Standard Level · maths-aa-sl · Interactive simulations
IB Mathematics: Analysis and Approaches SL Simulation Lab
45 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 (45 cards in all). Back to the IB Mathematics: Analysis and Approaches SL course →
1 · Number and algebra
- GeoGebraIB AA 1.1
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.
1.2Exponents and logarithms
1 sim- GeoGebraIn the lesson
The three laws of logarithms
Slide p and q and check each line: log(pq) = log p + log q, log(p/q) = log p − log q, log(p^q) = q log p.
1.3The binomial theorem
3 sims- GeoGebraIn the lesson
Binomial expansion, n = 1 to 6
Slide n from 1 to 6, then change a and b: match each coefficient to a row of Pascal's triangle times powers of a and b.
- GeoGebraIB AA 1.3
Pascal's triangle and nCr
Sliders n (row) and m (position in the row) pick out one entry of Pascal's triangle; a button resets both to 0.
- GeoGebraIB AA 1.3
Binomial approximation near x = 0
Vary a, n and the number of terms kept in the expansion of (1 + ax)^n and compare the cut-off polynomial with the true curve.
2 · Functions
- PhETIn the lesson
Graphing Lines
On Point-Slope, drag the point and the slope handle and watch y − y1 = m(x − x1) update; then try Slope-Intercept.
- GeoGebraIB AA 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
Restrict the domain, get an inverse
Slide left and right to shrink the domain until the green reflection in y = x passes the vertical line test.
- GeoGebraIB AA 2.2
Building the graph of g(h(x))
Move x0 along the x-axis: the construction carries it through h and then g, and the red point D marks g(h(x0)).
2.3Quadratic functions and equations
2 sims- GeoGebraIn the lesson
Three forms of a quadratic
Tick a form and move its sliders: p and q are the x-intercepts, (h, k) is the vertex, c is the y-intercept.
- GeoGebraIB AA 2.3
Discriminant and number of roots
Sliders a, b and c reshape the parabola so you can count its x-intercepts.
2.4Transformations of graphs
1 sim- GeoGebraIn the lesson
Transforming y = f(x) with sliders
In g(x) = a f(b(x − h)) + k, a stretches vertically, b scales x by 1/b, h and k translate. Try a = −1.
- GeoGebraIn the lesson
Remainder and factor theorems
Drag the slider to a value a: the vertical segment is the remainder f(a), and it vanishes when (x − a) is a factor.
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 AA 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.
3.3The unit circle and radian measure
2 sims- GeoGebraIn the lesson
Unit circle exact values
Drag the point round the circle; at π/6, π/4 and π/3 its coordinates (cos θ, sin θ) appear in exact form.
- GeoGebraIB AA 3.3
Radians and arc length
Drag the black points to change the angle and the radius and compare the arc lengths.
- GeoGebraIn the lesson
Amplitude, period and shift of sine
Slide A and ω: the amplitude is A and the period is 2π/ω; B lifts the midline. Tick Show properties to check.
- PhETIB AA 3.4
Trig Tour
Drag the point round the unit circle; choose sin, cos or tan to see its value and its graph drawn against the angle.
- GeoGebraIn the lesson
Every solution in the interval
Set a and the start and end of the interval, count where y = a cuts the curve, then tick Show solutions.
4 · Statistics and probability
4.1Descriptive 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 AA 4.1
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.
- GeoGebraIB AA 4.1
Frequency chart to cumulative frequency
Drag the blue points to change the class intervals and frequencies; the cumulative frequency graph and box plot redraw.
- GeoGebraIn the lesson
Why it is called least squares
Drag the two Drag Me points to shrink the sum of squares, then tick Show LSRL and Show Centroid.
- GeoGebraIB AA 4.2
Getting a feel for r
Choose the number of points with the slider, drag them anywhere, guess the correlation coefficient and then reveal it.
- GeoGebraIn the lesson
Venn diagram drawn to scale
Slide P(A ∩ B) and check P(A ∪ B) = P(A) + P(B) − P(A ∩ B); the overlap shrinks as the events separate.
- GeoGebraIB AA 4.3
Probability tree with rolling balls
A tree diagram with an adjustable probability on each branch; 100 balls roll through and are counted at each exit.
- GeoGebraIn the lesson
Build a distribution and find E(X)
Give each value a probability so the total is 1, run the simulation and watch the sample mean settle towards E(X).
4.5The binomial distribution
1 sim- PhETIB AA 4.5
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.
4.6The normal distribution
2 sims- GeoGebraIn the lesson
Normal probability as an area
Set a = μ − σ and b = μ + σ: the shaded area P(a < X < b) is about 0.68 whatever μ and σ are.
- GeoGebraIB AA 4.6
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 chord to tangent as h → 0
Tick secant line and show slopes, then slide h towards 0: (f(x+h) − f(x))/h closes in on the tangent's slope f'(x).
- PhETIB AA 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
The product rule as a growing area
Slide t and tick rate of change: the area uv grows by two strips, u·dv/dt and v·du/dt, which is the product rule.
- GeoGebraIB AA 5.2
Derivatives of sin(ax) and cos(ax)
Move the red point along the curve to see its gradient; one slider swaps sine and cosine, another sets a in f(x) = sin(ax).
- GeoGebraIn the lesson
Reading f, f′ and f″ together
Drag the point on the curve and tick Show f ' and Show f '': the tangent is flat where f ' = 0; f '' changes sign at the inflection.
5.4Optimization and kinematics
2 sims- GeoGebraIn the lesson
Open box: volume against cut size
Slide c to change the cut, then switch Function ON: V = c(l − 2c)(w − 2c) peaks where dV/dc = 0.
- GeoGebraIB AA 5.4
Particle motion: s, v and a
Press RESET then START: a particle moves along the vertical axis while position (blue), velocity (green) and acceleration (red) are graphed.
- GeoGebraIn the lesson
The family of antiderivatives F(x) + C
Slide C: every curve F(x) + C is the same shape shifted vertically, so all have the same gradient f(x) at each x.
- GeoGebraIn the lesson
Volume of revolution about the x-axis
Keep f(x) = sqrt(x) and slide b: the solid grows and the volume is π∫ y² dx from a to b, here π·b²/2 when a = 0.
- GeoGebraIB AA 5.6
Area between two curves
Drag the red points along the x-axis to set the limits; type your own two functions to see the area between them calculated.
- GeoGebraIB AA 5.6
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.
Each simulation stays the property of its source and is credited on the card inside the lesson. Back to the IB Mathematics: Analysis and Approaches SL course →