1.Let f(x)=a(x-h)2+k. The vertex of the graph of f is at (2, 3) and the graph passes through (1, 7) .
(a) Write down the value of h and of k .
(b) Find the value of a .
2.In an arithmetic sequence, the third term is 10 and the fi fth term is 16.
(a) Find the common difference.
(b) Find the fi rst term.
(c) Find the sum of the fi rst 20 terms of the sequence.
3.Let f(x)=x2 .
(a) Find ∫21( f(x) )dx .
(b) The following diagram shows part of the graph of f .
The shaded region R is enclosed by the graph of f , the x-axis and the lines x=1 and x=2 .
Find the volume of the solid formed when R is revolved 360°about the x-axis.
4.(a) Write down the value of
(i) log327 ;
(b) Hence, solve log327+log81/8-log164=log4x.
5.Celeste wishes to hire a taxicab from a company which has a large number of taxicabs.The taxicabs are randomly assigned by the company.
- The probability that a taxicab is yellow is 0.4.
- The probability that a taxicab is a Fiat is 0.3.
- The probability that a taxicab is yellow or a Fiat is 0.6.
Find the probability that the taxicab hired by Celeste is not a yellow Fiat.