Math AA SL Algebra Recap.notebook
Mathsl1 Channel
This presentation is not produced by IBO. It is simply a review I made for my students
in PEI, Canada in order to help refresh their memories before the IB exams. This
presentation is not an exhaustive list of the different sections and problem types in
ALGEBRA; it’s just an overview of some key concepts.
There are timestamps and downloadable notes in the video description. Be sure to
make use of YouTube’s many accessibility options including closed captioning, auto­
translating those closed captions, pausing, rewinding, and adjusting the speed.
There are often many different ways to solve a particular problem. If you have a
different (but valid) method that you are comfortable with, then use it. The questions in
this presentation are meant to illustrate the concepts at hand, however they do not
represent the trickiest problems that IB is likely to set. In order to best prepare for
problem solving, you’ll need to *do* a bunch of practice problems.
Enjoy!
Ian Toms
Algebra Review
Exponents and Logarithms
Exponent Rules for a>0 and b>0
Ex. ) Evaluate or simplify.
a)
d)
b)
c)
e)
Math AA SL Algebra Recap.notebook
Scientific Notation: a×10b where 1<a<10 and b
Mathsl1 Channel
Z.
Ex. ) Find the volume of a cube with side lengths of 4×1013m. Present your answer in
the form a×10b m3 where 1<a<10 and b Z.
Logarithms
The expression
asks, "what power needs to be applied to 2 to make 1/8?"
You must be able to change an equation from logarithmic to exponential form using the
fact that
.
Ex.) Solve to 3 significant figures:
If no base is shown on a logarithm, the base is assumed to be 10. Natural logs have a
base of e. In the real number system, you can only take the log of a positive number.
Logs are particularly useful for solving equations where the variable is in the
exponent.
Ex.) Solve
Log Laws
Other Facts
Math AA SL Algebra Recap.notebook
Mathsl1 Channel
Logarithmic Equations
"Converters" (not all terms are logs) ­ make a single log on one side (use log laws),
convert to exponential form, solve, check
"Droppers" (all terms logs) ­ create a single log of the same base on each
side (use log laws), drop the logs, solve, then check
ex.) Solve for x.
ex.) Solve for x.
Change of Base Rule
Let
a)
b)
and
. Write the following in terms of x and y only.
Math AA SL Algebra Recap.notebook
Mathsl1 Channel
Sequences and Series
Arithmetic Sequences have a common difference (increase/decrease through addition
of a fixed amount).
The nth term of an arithmetic sequence is given by:
The sum of the first n terms of an arithmetic series is given by:
Geometric Sequences have a common ratio (increase/decrease through multiplication
by a fixed amount).
The nth term of a geometric sequence is given by:
The sum of the first n terms of a geometric series is given by:
The sum of an infinite geometric series is given by:
iff r is between ­1 and 1
Ex.) An arithmetic sequence has u20 = 62 and S20 = 670. Find the value of u1 and the
value of d.
Ex.) A geometric sequence has u1 = 2 and a common ratio of 3. Which term number will
be the first to exceed 1000 000?
Math AA SL Algebra Recap.notebook
Mathsl1 Channel
Sigma Notation
Sigma means "sum". The expression
means the sum of the
terms for p­values from 4 to 7.
When there are many terms, write out the first few and look for a pattern.
For example,
Finance
Compound Interest: is geometric growth; is exponential growth
Ex.) Barrett invests $10 000 at 9% per annum, compounded quarterly.
a) Find the value after 10 years.
b) Find the effective annual interest rate.
c) Find the value after 10 years if he had invested at 9% P.A. with simple interest.
Math AA SL Algebra Recap.notebook
Mathsl1 Channel
Logic and "Show That" Questions
If the command term is "show that", simply do the problem. Don't work backward.
They're just being nice enough to tell you the answer in case you can't get it, but need
it for the next part of the question.
Ex. ) Show that
Binomial Expansion
Coefficients come from Pascal's triangle (which is built from combinations)
1
1
1
1
1
2
3
4
1
3
6
1
4
1
ex.) a) Expand
b) Hence, find the coefficient of x2 in
Math AA SL Algebra Recap.notebook
Look for patterns in your variables to find specific terms
ex.) Find the constant term in the expansion of
Mathsl1 Channel