# Year 12 Regular Problem Solving Classes

Liverpool

## Overview

A series of maths problem-solving sessions designed to give students the confidence to apply for university courses that require or take into consideration achievement in an admissions test.

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 and will help with preparations for taking advanced papers such as the MAT, TMUA 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 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 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
• To develop tenacity when dealing with maths problems

## Who will benefit from attending?

The course is designed for any A level Mathematics students who have an enquiring mind and wish to develop their problem solving ability for their A level studies and beyond.

It is particularly useful for those students who wish to make the first steps in preparing for university admissions tests such as the MAT, TMUA and STEP examinations.

## 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

## Materials and Equipment

While the classes are being held online, you will need access to suitable equipment. You are advised to use a headset or headphones with an inline microphone to provide the best sound quality and to prevent audio issues for other users. A laptop with a built-in webcam and microphone may be sufficient if you’re in a quiet area but please take the time to check this before the session. BBB is designed to be used on a variety of platforms but you will get the best experience via a desktop or laptop computer, running either Google Chrome or Mozilla Firefox as the browser.

Note: Internet Explorer and Edge are not suitable currently.

## 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 $$x^2–y^2=45$$?

## Study Schedule

Following on from several years of successful face-to-face problem-solving for Y12 students at the University of LIverpool, we have now devised an online version suitable for current restrictions.

We have tried to retain as much of our standard format as possible:

• a nominal start time of 5pm, with a few engaging starter problems: students can arrive any time between 5 and 5.30pm
• a set of themed and differentiated problems that students can try in small groups from 5.30 - 6.30pm
• plenty of qualified helpers to assist students in a constructive way, allowing them to collaborate whilst also demonstrating their ability as independent problem-solvers.

All safe-guarding procedures will be adhered to, and all student interactions recorded.

PLEASE NOTE THAT THESE SESSIONS ARE INTENDED TO BE INTERACTIVE AND COLLABORATIVE. STUDENTS MUST BE WILLING TO TURN ON THEIR CAMERA, SPEAK TO THEIR GROUP MEMBERS VIA A MICROPHONE AND WRITE ON A SHARED SCREEN. It is hoped that schools will be able to assist if students do not have the necessary technical equipment to be able to participate in this way, so that no students will miss out for these reasons.

These sessions are provided by the AMSP free of charge,

## Key Facts

#7991

Students

Year 12

##### Curriculum focus:

University admissions tests, A level Mathematics, A level Further Mathematics

##### Mathematical focus:

Pure, Problem solving

Student course

20 hours

North West

##### Venue:

University of Liverpool,
L69 7ZL

Mon 7th Dec 2020

##### Course times:

17:00 - 18:30

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