Maria Aneiros

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.

Evaluate a limit

Displacement-time graphs are given and the student should select the correct velocity-time graphs from a list. Includes linear, piecewise linear and quadratic displacement-time functions.

Adding several rational functions.

It is estimated that 30% of all CIT students cycle to college. If a random sample of eight CIT students is chosen, calculate the probability that...

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$X \sim \operatorname{Binomial}(n,p)$. Find $P(X=a)$, $P(X \leq b)$, $E[X],\;\operatorname{Var}(X)$.

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A student selects a card from a deck of 52 and rolls a dice once.

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Independent events in probability. Choose whether given three given pairs of events are independent or not.

A bag contains balls of three different colours. You're told how many there are of each, and asked the probability of picking a ball of a particular colour.

Previous throws don't affect the probability distribution of subsequent throws. Believing otherwise is the gambler's fallacy.

Given descriptions of some pairs of random events, pick the ones which are mutually exclusive.

Given the probability that a basketball shot misses the hoop, find the probability that it's on target - use the law of total probability.

First part asks for the probability of rolling an even number. Second part asks for the probability of not rolling either of two given numbers.

This question provides practice at adding, subtracting, dividing and multiplying complex numbers in rectangular form.

Using a given list of four complex numbers, find by inspection the one that is a root of a given cubic real polynomial and hence find the other roots.

Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

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.

Calculating complex numbers raised to an natural number exponent

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

Direct calculation of low positive and negative powers of complex numbers. Calculations involving a complex conjugate. Powers of $i$. Four parts.

Composite multiplication and division of complex numbers. Two parts.

Inverse and division of complex numbers.  Four parts.

This question provides practice at adding, subtracting, dividing and multiplying complex numbers in rectangular form.

Multiplication and addition of complex numbers. Four parts.

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

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

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

Multiple choice question. Given a randomised polynomial select the possibe ways of writing the domain of the function.