Number and Algebra

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

 
Amortization
 
 
Annuity
 
 
 

Equations and equation systems

 
Solving polynomial equations
 
 
Systems of linear equations
 
 
 

Laws of logarithms

 
Logarithms
 
 
Laws of logarithms
 
 
 

Rational exponents

 
 
Rational exponents
 
 
Rational exponents - alegraic manipulations
 
 
 

Sum of infinite geometric sequences

 
 
Infinite geometric sequences
 
 
Applications
 
 
 

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
 
 
 

Matrices

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

Eigenvalues and eigenvectors

 
 
Eigenvalues and eigenvectors
 
 
Powers of matrices

Editors

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