DHS Y4 Math 2 Supplementary Worksheet_Binomial Theorem

Math 1_Binomial Theorem (Compiled by Lim CH & J Goh) 1 Year 4 Mathematics 1 Binomial Theorem Supplementary Worksheet 1 Name : _________________________________ ( ) Class : _____ Date : __________ 1 (i) Write down and simplify the fourth term, in descending powers of x , in the expansion of n bax x  − . [2] (ii) If this fourth term is independent of x , find the value of n . [2] (iii) With the value of n found in part (ii), calculate the value of ab if the fourth term is equal to −160. [2] [2008 ACS (Barker Road) AMaths P1 (modified)] 2 Given that the coefficient of 4x in the expansion of 8 3 mx x  − is –13608, (i) find the value of the constant m , [4] (ii) hence find the term independent of x in the expansion of 4 21 x + 8 3 mx x  − . [3] [2008 ACS (I) AMaths P2] 3 Write down and simplify the first 3 terms, in ascending powers of x , in the expansion of 5 2 3 x − . Given that the first three terms in the expansion of ( ) 5 2 321      − + +xx px are 22 32qx qx+ − , find the value of p. [6] [2008 Anderson Sec AMaths P1] 4 (i) Write down the first three terms of the expansion, in ascending powers of x , of ( ) nax+1 , where a and n are constants. [2] (ii) Hence find the value of a and of n if ( ) 21 1 20 195 ... n ax x x+ = −+ + , taking up to the term in 2x . [6] [2008 Anglican High AMaths P1] 5 Given that ( ) 231 1 32 448 ... n px x x qx+ = − + ++ , find the value of p, of q and of n. [6] [2008 CHIJ St Nicholas Girls’ AMaths P1]

Math 1_Binomial Theorem (Compiled by Lim CH & J Goh) 2 6 (i) Write, in ascending powers of x, the first three terms in the expansion of .32 4      − x [2] (ii) The coefficients of x and x2 in the expansion of 4 2 32 ) (      − −xx p are in the ratio of 2 : 3. Find the value of p. [3] [ 2008 Balestier Hill Sec AMaths P2] 7 (i) Write down the first three terms in the expansion, in ascending powers of x , of 82 21       + px , where p is a constant. [2] ( ii) The first three terms in the expansion of 82 2 21 ) 2 (       + +pxqx , where p and q are integers, are 4 22 5 2x x+ − . Find the values of p and q , and show that 0< −q p .[6] [ 2008 Cedar Girls’ Sec AMaths P1] 8 Find in ascending powers of x , the first three terms in the expansion of (i) ( ) 5 2 x+ , (ii) ( ) 6 1 ax+ . Given that the coefficient of 2x in the expansion of ( ) 5 2 x+ ( ) 6 1 ax+ is 2960, find the possible value(s) of a . [5] [ 2008 CHIJ Toa Payoh Sec AMaths P1] 9 The coefficient of x in the expansion of n x     + 32 is 3 times the coefficient of 2x . (a) Find the value of n . [3] (b) Hence evaluate the coefficient of 2x in the expansion ( ) n xx      + −32 3 2 . [2] [ 2008 Commonwealth Sec AMaths P1] 10 (i) Find the term independent of x in the expansion of 8 32