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**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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