the magnetic field\\
			(Remember field direction = forces that a north pole experiences)
	\end{itemize}
\end{frame}

\begin{frame}{Uses of electro- and permanent magnets}
	\textbf{Permanent magnets:}
	\begin{itemize}	
		\item Uses in: Compasses, hard disks, motors, generators, microphones, speakers, credit cards, etc.
		\item Does not require a current to retain its magnetism
	\end{itemize}
	\textbf{Electromagnets:}
	\begin{itemize}	
		\item Temporary, could vary strength and direction of field
		\item Uses in: Electric bells, magnetic locks, relays, motors, generators, etc.
	\end{itemize}
\end{frame}


% TODO: Electromagnets and induction direction

\begin{frame}{Electric charge}
	\begin{itemize}
		\item There are positive and negative charges
		\item Measured in coulombs (\unit{\coulomb})
		\item Likes charges repel, opposite charges attract
		\item Rubbing \textrightarrow{} friction \textrightarrow{}\\transfer of electrons (negative charges) from one material into another
	\end{itemize}
\end{frame}

\begin{frame}{Detecting static and conductivity}
	\begin{columns}
		\column{0.5\textwidth}
		\hspace*{-1.5em}
		\includegraphics{gold-leaf.pdf}
		\column{0.5\textwidth}
		\textbf{Detecting static charges}
		
		No matter whether the charge is positive or negative, a charge brought \textbf{near} the \textbf{gold-leaf electroscope} causes the gold leaf to rise; the leaf falls back when the charge is removed.\\[\baselineskip]
		
		\textbf{Detecting conductivity}
		
		Draw a charged polythene strip firmly across the edge of the cap; the leaf should stay up even after the strip is removed.
		
		Touch the cap of the charged electroscope with different things (must be grounded). If the thing is a conductor, the leaf falls.
	\end{columns}
\end{frame}

% TODO: MISSING CONTENT
% Describe simple experiments to show the production of electrostatic charges by friction and to show the detection of electrostatic charges
% Explain that charging of solids by friction involves only a transfer of negative charge (electrons)

\begin{frame}{Electric fields}
	\begin{itemize}
		\item A region in which an electric charge experiences a force
		\item Direction of an electric field at a point is the direction of the force on a positive charge at that point
	\end{itemize}
\end{frame}

\begin{frame}{Electric field patterns}
	\begin{columns}
		\column{0.25\textwidth}
			\includegraphics[width=\textwidth]{electric-field-patterns-sphere.pdf}
			
			Around a charged conducting sphere
			
		\column{0.25\textwidth}
			\includegraphics[width=\textwidth]{electric-field-patterns-point.pdf}
			
			Around a point charge
			
		\column{0.45\textwidth}
			\includegraphics[width=\textwidth]{electric-field-patterns-opposite.pdf}
			
			Between two oppositely charged parallel conducting plates
	\end{columns}
\end{frame}

\begin{frame}{Charge by friction}
	Rubbing an object makes it charged because the friction causes electrons to be transferred from $A$ to the $B$, where $A$ becomes positive and $B$ becomes negative. Protons do not move.
\end{frame}

\begin{frame}{Conductors and insulators}
	\begin{itemize}
		\item Insulators: No free electrons, no free transfer of charge e.g. all simple molecular compounds, etc.
		
			An insulator can be charged by rubbing because the charge produced cannot move from where the rubbing occurs, i.e. the electric charge is static.
		\item Conductors: Free electrons, e.g. all metals, graphite, etc.
		\item Moving ions are not otherwise considered, but water is considered a conductor here.
	\end{itemize}
\end{frame}

\begin{frame}{Electric current}
	\mbox{}\hfill current = rate of flow of charge\hfill{}
	\begin{equation*}
		\text{current } I = \frac{\text{charge passing the point } Q}{\text{time } t}\hspace{2em}\text{ampere } \unit{\ampere} = \frac{\text{coulomb } \unit{\coulomb}}{\text{second } \unit{\second}}
	\end{equation*}\mbox{}
	
	\begin{itemize}
		\item Electrical conduction in metals is due to the movement of free electrons
		\item Conventional current is from positive to negative
		\item The flow of free electrons is from negative to positive
	\end{itemize}
\end{frame}

\begin{frame}{Ammeters}
	\begin{itemize}
		\item Always placed in \textbf{series} within a circuit
		\item Measures the current that passes through the point at which it's placed
		\item Has approximately \qty{0}{\ohm} resistance
		\item Has polarity: remember to connect it \emph{in the direction of the current}
		\item Could be analogue or digital
		\item Select the appropriate range before measurement
		\item Higher range means lower sensitivity, etc.
	\end{itemize}
\end{frame}

\begin{frame}{Electrical conduction}
	In a metal, each atom has one or more loosely held electrons that are free to move. When there is a potential difference across the ends of such a conductor, the free electrons drift slowly along it in the direction from the negative to the positive end. There is then a current of negative charge.
\end{frame}

\begin{frame}{DC and AC}
	\begin{columns}
	\column{0.575\textwidth}
	\begin{itemize}
		\item \textbf{Direct current:} electrons flow in one direction only \textrightarrow{} current in one direction only \& deflects ammeters in one direction only
		
		\item \textbf{Alternating current:} the direction of flow reverses regularly \textrightarrow{} current direction reverses \& deflects ammeters back and forth about the zero, if slow enough; doesn't register on the ammeter if too fast
			
			Frequency in hertz e.g. \qty{2}{\hertz} on the diagram; \qty{50}{\hertz} in the UK
		\item Batteries produce DC only; power supplies and generators could produce DC or AC, but we only learn about AC generators in IGCSE
		\item Iron-core transformers only work with AC!
	\end{itemize}
	\column{0.379\textwidth}
	\includegraphics[scale=0.68]{steady-dc.pdf}\\
	\includegraphics[scale=0.68]{ac.pdf}
	\hfill\mbox{}
	\end{columns}
\end{frame}

\begin{frame}{EMF and PD}
	\begin{align*}
	\text{EMF} &= \frac{\text{electrical work }W}{\text{charge }Q} = \text{units }\frac{\text{joule }\unit{\joule}}{\text{coulomb }\unit{\coulomb}} = \text{volt }\unit{\volt}\\
	&= \text{electrical work done by a source in moving a unit charge around a complete circuit}\\{}\\
	\text{PD} &= \frac{\text{electrical work }W}{\text{charge }Q} = \text{units }\frac{\text{joule }\unit{\joule}}{\text{coulomb }\unit{\coulomb}} = \text{volt }\unit{\volt}\\
	&= \text{electrical work done by a unit charge as it passes through a component}
	\end{align*}
\end{frame}

\begin{frame}{Voltmeters}
	\begin{itemize}
		\item Measures the PD across a component / some components / ``two points''
		\item Always placed in \textbf{parallel} with the component(s) that you're measuring
		\item Has polarity: remember to connect it \emph{in the direction of the current}

		\item Has extremely high resistance; almost doesn't affect the circuit
		\item Could be analogue or digital
		\item Select the appropriate range before measurement
		\item Higher range means lower sensitivity, etc.
	\end{itemize}
\end{frame}

\begin{frame}{Resistance}
	\begin{align*}
		\text{resistance }R &= \frac{\text{the potential difference across [a (group of) component(s)]}}{\text{the total current that goes through it}}\\ &= \frac{\text{voltage }V}{\text{current }I}\hspace{2em}\text{ohm } \unit{\ohm} = \frac{\text{volt } \unit{\volt}}{\text{ampere } \unit{\ampere}}
	\end{align*}
	
\end{frame}

\begin{frame}{Current--voltage graphs}
	Gradient = resistance
	
	\includegraphics{ohmic-and-diode.pdf}\includegraphics{lamp-and-thermistor.pdf}
	
	(The temperature of the thermistor is \emph{controlled} here)
\end{frame}

\begin{frame}{Resistance variance}
	For a metallic electrical conductor,
	\begin{itemize}
		\item resistance is directly proportional to length
		\item resistance is inversely proportional to cross-sectional area
	\end{itemize}
\end{frame}

\begin{frame}{Electrical energy and power}
	Energy in an electric circuit:\\
	Source of electrical energy \textrightarrow{} circuit components \textrightarrow{} surroundings
	\begin{align*}
		\text{power }P &= \text{current }I\times\text{voltage }V\\
		\text{energy }E &= \text{current }I\times\text{voltage }V\times\text{time }t\\
		&= \text{voltage }V\times\text{charge }Q
	\end{align*}
	
	Energy is in joules (\unit{\joule}) or kilowatt-hours (\unit{\kilo\watt\hour})\\
	Power is in watts (\unit{\watt})
	\begin{align*}
	\unit{\kilo\watt\hour}
	&= \text{the electrical energy used by a \qty{1}{\kilo\watt} appliance in \qty{1}{\hour}}\\
	&= \qty{3.6e6}{\joule}
	\end{align*}
\end{frame}

\begin{frame}{Circuit elements 1}
	TODO: I really don't know how to put this part in a revision resource... for now just read electrical\_symbols.pdf
	
	\includegraphics[scale=0.3]{circuit-components.jpg}
\end{frame}

\begin{frame}{Circuit elements 2}
	TODO: Same
	
	See page 216–219 on the Hodder textbook
\end{frame}

\begin{frame}{Series circuits}
	\begin{columns}
	\column{0.5\textwidth}
	\centering
	\includegraphics{series.pdf}
	\column{0.5\textwidth}
	\centering
	\includegraphics{series-pd.pdf}
	\end{columns}
	\begin{itemize}
		\item The current at every point is the same i.e. $I_A = I_B = I_C = I_D$
		\item The total PD across the components = the sum of individual PDs across each component i.e. $PD(X, Y) = PD(L_1) + PD(L_2) + PD(L_3)$
		\item The total resistance across the components = the sum of individual resistance across each component i.e. $R(X, Y) = R(L_1) + R(L_2) + R(L_3)$\\(remember, lamps etc.\ are resistors in some way or another)
	\end{itemize}
\end{frame}

\begin{frame}{Potential dividers}
	$V = IR$ $\therefore$ PD across a conductor must \textuparrow, as resistance \textuparrow, for a constant current\bigskip
	
	\begin{columns}
	\column{0.4\textwidth}
	\includegraphics{potential-divider.pdf}
	\column{0.5\textwidth}
	\begin{align*}
	I &= \frac{\text{emf}}{\text{total resistance}} = \frac{V}{R_1+R_2}\\
	V_1 &= I\times R_1=\frac{V\times R_1}{R_1+R_2}=V\times\frac{R_1}{R_1+R_2}\\
	V_2 &= I\times R_2=\frac{V\times R_2}{R_1+R_2}=V\times\frac{R_2}{R_1+R_2}\\
	\frac{V_1}{V_2} &= \frac{R_1}{R_2}
	\end{align*}
	\end{columns}
	
	Sometimes the potential divider may be variable e.g. if $R_1$ is a NTC thermistor, its resistance decrease when temperature rises, so the PD across $R_2$ increases and could be used to monitor temperature.
\end{frame}

\begin{frame}{Parallel circuits}
	\begin{columns}
	\column{0.5\textwidth}
	\centering
	\includegraphics{parallel.pdf}
	\column{0.5\textwidth}
	\centering
	\includegraphics{parallel-pd.pdf}
	\end{columns}
	\begin{itemize}
		\item The current in the main branch = the sum of the current in each sub branch i.e. $I_R = I_Q + I_P$, $\therefore$ $I_R > I_x\;\forall\;x\in\{P, Q\}$
		\item Sum of the currents into a junction ($\bullet$) = sum of currents out of the junction
		\item PD across entire circuit = PD in each branch i.e. $V_1 = V_2 = \qty{1.5}{\volt}$
		\item \alert{$R_{(P \text{ parallel with } Q)} = R_P\cdot R_Q / (R_P + R_Q)$} and $R_{(P \text{ parallel with } Q)} < R_x\;\forall\;x\in\{P,Q\}$
	\end{itemize}
\end{frame}

\begin{frame}{Why lamps are connected in parallel}
	\begin{itemize}
		\item The PD across each lamp is fixed (at the
supply EMF), so the lamp shines with the same brightness irrespective of how many other lamps are switched on (as long as your power supply can supply enough power)
		\item Each lamp can be turned on and off independently; if one lamp fails, the others can still be operated
	\end{itemize}
\end{frame}

\begin{frame}{Sources in series and parallel}
	\begin{columns}
		\column{0.5\textwidth}
		
		\begin{itemize}
			\item $EMF(A, B) = \qty{3}{\volt}$
			\item $EMF(X, Y) = \qty{0}{\volt}$
			\item $EMF(Q, P) = \qty{1.5}{\volt}$\ldots{}\\but the batteries last longer
		\end{itemize}
		
		\column{0.45\textwidth}
		
		\includegraphics{series-cell.pdf}\bigskip\bigskip
		
		\includegraphics[width=0.7\textwidth]{parallel-cell.pdf}
	\end{columns}
\end{frame}

% TODO: We really need past paper questions for this

\begin{frame}{Electrical safety}
	TODO: This is a very easy topic and I don't really want to spend time writing about it for now.
\end{frame}

\begin{frame}{Electromagnetic induction 1}
	\begin{itemize}
		\item Any EMF induced by movement produces a magnetic field that opposes that movement
			
			\begin{columns}
				\column{0.6\linewidth}
					\begin{itemize}
						\item When the magnet approaches the coil, north pole first, the induced EMF makes the coil behave like a magnet that repels the original magnet with an N pole.
						\item When the magnet leaves the coil, north pole last, the induced EMF makes the coil behave like a magnet that attracts the original magnet with an S pole.

					\end{itemize}
				\column{0.35\linewidth}
					\includegraphics{induce-oppose.pdf}
			\end{columns}
	\end{itemize}
\end{frame}

\begin{frame}{Electromagnetic induction 2}
	\begin{columns}
		\column{0.51\textwidth}
			When a straight wire moves at right angles to a magnetic field:
			
			\mbox{}
			\begin{itemize}
				\item Use the gesture as shown
				\item Point your thumb in the direction of the wire's movement
				\item Point your index finger in the direction of the magnetic field (N\textrightarrow S)
				\item The current is shown by the direction of your middle finger
			\end{itemize}
		\column{0.44\textwidth}
			\includegraphics{right-hand-rule.pdf}
	\end{columns}
\end{frame}

\begin{frame}{Electromagnetic induction 3}
	\begin{itemize}
		\item Factors affecting magnitude of induced EMF:
			\begin{itemize}
				\item Speed of relative motion\footnote{Only the component of the speed of relative motion that's in the direction of the ``motion''/thumb in the right-hand rule is counted}
				\item The strength of the magnet
				\item The number of turns on the coil
			\end{itemize}
	\end{itemize}
\end{frame}

\begin{frame}{AC generator}
\end{frame}

\begin{frame}{Magnetic effect of a current}
\end{frame}

\begin{frame}{Force on conductor with current}
\end{frame}

\begin{frame}{DC motor}
\end{frame}

\begin{frame}{Transformer}
\end{frame}

\definecolor{MainColor}{RGB}{180,40,45}
\definecolor{SubColor}{rgb}{0.9890909090909092, 0.9509090909090907, 0.952272727272727}
\csection{Nuclear physics}

\begin{frame}{The atom}
\end{frame}

\begin{frame}{Rutherford experiment}
\end{frame}

\begin{frame}{The nucleus}
\end{frame}

\begin{frame}{Fission and fusion}
\end{frame}

\begin{frame}{Nuclear reactors}
\end{frame}

\begin{frame}{Radiation types}
\end{frame}

\begin{frame}{Alpha decay}
\end{frame}

\begin{frame}{Beta decay}
\end{frame}

\begin{frame}{Gamma emissions}
\end{frame}

\begin{frame}{Deflection in EM fields}
\end{frame}

\begin{frame}{Ionizing radiation}
\end{frame}

\begin{frame}{Background radiation}
\end{frame}

\begin{frame}{Nuclear stability}
\end{frame}

\begin{frame}{Half-life}
\end{frame}

\begin{frame}{Nuclear safety}
\end{frame}

\definecolor{MainColor}{RGB}{227,103,42}
\definecolor{SubColor}{rgb}{0.9930290456431536, 0.9621576763485477, 0.9469709543568463}
\csection{Space physics}

\begin{frame}{The earth}
\end{frame}

\begin{frame}{Orbital speed}
\end{frame}

\begin{frame}{The moon}
\end{frame}

\begin{frame}{The solar system}
\end{frame}

\begin{frame}{The accretion model}
\end{frame}

\begin{frame}{Gravity}
\end{frame}

\begin{frame}{Light speed}
\end{frame}

\begin{frame}{The sun as a star}
\end{frame}

\begin{frame}{Hydrogen fusion}
\end{frame}

\begin{frame}{Stars basics}
	\begin{itemize}
	\item Galaxies are each made up of many billions of stars
	\item The Sun is a star in the galaxy known as the \textbf{Milky Way}
	\item The Sun is the closest star to us, by a wide margin
	\item Astronomical distances can be measured in light-years
	\end{itemize}
\end{frame}

\begin{frame}{Star life cycles}
	%\begin{columns}
	%\column{0ex}
	%\column{\textwidth}
	\begin{enumerate}
		\setlength{\itemsep}{-0.5\baselineskip}
		\item interstellar clouds of gas and dust that contain \ce{H2}
		\item internal grav attraction \textrightarrow{} collapses \& temperature\textuparrow{} \textrightarrow{} protostar
		\item inward force of grav attraction = outward force by high temperature at center\\\textrightarrow{} stable star
		\item runs out of \ce{H2} as nuclear fusion fuel
	\end{enumerate}
	{\usebeamercolor[fg]{structure}{SMALL}}\vspace*{-0.5\baselineskip}
	\begin{enumerate}
		\setlength{\itemsep}{-0.5\baselineskip}
		\item[5.] \textrightarrow{} right giant
		\item[6.] \textrightarrow{} planetary nebula w/ white dwarf star at center
	\end{enumerate}
	{\usebeamercolor[fg]{structure}{LARGE}}\vspace*{-0.5\baselineskip}
	\begin{enumerate}
		\setlength{\itemsep}{-0.5\baselineskip}
		\item[5.] \textrightarrow{} red supergiant
		\item[6.] \textrightarrow{} supernova\\
				\textrightarrow{} nebula containing \ce{H2} and new heavier elements\\w/ nutron star or black hole at center\\(the nebula from a supernova may form new stars with orbiting planets)
	\end{enumerate}
	%\end{columns}
\end{frame}

\begin{frame}{The universe}
\end{frame}

\begin{frame}{Redshift}
\end{frame}

\begin{frame}{CMBR}
\end{frame}

\begin{frame}{The Big Bang Theory}
	\begin{itemize}
		\item Initially: one point
		\item 13.7 billion years ago: the big bang, the huge explosion
		\item Ever-after: moving further
	\end{itemize}
\end{frame}

\begin{frame}{Universe expansion}
\end{frame}

\begin{frame}{The Hubble constant}
	\begin{align*}
		\text{Hubble constant } H_0 &= \frac{\text{speed at which the galaxy is moving away from earth } v}{\text{its distance from the earth } d}\\
		&\approx 2.2\times10^{-18} \text{ per second} \text{{} {} (memorize this)}
	\end{align*}	
	\begin{align*}
		\displaystyle \text{age of the universe } t = \frac{d}{v} &= \frac{1}{H_0}\\
		&\approx 14.4 \text{ billion years}\\
		\text{(The Big Bang started}& \text{ from a single point)}
	\end{align*}
	
	\textbf{Complete question~x.} % TODO: NOT INCLUDED
\end{frame}

\begin{frame}{Age of the universe}
\end{frame}

\definecolor{MainColor}{RGB}{0,0,0}
\definecolor{SubColor}{rgb}{0.97, 0.97, 0.97}
\csection{Exam technique}
\begin{frame}{Recap: Equivalent units}
	\begin{itemize}
		\item $\unit{\newton} = \unit{\kilo\gram\metre\per\second\squared}$ (Force)
		\item $\unit{\newton\second} = \unit{\kilo\gram\metre\per\second}$ (Impulse/momentum)
		\item TODO: Add more!
	\end{itemize}
	
	\textbf{Complete question~4.}
\end{frame}

\end{document}