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Video Lessons
In this section you will find all the video lessons regarding our first unit: Algebra.
Essential understandings:
Number and algebra allow us to represent patterns, show equivalencies and make generalizations which enable us to model real-world situations. Algebra is an abstraction of numerical concepts and employs variables which allow us to solve mathematical problems.
Suggested concepts embedded in this topic: Generalization, representation, modelling, equivalence, patterns, quantity AHL: Validity, systems.
Content-specific conceptual understandings:
• Modelling real-life situations with the structure of arithmetic and geometric sequences and series allows for prediction, analysis and interpretation.
• Different representations of numbers enable equivalent quantities to be compared and used in calculations with ease to an appropriate degree of accuracy.
• Numbers and formulae can appear in different, but equivalent, forms, or representations, which can help us to establish identities.
• Formulae are a generalization made on the basis of specific examples, which can then be extended to new examples.
• Logarithm laws provide the means to find inverses of exponential functions which model real-life situations.
• Patterns in numbers inform the development of algebraic tools that can be applied to find unknowns.
• The binomial theorem is a generalization which provides an efficient method for expanding binomial expressions.
AHL
• Proof serves to validate mathematical formulae and the equivalence of identities.
• Representing partial fractions and complex numbers in different forms allows us to easily carry out seemingly difficult calculations.
• The solution for systems of equations can be carried out by a variety of equivalent algebraic and
graphical methods.
MAA HL Subject guide IBO 2019
** Week 1: Aug 30th - Sept 5th **
Lesson 0 and Lesson 1 - Presumed knowledge
In this lesson you will learn or revise:
- the use of scientific notation.
- to operate numbers in scientific notation (+ - x /).
- To apply exponents to numbers written in scientific notation.
INSTRUCTIONS
Before you come to class
- Read from the subject guide the pages 20 - 25.
- Watch the video lesson: Lesson 0 (Note please ignore the comments regarding Kognity and Managebac)
In class:
- Introduction to the course
- Introduction to assessment
- First mock essay
- Self taught topics
Lesson 2 - Arithmetic Sequences
- the concept of sequence.
- to identify an arithmetic sequence.
- to find a general formula for an arithmetic sequence.
- to find the number of terms in an arithmetic sequence.
- to predict the nth term of an arithmetic sequence.
- to find the number of terms in an arithmetic series.
- to find the partial sum of an arithmetic series.
INSTRUCTIONS
Before Class:
- Watch: Video lesson for this session
Algebra - Lesson 2 - Algebraic sequences
Lesson 3 - Part II Series and Sigma notation
Lesson 3 - Part III Arithmetic Series
During class:
- Do: If there are any questions regarding the materials, please ask them during the first 10 minutes.
- Pay close attention to Further examples.
- Homework: Watch next lesson's video and read the assigned sections in preparation for next class.
** Week 2: Sept 6th - 12th **
Lesson 3: Geometric sequences
In this lesson you will learn:
- to identify a geometric sequence.
- to find a general formula for a geometric sequence.
- the concept of series.
- to read and write using appropriate notation (sigma notation).
- to identify an arithmetic series.
- to find a general formula for an arithmetic series.
INSTRUCTIONS
Before Class:
- Watch: Video lessons for this day:
Lesson 3 - Part I Geometric Sequences;
Please make sure to take a 5 minute break between videos. Stretch your arms, legs and torso!
During class:
- Do: If there are any questions regarding the materials, please ask them at this time.
- Homework: Watch next lesson's video and read the assigned sections in preparation for next class.
Lesson 4: Geometric Series and Convergence
In this lesson you will learn:
- to find the number of terms in a geometric sequence.
- to predict the nth term of a geometric sequence.
- to identify a geometric series.
- to find a general formula for a geometric series.
- to find the number of terms in a geometric series.
- to find the partial sum of a geometric series.
- applications of geometric sequences and series.
INSTRUCTIONS
Before Class:
- Watch: Video lessons for this day:
Lesson 4 - Part I Geometric Series
Lesson 4 - Part II Infinite Geometric Series and convergence.
During class:
- Please ask any questions you may have at this time.
- Worked examples.
Applications
In this lesson you will learn:
- Applications of sequences and series to real life situations.
INSTRUCTIONS
During class:
- If you have any questions please address them at this time.
- Further examples on Applications: compound interest, appreciation, depreciation, etc.
** Week 3: Sept 13 - Sep 19th **
Test 1
In this lesson you will reinforce your knowledge of sequences and series.
INSTRUCTIONS
Before Class:
- Put your observations and results from the exploration of the Koch snowflake into this shared document: Link
- Work on the study guide, share dwith you in the Google classroom.
- Review your notes on compound interest
During class:
- Test I: This test will be a mix of Paper 1 and Paper 2 style questions, that means you must bring your calculator to sit the test as well as a printed copy of the formula booklet.
- We will continue to develop pending and further examples on applications of sequences and series
Lesson Mini IA I
Friday
INSTRUCTIONS
Before Class:
- Read the subject guide's section on the toolkit i.e the internal assessment, paying special attention to the assessment criteria.
During class:
- Ask any relevant questions regarding the exploration/Toolkit.
- Read and mark the sample essay provided and compare your notes to the original scoring.
- Start to work on your first semester essay: Lacsap's fractions.
Homework:
- You will continue to work on this task at home. The expectation is that you will submit an essay. Please don't leave this task for last minute. Next week you will be given one more block to work on it.
** Week 4: Sept. 20th - Sept. 26th **
Lesson 5 - Proof I
Monday
In this lesson you will learn:
- the basics of Logic
- to prove simple statements using direct proof
INSTRUCTIONS
Before Class:
- Read: Complementary reading from Pearson. pages 204 - 218.
- Watch: Video lessons for this day:
Lesson 5 - Part I Basic Laws and simple proofs (Logic) (Optional)
Lesson 5 - Part II. Direct Proof
During class:
- Please ask any questions you may have at this time.
- Worked examples (Supplied in class)
Lesson 6 - Proof II
Wednesday
In this lesson you will learn:
- to prove simple statements using proof by contradiction
- to prove statements using the contrapositive
INSTRUCTIONS
Before Class:
- Read: Complementary reading from Pearson. pages 219 - 225.
- Watch: Video lessons for this day:
Lesson 6 - Part III Contradiction and Contrapositive
During class:
- Please ask any questions you may have at this time.
- Worked examples (Supplied in class)
Lesson 7: Proof by Mathematical induction I
Friday
In this lesson you will learn:
- to prove simple statements using proof by contradiction
- to prove statements using the contrapositive
INSTRUCTIONS
Before Class:
- Read: Complementary reading from Pearson. pages 226 - 234.
- Watch: Video lessons for this day:
Lesson 7 - Part I The process of Mathematical Induction
During class:
- Please ask any questions you may have at this time.
- Worked examples (Supplied in class)
** Week 6: Oct 26th - Oct. 30th. **
Lesson 8: Proof by Mathematical Induction II
Monday
In this lesson you will learn:
- to prove statements using Mathematical induction: divisibility and inequalities
INSTRUCTIONS
Before Class:
- Read: Complementary reading from Pearson. pages 226 - 234. (Pearson textbook available via Managebac.)
- Watch: Video lessons for this day:
Lesson 8 - Part II. Mathematical Induction to prove inequalities
During class:
- Please ask any questions you may have at this time.
- Worked examples (Supplied in class)
Lesson 9 - Binomial Theorem
Wednesday
In this lesson you will learn:
- the postulate of the binomial theorem
- to use the binomial theorem to expand binomials
- to use the binomial theorem to find a term in a binomial expansion
INSTRUCTIONS
Before Class:
- Watch: Video lessons for this day:
Lesson 9 - Part I
During class:
- Please ask any questions you may have at this time.
Lesson 10 - Binomial Theorem II
Friday
In this lesson you will learn:
- to find coefficients of specific terms in a binomial expansion
- to find the value of an unknown given the value of a term
- to find terms in a polynomial expansion resulting from the product of two binomial polynomials
INSTRUCTIONS
Before Class:
- Watch: Video lessons for this day:
Lesson 10 - Part I
During class:
- Please ask any questions you may have at this time.
- Worked examples (Supplied in class)
- Do: Please finish the Type I task LACSAP's Fractions
- Recommended reading: TOK Connection
Lesson 11 - Polynomial division
HL1: November 19th
HL2: November 20th
In this lesson you will learn:
- To use long division to factorize polynomials
- to find the roots of a polynomial/solve polynomial equations
- To use Synthetic division to factorize polynomials
NOTE: This topic IS NOT included in the syllabus however it is a very important tool of Algebra that will be useful in our study of Polynomials, thus you are required to be familiar with either of the two methods presented.
INSTRUCTIONS
Before Class:
- Read: Math is fun - Long division, Purple math - synthetic division
- Watch: Video lessons for this day:
Lesson 11 - Part I - Long Division
Part III - Systems of linear equations
During class:
- Please ask any questions you may have at this time.
- Worked examples (Supplied in class)
- Long division practice I, practice II
Lesson 12 - Simultaneous linear equations
HL1: November 24th
HL2: November 26th
In this lesson you will learn:
- To solve systems of 3 equations and 3 unknowns by elimination
- To solve systems of 3 equations and 3 unknowns by substitution
- To solve systems of 3 equations and 3 unknowns using technology (GDC)
INSTRUCTIONS
Before Class:
- Read: MAA HL Oxford. Page 205-208.
- Watch: Video lessons for this day:
Lesson 12 - part I
During class:
- Please ask any questions you may have at this time.
- Worked examples (Supplied in class)
- Discuss: what are the conditions for a system to have one, none, or an infinite number of solutions.
- Task I: General practice
** Week 14: November 22nd - November 26th **
Lesson 13 - Complex Numbers: Introduction
Monday
In this lesson you will learn:
- The relationship between complex numbers and quadratic equations.
- The definition of a complex number.
- to add, subtract and multiply complex numbers.
- to find the complex conjugate of a complex number.
- To divide two complex numbers.
- the concept of modulus of a complex number.
INSTRUCTIONS
Before Class:
- Read: MAA HL Pearson. Page 345 - 352
- Watch: Video lessons for this day:
Lesson 13 - Part I
During class:
- Please ask any questions you may have at this time.
- Work on the investigation: Introduction to complex numbers
- Discuss: How are complex numbers different from real numbers? What rules do you foresee not applying to complex numbers? Where in real life do we use complex numbers?
- MAAHL Pearson, page 354 - 356, exercise 8.1.
** Week 15: November 29th - December 3rd **
Lesson 14 - Polar form (Cis form)
Wednesday
In this lesson you will learn:
- The definition of modulus and argument
- How to write a complex number in Euler form
- How to write a number in Cis form
- How to find the principal argument
- the differences between principal argument and argument
- the properties of the modulus and the argument.
INSTRUCTIONS
Before Class:
- Read: MAA HL Pearson. Page 356-363
- Watch: Video lessons for this day:
Lesson 14 - Part I
Lesson 14 - Part II
During class:
- Please ask any questions you may have at this time.
- Worked examples (Supplied in class)
- Discuss: How are complex numbers different from real numbers? What rules do you foresee not applying to complex numbers? Where in real life do we use complex numbers?
- TMAAHL Pearson, page 363-364, Exercise 8.2
Lesson 15 - DeMoivre's Theorem
Friday
In this lesson you will learn:
- to apply DeMoivre's theorem to calculate powers of complex numbers
INSTRUCTIONS
Before Class:
- Read: MAA HL Pearson. Page 364-367
- Watch: Video lessons for this day:
Lesson 15 - Part I
Lesson 15 - Part II
During class:
- Please ask any questions you may have at this time.
- Worked examples (Supplied in class)
- Discuss: What are the properties of Cis form? How are these properties connected to the properties of the argument?
- Task I: Pearson MAA HL. page 373-374. Exercise 8.3.
** Week 16: December 6th - December 10th **
❄❅❆ *<]:}) HAPPY WINTER BREAK! ❆❅❄
Lesson 16 - Roots of polynomials I
Monday
In this lesson you will learn:
- to apply DeMoivre's to the calculation of fractional roots of complex numbers
- to solve equations of the form z^n=a+ib
- to understand the roots of a complex number as the vertices of a regular polygon
- to graph the roots of complex numbers on the complex plane
INSTRUCTIONS
Before Class:
- Read: MAA HL Oxford. Page 367-374
- Watch: Video lessons for this day:
Lesson 16 - Part I
During class:
- Please ask any questions you may have at this time.
- Worked examples (Supplied in class)
- Discuss: What relationships exist between pairs of complex roots?
- Task I: Pearson MAA HL. page 373-374. Exercise 8.3.
Lesson 17 - Roots of polynomials II
Wednesday
In this lesson you will learn:
- the Remainder theorem
- the factor theorem
- How to use the remainder and factor theorems to find the roots of polynomials.
INSTRUCTIONS
Before Class:
- Read: MAA HL Oxford. Page 178-190
- Watch: Video lessons for this day:
Lesson 17 - Part I
During class:
- Please ask any questions you may have at this time.
- IBID Mathematics Analysis and approaches HL exercise set A7.7.
- Worked examples (Supplied in class)
- Discuss: What relationships exists between pairs of complex roots?
- Task I: Oxford MAA HL. page 181. Exercise 3J. question 2.
- Task II: Oxford MAA HL. page 184. Exercise 3K. questions 6-10.
- Task III: Oxford MAA HL. page 190. Exercise 3L. questions 1-6, (a, b, and c only from each numeral)
Lesson 18: Revision
Friday
In this lesson you will review:
HL
- the Remainder theorem
- the factor theorem
- Algebra of complex numbers
INSTRUCTIONS
During class:
- Please ask any questions you may have at this time.
- Kahoot HL (we will play a kahoot Precalc Complex numbers review). (Game Pin: 09334462)
- Kahoot SL (we will play a kahoot IB Math Number and Algebra). (Game Pin: 0150606)
** Week 16: Dec 6th - Dec 8 **
TBD according to school end of year practices