Summary
IB SL AA Math Summary Notes
- Course
- Institution
Summary notes for the SL Math AA course for revision or a study guide.
[Show more]
Seller
Follow
anniechow
Content preview
IB SL MATHS SUMMARY NOTESLOGS AND EXPONENTIALS
INDEX NOTATION
34
Exponent/ power/ index
Base
INDEX LAWS
FRACTIONAL INDICES
1
𝑛
𝑎 𝑛 = √𝑎
𝑚 1 𝑚 𝑚
𝑛
𝑎𝑛 = (𝑎 )
𝑛 = ( √𝑎 )
EXPANSION AND FACTORISATION
- a(b+c) = ab + ac
- (a+b)(c+d) = ac+ad+bc+bd
- (a+b)(a-b) = a2-b2
- (a+b)2 = a2+2ab+b
- (a-b)2 = a2-2ab+b2
,EXPONENTIAL GRAPHS
𝑓(𝑥) = 𝑎 𝑥 EXPONENTIAL GROWTH FUNCTION 𝑓(𝑥) = 𝑎− 𝑥 EXPONENTIAL DECAY FUNCTION
1 1
Graph passes through (−1, ) and (1, 𝑎) Graph passes through (1, ) and (−1, 𝑎)
𝑎 𝑎
Graph passes through (0,1)
• Domain is all real x
• Range is all real positive numbers
• Y intercept is 1
• No x intercepts
BASE e
Base e = irrational number (2.718 …)
LOGARITHMS
𝑏 = 𝑎 𝑥 then loga b = x
e.g. 8 = 23 then log28 = 3
PROPERTIES OF LOGARITHMS
Rule i.e.
Logaa = 1 𝑎1 = 𝑎
Loga1 = 0 𝑎0 = 1
Loga𝑎𝑛 = n 𝑎𝑛 = 𝑎𝑛
WHEN ARE LOGS UNDEFINED?
Logab if b is negative
Loga0
,LOGARITHMIC FUNCTIONS
𝑦 = 𝑎𝑥
𝑦=𝑥
𝑦 = 𝑙𝑜𝑔a𝑥
Properties of 𝑦 = 𝑙𝑜𝑔a𝑥
• Domain: all positive real numbers
• Range: all real numbers
• X intercept 1
LOG BASE 10 AND NATURAL LOGS
Log to the base 10 Log10x = logx
Log to the base e (natural logs) Logex = lnx
EXPONENTIAL AND LOGARITHMIC FUNCTIONS
a logarithmic function is the inverse of the exponential function
If 𝑓(𝑥) = ⅇ 𝑥 then 𝑓 −1 (𝑥) = 𝑙𝑜𝑔ex
Loga𝑎 𝑥 = alogax = x
Lnex = elnx = x
Log of an exponential/ exponential of a log = x
LOG LAWS
**must learn by <3
Log x + log y = logxy
𝑥
Log x – log y = log
𝑦
Logxn = nlogx
, CHANGE OF BASE
SOLVING EXPONENTIAL EQUATIONS
- Take the ‘log’ of both sides
SOLVING LOGARITHMIC EQUATIONS
1. Ensure that both side of the equation are logarithms with the same base and the equating
the argument (the expression inside the bracket) i.e. “cancelling” the logs
Or
2. By using an exponent
** For both of these methods you must check that the solution/ solutions are possible.
You cannot have the log of a negative number
Sub your solution back into what was in the brackets of the log and then check the result is
positive
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller anniechow. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $10.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
75323 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now