<div>
<h2>QUESTION 1</h2>
<ol>
<li>
<p><strong>Solve for</strong> <em>x</em>:</p>
<ol>
<li>\(x^2 + x - 12 = 0\) <span>(3)</span></li>
<li>\(3x^2 - 2x = 6\) (answers correct to TWO decimal places) <span>(4)</span></li>
<li>\(\sqrt{2x + 1} = x - 1\) <span>(4)</span></li>
<li>\(x^2 - 3 > 2x\) <span>(4)</span></li>
</ol>
</li>
<li>
<p><strong>Solve for</strong> <em>x</em> and <em>y</em> <strong>simultaneously</strong>:</p>
<p>\(x + 2 = 2y\)</p>
<p>\(\frac{1}{x} + \frac{1}{y} = 1\)</p>
<p>(5)</p>
</li>
<li>
<p><strong>Given:</strong></p>
<p>\(2^{m+1} + 2^m = 3^{n^2} - 3^n\), where <em>m</em> and <em>n</em> are integers.</p>
<p><strong>Determine the value of</strong> \(m + n\).</p>
<p>(4)</p>
</li>
</ol>
<p style="text-align: right;">[24]</p>
</div>
**QUESTION 1**
1. **Solve for** *x*:
1.1.1 \(x^2 + x - 12 = 0\) *(3)*
1.1.2 \(3x^2 - 2x = 6\) *(answers correct to TWO decimal places)* *(4)*
1.1.3 \(\sqrt{2x + 1} = x - 1\) *(4)*
1.1.4 \(x^2 - 3 > 2x\) *(4)*
2. **Solve for** *x* **and** *y* **simultaneously**:
\(x + 2 = 2y\)
\(\frac{1}{x} + \frac{1}{y} = 1\)
*(5)*
3. **Given**:
\(2^{m+1} + 2^m = 3^{n^2} - 3^n\), where *m* and *n* are integers.
**Determine the value of** \(m + n\). *(4)*
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