Overview

The long running University of Leicester/AMSP Year 12 Mathematics Problem Solving course is intended for students whose extant enthusiasm, engagement and ability with the subject is already at a high level.

The primary aim of this course is the further development of such students’ mathematical insight, thinking and problem solving strategies. Participation in this course will enhance such students preparation for the TMUA, MAT and STEP and similar examinations. Most of the problems in the calculator free course are unstructured and challenging and based on the Y12 pure mathematics course.

These regular classes offer students the opportunity to develop mathematical problem-solving skills through discussion and collaboration. They are designed to help students to develop strategies and confidence when tackling unfamiliar problems in maths. 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 to 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 Test
• To provide a platform on which to build secure problem solving techniques

Content

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

• 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

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

Due to our funding arrangements, priority will be given to students from state-funded schools and colleges in the Leicester area.

Application to this course is via the University of Leicester School of Mathematical Sciences.

Study schedule

Key facts

• Reference:#13425
• Audience:Students
• Target year:Year 12
• Curriculum focus:University admissions tests
• Mathematical focus:Problem solving
• Format:Face-to-face
• Duration:20 hrs
• Region:East Midlands
• Venue:University of Leicester
• Start date:07 Oct 2024
• Course times:16:30 - 18:00
• Fee:Free