# 2006 A Level H2 Math

These Ten-Year-Series (TYS) worked solutions with video explanations for 2006 A Level H2 Mathematics are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.

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Paper 1
Paper 2
##### 2006 A Level H2 Math Paper 1 Question 3

The function $\text{g}$ is defined by $\text{g}:x\mapsto \frac{3}{x},x>0$.
Find, in a similar form, ${{\text{g}}^{2}}$ and ${{\text{g}}^{35}}$.

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##### 2006 A Level H2 Math Paper 1 Question 3 (FM)

Verify that if

${{v}_{n}}=n\left( n+1 \right)\left( n+2 \right)…\left( n+m \right)$.

then

${{v}_{n+1}}-{{v}_{n}}=\left( m+1 \right)\left( n+1 \right)\left( n+2 \right)…\left( n+m \right)$.

[2]

Given now that

${{u}_{n}}=\left( n+1 \right)\left( n+2 \right)…\left( n+m \right)$,

find $\sum\limits_{n=1}^{N}{{{u}_{n}}}$ in terms of $m$ and $N$.

[3]

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##### 2006 A Level H2 Math Paper 1 Question 6

Show that the equation

${{z}^{4}}-2{{z}^{3}}+6{{z}^{2}}-8z+8=0$

has a root of the form $k\text{i}$, where $k$ is real.

[3]

Hence solve the equation

${{z}^{4}}-2{{z}^{3}}+6{{z}^{2}}-8z+8=0$.

[3]

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##### 2006 A Level H2 Math Paper 2 Question 2

Given that $z=\frac{x}{{{\left( {{x}^{2}}+32 \right)}^{\frac{1}{2}}}}$, show that $\frac{\text{d}z}{\text{d}x}=\frac{32}{{{\left( {{x}^{2}}+32 \right)}^{\frac{3}{2}}}}$.

[3]

Find the exact value of the area of the region bounded by the curve $y=\frac{1}{{{\left( {{x}^{2}}+32 \right)}^{\frac{3}{2}}}}$, the $x$-axis and the lines $x=2$ and $x=7$.

[3]

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