Regular problem-solving classes in Norwich

Thursday 12th March 2020

Year 12 and 13 students, from schools and colleges in Norwich and the surrounding areas, have been spending their Saturdays in the University of East Anglia developing mathematical problem-solving skills through discussion and collaboration.

Regular problem-solving classes are designed to help students to develop strategies and confidence when tackling unfamiliar problems in maths, and will help with preparations for taking advanced papers such as the MAT, TMUA and STEP examinations. Delivered in different formats across the region and the country, classes greatly enrich students’ mathematical experience and help them to develop a better understanding of A level Mathematics and Further Mathematics.

The course covers a wide range of mathematical disciplines with problems, such as...

Number (digits and divisibility)

  • We looked at sequences such as factorials and their many applications when illustrating certain behaviours:
    Why \(2+100!\), \(3+100!\), \(4+100!\), ..., \(100+100!\) is a sequence of 99 consecutive numbers that doesn't include a prime number?
  • We looked at divisibility definition and what language needs to be used when making deductions about divisibility:
    Show that if \(m\) is a multiple of \(33\) and \(n\) is a multiple of \(7\) then \(mn\) is a multiple of \(231\)
    Show that if \(x-y\) is divisible by \(3\) then \(8x + 4y\) is divisible by \(6\)
  • We looked at the digits in a number:
    The sum of the digits of a four digit number is divisible by \(9\). Show that the number itself is divisible by \(9\).
    \(n\) is a two-digit number. The sum of the sum of its digits and the product of its digits is equal to \(n\). What are the possible values of \(n\)?

Algebra (forming and solving equations)

  • Why is the following attempt to solve the equation \(x^2 = 2x\) incorrect?
    \(x^2 = 2x\) (divide both sides by \(x\))
    \(x = 2\)
  • What is the difference between the two following questions?
    1. Solve \(xy - 3x + 4y = 12\)
    2. Solve, for \(x\), \(xy - 3x + 4y = 12\)

By Ian Clarke

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