Standard Level · maths-ai-sl · Interactive simulations
IB Mathematics: Applications and Interpretation SL Simulation Lab
39 unique simulations25 lessons2 sources
Every simulation here runs the real model — the applets a teacher would put on the board, from PhET and GeoGebra, not a video of one. Pick a topic, open a card inside its lesson to run it next to the notes, or jump straight to the source. A simulation that fits several lessons is listed under each of them (39 cards in all). Back to the IB Mathematics: Applications and Interpretation SL course →
1 · Number and algebra
- GeoGebraIB AI 1.1
Rounding on a number line
A number is placed on a scale; the green slider changes how many significant figures the scale is marked to.
- GeoGebraIB AI 1.2
Arithmetic series as an area
Enter a first term and common difference (1 to 5), drag the slider to add terms, then use the buttons to reflect and translate the staircase.
- GeoGebraIn the lesson
Compounding more often
Set the rate with the top slider, tick the blue box and raise M (compoundings a year): the step graph nears a smooth curve.
- GeoGebraIB AI 1.3
Paying off a loan
Drag the green blob to set the total term of a mortgage; the monthly repayment is calculated and shown on the graph.
1.4Exponents and logarithms
1 sim- GeoGebraIn the lesson
Exponential and log as inverses
Tick both curves and the axis of symmetry, then slide a: every point (x, y) on y = a^x mirrors to (y, x) on y = log_a x.
- GeoGebraIn the lesson
Two equations, one intersection
Use the slider bars to change each equation; the point where the two lines cross is the solution of the system.
2 · Functions
- PhETIB AI 2.1
Graphing Lines
Drag a point and a slope handle to build a line; the Point-Slope and Slope-Intercept screens write its equation live.
- GeoGebraIB AI 2.1
Gradients of perpendicular lines
Move the points that set the gradient of your line; a perpendicular line is drawn and you compare the two gradients.
- GeoGebraIn the lesson
A function and its inverse
Type f(x), press Reflect and run the horizontal line test: the mirror image in y = x is a function only if each line cuts f once.
- PhETIB AI 2.3
Curve Fitting
Drag data points onto the graph and fit a linear, quadratic or cubic curve; the fit statistics update as the points move.
- GeoGebraIB AI 2.4
Half-life decay
Type the initial amount (green box) and the half-life (blue box), then drag the red point along the decay curve.
2.5Modelling with sinusoidal functions
2 sims- GeoGebraIn the lesson
Ferris wheel height as a sine model
Change the radius, centre height and seconds per revolution: they set the amplitude, principal axis and period of the height graph.
- GeoGebraIB AI 2.5
Amplitude, period and shift of sine
Sliders change the amplitude, period and shifts of a sine curve.
- GeoGebraIn the lesson
Straightening an exponential with logs
Type a growth factor and an initial value: the points (x, log y) taken from the curve line up, with gradient log b and intercept log a.
3 · Geometry and trigonometry
- GeoGebraIn the lesson
Cone: volume, surface area and net
Move the sliders for h and r and follow the worked volume and total surface area; find the slant height on the net.
- GeoGebraIB AI 3.1
Angles inside a tetrahedron
A tetrahedron with base sides 8 cm and height 10 cm: drag the sliders to turn the view and tick the HINTS boxes.
3.2Trigonometry: sine and cosine rules
3 sims- GeoGebraIn the lesson
The sine rule in any triangle
Drag a vertex: the ratios a/sin A, b/sin B and c/sin C stay equal however the triangle changes.
- GeoGebraIB AA 3.2
Cosine rule in any triangle
Drag any vertex; the six parts of the triangle are shown together with c², a² + b² and a² + b² − 2ab cos γ.
- GeoGebraIB AA 3.2
The ambiguous case (SSA)
With angle A fixed, move point X to set side b and use the slider for side a; the possible triangles appear in red and green.
- GeoGebraIn the lesson
Bearings measured from north
Slide B to turn the arrow: the true bearing is measured clockwise from north (316°T); the compass form gives the acute angle (N44°W).
- GeoGebraIn the lesson
Adding, subtracting and scaling vectors
Drag A and B and tick each box: a + b joins tip to tail, a − b adds the reverse of b, and the slider k stretches or flips a.
- GeoGebraIn the lesson
Relative position and closest approach
Tick the boxes in turn: B relative to A is r_B − r_A, and the two are closest when that is perpendicular to the relative velocity.
4 · Statistics and probability
4.2Descriptive statistics
3 sims- PhETIn the lesson
Center and Variability
On Mean & Median, kick several balls, then drag one far out: the mean chases the outlier while the median barely moves.
- GeoGebraIB AI 4.2
Frequency chart to cumulative frequency
Drag the blue points to change the class intervals and frequencies; the cumulative frequency graph and box plot redraw.
- GeoGebraIB AI 4.2
Mean and SD under X → aX + b
Drag the data points, then use sliders a and b to transform every value by X → aX + b; mean and SD are shown for both sets.
- PhETIn the lesson
Least-Squares Regression
Drag points onto the graph, tick Best-Fit Line and read r; then drag one point away and watch the line and r change.
- GeoGebraIn the lesson
Tree diagram without replacement
Set the total and the number of blue balls, then move the step slider: the second-draw fractions change because the first ball is not replaced.
- GeoGebraIB AI 4.4
Venn diagram drawn to scale
Set P(A), P(B) and P(A ∩ B) directly; the two circles and their overlap are drawn to scale.
4.6Binomial and Poisson distributions
2 sims- GeoGebraIn the lesson
Binomial and Poisson side by side
Tick Binomial and slide n and p: the bars centre on np. Tick Poisson and raise λ: the peak follows λ and the spread widens.
- PhETIB AI 4.6
Plinko Probability
Drop balls through rows of pegs; set the number of rows and the chance of bouncing right, and compare the histogram with the ideal one.
4.7The normal distribution
2 sims- GeoGebraIn the lesson
Area under the normal curve
Type μ and σ, then drag the two red points: the shaded area is P(a < X < b), about 0.68 for μ ± σ and 0.95 for μ ± 2σ.
- GeoGebraIB AI 4.7
One standard deviation either side
100 random normal data points: randomise them, drag the movable lines to guess mean ± 1 SD, then tick Show Statistics.
5 · Calculus
- GeoGebraIn the lesson
From secant slope to tangent slope
Drag the red point along the curve towards the purple one: the secant's slope closes in on the tangent's slope, the derivative there.
- PhETIB AI 5.1
Calculus Grapher
Drag on the graph of f(x) to reshape it and watch the derivative graph redraw beneath; a tangent tool shows the slope at a point.
- GeoGebraIn the lesson
Tangent and normal at a point
Slide a to move P along y = x² and tick both boxes: the tangent has gradient 2a, the normal −1/(2a), so the two gradients multiply to −1.
- GeoGebraIB AI 5.2
Open box: volume against cut size
Sliders set the size of the cardboard and the cut size c; the box is drawn and its volume is plotted against c.
- GeoGebraIn the lesson
Definite integral as area
Type f(x) and slide the limits a and b: the shaded area equals F(b) − F(a), with the antiderivative F shown in the working.
- GeoGebraIB AI 5.3
Area so far is an antiderivative
g(x) is the area under f from a to x: tick Show f(t) and Show FTC, then drag the points x and a.
- GeoGebraIn the lesson
Trapezoidal rule strip by strip
Raise the number of trapezia and watch the sum close in on the exact area under the curve.
Each simulation stays the property of its source and is credited on the card inside the lesson. Back to the IB Mathematics: Applications and Interpretation SL course →