An object moves in a straight line, acceleration given by:

$\displaystyle f(t)=\frac{a}{(1+bt)^n}$. The object starts from rest. Find its maximum speed. 

Find the equation of a straight line which has a given slope or gradient $m$ and passes through the given point $(a,b)$.

There is a video in Show steps which goes through a similar example.

Match up equations with the corresponding lines on a graph.

This uses an embedded Geogebra graph of a line $y=mx+c$ with random coefficients set by NUMBAS.

Straightforward solving linear equations question

Straightforward solving linear equations question

Given the graph of the line determine the equation of the line.

Given the graph of the line determine the equation of the line.

Straightforward question: student must find the general solution to a second order constant coefficient ODE. Uses custom marking algorithm to check that both roots appear and that the solution is in the correct form (e.g. two arbitrary constants are present). Arbitrary constants can be any non space-separated string of characters. The algorithm also allows for the use of $e^x$ rather than $\exp(x)$.

Unit tests are also included, to check whether the algorithm accurately marks when the solution is correct; when it's correct but deviates from the 'answer'; when one or more roots is incorrect; or when the roots are correct but constants of integration have been forgotten.

Find the equation of a straight line which has a given gradient $m$ and passes through the given point $(a,b)$.

Finding x and y values for straight line graphs

Looking at gradients and values for x and y for straight-line graphs

Given the graph of the line determine the equation of the line.

Given one point and the gradient determine the equation of the line.

Identifying the gradient from a straight-line graph equation y=mx+c

Find the equation of a straight line which has a given slope or gradient $m$ and passes through the given point $(a,b)$.

There is a video in Show steps which goes through a similar example.

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No description given

Given one point and the gradient determine the equation of the line.

Given the graph of the line determine the equation of the line.

Straightforward question: student must find the general solution to a second order constant coefficient ODE. Uses custom marking algorithm to check that both roots appear and that the solution is in the correct form (e.g. two arbitrary constants are present). Arbitrary constants can be any non space-separated string of characters. The algorithm also allows for the use of $e^x$ rather than $\exp(x)$.

Unit tests are also included, to check whether the algorithm accurately marks when the solution is correct; when it's correct but deviates from the 'answer'; when one or more roots is incorrect; or when the roots are correct but constants of integration have been forgotten.

Express the equation of the given line in the form $y=mx+c$.

Express the equation of the given line in the form $y=mx+c$.

Find the equation of a straight line which has a given gradient $m$ and passes through the given point $(a,b)$.

Find the equation of the straight line which passes through the points $(a,b)$ and $(c,d)$.

Find the equation of the straight line perpendicular to the given line that passes through the given point $(a,b)$.

An object moves in a straight line, acceleration given by:

$\displaystyle f(t)=\frac{a}{(1+bt)^n}$. The object starts from rest. Find its maximum speed. 

Find the equation of the straight line parallel to the given line that passes through the given point $(a,b)$.