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.

Finding X-Y intercepts for quadratic and cubic equations.

A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Find a regression equation.

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Find a regression equation.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

All the answers in this question are equations. In order to mark each equation, Numbas needs to pick some values that satisfy the equation and some that don't, and check that the student's answer agrees with the expected answer.

Any equation with the same solution set as the expected answer will be marked correct.

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Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

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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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