Prelim Revision                Mixed questions               Exercise 2             Questions 11 - 20

 

 

 

 

11.        Find the point of intersection of the tangents to the parabola  y = x2 + 2    at the points P(-2,6) and Q(1,3).

 

            Hence, or otherwise, find the area bounded by the tangents and the arc PQ.

 

 

12.        Two banks one called Firstbank the other called Bestbank serve a small town.  Each month Firstbank loses ten percent of its customers to Bestbank, while Bestbank loses 15% of its customers to Firstbank. 

The marketing department of Firstbank claims that eventually they will have over 60% of the entire customer base of the town.  Are these claims justified, if, between them, the two banks have 20,000 customers?

 

 

13.        Given that  x2 + 2x – 3  is a factor of  f(x) = x4 + 2x3 – 7x2 + ax + b,  find a and b and hence factorise f(x) completely.

 

 

 

14.        Find the equation of the circle centre A(2,1), which passes through the origin.  A chord BC of the circle has midpoint M().  Find the co-ordinates of B and C.

 

 

15.        Evaluate:

 

a)                   b)        

 

 

 

 

 

 

 

16.        Find a given that:

 

 

 

 

17.        Three successive terms in a linear recurrence relations are: U1 = 1, U2 =, and U3 =

            If the relation is of the form  Un+1 = aUn + b, find the values of a and b, and any limit if one exists.

 

 

 

18.        If y = t2 – t show that

 

 

 

 

 

 

 

19.        If f(x) =   and  g(x) =  find h-1(x)  if h(x) = f(g(x)).

 

Show that h-1(h(x)) = x

 

 

 

 

 

20.       

 

 

 

 

 

 

           

 

 

The volume of the above box is given by   V(x) = 12x – 2x2   where the length x cm can vary from 1cm to 5cm. 

 

            Sketch the graph of V(x), and state the domain and range.

 

            Find the max. and min. volume of the box.