Find $\displaystyle \int x\sin(cx+d)\;dx,\;\;\int x\cos(cx+d)\;dx $ and hence $\displaystyle \int ax\sin(cx+d)+bx\cos(cx+d)\;dx$

Find $\displaystyle \int (ax)\ln(cx)\; dx $

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

5 indefinite integrals containing exponential functions

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Find roots and the area under a parabola

Function $f(x) = xe^{ax}$ is sketched and area shaded. Question is to determine the area under graph, exactly and (calculator) to 3 s.f. Area is above x-axis.

Question is to calculate the area bounded by a cubic and the $x$-axis. Requires finding the roots by solving a cubic equation. Calculator question

Graphs are given with areas underneath them shaded. The student is asked to select the correct integral which calculates its area.

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.

Rate of change problem involving velocity & acceleration

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.