Maximising the volume of a rectangular box

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This question guides students through the process of determining the dimensions of a box to minimise its surface area whilst meeting a specified volume.

Maximising the volume of a rectangular box

Finding the stationary points of a cubic with two turning points

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

Find the gradient of  $ \displaystyle ax^b+\frac{c}{x^{d}}+f$ at $x=n$

Q1 is true/false question covering some core facts, notation and basic examples.  Q2 has two functions for which second derivative needs to be determined.

Using simple substitution to find $\lim_{x \to a} bx+c$, $\lim_{x \to a} bx^2+cx+d$ and $\displaystyle \lim_{x \to a} \frac{bx+c}{dx+f}$ where $d\times a+f \neq 0$.

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 exercise will help you solve equations of type ax-b = c.

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