International Baccalaureate Mathematics Analysis and Approaches
Number and Algebra
These are the statements describing what students need to learn:
[Higher Level only statements are in blue]
- operations with numbers in the form a × 10k where 1 ≤ a < 10 and k is an integer
- arithmetic sequences and series. Use of the formulae for the nth term and the sum of the first n terms of the sequence. Use of sigma notation for sums of arithmetic sequences.
Analysis, interpretation and prediction where a model is not perfectly arithmetic in real life.
- geometric sequences and series. Use of the formulae for the nth term and the sum of the first n terms of the sequence. Use of sigma notation for the sums of geometric sequences
Use of sigma notation for the sums of geometric sequences.
- financial applications of geometric sequences and series: compound interest and annual depreciation
- laws of exponents with integer exponents. Introduction to logarithms with base 10 and e.
Numerical evaluation of logarithms using technology
- simple deductive proof, numerical and algebraic; how to lay out a left-hand side to right-hand side (LHS to RHS) proof. The symbols and notation for equality and identity
- laws of exponents with rational exponents.
Laws of logarithms
Change of base of a logarithm.
Solving exponential equations, including using logarithms
- Sum of infinite convergent geometric sequences.
- the binomial theorem including the expansion of (a+b)n,n ∈ N. Use of Pascal's triangle and nCr
- Counting principles, including permutations and combinations. Extension of the binomial theorem to fractional and negative indices, ie (a+b)n, n ∈ Q
- Partial fractions
- Complex numbers: the number i, where i2=-1.
Cartesian form z=a+bi; the terms real part, imaginary part, conjugate, modulus and argument. The complex plane.
- Modulus–argument (polar) form:
Sums, products and quotients in Cartesian, polar or Euler forms and their geometric interpretation.
- Complex conjugate roots of quadratic and polynomial equations with real coefficients. De Moivre’s theorem and its extension to rational exponents. Powers and roots of complex numbers.
- Proof by mathematical induction. Proof by contradiction. Use of a counterexample to show that a statement is not always true.
- Solutions of systems of linear equations (a maximum of three equations in three unknowns), including cases where there is a unique solution, an infinite number of solutions or no solution.
Click on a statement above for suggested resources and activities from Transum.