Finding the stationary points of a cubic with two turning points

Finding the stationary points of a rational function with specific features.

A graphical approach to aiding students in writing down a formal proof of discontinuity of a function at a given point.

Uses JSXgraph to sketch the graphs and involves some interaction/experimentation by students in finding appropriate intervals.

Find modulus and argument of two complex numbers. Then use De Moivre's Theorem to find negative powers of the complex numbers.

Find modulus and argument of two complex numbers. Then use De Moivre's Theorem to find positive powers of the complex numbers.

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

Given three vectors with integer components, find the corresponding magnitude and direction.

Given three vectors with integer components, find the corresponding magnitude and direction.

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

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

Refresher questions on topics in algebra that students beginning a maths undergraduate course should be familiar with.

Calculations involving elementary probability, and several questions designed to draw out misconceptions to do with probability.

Quiz covering basic arithmetic with complex numbers and solving roots for a quadratic with complex solutions

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

This uses an embedded Geogebra SHM graph with coefficients set by NUMBAS.

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

The subtraction algortihm using the borrow and pay back method with integers.

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.

Find the equation of a straight line which has a given slope or gradient $m$ and passes through the given point $(a,b)$.

There is a video in Show steps which goes through a similar example.

Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.

rebelmaths

Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.

rebelmaths

Implicit differentiation question with customised feedback to catch some common errors.

Implicit differentiation question with customised feedback to catch some common errors.

Given data on probabilities of three levels of success of three options and projections of the profits that the options will accrue depending on the level of success, find the expected monetary value (EMV) for each option and choose the one with the greatest EMV.

Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$  with coefficients in the real numbers. Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by: \[\phi(p(x))=p(a)+p(bx+c).\]Using the standard basis for range and domain find the matrix given by $\phi$.

Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$  with coefficients in the real numbers.

Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by:

$\phi(p(x))=ap(x) + (bx + c)p'(x) + (x ^ 2 + dx + f)p''(x)$

Using the standard basis for range and domain find the matrix given by $\phi$.

Simple probability question. Counting number of occurrences of an event in a sample space with given size and finding the probability of the event.

rebelmaths

Some impossible-looking questions about quadratic equations which can be solved with a bit of thinking.