This document acts as an index for the extensive collection of arithmetic example sheets which will eventually be added to this site. The example sheets all contain 20 individual exercises which may be downloaded, printed and handed out to students as required. When all exercises have been completed it is expected that there will be over 6000 individual examples for students to work out!

The individual exercises in each group are all of the same kind; separate corresponding answer sheets are available for checking student work. The main categories - more or less in ascending order of difficulty are -

• Whole Numbers The sets of exercises in this group are all to be done without the aid of calculator or other tool - these are all about mental arithmetic, learning to spot patterns and use a range of short-cuts and tricks without using any mechanical or electronic tools -
  1. Addition - up to four digit numbers.
  2. Subtraction - up to four digit numbers.
  3. Factors - ie expressions involving only addition and subtraction.
  4. Multiplication
  5. Division - including remainder and modulus operators.
  6. Terms - not involving addition or subtraction.
  7. Simple Expressions - expressions with any of the above operators - but not involving powers.
  8. Powers - examples requiring simplification of exponent expressions before (depending on the exercise) evaluation of the answers
  9. Expressions - of arbitrary complexity, containing all of the above!
• Rational Numbers The sets of exercises in this group should, again, all be done without the aid of a calculator; once more these are all about mental arithmetic and exact answers - building on the tricks and short-cuts found when dealing with simple whole numbers -
  1. Normalisation - exercises in which the objective is to normalise the given numbers so that the numerator and denominator have no common factors.
  2. Multiplication - NOT YET AVAILABLE!
  3. Division - NOT YET AVAILABLE!
  4. Addition - NOT YET AVAILABLE!
  5. Subtraction - NOT YET AVAILABLE!
  6. Expressions - NOT YET AVAILABLE!
• Real Numbers While the results for examples in this group are arbitrary real numbers, students should be encouraged only to resort to the use of a calculator or other aid in the final stages of evaluating an answer. This is to impress upon them that calculators can introduce quite alarming rounding errors if used unwisely (some of the later exercises are written to bring out this possibility when evaluating answers) -
  1. Factors - NOT YET AVAILABLE!
  2. Terms - NOT YET AVAILABLE!
  3. Simple Expressions - NOT YET AVAILABLE!
  4. Powers - NOT YET AVAILABLE!
  5. Expressions - NOT YET AVAILABLE!
• Logarithms/Exponents Should a student be interested in looking at statistics or more advanced mathematics, some knowledge of logarithms (both natural and to other bases) will be essential. The use of logarithms is therefore introduced here in conjunction with their exponent counterparts -
  1. Simple Logarithms - NOT YET AVAILABLE!
  2. Exponentiation - NOT YET AVAILABLE!
  3. Natural Logarithms - NOT YET AVAILABLE!
  4. Different Bases - NOT YET AVAILABLE!
  5. Expression Evaluation - NOT YET AVAILABLE!
• Complex Numbers Complex numbers are introduced here as an extension of real numbers with the intention of de-mystifying their use when learning algebraic number manipulation, leading into trigonometry and engineering mathematics generally -
  1. Factors - NOT YET AVAILABLE!
  2. Terms - NOT YET AVAILABLE!
  3. Expressions - NOT YET AVAILABLE!
  4. Coordinates - NOT YET AVAILABLE!
  5. Conjugates - NOT YET AVAILABLE!
  6. Angles - NOT YET AVAILABLE!
  7. Hyperbolic Functions - NOT YET AVAILABLE!