# 2005 A Level H2 Math

2021

2022

2023

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004

2003

2002

2001

2000

1995

1994

1993

1991

1990

1986

1984

1983

1982

### Â  Â 1971-1980

1978

1977

1973

Paper 1
Paper 2
##### 2005 A Level H2 Math Paper 2 Question 1

Verify that $z=\text{i}$ is a root of the equation

${{z}^{4}}-2{{z}^{3}}+6{{z}^{2}}-2z+5=0$.

[1]

Hence determine the other roots.

[4]

##### 2005 A Level H2 Math Paper 2 Question 4

It is given that $a$, $b$, $c$ are the first three terms of a geometric progression. It is also given that $a$, $c$, $b$ are the first three terms of an arithmetic progression.

(i)

Show that ${{b}^{2}}=ac$ and $c=\frac{a+b}{2}$.

[2]

(i) Show that ${{b}^{2}}=ac$ and $c=\frac{a+b}{2}$.

[2]

(ii)

Hence show that $2{{\left( \frac{b}{a} \right)}^{2}}-\left( \frac{b}{a} \right)-1=0$.

[2]

(ii) Hence show that $2{{\left( \frac{b}{a} \right)}^{2}}-\left( \frac{b}{a} \right)-1=0$.

[2]

(iii)

Given that the sum to infinity of the geometric progression is $S$, find $S$ in terms of $a$.

[4]

(iii) Given that the sum to infinity of the geometric progression is $S$, find $S$ in terms of $a$.

[4]