Apart from the errors, here is some LaTeX advice to improve the LaTeX version, some very subtle, others not so subtle.i did upload the 'clean' version
1. Not so subtle: Don't break mathematical expressions like in 11a:
![11a.png](/data/attachments/39/39821-19603d8ae138e266c7f1b700495740fc.jpg)
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.
![11abetter.png](/data/attachments/39/39822-46561645af2e22e25496e740588a8c3a.jpg)
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:
![Cambridge4A1b.png](/data/attachments/39/39823-4459f49ae96ba4f8468c50378601ac7c.jpg)
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:
![12biii.png](/data/attachments/39/39824-55994a305a679a7b59c58fefb0780cd9.jpg)
this code
Code:
$$\int_0^\frac{\pi}{2}\frac{x}{1+\cos x+\sin x}\ \!dx$$
![12biii-small-space-before-dx.png](/data/attachments/39/39825-e07ebf16f82607f26b5cd352f36cece8.jpg)
3. Subtle: smaller tilde for vector.
See in the original:
![q3-vector-original.png](/data/attachments/39/39826-07b987592002272521eb19ee7410849f.jpg)
your LaTeX version has a huge tilde:
![q3-vector-huge-latex.png](/data/attachments/39/39827-36c4a4d621ede5d5c7194df8759d63d8.jpg)
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}
![q3-vector-small-tilde-latex.png](/data/attachments/39/39828-878bedb843b104c048f028fdd54585ac.jpg)
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