The answer to this question is a differential equation involving $y''$, $y'$ and $y$.

A variable value generator for $y$ ensures that the right values are tested to check that the student's answer is equivalent to the expected equation.

Match up equations with the corresponding lines on a graph.

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Given the graph the student enters the equation

Ready to use

Given the graph the student enters the equation

Ready to use

Given the graph the student enters the equation

Ready to use

Given the graph the student enters the equation

Ready to use

Given the graph the student enters the equation

Ready to use

Given the graph the student enters the equation

Ready to use

Find a regression equation.

Solving a differential equation of the form $\frac{dy}{dx}=\frac{ax^n}{y}$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=axy^2$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=axy$ using separation of variables.

Here you'll see a first example of how a map can arise from a system of differential equations and gain some first insight into the dynamics of 1D maps.

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Solve a Differential equation with 3 simple linear factors

Solve equation involving exponential function

Solve equation involving exponential function.

Solve equation involving exponential function.

Solve equation involving logarithmic function.

Solve equation involving logarithmic function.

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Set up and solve an equation = 1, to ensure a function is a CRV

Find the equation of a line given a point and a parallel line.

Find the equation of a line given a point and a parallel or perpendicular line.

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A function $f(x) = cln(ax^2+bx) -x$ is sketched and tangent is also drawn. The equation of the tangent line is asked for and $x$-coordinate for horizontal tangent is asked for. Calculator.

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.