Add Maths 2010 May-June Paper 11

1. Show that $\frac{1}{1-\cos \theta}+\frac{1}{1+\cos \theta}=2 \operatorname{cosec}^{2} \theta$ . [3]

2. Express $\lg a+3 \lg b-3$ as a single logarithm. [3]

3. (a) Shade the region corresponding to the set given below each Venn diagram.

(b) Given that $P=\left\{p: \tan p=1\right.$ for $\left.0^{\circ} \leqslant p \leqslant 540^{\circ}\right\}$ , find $n (P)$ .

4. (a) Solve the equation $16^{3 x-2}=8^{2 x}$

(b) Given that $\frac{\sqrt{a^{\frac{4}{3}} b^{-\frac{2}{5}}}}{a^{-\frac{1}{3}} b^{\frac{3}{5}}}=a^{p} b^{q},$ find the value of $p$ and of $q$

5. (i)

On the diagram above, sketch the curve $y=1+3 \sin 2 x$ for $0^{\circ} \leqslant x \leqslant 180^{\circ}$
(ii)

On the diagram above, sketch the curve $y=|1+3 \sin 2 x|$ for $0^{\circ} \leqslant x \leqslant 180^{\circ}$ .

(iii) Write down the number of solutions of the equation $|1+3 \sin 2 x|=1$ for $0^{\circ} \leqslant x \leqslant 180^{\circ}$ .