# Scientific notation

## Writing a number in scientific notation

## Multiplication and division

## Addition and subtraction

## Powers

# Arithmetic sequences and series

## Sequences and their notation

## Arithmetic sequences

## Sigma notation

## Arithmetic series

# Geometric sequences and series

## Geometric sequences

## Geometric series

## Applications

# Financial applications

## Interest compounded annually

## Compound interest – other compounding intervals

## Annual depreciation

# Exponents and logarithms

## Roots

Roots of numbers and algebraic expressions in radical form **can be written in an equivalent form using rational exponents**. Writing roots as exponents allows you to apply exponent rules to your work with roots.

For rational exponents:

\(a^{1/n} = a√n , a>0\)

## Logarithms

You learned that \(a^x=b\) **(exponential form)** is equivalent to \(log_ab=x \space for \space a>0, \space a≠1 \space and \space b>0\)

**You will be able to use your calculator to evaluate logarithms in the exam**. However, you need to understand the properties of logarithms when simplifying algebraic expressions such as \(log_a^3\).

The following properties of logarithms are useful for working with logarithms but are not included in the IB formula booklet. You should memorize them or be able to derive them from the definition of a logarithm:

\(log_a1=0\)

\(log_aa=1\)

\(e^{ln (m)} = m\)

The laws of logarithms are given in the IB formula booklet and do not need to be memorized. When you use these laws it’s important to remember that they only apply to logarithms with the same base.

**Exam questions** involving logarithm laws **will only be asked for base 10 and base e.**

**Logarithms can be always calculated using a calculator.**

## Laws of exponents (Should be prior knowledge but also given in the formula booklet)

\(a^m×a^n=a^{(m+n)}\)

\(\frac{a^m}{a^n}=a^{m-n}\)

\({\left( {{a^m}} \right)^n} = {a^{m \times n}}\)

\(\left(ab\right)^m=a^mb^m\)

\({\left( {\dfrac{a}{b}} \right)^m} = \dfrac{{{a^m}}}{{{b^m}}}\)

\(a^{-m}=\frac1{a^m}\)

\(a^0=1\)

## Tips

- You can always use your calculator, having trouble solving something? use the graphing function on your GDC
- Always read and answer the question (ATFQ! - Mr Header SKC)

# Approximation

## Rounding

## Significant figures

## Estimation and percentage error

# Amortization and annuity

# Equations and equation systems

# Laws of logarithms

# Rational exponents

# Sum of infinite geometric sequences

# Introduction to complex numbers

# Further complex numbers

# Matrices

# Eigenvalues and eigenvectors

# Editors

- CD_FER - 616 words.

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