A-Level · 9231 · Interactive simulations
37 unique simulations20 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 (37 cards in all). Back to the A Level Further Mathematics course →
Slide c and d: the vertical asymptote sits at x = −d/c. Slide a: the horizontal asymptote is y = a/c.
Slider p changes the degree of the numerator of a rational function; watch how the curve behaves for large |x|.
Set the slider to n = 20, raise the maximum to 1000 and watch the sum of the first n terms of 1/(r(r + 1)) creep towards 1.
Reveal the common point, then move slider a until there is no unique solution and slider b to get a whole line of solutions.
Set the entries of matrix A, then drag the vertices of the left-hand polygon and compare its area with that of its image.
Set a and b, then drag the θ slider to trace the curve. Compare a > b, a = b (a cardioid) and a < b.
Set the start and stop angles with sliders or input boxes and change the number of sectors approximating the area.
Drag the θ slider at the bottom right: the Cartesian graph of r against θ and the polar curve are drawn together.
Change the components of u and v: u × v stays perpendicular to both, with length |u||v| sin θ, the area of their parallelogram.
Click through the steps: points A and B, the direction vectors, their vector product and the projection giving the distance.
Drag the components of three vectors a, b and c, show the parallelepiped and step through the volume calculation.
Place the blue arrow (the induction step) at each number in turn: it passes "true" from n to n + 1, starting from the base case.
Compare the graph of cosh(ax) with the two exponential terms it is made from: their sum gives a curve with minimum value 1.
Traces the point (cos t, sin t) on the circle x² + y² = 1 and (cosh t, sinh t) on the hyperbola x² − y² = 1.
Rotate the unit vector v until Av lies along the same line: the stretch factor is the eigenvalue. Then change a, b, c, d.
Blue lines through the origin are mapped by the matrix M to the red lines; the invariant lines can be displayed.
Move the green slider to trace the parametric curve, then the blue slider to see the gradient, tangent and normal.
Type a polynomial equation in x and y, then drag the red point C round the curve; P plots the gradient at C.
Halve the interval again and again: the length of the polygonal path closes in on the arc length integral.
Slide the points a and b to change the interval, or type a new f(x) in the input field.
Change the number of segments with the slider and the end values of the parameter with sliders or input boxes.
Move the blue point c and the slider n: the n roots sit on one circle, equally spaced at angles of 2π/n.
Drag two complex numbers on the Argand diagram and compare their moduli and arguments with those of the product.
Move the a, b, c sliders: when b² > 4ac the solution dies away without oscillating; when b² < 4ac it oscillates.
Fire at 30° and at 60° with the same speed: the range is the same, but the steeper shot flies higher and for longer.
Change the angle of projection and the initial speed and watch the path of the projectile being traced.
A plank on a pivot: place masses at chosen distances and see whether it balances.
Use the sliders and buttons to show the velocity and acceleration vectors, then use the diagram to derive v = rω and a = rω².
Adjust the speed of the ball and watch the radius of its horizontal circle change.
Pull the spring with the applied-force slider and change the spring constant: the extension is proportional to the force.
Hang masses on springs of adjustable stiffness, measure the equilibrium extension and follow the energy as they oscillate.
On Explore 1D set the masses, velocities and elasticity, then play: elasticity is the coefficient of restitution e as a percentage.
Vary the coefficient of restitution, the starting positions and the launch speed; the displacement–time graph shows every collision.
Raise n for narrower bars, then change m: P(0 ≤ X ≤ m) is the total bar area, which becomes the area under f(x).
Change the degrees of freedom and drag the critical values: for small ν the tails are heavier, so critical values lie further out.
Take new samples and watch the interval move while the population mean stays fixed; vary the % level and the sample size.
Slide the purple point (the test statistic): reject H₀ once the purple p-value area is smaller than the blue area α.
Each simulation stays the property of its source and is credited on the card inside the lesson. Back to the A Level Further Mathematics course →