Summer Work + Reading: A-Level Mathematics
1. COMPULSORY TASK – STRENGTHENING MATHEMATICAL FOUNDATIONS
A Level Mathematics moves quickly and assumes confidence with algebraic manipulation. Many students find that difficulties in Year 12 arise not because of new concepts, but because of gaps in core skills from IGCSE.
Please review and practise the following topics:
a) Review the IGCSE basics:
Using Save My Exams or similar revision resources:
• Algebraic manipulation (expanding, factorising, simplifying)
• Solving linear and quadratic equations
• Completing the square
• Indices and surds
• Simultaneous equations
• Coordinate geometry
• Trigonometry and exact values
• Functions and graphs
Students are encouraged to revisit key IGCSE Extended Mathematics topics using past paper questions to strengthen fluency and algebraic confidence before starting A Level Mathematic
b) Attempt transition-style questions:
Using:
Dr Frost Maths → GCSE to A Level Transition materials
CorbettMaths → Maths A-level Basic Exercise with answers
Suggested topics:
• Algebraic fractions
• Functions and composite functions
• Coordinate geometry
• Graph transformations
• Trigonometric identities
• Introduction to differentiation
If you wish to consolidate your Mathematics knowledge moving to A Level, there is an optional bridging book which supports the move from IGCSE to A Level:
Head Start to A-Level Maths (CGP)
ISBN: 978-1782947929
2. OPTIONAL TASK – SUBJECT WIDER READING
Please pick one of the following books to read:
a) Alex's Adventures in Numberland – Alex Bellos
ISBN: 978-1408809594
A fascinating journey through mathematics in culture, puzzles, and real-life applications.
b) The Simpsons and Their Mathematical Secrets – Simon Singh
ISBN: 978-1408831311
Shows how mathematics appears unexpectedly in popular culture.
3. FOR INTEREST – MATHEMATICS YOUTUBE CHANNELS
For Curiosity:
i. Numberphile
Outstanding mathematics channel featuring fascinating mathematical ideas and interviews with mathematicians.
ii. 3Blue1Brown
Beautiful visual explanations of mathematical concepts including calculus, linear algebra, and probability.
For A Level Content: i. TLMaths
One of the strongest A-Level Mathematics channels with clear topic-by-topic teaching.
ii. ExamSolutions
Excellent worked examples and examination-style questions.
iii. Bicen Maths
Strong A-Level explanations and exam preparation.