Summer Work + Reading: A-level Further Mathematics
1. COMPULSORY TASK – DEVELOPING MATHEMATICAL THINKING
Further Mathematics is designed for students who enjoy mathematics and are excited by problem solving beyond standard methods. Success depends on strong algebraic fluency and curiosity rather than simply learning procedures.
Please complete the following:
a) Strengthen core skills:
Review:
• Algebraic manipulation
• Trigonometry
• Coordinate geometry
• Functions
• Sequences and series
• Proof techniques
• Mathematical reasoning
b) Attempt enrichment and problem-solving activities:
Using:
NRICH Sixth Form Problem Solving Activities
NRICH Post 16 Curriculum
Underground Mathematics
Suggested areas:
• Logic problems
• Mathematical proof
• Sequences and patterns
• Geometry investigations
• Introductory matrices and vectors
If you wish to consolidate your understanding moving into Further Mathematics, an optional bridging text is:
Head Start to A-Level Further Maths (CGP)
ISBN: 978-1782947936
2. OPTIONAL TASK – SUBJECT WIDER READING
Please pick one of the following books to read:
a) How Not To Be Wrong – Jordan Ellenberg
ISBN: 978-0143127536
Shows how mathematical thinking helps us understand everyday life and decision-making.
b) Things to Make and Do in the Fourth Dimension – Matt Parker
ISBN: 978-0141975979
A highly entertaining journey through strange mathematical ideas.
3. FOR INTEREST – FURTHER MATHEMATICS YOUTUBE CHANNELS
For Curiosity:
i. Mathologer
Excellent for elegant proofs and advanced mathematical concepts.
ii. Michael Penn
Challenging but highly rewarding mathematics explanations.
For A Level Content:
i. TLMaths
Includes Further Mathematics content aligned to A-Level specifications.
ii. ExamSolutions
Strong worked examples and topic explanations.
iii. Khan Academy (Advanced Mathematics)
Useful for extending understanding of calculus and linear algebra.