Detailed Plan for year 1 (grade 11) Week commencing: 2021
Topic
Proof
1.3
Binomial Theorem
1.4
1.6 Simple deductive proof 1.15 Proof by induction, proof by contradiction, counterexample. 1.9 The binomial theorem: expansion of (a+b),n∈ℕ.
Arithmetic and Geometric sequences
Applications
Sep 5
Sep 12
Use of Pascal’s triangle and nCr. 1.10 Extension to fractional and negative indices. 1.11 Partial fractions.
Sep 19
Functional relationships Functions
2.1 2.2, 2.3
TOK links
TOK: 1. Is all knowledge concerned Arithmetic sequences and series. with and use Use of the formulae for the nth term and the sum of the firstidentification n of patterns? Consider terms of the sequence. Fibonacci numbers and Use of sigma notation for sums of arithmetic sequences. connections with the golden Applications. Analysis, interpretation and prediction where a model isratio. not perfectly arithmetic in real life. 2. How do mathematicians 1.3 reconcile the fact that some Geometric sequences and series. conclusions seem to conflict Use of the formulae for the n th term and the sum of the first n intuitions? with our terms of the sequence. Consider for instance that a Use of sigma notation for the sums of geometric sequences. finite area can be bounded Applications by an infinite perimeter. 1.4 3. How have technological Financial applications of geometric sequences and series: advances affected the - compound interest nature and practice of - annual depreciation. mathematics? Consider the use of financial packages for 1.8 instance. Sum of infinite convergent geometric sequences. IM: Aryabhatta is sometimes considered the “father of algebra”–compare with alKhawarizmi; the use of several alphabets in mathematical notation (for example the use of capital sigma for the sum).
1.2
Arithmetic and Geometric series
Sep 26
Syllabus reference
1.1 1.2
Number patterns and sigma notation Aug 29
Textbook Reference
2.1 Equations of straight lines, gradient, intercepts, parallel and perpendicular lines. 2.2 Concept of a function, inverse function.
5
TOK: Is mathematical reasoning different from scientific reasoning, or reasoning in other Areas of Knowledge? TOK: 1. How have notable individuals shaped the development of mathematics as an area of knowledge? Consider Pascal and “his” triangle.
TOK: Descartes showed that geometric problems could be solved algebraically and vice versa. What does this tell us about mathematical
