Paul Howes

What is the function of the given graph?

$I$ compact interval. $\displaystyle g: I \rightarrow I, g(x)=\frac{ax}{x^2+b^2}$. Find stationary points and local maxima, minima. Using limits, has $g$ a global max, min? 

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

5 questions on finding local and global maxima and minima on compact intervals and on the real line for differentiable functions.

Given a graph of some function f, the student is asked for values of $f$ and its inverse. Function is cubic and invertible.

Finding the stationary points of a cubic with two turning points

Choose the graph that represents the differential of the given graph

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Using Pythagoras' theorem to determine a non-hypotenuse side, where side lengths include surds and students enter using sqrt syntax

Converting Radians to Degrees

Converting Degrees to Radians

Areas of triangles

rebelmaths

Given the original formula the student enters the transformed formula

Recall and use of formulae for volume and surface area of a sphere.

Finding surface area and volume, given formulae.

Area and circumference of circles

Using Pythagoras' theorem to determine the hypotenuse, where side lengths include surds and students enter using sqrt syntax

Given the original formula the student enters the transformed formula

Finding lengths of sides of triangles

This question asks a student to draw a straight line graph by dragging points.

Converting to standard form in both positive and negative powers

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$I$ compact interval. $\displaystyle g: I\rightarrow I, g(x)=\frac{x^2}{(x-c)^{a/b}}$. Are there stationary points and local maxima, minima? Has $g$ a global max, global min? 

$g: \mathbb{R} \rightarrow \mathbb{R}, g(x)=\frac{ax}{x^2+b^2}$. Find stationary points and local maxima, minima. Using limits, has $g$ a global max, min? 

$I$ compact interval, $g:I\rightarrow I$, $g(x)=(x-a)(x-b)^2$. Stationary points in interval. Find local and global maxima and minima of $g$ on $I$. 

$I$ compact interval, $g:I\rightarrow I,\;g(x)=ax^3+bx^2+cx+d$. Find stationary points, local and global maxima and minima of $g$ on $I$

$I$ compact interval, $g:I\rightarrow I,\;g(x)=ax^3+bx^2+cx+d$. Find stationary points, local and global maxima and minima of $g$ on $I$