Overview

Throughout the Summer Term of 2024, the AMSP will be running a series of interactive online problem-solving sessions for Year 12 students, designed to give them the confidence to apply for university courses in mathematics or related fields, particularly those which might require or take into consideration achievement in an admissions test. The organisers are based in the North West but anyone is welcome to apply.

These regular classes offer students the opportunity to develop mathematical problem-solving skills through discussion and collaboration. They are designed to help students develop strategies and confidence when tackling unfamiliar problems in maths and will help with preparations for taking advanced papers such as the MAT, TMUA, AEA and STEP examinations.

At the same time, the problems used in the course are fun and rewarding. Attending the sessions will greatly enrich students’ mathematical experience and help them develop a better understanding of A-level Mathematics.

Aims

• To develop initial strategies when dealing with maths problems
• To develop confidence when dealing with maths problems
• To develop resilience when dealing with maths problems
• To provide some initial information about the problem-solving involved in university admissions tests
• To provide a platform on which to build secure problem-solving techniques

Who will benefit from attending?

The course is designed for any A-level Mathematics student with an enquiring mind who wishes to develop their problem-solving abilities for their A-level studies and beyond.

It would be particularly useful for students wishing to make the first steps in preparing for university admissions tests such as the MAT, TMUA, AEA and STEP examinations.

Content

The course covers a wide range of mathematical disciplines with problems. These can include:

• Logic: truth, falsity and evaluating propositions
• Algebra: the difference between two squares and other identities
• Geometry: angles, triangle and circles
• Number: digits and divisibility
• Algebra: forming and solving equations
• Combinatorics: systematic counting
• Number: prime factorisation, fractions and irrationals
• Algebra: sequences and series
• Number: indices and logarithms
• Algebra: quadratics, cubics and other polynomials
• Geometry: trigonometry
• Combinatorics: further systematic counting and placement
• Geometry: coordinates and vectors
• Calculus: curve sketching and differentiation
• Calculus: integration
• Combinatorics: the binomial expansion

Materials and equipment

Participants will need access to suitable equipment. They are advised to use a headset or headphones with an inline microphone to provide the best sound quality and prevent audio issues for other users. A laptop with a built-in webcam and microphone will usually be sufficient for those in a quiet area but please take the time to check this before the session. We shall use the online classroom system BigBlueButton (BBB), which is designed to be used on a variety of platforms, but you will get the best experience via a desktop or laptop computer running Google Chrome or Mozilla Firefox.

Note: Internet Explorer and Edge are not suitable currently.

Access to GeoGebra or Desmos might also be useful.

Other information

The following problems provide a taste of the sort of problem solving that will be encountered in the classes:

Problem 1: How many primes greater than two can be found that are one less than a square number?

Problem 2: How many pairs of integers can you find that satisfy the equation \(x^2–y^2=45\)?

Eligibility

Key facts

• Reference:#12626
• Audience:Students
• Target year:Year 12
• Curriculum focus:University admissions tests, A level Mathematics, A level Further Mathematics
• Mathematical focus:Problem solving, Pure, Reasoning
• Format:Online
• Duration:Summer Term
• Study days:12
• Online sessions:12
• Region:North West
• Venue:Online
• Start date:07 May 2024
• Course times:16:30 - 18:00
• Fee:Free