Download MI4 PS06 - F16

MI - 4
Teacher (circle):
NC
NC
NC
1)
Condie
Problem Set: 6
Dowling
Loo
means you have to show all work done by hand, with no calculator use.
Find exact value for log(100!) – log(99!).
2)
Given MAX with mA  36 , x  17, and a  13 , solve for the length of side m to the nearest
tenth.
3)
Solve each equation for n:
 2n 
 2n  1
a) 13  
  7

 n  2
 n3 
NC
ID Number____________
Mods: __________
4)
 3n  1  3n  1
b) 4  


 n   n 1 
Find the sum of each series, leaving complex answers in a + bi form. You may again assume
that for complex numbers a  bi, with a  bi  1 our formula for the sum of infinite
geometric series is valid.

i
a)   
n 1  2 
5)
1 i 
b)  

n 1  2 
n

n
In triangle ABC, a  12, b  10, and c  9 . Find the measure of the largest angle in triangle
ABC.
f ( x)  f ( x)
.
2
Determine (if possible), whether g is an even function or an odd function. Show your reasoning.
NC
6)
NC
7)
Let f be a function whose domain includes all real numbers. Define g ( x) 
Erik wants to form 4-digit integers using only the digits 1, 2, 3, and 4. He is allowed to
repeat digits. What is the probability that he forms a 4-digit integer where at least one digit
repeats? Express your answer as a common fraction.
PS 6.1
Rev. 16
MI - 4
Teacher (circle):
NC
Problem Set: 6
Dowling
Loo
Condie
ID Number____________
Mods: __________
8) Suppose that an isosceles triangle has two sides of length a and one side of length c.
a. Find the area of the triangle in terms of a and c. Simplify as much as you can.
b. A well-known formula for the area of a triangle is called Hero’s Formula. It is given by
s(s  a)(s  b)(s  c), where s 
abc
.
2
Use this formula to find the area of the isosceles triangle from part a.
Note: You may not use this formula in part a.
NC
9) The sum of a number, a, and its reciprocal is 1. Let an be the sum of the nth power of a and its
reciprocal. That is, an  a n 
1
.
an
a. Find the sequence an n 1
3
b. Find the value of a6
NC
 2x  4 
10) Let f ( x)  ln 
 .
 3x 
a. Find the domain of f.
b. Find all x for which f ( x )  0
NC
11) Find the last two digits of the number 112016 .
PS 6.2
Rev. 16