Apart from the errors, here is some LaTeX advice to improve the LaTeX version, some very subtle, others not so subtle.
1. Not so subtle: Don't break mathematical expressions like in 11a:
Try this code
Code:
By first writing $\sqrt3+i$ and $\sqrt3-i$ in exponential form,\\
express $(\sqrt3+i)^{12}+(\sqrt3-i)^{12}$ in the form of $a^b$ where $a$ and $b$ are integers.
Other questions in the LaTeX version with broken mathematical expressions: 12bii, 12c, 13aii
2. Subtle: Space before dx in integrals. I use Cambridge Ex4A Q1b as an example and I make this picture big so you can see clearly a space before the dx:
It's not a big space. You can use \ \! to make a space and then bring it back a bit.
So in 12biii instead of this:
this code
Code:
$$\int_0^\frac{\pi}{2}\frac{x}{1+\cos x+\sin x}\ \!dx$$
3. Subtle: smaller tilde for vector.
See in the original:
your LaTeX version has a huge tilde:
so how to make a smaller tilde in LaTeX?
This code:
Code:
\documentclass{article}
\usepackage{accents}
\newcommand{\ut}[1]{\underaccent{\tilde}{#1}}
\renewcommand{\vec}[1]{\ut{#1}}
\begin{document}
$\vec r(t)$
\end{document}
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