1. Oxbridge Maths (and related subjects) APN, January 2012

2. Administration  What’s involved (Numbers will decrease)  Career Intention sheet  Oxbridge Research (eg cwk/ exams)  APN Web Contact details and useful info How oxbridge admissions really work UNIQ Summer School (Deadline 23 Feb) Interviews, Content, STEP and AEA Other info: Crompton House (Oxford: March) Open days: Info coming soon MEI Support Information

3. Administration  Maths and medicine Maths and medicine  Institute of Physics Institute of Physics  Maths, Biology, Chemistry, Physics, Engineering (STEM link) Maths, Biology, Chemistry, Physics, Engineering  Maths of engineering Maths of engineering  Cambridge Millenium Maths Project Cambridge Millenium Maths Project  Oxford Admissions Entrance Test Oxford Admissions Entrance Test  Maths off the beaten track (APN) Maths off the beaten track (APN)  Andy's hotlinks (Motivation & Oxbridge etc) Andy's hotlinks (Motivation & Oxbridge etc)  Ozone in college

4. Andy’s Website

5. A proof that 1 = 2 Step 1: Let a = b. Step 2: Then a 2 = ab. Step 3: So a 2 + a 2 = a 2 + ab. Step 4: In other words 2a 2 = a 2 + ab. Step 5: So2a 2 – 2ab = a 2 + ab – 2ab Step 6: and 2a 2 – 2ab = a 2 – ab. Step 7: So 2(a 2 – ab ) = a 2 – ab. Step 8: Cancelling the (a 2 – ab) from both sides gives 1 = 2.

6. Correct procedure in equations

7. Example for discussion Solve for x the following equations, commenting upon any special cases that arise in the two cases. (i) ax + b = bx + c (ii) ax + a 2 = b 2 – bx

8. STEP and AEA Principles  how to write mathematics in “good style”  understanding key symbols and using them correctly  ‘exact’ values  reasoning, conciseness and clarity

9. Common symbols to use:

10. Week 1: Problems to bite on Please see handout.