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Binomial Functions

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   1 Binomial & Functions Test SL Name:__________________________ Date: 6 th  October 2014 Total: /42 marks Answer all questions on this question paper.   Unless otherwise stated in the question, all numerical answers should be given exactly or correct to three significant figures. 1.  Find the coefficient of a 5 b 7   in the expansion of ( a  + b ) 12 .   Working:  Answer:  ...................................................................... (Total 4 marks) 2.  Determine the constant term in the expansion of Working:  Answer:  .................................................................... (Total 4 marks) .2  –  92        x x   2 3.  When the expression (2 + ax ) 10  is expanded, the coefficient of the term in  x 3  is 414 720. Find the value of a . Working:  Answer  : …………………………………………..   (Total 6 marks) 4.  Consider the functions  f :  x 4(  x  –   1) and  g :  x .  (a) Find  g   –  1 . (b) Solve the equation (  f   °   g   –  1 ) (  x ) = 4. Working:  Answers : (a) .................................................................. (b) .................................................................. (Total 6 marks)   2  –  6  x   3 5.  Consider the functions  f   (  x ) = 2  x  and  g   (  x ) = ,  x  3. (a) Calculate (  f    ◦  g  ) (4). (b) Find  g  − 1 (  x ). (c) Write down the domain of  g  − 1 . (Total 6 marks) 6.  Let  f   (  x ) = ,  x      − 4 and  g   (  x ) =  x 2 ,  x     . (a) Find (  g    ◦  f   ) (3). (b) Find  f − 1 (  x ). (c) Write down the domain of  f − 1 . (Total 6 marks) 31   x   Answers:Working: (a) .....................................................(b) .....................................................(c) ..................................................... 4   x  Answers:Working: (a) .....................................................(b) .....................................................(c) .....................................................   4 7.  The diagram shows parts of the graphs of  y =  x 2  and  y  = 5  –   3(  x    –   4) 2 . The graph of  y = x 2  may be transformed into the graph of   y  = 5  –   3(  x    –   4) 2  by these transformations. A reflection in the line  y  = 0 followed by a vertical stretch with scale factor k    followed by a horizontal translation of  p  units followed by a vertical translation of q  units. Write down the value of (a) k  ; (b)  p ; (c) q.   Working:  Answers : (a) .................................................................. (b) .................................................................. (c) .................................................................. (Total 4 marks) 2468  –2  0 2 4 6  y x y = x 22  y x = 5 – 3(–4)
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