This question asks you to place a point on a number line.

This question allows you to practice plotting points on graphs.

This question allows you to practice placing points on a number line.

This question allows you to practice identifying points on graphs.

This question allows you to practice identifying points on graphs.

Slope of a curve at a point

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

Slope of a curve at a point

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

Missing: Application with bacteria, turning points, difficult chain rule

Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

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.

Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it at a given point.

The word problem is about the costs of sweets in a sweet shop.

Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it at a given point.

The word problem is about the costs of sweets in a sweet shop.

Application of differentitaion in geology. A projectile problem.

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.

Slope of a curve at a point

Student is asked to drag points onto the unit circle, to represent sin(x) and cos(x), where x is a multiple of 45 degrees.

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

rebel

rebelmaths

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.

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.

Student is asked to drag points onto the unit circle, to represent sin(x) and cos(x), where x is a multiple of 45 degrees.

A function of the form f(x)= sin(ax+b) is given and plotted. A few points are plotted on the curve. $x$-coordinates are provided for two of them and $y$-coordinate provided for third. Student is required to determine other coordinates.

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.