IB Mathematics: Applications and Interpretation Ultimate Guide

Natural Numbers (N)

The set of positive counting numbers, starting from 1.

Integers (Z)

The set of all whole numbers, including negative numbers and zero.

Rational Numbers (Q)

Numbers that can be expressed as fractions a/b, where a and b are integers.

Irrational Numbers

Numbers that cannot be expressed as fractions; their decimal representations are non-terminating and non-repeating.

Real Numbers (R)

The set of all rational and irrational numbers.

Rounding Up

When rounding, numbers greater than 4 are rounded up, and numbers 4 or less are rounded down.

Significant Figures (s.f.)

Digits in a number that are significant, including all non-zero digits, zeros between non-zero digits, and trailing zeros in decimals.

Addition/Subtraction with s.f.

The result should have the same number of decimal places as the number with the fewest decimal places.

Multiplication/Division with s.f.

The result should have the same number of significant figures as the number with the fewest significant figures.

Scientific Notation

A way of expressing numbers as a product of a coefficient (1 ≤ a < 10) and a power of ten.

Percentage Error

The accuracy of an approximate value compared to the exact value, expressed as a percentage.

Arithmetic Sequences

A sequence with a constant difference between consecutive terms.

Geometric Sequences

A sequence with a constant ratio between consecutive terms.

Sigma Notation

A compact way to represent the summation of a sequence using the Greek letter Σ.

Exponent Rules

Mathematical rules that define how to handle operations on exponents.

Logarithms

The inverse operations of exponentiation, showing the exponent needed to produce a certain number.

Binomial Theorem

A formula for expanding expressions of the form (a + b)ⁿ.

Compound Interest

Interest calculated on the initial principal and the accumulated interest from previous periods.

Depreciation

The reduction in the value of an asset over time.

Functions

Mathematical relationships where each input has one output, often expressed as f(x).

Linear Functions

Functions characterized by a constant rate of change leading to straight-line graphs.

Quadratic Functions

Functions that involve the square of the variable, usually forming parabolic shapes.

Trigonometry

The study of relationships between angles and sides in triangles.

Probability

A numerical description of how likely an event is to occur, ranging from 0 (impossible) to 1 (certain).

Normal Distribution

A continuous probability distribution that is symmetric around the mean, showing that data near the mean are more frequent.

Expected Value

The average or mean value of a random variable in a probability distribution.

Bayes' Theorem

A formula that describes how to update the probability of a hypothesis based on new evidence.