Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

Some questions that use the quantities extension to handle units.

Asks the student to add two single-digit numbers, one of which might be negative.

This uses an embedded Geogebra graph of a polar function with random coefficients set by NUMBAS.

Quadratic equation

An example of using the GeoGebra extension to ask the student to create a geometric construction, with marking and steps.

Unit conversion

An example of using the GeoGebra extension to ask the student to create a geometric construction, with marking and steps.

Recognising that $(x-a)^2+(y-b)^2=r^2$ is a circle of radius $r$ with centre $(a,b)$ 

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

Apply and combine logarithm laws in a given equation to find the value of $x$.

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Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

Solve for $x$:  $\log_{a}(x+b)- \log_{a}(x+c)=d$

Angle conversion

Quadratic equation

Unit conversion

Collecting like terms

Collecting like terms

Power rule

Transpose equation

Product rule

Transpose equation

Percentages

BODMAS

Significant figures

Linear equations

Quotient rule

Product rule