Download PS #2

IMSA
(1)
(b)
(3)
(4)
(5)
(6)
(7)
Prob. Set #2
DUE: Friday, September 4th Fall 2015
Let f (x)  x 3  3x  4 .
(a)
(2)
MI-4
f (2  h)  f (2  h)
.
2h
If h were very close to 0, what would your answer to Question 1a be close to? Why?
Simplify the expression
Let g(x)  x 5 14x 4  67x 3 108x 2  34x 156 . Given that 3 and 5  i are zeroes of g (x ) , find all the
remaining zeroes.
The sum of an infinite geometric series an n1 is 48 and a2  9 . Find all possible pairs a1 , r  of the
first term and the common ratio.

Find the inverse of each function:
2x  5
(a)
(b) g(x)  log7 (2x  3)  2
f (x) 
5x  3
(c)
h(x) 
7  3x5  2
4th
4
Find all possible values of sin( x) cosx if sin(x)  cos x 
8
.
15
3
(b)
Find all possible values of sin( x)  cosx if sin(x)cos x  .
7
1
1
1
1



 3.
Solve for x:
log 3 (x) log 25 (x) log 9 (x) log 5 (x)
(a)
In how many different ways can 7 boys and 5 girls stand in a circle under the following condition? Show
thinking!
a.
Anyone can stand next to anyone else (i.e., there are no special conditions).
b.
No one is standing next to someone of the same gender.
c.
The seven boys must stand together and the five girls must stand together
d.
The five girls must stand together.
(8)
Consider the sequence of squares formed by
connecting the midpoints of a square whose sides
are four inches long.
a) Find the length of A3B3.
b)
Find a formula for the length of AnBn.
c)
Find the area of AnBnCnDn.
A2
A1
A3
B3
B2
D2
C3
B1
P.S. 2.1
D1
D3
C2
C1
IMSA
MI-4
Prob. Set #2
DUE: Friday, September 4th Fall 2015
9. Write using summation notation:
a) 5 + 2 + 1 + 4 . . . . . . . . . . +100
b) 32 +24+18+ . . . . . . . + 81/8
10. The Fibonacci sequence ƒn begins 1, 1, 2, 3, 5, 8, … where an  an2  an1 .
f
a) Find the first eight ratios n 1 of successive terms of the Fibonacci sequence. State each ratio to 8
fn
decimal places.
b) Solve x 2  x  1  0 exactly. Guess: How are parts (a) and (b) related?
c) State another interesting piece of information about the Fibonacci sequence. (Search,
ask, and state something true about this sequence.)
P.S. 2.2