Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

Differentiate $\displaystyle \cos(e^{ax}+bx^2+c)$.

Contains a video solving a similar example.

Express $\displaystyle \frac{a}{x + b} \pm  \frac{c}{x + d}$ as an algebraic single fraction over a common denominator. 

Contains a video in Show steps.

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.

Factorise $\displaystyle{ax ^ 2 + bx + c}$ into linear factors. 

Find $c$ and $d$ such that $x^2+ax+b = (x+c)^2+d$.

Calculations of the lengths of two 3D vectors, the distance between their terminal points, their sum, difference, and dot and cross products.

Product of one of 2, 3, 5, 9, or 10 by a number up to 10. With hints to learn calculation rather than memorisation.

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.

test description

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The student is asked to factorise a quadratic $x^2 + ax + b$. A custom marking script uses pattern matching to ensure that the student's answer is of the form $(x+a)(x+b)$, $(x+a)^2$, or $x(x+a)$.

To find the script, look in the Scripts tab of part a.

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

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

Fill in the blank on this statement (1 mark)

Two multiple choice questions for Tearoom Trade

Multiple response question (3 correct out of 6). Selection of questions from a pool. Adapted from Mario's True/False template.

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

No description given