M1 Worked solutions

January 2010

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpMzIzMjNhZmYtMTM5NC00NzA4LWJmNWYtM2NhMmNkYWE4YmRh&hl=en_US

May 2009

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpMGUwMTJmNjEtYTU2Ny00NTVjLWI1NDYtM2VlOWFjMjRjNWVj&hl=en_US

January 2009

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpNTVhNTA1MTMtY2I2Ny00NWQ3LWIwOTAtZmU0NmQ2MDI5ODhm&hl=en_US

May 2008

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpM2IzODJlZjAtYjE0Mi00NzdkLWE4NTEtYTMzNDRkZjJlYjcz&hl=en_US

January 2008

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpY2VjYWQwZTMtMWEwNC00Zjc5LTliYTAtMWUwZTRlNzAyNTBj&hl=en_US

June 2007

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpMDRmYTYwMzItOTc5NC00ZjkyLTgzYTktYmFmNWI4YmFiOGFk&hl=en_US

January 2007

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpY2E0MjMxZjAtYjNiZS00YmI2LTk0YjYtZTQwZTViMzQ0N2E5&hl=en_US

June 2006

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpMGRjZWQ2YzItNWFlZS00NmYwLTgyMjctNmVhMjg0YzFjNTA2&hl=en_US

January 2006

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpZDhiNDc5ZDQtZGIzYy00ZGVlLThmMDktZDdkZTQ0NGM1NzMy&hl=en_US

M1 Connected particles 17/11/11

• Examples involving pulleys, cars and trailers

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpN2QxYWU3ZjktMjkwNS00M2ZkLWFiYzYtMjYwNzUxMzYwZmNi&hl=en_US

M1 Moments 16/11/11

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpZGQzNmE2ZGMtMjBiYy00ZTc2LTg5MDQtMzNlNTVhMGRjZTg4&hl=en_US

M1 Collisions, guns and jerks 10/11/11

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpYTY4NjY5NTMtNTI1ZC00ZjI0LTkxMmEtMmU1MTE3OGU2NTQ2&hl=en_US

M1 Momentum and impulse 09/11/11

• Momentum = mass x velocity
• Finding changes in momentum
• Impulse = force x time = change in momentum
• Principle of conservation of momentum
• Collisions

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpZjIwMzJmYzktMGYwYy00NTVjLWEyMmEtYzVkOWNlYTM5NjFh&hl=en_US

M1 Newton's laws 02/11/11

• Defining Newton's laws
• With particular focus on Newton's second law
• Using N2L to solve problems

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpMjcxNzlhNzctNTkyZS00YzM0LWI3NjEtY2ZlZDFkOGNiMWZh&hl=en_US

M1 Types of forces 12/10/11

• Types of forces acting in different situations
• Weight, normal reactions, tension, thrust, friction
• Friction - maximum friction, coefficient of friction
• Solving forces problems (in equilibrium) involving friction

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpYTE4YTU1Y2EtMzkwMi00ZmQ3LTlhNTMtZTRmZmU0MzRhZDU0&hl=en_US

M1 Intro to forces 06/10/11

• Resultant of two forces
• Resolving into horizontal and vertical components
• Resultant of three or more forces
• Equilibrium

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpZDZkYTAzMjMtODhkYy00NTdlLThmNDgtMzE0YzZjMGNlODNj&hl=en_US

M1 Equations of motion and vectors review 05/10/11

• A quick look at displacement,velocity,acceleration-time graphs
• Questions using equations of motion
• Questions using vectors

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpODk2YjM0OTItYTgzOS00NzdiLWIyODMtNTY0M2Q5Mjk5ZDE4&hl=en_US

M1 Vertical motion 29/09/11

• Horizontal motion question
• Vertical motion - acceleration due to gravity
• Importance of defining direction
• Vertical motion examples

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpZDJiOTk4OGEtMGY5My00ZTM0LTk3NGMtOTg2Y2Q4Yjg5ZjYy&hl=en_US

M1 Equations of motion 28/09/11

• Deriving equations of motion
• Examples of using equations of motion

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpYzRjNmM2ZTQtYmI1My00Yzk0LWJjNjUtZWViODE0OWQ5NmRj&hl=en_US

M1 Vectors M1 questions 22/09/11

• A couple of past M1 questions

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpY2Q0YjA2YjItOWU0Yi00OTE5LWEyMDYtMzllYzRkNjljZjQ0&hl=en_US

M1 Applications of vectors 21/09/11

• Finding magnitude and direction from i-j form vector
• i and j components of a vector
• Unit vector
• Displacement vectors
• Position vectors
• Velocity vectors
• Acceleration vectors
• Problems involving position, displacement, velocity and acceleration vectors

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpMGY4ZmMxZGItMjc1Yy00NzMzLWE2MzItYjU1ZTU0OGVkMzk0&hl=en_US

M1 More vectors 15/09/11

• Intro to i and j vectors
• Parallel vectors
• Magnitude of a vector
• Direction of a vector
• Homework set

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpMGJiNmM4YTAtNmVjNi00YWM1LWJhN2YtZGE1YzM3ZjA5NjU4&hl=en_US

M1 Introduction to vectors 14/09/11

• Problems involving bearings - using cosine rule and sine rule
• Taking care with sine rule - ambiguity of angle solutions
• Basic revision of vectors (GCSE level)
• Scalar quantities / Vector quantities
• Resultant of two vectors

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpNTkwNTA5ZTktMDA5NC00OWE4LWFhNDctMWVlY2M4ZWU5NjY2&hl=en_US

Support for summer work

In addition to the support on the Year 12 Maths blog...

http://wellingmaths12.blogspot.com/

Here is one more link for support for the Further Maths summer work:

Trigonometry

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpYzY1MmZiNGQtMTkxMy00MTNhLThmMzYtOTIwMzUzMWUxOTVk&hl=en_US

Course info and summer work

Follow this link to the information sheet about A-Level Further Mathematics at Welling School:
https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpOGVhZTlkNGUtNzExMC00MDI2LWFmZTktOGY3MjY1ZmE2MjU0&hl=en_US

And follow this link to the summer work that must be completed and handed in at the first A-Level Further Mathetmatics lesson in September:
https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpNGI1OWYxYWEtYzhmNi00YzU1LWI2MDgtYjkyY2I1NjNiMTRi&hl=en_US

Change to Year 13 blog

Any further posts relating to current Year 12 will be on the Year 13 blog:
www.wellingfurthermaths13.blogspot.com

M1 Forces 30/03/11

• resolving into components


• problems involving forces in equilibrium


• on a slope

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpNmVlNGY3MzUtZTY3OS00N2VmLTg2YjMtYjQxZDY2ZjI2NGQ4&hl=en

D1 Route inspection 23/03/11

• Graphs, Semi-Eulerian, Eulerian, Valency of nodes etc.
• Route inpection algorithm
• Identifying odd vertices, possible pairings, identifying shortest route
• Starting / finishing at same point
• Starting / finishing at different points
• Example of exam question using route inspection

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpOTY1MTQ1NjAtNWU2NS00NmYwLTlhZGEtMDkwN2FlNWZmOGVi&hl=en

D1 Critical path analysis2 17/03/11

• Cascade (Gantt) chart
• Scheduling

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpNWM1MzFiZjUtZTFlMC00NTJhLWI3MWYtYTQ0OWQ2ZDMyMzYy&hl=en

D1 Critical path analysis 09/03/11

• Precedence/dependence tables
• Drawing an activity network
• Dummy activities
• Earliest and latest event times
• Critical events and slack
• Critical activities and float
• Critical paths

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpMzlhYjg0NzQtMjFkZC00ZmE3LTkzZDEtNmVmZDczOTZjZjlm&hl=en

D1 Matchings 02/03/11

• Worked through examples from Chapter 7 Matchings

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpNDZjZWYyOWMtZTg3ZS00NGM4LWE1MzMtYWMwZGM0OTA1Yzkx&hl=en

D1 Linear programming - algebraic / simplex 09/02/11

• Recap graphical method
• Link to algebraic
• Slack variables
• Simplex method

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpYzlmMDI2OTYtNjZkNi00Y2EzLThlOTctOGI3M2RmMWQ3YTJi&hl=en

D1 Linear programming 02/02/11

• Regions from inequalities
• Linear programming solved graphically

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpZTIwMjA3ODItN2E0OC00N2Y3LWFiOTAtOWFiNGI3Y2E0NTBk&hl=en

M1 Vectors exam questions 05/01/11

A few past M1 questions using vectors

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpYjhhYzQ0MGUtZDQ4YS00ODk4LTk5NTQtZGM1NjAyN2YyZDE4&hl=en