Number and Algebra

Scientific notation


Writing a number in scientific notation


Multiplication and division


Addition and subtraction




Arithmetic sequences and series


Sequences and their notation


Arithmetic sequences


Sigma notation


Arithmetic series


Geometric sequences and series


Geometric sequences


Geometric series




Financial applications


Interest compounded annually


Compound interest – other compounding intervals


Annual depreciation


Exponents and logarithms


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:

\(a^{1/n} = a√n , a>0\)



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:



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

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)



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


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





  • 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)







Significant figures


Estimation and percentage error


Amortization and annuity


Equations and equation systems

Solving polynomial equations
Systems of linear equations

Laws of logarithms

Laws of logarithms

Rational exponents

Rational exponents
Rational exponents - alegraic manipulations

Sum of infinite geometric sequences

Infinite geometric sequences

Introduction to complex numbers

Complex solutions to quadratic equations
Cartesian form of complex numbers
Powers of complex numbers
Graphing in the complex plane

Further complex numbers

Polar and Euler forms
Multiplication and division
Powers of complex numbers
Geometric interpretations
Addition of sinusoidal functions


Definitions and equality
Addition, subtraction, multiplication by a scalar
Matrix multiplication
Matrix algebra

Eigenvalues and eigenvectors

Eigenvalues and eigenvectors
Powers of matrices


View count: 1970