To provide a complete solution to the problem:
### a) Calculate Emyr's Percentage Score
To determine Emyr's percentage score in the exam, we use the formula for percentage:
[tex]\[ \text{Percentage score} = \left( \frac{\text{Exam score}}{\text{Total possible score}} \right) \times 100 \][/tex]
Given:
- Exam score = 112
- Total possible score = 200
Substitute these values into the formula:
[tex]\[ \text{Percentage score} = \left( \frac{112}{200} \right) \times 100 \][/tex]
First, perform the division within the parentheses:
[tex]\[ \frac{112}{200} = 0.56 \][/tex]
Now, multiply by 100 to convert the decimal to a percentage:
[tex]\[ 0.56 \times 100 = 56\% \][/tex]
So, Emyr's percentage score is 56%.
### b) Determine Emyr's Result
To find Emyr's result based on his percentage score, we refer to the given grading table:
[tex]\[
\begin{tabular}{|c|c|}
\hline Percentage & Result \\
\hline $15 \%-29 \%$ & D \\
\hline $30 \%-49 \%$ & C \\
\hline $50 \%-64 \%$ & B \\
\hline $65 \%-79 \%$ & A \\
\hline $80 \%-100 \%$ & A$^*$ \\
\hline
\end{tabular}
\][/tex]
We observe that a percentage score of 56% falls in the range of 50% to 64%, which corresponds to the grade "B".
Therefore, Emyr's result is:
[tex]\[
\boxed{B}
\][/tex]
