1. (a) Expand (1 + 2x 2 ) in ascending powers of x up to and including the term in x 3. (3)

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1 Binomial - Core 4 Revision (a) Epand ( ) powers of up to and including the term in State the range of values of for which the full epansion is valid () (Total 4 marks) (a) Epress as the sum of two partial fractions ( )( ) Hence epand ( )( ) in a series of ascending powers of up to and including the term in State the range of values of for which the full epansion in part is valid () (a) Obtain the binomial epansion of ( = ) powers of up to and including the term in State the range of values of for which the full epansion is valid () 4 (a) Obtain the binomial epansion of ( ) as far as the term in Hence, or otherwise, find the series epansion of (8 4) as far as the term in 5 (a) Epand 6 ( ) in a series of ascending powers of up to the term in ² State the values of for which the full epansion is valid (5) () (Total 6 marks) South Wolds Comprehensive School

2 6 (a) Epress 8 ( )( ) A B Obtain the first three terms in the epansion of powers of Show that the first three terms in the epansion of are powers of are 4 8 (d) Hence or otherwise, obtain the first three terms in the epansion of ascending powers of 8 ( )( ) in (e) State the range of values of for which the epansion in part (d) is valid (Total marks) 7 (a) Find the binomial epansion of ( ) up to the term in Hence, or otherwise, obtain the binomial epansion of simplified form up to the term in, in Use your answer to part with = 0 to show that 5 8 (a) (i) Obtain the binomial epansion of ( ) up to and including the term in Hence, or otherwise, show that 4 7 for small values of Obtain the binomial epansion of ( ) up to and including the term in Given that ( ) ( ) the values of A, B and C A B C, find can be written ( ) ( ) ( ) (5) South Wolds Comprehensive School

3 (d) Hence find the binomial epansion of ( ) ( ) up to and including the term in (a) Obtain the binomial epansion of ( ) as far as the term in (i) Hence, or otherwise, find the series epansion of ( 4 ) as far as the term in Find the range of values of for which this epansion is valid () (Total 6 marks) 0 (a) (i) Find the binomial epansion of ( ) up to the term in Hence, or otherwise, obtain the binomial epansion of up to the term in Epress 4 ( ) ( ) in partial fractions (i) Find the binomial epansion of 4 ( )( ) up to the term in Find the range of values of for which the binomial epansion of valid 4 is ( )( ) (Total marks) (a) Obtain the binomial epansion of ( ) up to and including the term in Hence obtain the binomial epansion of 5 up to and including the term in (d) Find the range of values of for which the binomial epansion of 5 would be valid Given that is small, show that 4 a b c, where a, b and c are integers 5 South Wolds Comprehensive School

4 (a) Obtain the first four terms of the binomial epansion of ( 8) a b c, where a, b and c are integers State the range of values of for which the full epansion is valid () (a) Determine the binomial epansion of 0 including the term in, powers of, up to and Show that the coefficient of n in this epansion is K(n )(n ) n 0 for a rational number K whose value is to be determined Determine the value of correct to fourteen decimal places 0 4 (a) (i) Obtain the first four terms in the binomial epansion of powers of Show that the first four terms in the binomial epansion of powers of are Epress 8 7 ( ) ( ) A B Hence obtain the first four terms in the epansion of powers of 8 7 ( )( ) (Total marks) South Wolds Comprehensive School 4

5 5 The function f is given by f() = ( )(4 ) (a) Epress f() in partial fractions (i) Show that the first three terms in the epansion of powers of are Obtain a similar epansion for (iii) Hence, or otherwise, obtain the first three terms in the epansion of f() powers of (iv) Find the range of values of for which the epansion of f() powers of is valid 4 A 6 (a) Epress ( )( ) B (i) Show that the first three terms in the epansion of (Total 4 marks) powers of are 4 8 Obtain also the first three terms in the epansion of powers of Hence, or otherwise, obtain the first three terms in the epansion of 4 ( )( ) powers of (Total 0 marks) South Wolds Comprehensive School 5