Express $\displaystyle \frac{a}{x + b} + \frac{cx+d}{x^2 +px+ q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{a}{x + b} +\frac{c}{(x + b)^2}$ as an algebraic single fraction.

Express $\displaystyle \frac{a}{x + b} +\frac{cx+d}{(x + b)^2}$ as an algebraic single fraction.

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.

The derivative of $\displaystyle x ^ {m}(ax^2+b)^{n}$ is of the form $\displaystyle x^{m-1}(ax^2+b)^{n-1}g(x)$. Find $g(x)$.

Differentiate $\displaystyle \ln((ax+b)^{m})$

Differentiate

\[ \sqrt{a x^m+b})\]

Differentiate $\displaystyle e^{ax^{m} +bx^2+c}$

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.

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

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

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

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

dddddd

test description

No description given

This is supposed to demonstrate allowing one of two different free variables in the student's answer, but only marked as correct if the same free variable is used in all gaps. The custom marking algorithm should extend to any number of gaps, and one could add more alternative answers to allow for more free variable names. It doesn't allow just any free variable name.

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

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

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

No description given

No description given

No description given

No description given