Math 230 Exams

Midterm 1, Thursday 6th October, 14.00-15.20, Location  IBLC 261


The midterm will cover chapters 1, 2.1, 2.3 and more from class. (Homeworks 1, 2, 3.) It is a closed-book exam: no books, notes, or calculators may be used.

The topics covered are: problem solving, word puzzles, numeric puzzles, natural numbers, integers, rational numbers, fractions, multiples and factors, division theorem, divisibility and testing for factors 2 to 10, prime numbers, fundamental theorem of arithmetic, prime factorisation, infinity of primes, twin primes question, Goldbach question, greatest common divisor and co-prime numbers, least common multiple, Euclidean algorithm, Bezout's identity.

More detail on what we have learned is here

Extra office hours:  Tuesday 4th October, 5-6pm

Practice questions:  Lots of them with solutions are here!

Some study hints: here and here. A summary of the exam relevant ones are

  1. To study efficiently make sure you know the definitions, the algorithms/methods for computing things, the formulas for things, and results/proof methods we use most often. Perhaps write them in your own words, or explain them to a friend.
  2. Do the lecture examples, practice questions and old homeworks again without looking at the answers.
  3. Go through the posted homework solutions to gain another point of view on solving the questions.
  4. In the exam: If you get stuck on a problem in the exam then write down relevant definitions accurately. This will help to inspire you and pick up points for working. If you use a result from class say "From the result in class..." then state the result so the grader knows this isn't made up.

Midterm 2, Thursday 3rd November, 14.00-15.20, Location IBLC 261


The midterm will cover chapters 2.4, 2.5 and much more from class. (Homeworks 4, 5, 6.) It is a closed-book exam: no books, notes, or calculators may be used.

The topics covered are: definition of congruence, congruence classes, calculating least nonnegative residue, finding a missing modulus, three useful properties of congruence, solving congruences of the form x+b, solving congruences of the form ax,  symmetry theorem for congruence, encrypting/decrypting using the Caesar cipher,  encrypting/decrypting using the shift cipher, encrypting/decrypting using the affine cipher, encrypting/decrypting using the stream cipher, encrypting/decrypting using the block cipher.

More detail on what we have learned is here

Extra office hours:  Tuesday 1st November, 5-6pm

Practice questions:  More of them with solutions are here!

Some study hints: here and here. A summary of the exam relevant ones are

  1. To study efficiently make sure you know the definitions, the algorithms/methods for computing things, the formulas for things, and results/proof methods we use most often. Perhaps write them in your own words, or explain them to a friend.
  2. Do the lecture examples, practice questions and old homeworks again without looking at the answers.
  3. Go through the posted homework solutions to gain another point of view on solving the questions.
  4. In the exam: If you get stuck on a problem in the exam then write down relevant definitions accurately. This will help to inspire you and pick up points for working. If you use a result from class say "From the result in class..." then state the result so the grader knows this isn't made up.

Final exam, Saturday 10th December, 15.30-18.00, Location MATH 100

The final will cover the whole course, which is chapters 1, 2.1, 2.3, 2.4, 2.5, 5.4 and much more from class. (Homeworks 1-8.) It is a closed-book exam: no books, notes, or calculators may be used.

The topics covered are: problem solving, word puzzles, numeric puzzles, natural numbers, integers, rational numbers, fractions, multiples and factors, division theorem, divisibility and testing for factors 2 to 10, prime numbers, fundamental theorem of arithmetic, prime factorisation, infinity of primes, twin primes question, Goldbach question, greatest common divisor and co-prime numbers, least common multiple, Euclidean algorithm, Bezout's identity.

Definition of congruence, congruence classes, calculating least nonnegative residue, finding a missing modulus, three useful properties of congruence, solving congruences of the form x+b, solving congruences of the form ax,  symmetry theorem for congruence, encrypting/decrypting using the Caesar cipher,  encrypting/decrypting using the shift cipher, encrypting/decrypting using the affine cipher, encrypting/decrypting using the stream cipher, encrypting/decrypting using the block cipher.

Zero divisors, ASCII: finding a check/missing digit, detecting an error, guaranteed detection of one digit and not of 2 digits, ISBN: finding a check/missing digit, detecting an error, guaranteed detection of one digit, SIN: finding a check digit, detecting an error, UPC: detecting an error, Credit cards: finding the check digit; simple closed curve, interior/exterior for polygons and polyhedra, convex/concave for polygons/polyhedra, vertices edges and faces, equilateral, equiangular, regular polygons, infinitely many regular polygons, Euler's characteristic formula theorem, degree and edge theorem, polyhedra and regular polyhedra, edge theorems for regular polyhedra, 5 regular polyhedra.

More detail on what we have learned is here

Office hours: Friday 9th December 1-3pm

Practice questions: In addition to the ones for the previous midterms here are some more.

Some study hints: here and here. A summary of the exam relevant ones are

  1. To study efficiently make sure you know the definitions, the algorithms/methods for computing things, the formulas for things, and results/proof methods we use most often. Perhaps write them in your own words, or explain them to a friend.
  2. Do the lecture examples, practice questions and old homeworks again without looking at the answers.
  3. Go through the posted homework solutions to gain another point of view on solving the questions.
  4. In the exam: If you get stuck on a problem in the exam then write down relevant definitions accurately. This will help to inspire you and pick up points for working. If you use a result from class say "From the result in class..." then state the result so the grader knows this isn't made up.

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