SAT Subject Test Mathematics Level 2

Using   the defining    equation     with   n   =   3,  you have

Thus,   .

Use the calculator:  .  Thus,   x 4     ≈   5.29.

39 . D
The area of any triangle is . Call the base of triangle ABC side AC and say that the
height drawn from point B to base AC meets base AC at point D.

Base    AC  of  triangle    ABC is  a   radius  of  the circle. The area    of  the semicircle  is  8π. So  if  the

radius  of  the semicircle  is  r   (in particular, r   =   AC  =   BC),    then     ,  πr^2    =   16π,    r^2     =    16 ,

and r   =   4.  So  AC  =   4   and BC  =   4.

You can find    the height  BD  of  the triangle    in  terms   of  θ   by  saying  that     ,  so  BD  =

BC  sin θ   =   4   sin θ.  Thus    the base    AC  is  4,  and the height  BD  is  4   sin θ.  The area    of  the triangle    is

40 . B

When    two or  more    events  are independent,    the probability that    all the events  occur   is  equal

to  the product of  the probabilities   that    each    event   occurs. The decimal equivalent  of  70% is

0.7.    In  this    question,   the probability that    a   person  selected    at  random  from    each    room    is  a

senior  at  university  X   is  0.7.    So  the probability that    each    of  the 3   people  selected    is  a   senior  at

university  X   is  (0.7)(0.7)(0.7) =   0.343.

41 . E