Student is asked to sketch square root graph, by plotting several points and selecting the correct graph.

Student sketches 1/x, by plotting several points and then selecting the graph from a list

Given a graph of a cubic, the student is asked how many stationary points f has.

$f(x)=   c\ln(ax^2+bx)-x$ is sketched. A tangent is also sketched. The equation of the tangent line is asked for. Shorter because in the original, I also ask for the $x$-coordinate of the maximum point.

A graph (of a cubic) is given. The question is to determine the number of roots and number of stationary points the graph has. Non-calculator. Advice is given.

A cubic with a maximum and minimum point is given. Question is to determine coordinates of the minimum and maximum point. Non-calculator. Advice is given.

Implicit differentiation.

Given $x^2+y^2+dxy +ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.

Differentiate

\[ \sqrt{a x^m+b})\]

Finding the stationary points of a cubic with two turning points

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

Given the original price of a smartphone and the rate at which it decreases, calculate its price after a given number of months. In the second part, calculate the time remaining until the price goes below a certain point.

Students enter equation and turning point

Students enter equation and turning point

Given the original price of a smartphone and the rate at which it decreases, calculate its price after a given number of months. In the second part, calculate the time remaining until the price goes below a certain point.

Assesses basic differentiation and finding turning points of curves.

Students enter equation and turning point

Divergence of vector fields.

Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.

Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

rebel

rebelmaths

Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

rebel

rebelmaths

Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

rebel

rebelmaths

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.

Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

rebel

rebelmaths

Questions asking you to find the equation of a line between two points, in Cartesian coordinates.

Elementary examples of multiplication and addition of complex numbers. Four parts.

Students enter equation and turning point

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=x^2-y^2$, and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point.

If you want to modify $f(x,y)$ simply change the definition of  $f(x,y)$ and that of the variable  str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$.