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

Students must find $\int \frac{1}{x-a} \, dx$.

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

A simple situational question about a box of chocolates, asking how many of each type there are, what percentage of the box they represent, the probability of picking one and ratios of different types.

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$.

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx $ and hence find $\displaystyle \int (ax+b)^2\sin(cx+d)\; dx $ 

Also two other questions on integrating by parts.

Find  $\displaystyle \int\cosh(ax+b)\;dx,\;\;\int x\sinh(cx+d)\;dx$

Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$, $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$, $\int_0^{r}x ^ {2}e^{t x}\;dx$

Evaluate $\int_0^{\,m}e^{ax}\;dx$, $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$. 

Finding areas under graphs using definite integration.

This is an old demo. For a demonstration of Numbas's current features, please see the newest demo exam.

A few questions which show off various features of Numbas.

Find $\displaystyle I=\int \frac{2 a x + b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.

Simple exercises introducing the fundamental set operations, and NUMBAS syntax for sets.

This test contains questions from Lecture Unit 1.1: General Principles.

Demonstration of the written number extension, which converts whole numbers to words.

Simple exercises introducing the fundamental set operations, and NUMBAS syntax for sets.

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Calculate the concentration of a dilute acid given the amount and concentration of dilute alkali to neutralise it. Cribbed from this Bitesize problem.

There are steps to break down the calculation, and the student must give units at each step.

Preparing solutions to given concentrations/dilutions.

Standard simple integrals asked for (1/x, sin(x), cos(x), x^2, x, e^x)

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