AP Calculus woes (already)

Test Preparation AP Mathematics & Computer Science
1

<p>Alright... so I sat down to work on my AP Calculus summer work, and realized that I've completely forgotten much of what'll be on the test next year! Can anyone point me in the right direction/briefly explain the concepts behind some of these problems? (answers aren't necessarily required, just a helpful hand!)</p>

<p>Question 1:
given: g(x)= radical(x-2)
What is g(g(x))?
How can you have a radical beneath another radical? What are you supposed to do? I've never seen this before...</p>

<p>Question 2:
Factor: 5x^2(x+3)^-4 - 10x(x+3)^-7
Where do you begin here? Is it some version of factor by grouping?</p>

<p>Question 3:
Simplify: log(base 1/2) 8
Can someone briefly explain how to work log problems? We did them in Algebra II two years ago...</p>

<p>Question 4:
Simplify: e^(l+lnx)
This one just... leaves me flummoxed.</p>

<p>Thanks to any takers!</p>

2

<p>Question 1: A radical under a radical is fine. Leave it.</p>

<p>Question 4: e^(a+b)=(e^a)(e^b)</p>

3

<p>Question 3: use change of base formula log(8)/log(1/2) in calc will give you -3
or without a calc, think of it as “what is the exponent that turns base 1/2 into 8?” -3 is your answer</p>

4

<p>Question 4
e^(l+lnx)
(e)(e^lnx)
(e)(x)
ex</p>

5

<p>Thank you all!</p>

6

<p>and one more question:</p>

<p>If I have
1 over
radical(x^2 +3x -1)</p>

<p>how could I rationalize that denominator?</p>

7

<p>You just multiply the numerator and the denominator by the denominator.
√(x) * √(x) = x</p>