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ExaminerPrepexaminerprep.com · IB Maths simulations: 28 Free Interactive Models

Free · 28 interactive models

IB Maths simulations

Interactive models for IB Maths Analysis and Approaches, SL and HL: series, functions, trigonometry, vectors, probability and calculus you can drag and explore.

Also: IB Physics simulations · IGCSE Physics simulations · the original 71 IB Physics & Maths simulations

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1 · Number and algebra

Arithmetic and geometric series

Arithmetic and geometric seriesOpen →1

Compound interest and depreciation

Change the principal, rate, compounding frequency and time to compare simple, compound and continuous models, for growth or for depreciation. Drag acrOpen →1

Proof by induction

Step through the base case and inductive step for three statements, watching the dominoes and the algebra together. Remove a step to see why both are Open →1

Permutations and combinations

Pick n objects and r of them, then step through every ordered arrangement. Each row of the grid is one unordered selection with its r! orderings, whicOpen →1

De Moivre's theorem

Set z = r(cos θ + i sin θ) and watch its powers zⁿ spiral round the Argand diagram, or switch mode to see the n nth roots of a number form a regular pOpen →1

Systems of linear equations

Systems of linear equationsOpen →

2 · Functions

Composite functions

Pick f and g, then drag an x-value through two function machines to see how f∘g and g∘f differ in formula, graph, domain and range.Open →2

Exponential models

Adjust A, k and c in y = A·e^(kt) + c to fit a set of data points, drag the points to make your own data, and see how the half-life or doubling time dOpen →2

Modulus functions and inequalities

Compare y = f(x), y = |f(x)| and y = f(|x|) for linear, quadratic and cubic functions, then solve an inequality against a straight line by seeing wherOpen →2

Polynomials and the factor theorem

Polynomials and the factor theoremOpen →

3 · Geometry and trigonometry

Transformations of trigonometric graphs

Change a, b, c and d in y = a sin(b(x − c)) + d and watch the amplitude, period, phase shift and principal axis change against the base graph. Drag thOpen →3

Solving trigonometric equations

Choose sin x, cos x or tan x, set the value k and an interval, and watch every solution appear on the graph and on the unit circle. Drag up and down oOpen →3

Volume and surface area of 3D solids

Choose a solid, change its dimensions and rotate it to see how the volume and total surface area formulas respond.Open →3

Ambiguous case of the sine rule

Fix angle A and side b, then change side a: watch side a swing from C and see whether it meets the base zero, one or two times, with both possible angOpen →3

Vector equations of lines in 3D

Build two lines r = a + λb from integer vectors, rotate the 3D view, and see whether they intersect, are parallel or are skew, together with the acuteOpen →3

Compound angle and double angle identities

A right-angled triangle of hypotenuse 1 is rotated through angle A inside a rectangle, so the heights and widths add up to sin(A + B) and cos(A + B). Open →

4 · Statistics and probability

Venn diagrams and conditional probability

Choose P(A), P(B) and P(A ∩ B) and watch the Venn diagram reshape. Shade any region, read off P(A | B), and test whether the events are independent orOpen →4

Discrete random variables

Build your own probability distribution table, see its bar chart, E(X) and Var(X), then run thousands of random trials to watch the sample mean settleOpen →4

Continuous random variables

Pick a probability density function, then drag a and b on the graph (or use the sliders) to shade P(a < X < b) as an area under f(x). The lower graph Open →4

Bayes' theorem: medical test

Set how common a condition is and how accurate a test is, then see through a tree diagram and 1000 people how likely a positive result really means haOpen →4

Standard deviation and outliers

Drag the data points on the top number line and watch the mean, standard deviation, quartiles and 1.5 × IQR fences respond. The lower line shows the tOpen →

5 · Calculus

Chain and product rules

Pick a composite or product function, drag the point along the curve and watch the tangent gradient being assembled step by step from the chain rule oOpen →5

Second derivative and points of inflexion

Graph f, f′ and f″ together and drag the point along the curve to see where f is concave up or down, where the stationary points are and where the poiOpen →5

Trapezoidal rule and Riemann sums

Split the area under a curve into n trapezia or rectangles and watch how the approximation, the exact integral and the error change as n grows.Open →5

Displacement and distance travelled

Watch a particle move along a line while the area under its velocity–time graph builds up: signed area gives displacement, total area gives distance tOpen →5

Euler's method and differential equations

Pick a differential equation, drag the starting point on the slope field and watch Euler's method take tangent steps. Compare each estimate with the eOpen →5

Implicit differentiation

Choose a curve defined by an equation in x and y, drag a point along it and see dy/dx found by implicit differentiation, together with the tangent linOpen →5

Related rates of change

Watch a sliding ladder, a filling cone and a growing circle, pause at any moment, and see how one known rate fixes another through the chain rule.Open →

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