Free maths tools for IB Maths

Calculators that show the working, not just the answer. Each one has a worked example, the mistakes that cost marks, the keystrokes for your own calculator and links to the notes and practice questions.

Probability distributions

• Normal distribution calculatorP(X < b), P(X > a) and P(a < X < b) for X ~ N(μ, σ²), with the z-scores and a shaded curve.
• Inverse normal calculatorFind x from a probability, or an unknown mean μ or standard deviation σ, with the z-value and working.
• Binomial distribution calculatorP(X = r), P(X ≤ r), P(X ≥ r) and ranges for X ~ B(n, p), as an exact sum, with a bar chart.
• Poisson distribution calculatorP(X = r), P(X ≤ r), P(X ≥ r) and ranges for X ~ Po(λ), exact, with a bar chart.

Statistical tests

• Chi-squared test calculatorχ² test for independence (contingency table) or goodness of fit: expected values, χ², degrees of freedom and the p-value.
• t-test calculatorTwo-sample (pooled or Welch), one-sample and paired t-tests from your data: t, degrees of freedom and the p-value.
• Confidence interval calculatorA confidence interval for a mean, using t (σ unknown) or z (σ known), from summary statistics or your data.

Data and statistics

• Standard deviation calculatorσ and s (divide by n or n − 1), the variance, mean, quartiles and a box plot, from a list or a frequency table.
• Mean, median and mode calculatorMean, median, mode, range, quartiles and the interquartile range, from a list or a frequency table, with a box plot.
• Correlation and regression calculatorPearson's r, the regression line of y on x (and x on y) and Spearman's rank, with a scatter graph.

Matrices, vectors and complex numbers

• Matrix calculatorDeterminant, inverse, transpose, powers, sums and products of 2 × 2 and 3 × 3 matrices, in exact fractions.
• Complex number calculatorModulus, argument and polar form, arithmetic with two complex numbers, powers (De Moivre) and nth roots, on an Argand diagram.
• Vector calculatorMagnitude, unit vector, sum and difference, scalar product, the angle between two vectors and the vector product, in 2D or 3D.

In class

Every tool works on the board: change one number and the answer, the working and the graph update. “Copy link to these numbers” gives you a link that opens the tool with the same numbers, to share with your class. Answers are rounded to 3 significant figures; switch to 4 or 6, or full accuracy, under each tool.

In the exam

These tools are for learning and checking. In the exam you need your own calculator and your written working, so practise both: calculator guides show the keystrokes step by step. For graphs, regression models and anything you can type as an equation, use the free Grapher.