# Monthly Archives: September 2017

## HCI/2013/I/Q1 Inequalities

Given that a is a positive real number, solve the inequality

## MJC/2013/P1/Q6 Functions

The functions f and g are defined as follows:

Where λ is a constant.

(i) Given that gf exists, find the largest value of λ.

In the rest of the questions, use the value of λ found in part (i).

(ii) On the same diagram, sketch the graph of   and  , showing clearly the relationship between the graphs.

(iii) Hence find the exact solution of

## Finding the Range of a Composite Function I

Two functions f and g are defined as follows:

Determine, with reasons, whether fg and gf exist. If the composite function exists, give the rule, domain and range in exact form.

## Binomial Theorem: Finding the unknown Coefficient and Power

The binomial expansion of , where n is a positive integer, in ascending power of x, is . Find the value of n and of k.

## Binomial Theorem: Finding the unknown power

In the expansion of in the ascending power of , the coefficient of the third term is 121. Find the value of n.

## Binomial Theorem Basics

Find, in ascending powers of x, the first four terms in the expansion of .

Things to note:

Expansion by binomial theorem is all about pattern recognition. Note that the numbers in light blue are in ascending or descending down the expansion.

## Finding the Complex Roots of Equation with Real Coefficients

Given that the equation  has a root of 1-2i, solve the equation.

## GCE/2010/I/Q5 National Exam Question on Modulus Graph

(i) Sketch the curve  for

(ii) Find the -coordinates of the points of intersection of the curve  and the line y=27.

## ACS(I)/2015/I/Q3 Modulus Function

Solve the equation