Find the points of intersection of a straight line and a circle.

Calculate a repeated integral of the form $\displaystyle I=\int_0^1\;dx\;\int_0^{x^{m-1}}mf(x^m+a)dy$

The $y$ integral is trivial, and the $x$ integral is of the form $g'(x)f'(g(x))$, so it straightforwardly integrates to $f(g(x))$.

Calculate a repeated integral of the form $\displaystyle I=\int_0^1\;dx\;\int_0^{x^{m-1}}mf(x^m+a)dy$

The $y$ integral is trivial, and the $x$ integral is of the form $g'(x)f'(g(x))$, so it straightforwardly integrates to $f(g(x))$.

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.

Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by substitution 3 with parts' by Joshua Boddy.

Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by elimination 1 with parts' by Joshua Boddy.

Tests Algebra, Graphing Straight Lines, Probability, Statistics

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.

Tests the ability to find the gradient and intercept of a straight line graph.

A graph of a straight line $f$ is given. Questions include determining values of $f$, of $f$ inverse, and determing 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.

A graph of a straight line $f$ is given. Questions include determining values of $f$, of $f$ inverse, and determining the equation of the line.

A graph of a straight line $f$ is given. Questions include determining values of $f$, of $f$ inverse, and determing the equation of the line.

A graph of a straight line $f$ is given. Questions include determining values of $f$, of $f$ inverse, and determing the equation of the line. Non-calculator. Detail advice is given.

Straight line graph formula

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

Match up equations with the corresponding lines on a graph.

This question asks a student to draw a straight line graph by dragging points.

This question asks a student to draw a straight line graph by dragging points.

This question asks a student to draw a straight line graph by dragging points.

This question asks a student to draw a straight line graph by dragging points.

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

Finding x and y values for straight line graphs

Finding x and y values for straight line graphs

Completing a table of x and y values from a straight line graph equation.

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

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

Identifying straight-line equations, and correlations.

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

This question asks a student to draw a straight line graph by dragging points.