Converting integers from one base to another. Includes binary to decimal.

Cramers Rule applied to 3 simultaneous equations

Create a truth table for a logical expression of the form $((a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d))\operatorname{op4}e $ where each of $a, \;b,\;c,\;d,\;e$ can be one the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3},\;\operatorname{op4}$ one of $\lor,\;\land,\;\to$.

For example: $((q \lor \neg p) \to (p \land \neg q)) \lor \neg q$

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Simple application of "Power Rule" to differentiate polynomials.

Some co-efficients and powers are non-integer and some may be negative.

Simple application of "Power Rule" to differentiate single term functions.

Some co-efficients and powers are non-integer and some may be negative.

rebelmaths

Printing errors in the work produced by a particular film occur randomly at an average rate of p per page.

i.What is the probability that a one page document will contain x1 printing error(s)?

ii.If a n page document is printed, calculate the probability of having more than x2 errors. Assume a Poisson distribution.

This is a copy of a question by Ben Brawn. It replaces the JavaScript construction of the diagram with Eukleides.

This is a copy of a question by Ben Brawn. It replaces the JavaScript construction of the diagram with JSXGraph+JME.

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant

These practice questions cover:

• resolving axial forces in a truss structure
• stress & strain in a closed thin-walled pressure vessel (an example of 2D plane stress)
• use of Mohr's circle for determining principal stresses for a 2D plane stress case
• calculation of invariants for general 3D stress case, leading to von Mises stress and principal stresses

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

A function which renders the factorisation of a number in LaTeX.

Rearrange equations to make $x$ the subject.

Substitute a given value into a formula, and substitute an expression in terms of $x$ into a formula.

Rearrange equations to make $x$ the subject.

Two questions on solving systems of simultaneous equations.

Simple exercise in collecting terms in different powers of \(x\)

As it says on the tin!

Random terms including powers of x.

9 questions: Expanding out expressions such  $(ax+b)(cx+d)$ etc.

Quotient and remainder, polynomial division.

Dividing powers of x - set out as a fraction

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Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

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Looking at gradients and values for x and y for straight-line graphs