Sketch a function graph by using fist and second derivatives.

This demonstrates how to construct a JSXGraph diagram in JME code.

The construction shows a triangle and its orthocentre, circumcentre and centroid. They are always collinear. You can move the vertices of the triangle.

Students are asked to draw a hyperbola from an equation by drawing a table of graphs and plotting them.

Students are asked to draw an exponential from an equation by drawing a table of graphs and plotting them.

Students are asked to draw a parabola from an equation by drawing a table of graphs and plotting them.

Students are given the equation of a parabola and asked to identify its graph. They are given the parabolic curve, an exponential, a hyperbola and a line to choose from.

Finding areas under graphs using definite integration.

Rotate the graph of  $y=a\ln(bx)$  by $2\pi$ radians about the $y$-axis between $y=c$ and $y=d$. Find the volume of revolution.

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JSXGraph code based on original by Christian Lawson-Perfect

Numbas representation of the Metacentric Height fluid mechanics laboratory for first year Engineering students. 

Students should answer this question after completing the laboratory and the associated Excel template, including the relevant plots. 

The first question tests their capacity to correctly calculate metacentric heights, the remaining questions evaluate their graph interpretation skills. 

A quadratic is and a graph of it is given. A tangent is also sketched. The equation of the tangent line is asked for.

$f(x)= ae^{-bt}+c$ is given and plotted. A few points are plotted on the curve. $x$-coordinates are provided for two of them and $y$-coordinate provided for third. Student is required to determine other coordinates.

A quadratic is and a graph of it is given. A tangent is also sketch. The equation of the tangent line is asked for.

A quadratic equation (equivalent to $(x+a)^2-b$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

Solve the equation  5x - 8 = 32

A quadratic function is given. The graph of the function is drawn with three coordinates on the graph, without any x or y ticks.  The $x$ coordinate is given for a couple and $y$ coordinate given for the third, and coordinates are asked for.

A graph of an (invertible) cubic is given. The question is to determine values of $f$ from graph.

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Four sinusoidal graphs are given. Student should select the one which is sine and cosine.

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

A quadratic is and a graph of it is given. A tangent is also sketch. The equation of the tangent line is asked for.

Question is to calculate the area bounded by a cubic and the $x$-axis. Requires finding the roots by solving a cubic equation. Calculator question

Function $f(x) = xe^{ax}$ is sketched and area shaded. Question is to determine the area under graph, exactly and (calculator) to 3 s.f. Area is above x-axis.

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.