This question demonstrates how to plot a graph of a function using JSXGraph.

Shear and bending moment diagram for a beam loaded with an arbitrary parabolic distributed load described with a loading function.  Integrate to find reactions and equations for shear and bending moment.

Example of an explore mode question. Student is given a 3x3 matrix and is asked to find the characteristic polynomial and eigenvalues, and then eigenvectors for each eigenvalue. The part asking for eigenvectors can be repeated as often as the student wants, to be used for different eigenvalues.

Assessed: calculating characteristic polynomial and eigenvectors.

Feature: any correct eigenvalue will be recognised by the marking algorithm, even multiples of the obvious one(s) (which can be read off from the reduced row echelon form)

Randomisation: Not randomised, just using particular matrices. I am still working on how to randomise this for 3x3; a randomised 2x2 version exists. I have several different versions for 3x3 (not all published yet), so I could make a random choice between these in a test.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".

Find the area, first moment of area, and coordinates of a general spandrel.  The area may be above or below the function.

Example of an explore mode question. Student is given a 2x2 matrix with eigenvalues and eigenvectors, and is asked to decide if the matrix is invertible. If yes, second and third parts are offered where the student should give the eigenvalues and eigenvectors of the inverse matrix.

Assessed: remembering link between 0 eigenvalue and invertibility. Remembering link between eigenvalues and eigenvectors of matrix and its inverse.

Randomisation: a random true/false for invertibility is created, and the eigenvalues a and b are randomised (condition: two different evalues, and a=0 iff invertibility is false), and a random invertible 2x2 matrix with determinant 1 or -1 is created (via random elementary row operations) to change base from diag(a,b) to the matrix for the question. Determinant 1 or -1 ensures that we keep integer entries.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".

Definite integation of basic functions.

This test will assess a students ability to work with piecewise and composite functions.

No description given

No description given

No description given

No description given

No description given

Complementary function/particular integral for forced simple harmonic motion (non-resonant)

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

Compute a table of values for a quadratic function. A JSXgraph plot shows the curve going through the entered values.

No description given

No description given

Given a randomised rational function select the possible ways of writing the domain of the function.

Given a randomised rational function select the possible ways of writing the domain of the function.

No description given

Simple application of "Power Rule" to differentiate single term functions.

Some co-efficients and powers are non-integer and some may be negative.

A function which renders the factorisation of a number in LaTeX.

No description given

Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.

rebelmaths

Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.

rebelmaths

Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.

rebelmaths

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

Missing: Application with bacteria, turning points, difficult chain rule

This question is to test if you know how to use your calculator correctly.

given trig function applied to tides. students need to find max depth, time of low tide and times between which a boat of given depth can use the port.