1.INTRODUCING BINOMIAL EXPANSION
2.USING GRAPHICS CALCULATOR TO FIND COEFFICIENTS
3.BINOMIAL EXPANSION WITH NATURAL POWERS
4.FINDING CERTAIN TERMS OF OUR EXPANSION
5.BINOMIAL EXPANSION WITH INTEGER POWERS
6.ARRANGEMENTS AND FACTORIALS
7.FACTORIALS AND PERMUTATIONS
8.COMBINATIONS
9.LINKING COMBINATIONS AND BINOMIAL COEFFICIENTS
10.PROOF OF COMBINATIONS PROPERTY
11.DEDUCTIVE PROOFS
12.DISPROVING BY COUNTEREXAMPLE
13.PROVING BY CONTRADICTION
14.PROVING BY INDUCTION
15.FACTORIAL PROOF BY INDUCTION
16.DIVISIBILITY PROOF BY INDUCTION
17.DERIVATIVE PROOF BY INDUCTION
18.PROOF OF SUMS BY INDUCTION
19.PROOF OF BINOMIAL THEOREM BY INDUCTION
The Unit 9 Resource Bundle Get your classroom time back with materials designed for the thinking process.
✅ 19 Printable Worksheets
✅ Complete Worked Solutions
✅ Delivered via Email (PDF)
A Note from the Creator: I’ve priced this bundle at $9.99, roughly the cost of two cups of coffee. While the caffeine keeps me fueled to build these courses between my own teaching shifts, these PDFs are here to help you stop racing the bell and start mentoring again.
Binomial And Proof
• Covers: This module provides a comprehensive exploration of binomial expansion, arrangements, selections, and various proof techniques. It begins with binomial expansion, covering its introduction, using graphics calculators for coefficients, expanding with natural and integer powers, and finding specific terms. The module then delves into arrangements and selections, explaining factorials, permutations, and combinations, and linking these concepts to binomial coefficients. Finally, it provides an in-depth look at proof methods, including deductive proofs, disproving by counterexample, proof by contradiction, and extensive coverage of proof by induction (for factorials, divisibility, derivatives, and sums), culminating in the proof of the Binomial Theorem.
• Outcomes: Perform binomial expansions for expressions with both natural and integer powers. Efficiently find specific terms within a binomial expansion. Understand and apply factorials, permutations, and combinations to solve problems involving arrangements and selections. Formulate and execute various mathematical proofs, including deductive, contradiction, and counterexample methods. Master the technique of proof by induction for a range of mathematical statements, including those involving factorials, divisibility, derivatives, and sums. Understand and prove the Binomial Theorem.
TESTIMONIAL
"I enjoyed the structure of the questions and answers, and the quantity of questions that were available in order to practise the skills that I attained. I gained an understanding of algebra and calculus from a different angle than ways that I have been taught by previous teachers. Anyone who is looking to achieve in algebra and calculus and cannot attend school for any reason should definitely enroll in this course"
🎓 Q. C. – Year 12 Student
