Given a linear programming problem in standard form, write down the dual problem.

Nature of fixed points of a 2D dynamical system.

These examples are either centres or spirals.

Compute a table of values for a quadratic function. A JSXgraph (the graph paper) plot shows the curve going through the entered values. The student input is now disconnected from the graph so that they slide the points usually after they input the values and the answer fields are not updated.

Given a linear programming problem in standard form, write down the dual problem.

Given a linear programming problem in standard form, write down the dual problem.

Compute a table of values for an exponential function. The student input is now disconnected from the graph so that they slide the points on the graph after they input the values and the answer fields are not updated. Now includes a graph in advice.

Compute a table of values for a quadratic function. A JSXgraph (the graph paper) plot shows the curve going through the entered values. The student input is now disconnected from the graph so that they slide the points usually after they input the values and the answer fields are not updated.

This question uses the vis.js library to plot 3D functions and data sets.

As well as JME functions to make plots, you can use javascript functions to get more control over how the plots are rendered.

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

Compute a table of values for a quadratic function. A JSXgraph (the graph paper) plot shows the curve going through the entered values. The student input is now disconnected from the graph so that they slide the points usually after they input the values and the answer fields are not updated.

Compute a table of values for a quadratic function. A JSXgraph (the graph paper) plot shows the curve going through the entered values. The student input is now disconnected from the graph so that they slide the points usually after they input the values and the answer fields are not updated.

Compute a table of values for a quadratic function. The student input is now disconnected from the graph so that they slide the points on the graph after they input the values and the answer fields are not updated. Now includes a graph in advice.

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

Calculate the functional value at a point.

Calculate the functional value at a point.

The derivative of $\displaystyle x ^ {m}(ax^2+b)^{n}$ is of the form $\displaystyle x^{m-1}(ax^2+b)^{n-1}g(x)$. Find $g(x)$.

Finding the zero of a non-polynomial function

Some simple questions around injectivity, surjectivity, bijectivity (and the inverse function) of linear functions $\mathbb R\to \mathbb R$ (i.e., $x\mapsto mx+b$ for some real numbers $m$, $b$).

More work on differentiation with trigonometric functions

Introductory function notions

This assessment reviews some of the material covered in the first lecture session. 

What is the function of the given graph?

Gives students an introduction to the injective property of functions

Introduces students to the floor and ceiling functions

Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

Determine the largest possible domain of a rational function.

Determine if a function is odd, even or neither. 

Small demo using the JME implementation of JSXGraph inline in a multiple choice question. This version uses a JME variable to store the expressions and then calls a function wherever a plot is required.

This question is the one described in method 1 of the example "Apply a standard integral" in the Numbas documentation.

The student is shown a randomly chosen function to integrate. The function is one of $e^{kx}$, $x^k$, $\cos(kx)$, $\sin(kx)$, with $k$ a randomly chosen integer.

Differentiate $ (a+bx) ^ {m} \sin(nx)$

The derivative of $\displaystyle x ^ {m}(ax^2+b)^{n}$ is of the form $\displaystyle x^{m-1}(ax^2+b)^{n-1}g(x)$. Find $g(x)$.