From 3d6ea49818f9ab00bda199e89358861f5007cbbc Mon Sep 17 00:00:00 2001
From: Mohit Agarwal <mohit.agarwal@sky.com>
Date: Sat, 13 Nov 2021 11:27:51 +0000
Subject: Working on questions

---
 tests/1-data-rep/questions.tex | 139 ++++++++++++++++++++++++++++++++++++-----
 1 file changed, 125 insertions(+), 14 deletions(-)

(limited to 'tests/1-data-rep/questions.tex')

diff --git a/tests/1-data-rep/questions.tex b/tests/1-data-rep/questions.tex
index 489ae8a..bc32ed8 100644
--- a/tests/1-data-rep/questions.tex
+++ b/tests/1-data-rep/questions.tex
@@ -2,16 +2,29 @@
 
     \question Lucy records using her camera. The camera saves the
     audio and video parts of the recording seperately. Lucy transfers
-    recording to her computer. The audio file has a size of 12.8 kB.
-    Audio is recorded at a sample rate of 320 kB per second. The audio
+    recording to her computer. The audio file has a size of 19 MB.
+    Audio is recorded at a sample rate of 45 kHz. The audio
     resolution is 32 bits.
 
     \begin{parts}
 
-        \part[5] In minutes, how many seconds was the recording.
+        \part[5] In minutes and seconds, how long was the recording.
+
+        \begin{solution}
+        \begin{align*}
+            size &= sample\ rate\times sample\ resolution\times length\\
+            18000000 \times 8 &=  45000\times32\times length\\
+            18000000 &= 45000\times4\times length\\
+            18000 &= 45\times4\times length\\
+            18000 &= 180\times length\\
+            length &= 100\ seconds\\
+            &= 1\ minute\ 40\ seconds\\
+        \end{align*}
+        \end{solution}
+
         \vspace{\stretch{1}}
 
-        \part[5] A video file consists of many still frames. Each
+        \part[4] A video file consists of many still frames. Each
         frame is a normal image. The size of a video file can
         therefore be expressed as:
 
@@ -21,40 +34,138 @@
         \end{align*}
 
         If each frame is 1920 pixels wide and 1080 pixels high in
-        resolution, and the bit depth of 24 bits, what is the file
-        size of the video file. 
+        resolution, the bit depth of 24 bits, and her camera records
+        30 frames each second. What is the file size of the video
+        file, rounded to 3 significant figures, in bytes, with some
+        sensible unit prefix?
+
+        \begin{solution}
+
+            Allow error carried forward for time
+            \begin{align*}
+            size &= length\times frames\ per\ second\times
+            resolution\times colour\ depth\\
+            &= 100\times 30 \times 1920\times1080\times24\\
+            &= 149299200000\ bits\\
+            &= 18662400000\ bytes\\
+            &\approx 18.7\ GB
+            \end{align*}
+            Three points for correct calculation. One point for
+            correct rounding and unit prefix. Accept other suitable
+            unit prefix.
+        \end{solution}
         \vspace{\stretch{1}}
-        
+
         \pagebreak
 
         \part[1] Lucy combines the audio and video to form a file. She
         then runs a lossy compression algorithm on the resulting file.
         What is lossy compression?
-        \vspace{\stretch{1}}
 
-        \part[3] The file size after compression is reduced by 20\%.
-        What is the final file size?
+        \begin{solution}
+            Reducing the size of a file by removing data.
+        \end{solution}
         \vspace{\stretch{1}}
 
+        \part[3] The file size after compression is reduced by 95\%.
+        What is the final file size? Use your rounded value for
+        video file size. Once more leave your answer rounded to 3
+        significant figures, in bytes, with a suitable unit prefix.
+
+        \begin{solution}
+
+            Allow error carried forward for size
+            \begin{align*}
+                Compressed\ Size &=
+                18.7\times 10^9 + 19\times 10^6 * 0.05\\
+                &= 935950000\\
+                &= 0.93595\ GB\\
+                &\approx 0.936\ GB
+            \end{align*}
+            Two points for correct calculation. One point for
+            correct rounding and unit prefix. Accept other suitable
+            unit prefix.
+        \end{solution}
+        \vspace{\stretch{2}}
+
         \part[1] State an assumption made for part (d).
+
+        \begin{solution}
+            There is no metadata or other factor that would influence
+            the file size.
+        \end{solution}
+        \vspace{\stretch{1}}
+
+        \pagebreak
+
+        \part[3] Using your rounded value for the total compressed
+        file size, and the length of recording, find a value for the
+        size of a compressed video with sound per second.
+
+        Leave your answer rounded to 3 significant figures, with a
+        suitable unit and prefix.
+
+        \begin{solution}
+
+            Allow error carried forward for size or time
+            \begin{align*}
+                Rate &= size \div time\\
+                &= 0.936\ GB \div 100\\
+                &= 9.36\ MB/s
+            \end{align*}
+            Two points for correct calculation. One point for correct
+            unit and unit prefix. Accept other suitable unit prefix.
+        \end{solution}
+
+        \vspace{\stretch{1}}
+
+        \part[3] Lucy wants to record 1 hour of video. Estimate how
+        much space this will take on her hard drive when the video and
+        audio are combined and compressed, using your answer to (f).
+
+        Leave your answer rounded to 3 significant figures, in bytes,
+        with a suitable unit prefix. 
+        \begin{solution}
+
+            Allow error carried forward for size or time
+            \begin{align*}
+                Size &= rate \times time\\
+                &= 9.36 \times 60\times 60\\
+                &\approx 33.7\ GB
+            \end{align*}
+            Two points for correct calculation. One point for correct
+            unit and unit prefix. Accept other suitable unit prefix.
+        \end{solution}
+
         \vspace{\stretch{1}}
 
     \end{parts}
     \droptotalpoints
     \pagebreak
 
-    \question Let us say there is a string:
+    \question Let us say there are some bits:
 
-    \verb|Hi|
+    \centering
+    000110111100000001111111001
 
     \vspace{1cm}
 
     \begin{parts}
 
-        \part[2] If the string is encoded in 8 bit ascii, how much
-        space does the string take in bytes to store?
+        \part[2] Using run length encoding represent these bits.
+        \vspace{\stretch{1}}
+
+        \part[2] Computers store information in binary. Let us say
+        that a run is represented by 5 bits: 4 bits for the length of
+        the run, and 1 bit for the bit in the run. For example 00000
+        which is 5 zeroes would be 10010, using the first to bits to
+        represent the 5 and the final bit to represent the 0.
+        Represent your encoding in this format.
+        \vspace{\stretch{1}}
 
     \end{parts}
+    \droptotalpoints
+    \pagebreak
 
 
 \end{questions}
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