IBDP Maths AA - Number and Algebra

Standard form

A way to represent numbers as ax10^k where a is between 1 and 10, and k is an integer indicating how many times a is multiplied or divided by 10.

Laws of indices

Rules to simplify expressions with exponents, including laws for multiplication, division, addition, subtraction, and powers of powers.

Partial fractions

A method to simplify rational expressions into the sum of fractions with constant numerators, aiding in integration of rational functions.

Logarithms

The inverse of exponents, where loga b = x if a^x = b, with key laws like loga xy = loga x + loga y.

Arithmetic Sequences & Series

Sequences with a constant difference between terms, with nth term formula An = a + (n-1)d and series sum formula Sn = n/2(2a + (n-1)d).

Geometric Sequences & Series

Sequences with a common ratio between terms, with nth term formula An = ar^(n-1) and series sum formula Sn = a(1-r^n)/(1-r).

Proof by Deduction

Showing a result is true for all integers, consecutive integers, or even/odd numbers.

Proof by Induction

Proving a result for a set of integers by showing it's true for one integer and the next.

Proof by Contradiction

Proving a result by showing the negation of the result is false.

Binomial Theorem

A method to expand a two-term expression raised to a power using the formula (a + b)^n = Σ(n choose k) a^(n-k) b^k.

Permutations

Number of possible arrangements when order matters, calculated using nPr = n!/(n-r)!.

Combinations

Number of possible arrangements when order doesn't matter, calculated using nCr = n!/(r!(n-r)!).

Complex Numbers

Numbers represented in the complex plane, with Cartesian form z = a + bi, and operations like addition, subtraction, multiplication, and division.