REVIEW
IBMYP5 MAT-ADD10 - IGCSE 0606 REVIEW
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SERIES CONTENT
This series of slides is an aggregate of:
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| Information, Explanation & Demonstration |
| Thinking, Conversation & Discussion |
| Thinking on your feet |
| Exercises that “All must” complete Level 1 - 4 |
| Exercises that “Most will” complete Level 4 - 6 |
| Exercises that “Some do” complete Level 6+ |
| Exercises that “Few can” complete Level 7+ |
Share | Tutorial Video Link ToK |
SERIES ICONS
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IGNITION
“A Conceptual Approach”...
~ DISCUSS Transferable Thinking
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TOPIC CONTENT
A summary of the Knowledge & Skills ...
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TOPIC CONTENT
A summary of the Knowledge & Skills ...
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“Transferable Thinking”
~ DISCUSS What do we know about… Transferable Thinking
Session Content
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IGCSE
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TERMS & VOCABULARY
Required for this topic...
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IGCSE
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C, C & C… Explain
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IGCSE
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
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Solution...
Your turn… Experiment
Solve this question in your notebook…
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IGCSE
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All learners must complete…LEVEL 1-4
All must… Exercise
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“Transferable Thinking”
~ DISCUSS What do we know about… Transferable Thinking
Session Content
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IGCSE
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TERMS & VOCABULARY
Required for this topic...
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IGCSE
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C, C & C… Explain
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
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Solution...
Your turn… Experiment
Solve this question in your notebook…
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IGCSE
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All learners must complete…LEVEL 1-4
All must… Exercise
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“Transferable Thinking”
~ DISCUSS What do we know about… Transferable Thinking
Session Content
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IGCSE
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TERMS & VOCABULARY
Required for this topic...
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IGCSE
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C, C & C… Explain
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IGCSE
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
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Solution...
Your turn… Experiment
Solve this question in your notebook…
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IGCSE
0606
All learners must complete…LEVEL 1-4
All must… Exercise
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“Transferable Thinking”
~ DISCUSS What do we know about… Transferable Thinking
Session Content
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IGCSE
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TERMS & VOCABULARY
Required for this topic...
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IGCSE
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C, C & C… Explain
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
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Solution...
Your turn… Experiment
Solve this question in your notebook…
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IGCSE
0606
All learners must complete…LEVEL 1-4
All must… Exercise
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“Transferable Thinking”
~ DISCUSS What do we know about… Transferable Thinking
Session Content
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IGCSE
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TERMS & VOCABULARY
Required for this topic...
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IGCSE
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C, C & C… Explain
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
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Solution...
Your turn… Experiment
Solve this question in your notebook…
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IGCSE
0606
All learners must complete…LEVEL 1-4
All must… Exercise
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“Transferable Thinking”
~ DISCUSS What do we know about… Transferable Thinking
Session Content
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IGCSE
0606
TERMS & VOCABULARY
Required for this topic...
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C, C & C… Explain
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
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Solution...
Your turn… Experiment
Solve this question in your notebook…
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IGCSE
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All learners must complete…LEVEL 1-4
All must… Exercise
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“Transferable Thinking”
~ DISCUSS What do we know about… Transferable Thinking
Session Content
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IGCSE
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TERMS & VOCABULARY
Required for this topic...
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IGCSE
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C, C & C… Explain
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
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Solution...
Your turn… Experiment
Solve this question in your notebook…
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IGCSE
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All learners must complete…LEVEL 1-4
All must… Exercise
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“Transferable Thinking”
~ DISCUSS What do we know about… Transferable Thinking
Session Content
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IGCSE
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TERMS & VOCABULARY
Required for this topic...
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IGCSE
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C, C & C… Explain
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
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Solution...
Your turn… Experiment
Solve this question in your notebook…
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IGCSE
0606
All learners must complete…LEVEL 1-4
All must… Exercise
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“Transferable Thinking”
~ DISCUSS What do we know about… Transferable Thinking
Session Content
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IGCSE
0606
TERMS & VOCABULARY
Required for this topic...
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IGCSE
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C, C & C… Explain
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
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Solution...
Your turn… Experiment
Solve this question in your notebook…
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IGCSE
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All learners must complete…LEVEL 1-4
All must… Exercise
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“Transferable Thinking”
~ DISCUSS What do we know about… Transferable Thinking
Session Content
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IGCSE
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TERMS & VOCABULARY
Required for this topic...
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IGCSE
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C, C & C… Explain
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
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Solution...
Your turn… Experiment
Solve this question in your notebook…
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IGCSE
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All learners must complete…LEVEL 1-4
All must… Exercise
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PORTFOLIO
Evidence of thinking & learning:
*Assignments
*Notes
*Definitions
*Formulae
*Examples & Solutions
Take a photo of your Evidence of Thinking & Learning and paste it into the daily portfolio Google Doc. Submit this in our Google Classroom by the end of this class.
Take a photo of your Evidence of Thinking & Learning and paste it into your daily portfolio Google Doc.
Submit this in our Google Classroom at the end of each class.
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3-2-1 Reflection
In your portfolio, reflect on this session and answer the following: | |
3 2 1 | Three things that You learnt from this lesson… |
Two things that You found interesting and would like to know more about… | |
One thing that You still have a question about… | |
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“Transferable Thinking”
~ DISCUSS What do we know about… Transferable Thinking
Session Content
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SERIES & BINOMIAL THEOREM
and properties of the coefficients is not required);
Learning Objectives
In this session, we are thinking & learning about…
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SERIES & BINOMIAL THEOREM
How do we expand (a + b)n, where n is a positive integer?
The coefficients of the binomial expansion of (a + b)n for n = 0 to 8 are illustrated in the book 'Precious Mirror', which was written by Zhu Shijie in 1303.
IGNITION
“A Conceptual Approach”...
~ DISCUSS Transferable Thinking
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SERIES & BINOMIAL THEOREM
The discovery of this triangle can be traced back to many mathematicians. The earliest one recorded was by an ancient Indian mathematician Acharya Pingala, who published the book 'Chandas Shastra' between the 3rd and 2nd century B.C.
IGNITION
“A Conceptual Approach”...
~ DISCUSS Transferable Thinking
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SERIES & BINOMIAL THEOREM
In China, it was known as Yang Hui's (1238-1298) triangle, although the Chinese mathematician fia Xian (1010-1070) discovered it two centuries earlier.
IGNITION
“A Conceptual Approach”...
~ DISCUSS Transferable Thinking
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SERIES & BINOMIAL THEOREM
In the Western world, we know it as Pascal's Triangle, named after the French mathematician Blaise Pascal (1623-1662). Can the triangle be used when n > 8? In this chapter, we will learn how to expand (a + b)n using the Binomial Theorem.
IGNITION
“A Conceptual Approach”...
~ DISCUSS Transferable Thinking
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SERIES & BINOMIAL THEOREM
Learning Objectives
In this session, we are thinking & learning about…
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SERIES & BINOMIAL THEOREM
IGNITION
“A Conceptual Approach”...
~ DISCUSS Transferable Thinking
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IGCSE
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SERIES & BINOMIAL THEOREM
Binomial Theorem - Pascal’s Triangle
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Binomial Theorem
Your turn… Experiment
Solve this question in your notebook…
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SERIES & BINOMIAL THEOREM
Binomial Theorem
Your turn… Experiment
Solve this question in your notebook…
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SERIES & BINOMIAL THEOREM
Binomial Theorem
Solve in your notebook...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Binomial Theorem
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Binomial Theorem
Solve in your notebook...
Your turn… Experiment
Solve this question in your notebook…
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SERIES & BINOMIAL THEOREM
Binomial Theorem
DISCUSS
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SERIES & BINOMIAL THEOREM
Binomial Theorem - Coefficients
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Binomial Theorem - Coefficients
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Binomial Theorem - Coefficients
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Binomial Theorem - Coefficients
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Binomial Theorem - Coefficients
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Binomial Theorem - Coefficients
Solve in your notebook…
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Binomial Theorem - Coefficients
(a)
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Binomial Theorem - Coefficients
(b)
Solution...
Demo… Example
Step-by-Step Example…
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IGCSE
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SERIES & BINOMIAL THEOREM
Binomial Theorem - Coefficients
Solve in your notebook…
Your turn… Experiment
Solve this question in your notebook…
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SERIES & BINOMIAL THEOREM
Binomial Theorem
Compare & Contrast
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SERIES & BINOMIAL THEOREM
Binomial Theorem - Formula
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
In general…
Binomial Theorem - Formula
FORMULA
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SERIES & BINOMIAL THEOREM
Binomial Theorem - Coefficients
Solve in your notebook…
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Binomial Theorem - Coefficients
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Binomial Theorem
Your turn… Experiment
Solve this question in your notebook…
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IGCSE
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SERIES & BINOMIAL THEOREM
Binomial Theorem
Solve in your notebook…
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Binomial Theorem
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Binomial Theorem
Solve in your notebook…
Your turn… Experiment
Solve this question in your notebook…
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SERIES & BINOMIAL THEOREM
Binomial Theorem
Solve in your notebook…
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Binomial Theorem
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Binomial Theorem
Solve in your notebook…
Solution...
Your turn… Experiment
Solve this question in your notebook…
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SERIES & BINOMIAL THEOREM
Binomial Theorem
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Binomial Theorem
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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IGCSE
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SERIES & BINOMIAL THEOREM
Binomial Theorem
Solve in your notebook…
Solution...
Your turn… Experiment
Solve this question in your notebook…
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IGCSE
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SERIES & BINOMIAL THEOREM
Binomial Theorem
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Binomial Theorem
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Binomial Theorem
Solve in your notebook…
Solution...
Your turn… Experiment
Solve this question in your notebook…
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TERMS & VOCABULARY
Required for this topic...
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SERIES & BINOMIAL THEOREM
C, C & C… Explain
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Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Solve in your notebook…
Solution...
Your turn… Experiment
Solve this question in your notebook…
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TERMS & VOCABULARY
Required for this topic...
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SERIES & BINOMIAL THEOREM
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Solve in your notebook…
Solution...
Your turn… Experiment
Solve this question in your notebook…
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TERMS & VOCABULARY
Required for this topic...
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SERIES & BINOMIAL THEOREM
Arithmetic Sequence or Progression
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Arithmetic Sequence or Progression
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Arithmetic Sequence or Progression
FORMULA
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SERIES & BINOMIAL THEOREM
Arithmetic Sequence or Progression
Solve in your notebook…
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Arithmetic Sequence or Progression
Solve in your notebook…
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Arithmetic Sequence or Progression
Solve in your notebook…
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Arithmetic Sequence or Progression
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Arithmetic Sequence or Progression
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Arithmetic Sequence or Progression
MATHS PROOF
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SERIES & BINOMIAL THEOREM
Arithmetic Sequence or Progression
MATHS PROOF
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SERIES & BINOMIAL THEOREM
Arithmetic Sequence or Progression
Solve in your notebook…
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Arithmetic Sequence or Progression
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Arithmetic Sequence or Progression
Solve in your notebook…
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Arithmetic Sequence or Progression
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Arithmetic Sequence or Progression
Solve in your notebook…
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Arithmetic Sequence or Progression
(a)
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Arithmetic Sequence or Progression
(b)
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Geometric Sequence or Progressions
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Geometric Sequence or Progressions
C, C & C… Explain
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Geometric Sequence or Progressions
FORMULA
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SERIES & BINOMIAL THEOREM
Geometric Sequence or Progressions
Solve in your notebook…
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Geometric Sequence or Progressions
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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Geometric Sequence or Progressions
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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Geometric Sequence or Progressions
Solve in your notebook…
Demo… Example
Step-by-Step Example…
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Geometric Sequence or Progressions
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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Geometric Sequence or Progressions
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Geometric Sequence or Progressions
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Geometric Sequence or Progressions
MATHS PROOF
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SERIES & BINOMIAL THEOREM
Geometric Sequence or Progressions
MATHS PROOF
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Geometric Sequence or Progressions
Solve in your notebook…
Demo… Example
Step-by-Step Example…
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Geometric Sequence or Progressions
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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Geometric Sequence or Progressions
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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Geometric Sequence or Progressions
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Infinite Geometric Series
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Infinite Geometric Series
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Infinite Geometric Series
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Infinite Geometric Series
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Infinite Geometric Series
FORMULA
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SERIES & BINOMIAL THEOREM
Infinite Geometric Series
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Infinite Geometric Series
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Infinite Geometric Series
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Infinite Geometric Series
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Infinite Geometric Series
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Infinite Geometric Series
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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Further Arithmetic & Geometric Series
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Further Arithmetic & Geometric Series
Solve in your notebook…
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Further Arithmetic & Geometric Series
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Further Arithmetic & Geometric Series
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Further Arithmetic & Geometric Series
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Further Arithmetic & Geometric Series
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Further Arithmetic & Geometric Series
SUMMARY
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SERIES & BINOMIAL THEOREM
Further Arithmetic & Geometric Series
SUMMARY
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SERIES & BINOMIAL THEOREM
Further Arithmetic & Geometric Series
SUMMARY
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SERIES & BINOMIAL THEOREM
Further Arithmetic & Geometric Series
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Geometric Sequence or Progressions
Solve in your notebook…
Solution...
Your turn… Experiment
Solve this question in your notebook…
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SERIES & BINOMIAL THEOREM
Geometric Sequence or Progressions
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Geometric Sequence or Progressions
Solve in your notebook…
Solution...
Your turn… Experiment
Solve this question in your notebook…
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SERIES & BINOMIAL THEOREM
Geometric Sequence or Progressions
C, C & C… Explain
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SERIES & BINOMIAL THEOREM
Geometric Sequence or Progressions
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
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SERIES & BINOMIAL THEOREM
Geometric Sequence or Progressions
Solve in your notebook…
Solution...
Your turn… Experiment
Solve this question in your notebook…
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SERIES & BINOMIAL THEOREM
Geometric Sequence or Progressions
C, C & C… Explain
180
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SERIES & BINOMIAL THEOREM
Geometric Sequence or Progressions
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
181
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SERIES & BINOMIAL THEOREM
Geometric Sequence or Progressions
Solve in your notebook…
Solution...
Your turn… Experiment
Solve this question in your notebook…
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SERIES & BINOMIAL THEOREM
Arithmetic Series
C, C & C… Explain
183
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SERIES & BINOMIAL THEOREM
Arithmetic Series
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
184
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SERIES & BINOMIAL THEOREM
Arithmetic Series
Solve in your notebook…
Solution...
Your turn… Experiment
Solve this question in your notebook…
185
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SERIES & BINOMIAL THEOREM
Arithmetic Series
C, C & C… Explain
186
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SERIES & BINOMIAL THEOREM
Arithmetic Series
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
187
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SERIES & BINOMIAL THEOREM
Arithmetic Series
Solve in your notebook…
Solution...
Your turn… Experiment
Solve this question in your notebook…
188
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SERIES & BINOMIAL THEOREM
Solve in your notebook…
Solution...
Demo… Example
Step-by-Step Example…
189
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SERIES & BINOMIAL THEOREM
Solve in your notebook…
Solution...
Your turn… Experiment
Solve this question in your notebook…
190
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SERIES & BINOMIAL THEOREM
All learners must complete…LEVEL 1-4
All must… Exercise
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PORTFOLIO
Evidence of thinking & learning:
*Assignments
*Notes
*Definitions
*Formulae
*Examples & Solutions
Take a photo of your Evidence of Thinking & Learning and paste it into the daily portfolio Google Doc. Submit this in our Google Classroom by the end of this class.
Take a photo of your Evidence of Thinking & Learning and paste it into your daily portfolio Google Doc.
Submit this in our Google Classroom at the end of each class.
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3-2-1 Reflection
In your portfolio, reflect on this session and answer the following: | |
3 2 1 | Three things that You learnt from this lesson… |
Two things that You found interesting and would like to know more about… | |
One thing that You still have a question about… | |
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“Transferable Thinking”
~ DISCUSS What do we know about… Transferable Thinking
Session Content
194
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Learning Objectives
In this session, we are thinking & learning about…
195
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Learning Objectives
In this session, we are thinking & learning about…
196
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Summary Recap
C, C & C… Explain
197
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Summary Recap
C, C & C… Explain
198
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Summary Recap
C, C & C… Explain
199
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Summary Recap
C, C & C… Explain
200
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Summary Recap
C, C & C… Explain
201
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Summary Recap
C, C & C… Explain
202
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Further Vector Notation
C, C & C… Explain
203
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Further Vector Notation
Solve in your notebook...
Demo… Example
Step-by-Step Example…
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Further Vector Notation
C, C & C… Explain
205
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Further Vector Notation
Solve in your notebook...
Demo… Example
Step-by-Step Example…
206
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Further Vector Notation
Solve in your notebook...
Demo… Example
Step-by-Step Example…
207
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Further Vector Notation
Solution… (Step 1/3)
Demo… Example
Step-by-Step Example…
208
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Further Vector Notation
Solution… (Step 2/3)
Demo… Example
Step-by-Step Example…
209
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Further Vector Notation
Solution… (Step 3/3)
Demo… Example
Step-by-Step Example…
210
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Position Vectors
C, C & C… Explain
211
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Position Vectors
C, C & C… Explain
212
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Position Vectors
Solve in your notebook…
HINT: Sketch the context.
Demo… Example
Step-by-Step Example…
213
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Position Vectors
Solution...
Demo… Example
Step-by-Step Example…
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Position Vectors
Solve in your notebook...
Demo… Example
Step-by-Step Example…
215
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Position Vectors
Solution...
Demo… Example
Step-by-Step Example…
216
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Position Vectors
Solution - HENCE…
Demo… Example
Step-by-Step Example…
217
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Vector Geometry
Demo… Example
Step-by-Step Example…
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Vector Geometry
Solution… (a)
Demo… Example
Step-by-Step Example…
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Vector Geometry
Solution… (b)
Demo… Example
Step-by-Step Example…
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Vector Geometry
Solution… (c)
Demo… Example
Step-by-Step Example…
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Vector Geometry
Solution… (d-1/4)
Demo… Example
Step-by-Step Example…
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Vector Geometry
Solution… (d-2/4)
Demo… Example
Step-by-Step Example…
223
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Vector Geometry
Solution… (d-3/4)
Demo… Example
Step-by-Step Example…
224
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Vector Geometry
Solution… (d-4/4)
Demo… Example
Step-by-Step Example…
225
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Vector Geometry
Solve in your notebook...
Demo… Example
Step-by-Step Example…
226
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Vector Geometry
Solution… (a)
Demo… Example
Step-by-Step Example…
227
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Vector Geometry
Solution… (b-i)
Demo… Example
Step-by-Step Example…
228
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Vector Geometry
Solution… (b-ii)
Demo… Example
Step-by-Step Example…
229
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Vector Geometry
Solution… (c-1)
Demo… Example
Step-by-Step Example…
230
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Vector Geometry
Solution… (c-2)
Demo… Example
Step-by-Step Example…
231
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Constant Velocity Problems
C, C & C… Explain
232
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You may already know the formula for an object moving with constant speed:
Similarly, the formula for an object moving with constant velocity:
Constant Velocity Problems
C, C & C… Explain
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Constant Velocity Problems
C, C & C… Explain
234
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Constant Velocity Problems
C, C & C… Explain
235
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Constant Velocity Problems
Solve in your notebook...
Demo… Example
Step-by-Step Example…
236
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Constant Velocity Problems
Solutions...
Demo… Example
Step-by-Step Example…
237
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Constant Velocity Problems
C, C & C… Explain
238
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Constant Velocity Problems
C, C & C… Explain
239
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Constant Velocity Problems
C, C & C… Explain
240
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Constant Velocity Problems
SUMMARY
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Critical Connections
What did we explore last session…? How can we apply this Knowledge & Understanding…? …Any Q’s? |
Thinking on your feet...
~ DISCUSS Concepts & Contexts
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Constant Velocity Problems
C, C & C… Explain
243
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Position Vectors
C, C & C… Explain
244
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Position Vectors
Solve in your notebook...
Demo… Example
Step-by-Step Example…
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Position Vectors
C, C & C… Explain
246
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Position Vectors
Solve in your notebook...
Demo… Example
Step-by-Step Example…
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Summary
C, C & C… Explain
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Summary
C, C & C… Explain
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Summary
C, C & C… Explain
250
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C, C & C… Explain
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C, C & C… Explain
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Linear Equations in 3 Forms
C, C & C… Explain
253
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Working with Vectors
C, C & C… Explain
254
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Working with Vectors
C, C & C… Explain
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Working with Vectors
C, C & C… Explain
256
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Working with Vectors
C, C & C… Explain
257
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Vectors with Value
C, C & C… Explain
258
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Vectors with Value
C, C & C… Explain
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Vectors with Value
C, C & C… Explain
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Vectors with Value
C, C & C… Explain
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Vectors with Value
C, C & C… Explain
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Vectors with Value
C, C & C… Explain
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Vectors with Value
C, C & C… Explain
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We can further divide vector into two types…
Equations of Lines
C, C & C… Explain
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Equations of Lines
C, C & C… Explain
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Equations of Lines
C, C & C… Explain
267
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Equations of Lines
C, C & C… Explain
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Equations of Lines
C, C & C… Explain
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C, C & C… Explain
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Geometric Representation - Definition
C, C & C… Explain
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Geometric Representation
C, C & C… Explain
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Geometric Representation
C, C & C… Explain
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Equal Vectors
C, C & C… Explain
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Equal Vectors
C, C & C… Explain
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Addition of Vectors
C, C & C… Explain
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Addition of Vectors
C, C & C… Explain
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Addition of Vectors
C, C & C… Explain
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C, C & C… Explain
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C, C & C… Explain
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C, C & C… Explain
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If we can consider the Cartesian Plane, any vector on the plane can be moved so as to start from the origin O.
C, C & C… Explain
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Thus any vector on the plane can be written in the form OA.
Suppose that the coordinates of the point A are: A (a,b)
C, C & C… Explain
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C, C & C… Explain
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
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Solution...
Demo… Example
Step-by-Step Example…
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Vectors on The Cartesian Plane
C, C & C… Explain
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
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C, C & C… Explain
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
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C, C & C… Explain
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
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C, C & C… Explain
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
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C, C & C… Explain
295
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
296
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Points & Vectors
C, C & C… Explain
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
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Dot Product - Angle Between Vectors
C, C & C… Explain
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Dot Product - Angle Between Vectors
C, C & C… Explain
300
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Dot Product - Angle Between Vectors
C, C & C… Explain
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Dot Product - Angle Between Vectors
C, C & C… Explain
302
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Dot Product - Angle Between Vectors
C, C & C… Explain
303
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Dot Product - Angle Between Vectors
C, C & C… Explain
304
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Dot Product - Angle Between Vectors
C, C & C… Explain
305
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Dot Product - Angle Between Vectors
C, C & C… Explain
306
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Dot Product - Angle Between Vectors
C, C & C… Explain
307
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Dot Product - Angle Between Vectors
C, C & C… Explain
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Dot Product - Angle Between Vectors
Solve in your notebook...
Demo… Example
Step-by-Step Example…
309
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Dot Product - Angle Between Vectors
Solve in your notebook…
Demo… Example
Step-by-Step Example…
310
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Dot Product - Angle Between Vectors
Solution...
Demo… Example
Step-by-Step Example…
311
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Dot Product - Angle Between Vectors
Solution...
Demo… Example
Step-by-Step Example…
312
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Dot Product - Angle Between Vectors
Solve in your notebook...
Demo… Example
Step-by-Step Example…
313
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Dot Product - Angle Between Vectors
Solution...
Demo… Example
Step-by-Step Example…
314
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C, C & C… Explain
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Can the cross product exist in 2 dimensions?
By definition the cross product does not exist in 2 dimensions as the cross product of 2 vectors yields another vector which is in direction perpendicular to the vectors participating in the cross product.
IGNITION
“A Conceptual Approach”...
~ DISCUSS Transferable Thinking
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Cross product is a binary operation on two vectors in three-dimensional space.
It results in a vector that is perpendicular to both vectors. The Vector product of two vectors, a and b, is denoted by a × b.
IGNITION
“A Conceptual Approach”...
~ DISCUSS Transferable Thinking
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Its resultant vector is perpendicular to a and b.
Vector products are also called cross products.
Cross product of two vectors will give the resultant a vector and calculated using the Right-hand Rule.
IGNITION
“A Conceptual Approach”...
~ DISCUSS Transferable Thinking
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Can the cross product exist in 2 dimensions?
Actually, there is a cross product defined in all dimensions. However, the result is an antisymmetric tensor: (u x v)_ij = u_i v_j - u_j v_i. In any dimension, there is an operation called the Hodge dual that relates an antisymmetric tensor of rank p with another of rank n - p where n is the dimension of the space.
This is done by using the totally antisymmetric tensor of rank n, eps: given a tensor a_ijk…m of rank p, you define b_qr…t of rank n - p by b_qr…t = eps_qr…tijk…m a_ijk…m, eps defined by eps_1234…n = 1.
When you apply this to the cross product in 3 d, the tensor of rank 2 becomes a vector of rank 3 - 2 = 1 (actually a pseudovector).
In 2d, the tensor becomes a scalar of rank 2 - 2 = 0.
In 4 and higher dimensions, the Hodge dual gives you a tensor of higher rank, there is not much point in using this!
You might have seen the cross product in 4d, in the definition of F_mu nu in Maxwell’s theory.
IGNITION
“A Conceptual Approach”...
~ DISCUSS Transferable Thinking
319
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Cross Product - 3D Vectors
C, C & C… Explain
320
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Cross Product - 3D Vectors
C, C & C… Explain
321
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Cross Product - 3D Vectors
C, C & C… Explain
322
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Cross Product - 3D Vectors
C, C & C… Explain
323
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Cross Product - 3D Vectors
C, C & C… Explain
324
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Cross Product - 3D Vectors
C, C & C… Explain
325
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Cross Product - 3D Vectors
C, C & C… Explain
326
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Cross Product - 3D Vectors
C, C & C… Explain
327
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Cross Product - 3D Vectors
C, C & C… Explain
328
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Cross Product - 3D Vectors
Solve in your notebook…
Demo… Example
Step-by-Step Example…
329
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Cross Product - 3D Vectors
Solution...
Demo… Example
Step-by-Step Example…
330
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Cross Product - 3D Vectors
Solution...
Demo… Example
Step-by-Step Example…
331
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Cross Product - 3D Vectors
C, C & C… Explain
332
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Cross Product - 3D Vectors
Solve in your notebook...
Demo… Example
Step-by-Step Example…
333
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Cross Product - 3D Vectors
Solution...
Demo… Example
Step-by-Step Example…
334
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Cross Product - 3D Vectors
Solution...
Demo… Example
Step-by-Step Example…
335
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Cross Product - 3D Vectors
Solution...
Demo… Example
Step-by-Step Example…
336
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Cross Product - Magnitude
C, C & C… Explain
337
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Cross Product - Magnitude
C, C & C… Explain
338
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Cross Product - Magnitude
C, C & C… Explain
339
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IGCSE
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Cross Product - 3D Vectors
C, C & C… Explain
340
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Cross Product - 3D Vectors
FIND the AREA of the parallelogram determined by vectors u and v.
Solve in your notebook...
Demo… Example
Step-by-Step Example…
341
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Cross Product - 3D Vectors
Solve in your notebook…
Demo… Example
Step-by-Step Example…
342
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Cross Product - 3D Vectors
Solution...
Demo… Example
Step-by-Step Example…
343
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IGCSE
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Planes
C, C & C… Explain
344
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
345
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Cross Product - 3D Vectors
C, C & C… Explain
346
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C, C & C… Explain
347
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
348
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C, C & C… Explain
349
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
350
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C, C & C… Explain
351
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
352
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C, C & C… Explain
353
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C, C & C… Explain
354
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
355
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Solution...
Your turn… Experiment
Solve this question in your notebook…
356
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All learners must complete…LEVEL 1-4
All must… Exercise
357
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PORTFOLIO
Evidence of thinking & learning:
*Assignments
*Notes
*Definitions
*Formulae
*Examples & Solutions
Take a photo of your Evidence of Thinking & Learning and paste it into the daily portfolio Google Doc. Submit this in our Google Classroom by the end of this class.
Take a photo of your Evidence of Thinking & Learning and paste it into your daily portfolio Google Doc.
Submit this in our Google Classroom at the end of each class.
358
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3-2-1 Reflection
In your portfolio, reflect on this session and answer the following: | |
3 2 1 | Three things that You learnt from this lesson… |
Two things that You found interesting and would like to know more about… | |
One thing that You still have a question about… | |
359
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“Transferable Thinking”
~ DISCUSS What do we know about… Transferable Thinking
Session Content
360
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TERMS & VOCABULARY
Required for this topic...
361
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VECTORS & RELATIVE VELOCITY
What is a matrix?
C, C & C… Explain
362
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VECTORS & RELATIVE VELOCITY
Operations with Matrices - Addition
C, C & C… Explain
363
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VECTORS & RELATIVE VELOCITY
Operations with Matrices - Addition
Demo… Example
Step-by-Step Example…
364
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VECTORS & RELATIVE VELOCITY
Operations with Matrices - Subtraction
C, C & C… Explain
365
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VECTORS & RELATIVE VELOCITY
Operations with Matrices - Negatives
C, C & C… Explain
366
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VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplication by a Constant
C, C & C… Explain
367
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VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by Another Matrix
C, C & C… Explain
368
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VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by Another Matrix
C, C & C… Explain
369
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VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by Another Matrix
C, C & C… Explain
370
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VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by Another Matrix
C, C & C… Explain
371
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VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by Another Matrix
C, C & C… Explain
372
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VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by Another Matrix
C, C & C… Explain
373
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VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by Another Matrix
C, C & C… Explain
374
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VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by Another Matrix
C, C & C… Explain
375
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VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by Another Matrix
C, C & C… Explain
376
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VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by Another Matrix
C, C & C… Explain
377
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VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by Another Matrix
C, C & C… Explain
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VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by Another Matrix
C, C & C… Explain
379
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IGCSE
0606
VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by Another Matrix
C, C & C… Explain
380
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IGCSE
0606
VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by Another Matrix
C, C & C… Explain
381
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IGCSE
0606
VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by Another Matrix
C, C & C… Explain
382
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IGCSE
0606
VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by Another Matrix
C, C & C… Explain
383
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IGCSE
0606
VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by Another Matrix
C, C & C… Explain
384
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IGCSE
0606
VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by Another Matrix
C, C & C… Explain
385
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IGCSE
0606
VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by Another Matrix
C, C & C… Explain
386
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IGCSE
0606
VECTORS & RELATIVE VELOCITY
Operations with Matrices - Order of Multiplication
C, C & C… Explain
387
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IGCSE
0606
VECTORS & RELATIVE VELOCITY
Operations with Matrices - Order of Multiplication
C, C & C… Explain
388
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IGCSE
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VECTORS & RELATIVE VELOCITY
Operations with Matrices - Order of Multiplication
Solve in your notebook...
Demo… Example
Step-by-Step Example…
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VECTORS & RELATIVE VELOCITY
There are exceptional conditions (such as when one matrix is The Identity Matrix) when the products will be the same, but not usually.
Operations with Matrices - Order of Multiplication
C, C & C… Explain
390
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IGCSE
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VECTORS & RELATIVE VELOCITY
Operations with Matrices - Division
C, C & C… Explain
391
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IGCSE
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VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by an Inverse
C, C & C… Explain
392
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IGCSE
0606
VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by an Inverse
C, C & C… Explain
393
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IGCSE
0606
VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by an Inverse
C, C & C… Explain
394
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IGCSE
0606
VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by an Inverse
C, C & C… Explain
395
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IGCSE
0606
VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by an Inverse
C, C & C… Explain
396
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IGCSE
0606
VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by an Inverse
C, C & C… Explain
397
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IGCSE
0606
VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by an Inverse
C, C & C… Explain
398
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IGCSE
0606
VECTORS & RELATIVE VELOCITY
Operations with Matrices - Multiplying by an Inverse
C, C & C… Explain
399
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IGCSE
0606
VECTORS & RELATIVE VELOCITY
Operations with Matrices - Transposing
C, C & C… Explain
400
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IGCSE
0606
VECTORS & RELATIVE VELOCITY
Operations with Matrices - Notation
C, C & C… Explain
401
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IGCSE
0606
VECTORS & RELATIVE VELOCITY
Operations with Matrices - Notation
C, C & C… Explain
402
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IGCSE
0606
VECTORS & RELATIVE VELOCITY
Operations with Matrices
Solve in your notebook...
Demo… Example
Step-by-Step Example…
403
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0606
Solution...
Your turn… Experiment
Solve this question in your notebook…
404
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All learners must complete…LEVEL 1-4
All must… Exercise
405
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3-2-1 Reflection
In your portfolio, reflect on this session and answer the following: | |
3 2 1 | Three things that You learnt from this lesson… |
Two things that You found interesting and would like to know more about… | |
One thing that You still have a question about… | |
406
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“Transferable Thinking”
~ DISCUSS What do we know about… Transferable Thinking
Session Content
407
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TERMS & VOCABULARY
Required for this topic...
408
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IGCSE
0606
C, C & C… Explain
409
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IGCSE
0606
Solve in your notebook...
Demo… Example
Step-by-Step Example…
410
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Solution...
Your turn… Experiment
Solve this question in your notebook…
411
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IGCSE
0606
All learners must complete…LEVEL 1-4
All must… Exercise
412
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“Transferable Thinking”
~ DISCUSS What do we know about… Transferable Thinking
Session Content
413
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IGCSE
0606
TERMS & VOCABULARY
Required for this topic...
414
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IGCSE
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C, C & C… Explain
415
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IGCSE
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
416
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Solution...
Your turn… Experiment
Solve this question in your notebook…
417
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IGCSE
0606
All learners must complete…LEVEL 1-4
All must… Exercise
418
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Critical Connections
Links to other subjects...
~ DISCUSS Concepts & Contexts
419
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TERMS & VOCABULARY
Required for this topic...
420
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CONCEPTS & CONTEXTS
Key Concept: |
Related Concept(s): |
Global Context: |
421
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International Mindedness
422
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ESSENTIAL UNDERSTANDINGS
In this topic, we are exploring…
423
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Learner Profile
The Learner Profile we will develop and refine...
424
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Approaches To Learning
The ATLS we will develop and refine…
425
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STATEMENT OF INQUIRY
Students will understand that...
...through inquiry into...
426
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Skill: |
Factual: |
Concept: |
Debatable: |
INQUIRY Q’s
427
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Areas of Knowledge
~ DISCUSS“How you know what you think you know.”
428
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Prior Knowledge
~ SHARE What is your prior knowledge…?
429
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3D World
~ DISCUSS How can we use this in the 3D World…?
430
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IGNITION
“A Conceptual Approach”...
~ DISCUSS Transferable Thinking
431
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Learning Objectives
In this session, we are thinking & learning about…
432
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Success Criteria
By the end of this session, you need to be able to...
433
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C, C & C… Explain
434
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
435
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Solution...
Your turn… Experiment
Solve this question in your notebook…
436
©
All learners must complete…LEVEL 1-4
All must… Exercise
437
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C, C & C… Explain
438
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
439
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Solution...
Your turn… Experiment
Solve this question in your notebook…
440
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Most learners will complete…LEVEL 4-6
Most will… Exercise
441
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C, C & C… Explain
442
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
443
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Solution...
Your turn… Experiment
Solve this question in your notebook…
444
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Some learners can complete…LEVEL 6+
Some can… Exercise
445
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C, C & C… Explain
446
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Solve in your notebook...
Demo… Example
Step-by-Step Example…
447
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Solution...
Your turn… Experiment
Solve this question in your notebook…
448
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Few learners do complete…LEVEL 7+
Few do… Exercise
Solve this question in your notebook…
449
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MATHS PROOF
450
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TECHNOLOGY
TI-Nspire Step-By-Step...
7x5
451
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VIDEO LINK
452
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PORTFOLIO
Evidence of thinking & learning:
*Assignments
*Notes
*Definitions
*Formulae
*Examples & Solutions
Take a photo of your Evidence of Thinking & Learning and paste it into the daily portfolio Google Doc. Submit this in our Google Classroom by the end of this class.
Take a photo of your Evidence of Thinking & Learning and paste it into your daily portfolio Google Doc.
Submit this in our Google Classroom at the end of each class.
453
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Feedback-&-Forward
In your portfolio, reflect on this session and answer the following: | |
| What went well for You? |
| What would You do differently next time? How could You change it? |
| What do You want to know more about on this topic? |
454
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3-2-1 Reflection
In your portfolio, reflect on this session and answer the following: | |
3 2 1 | Three things that You learnt from this lesson… |
Two things that You found interesting and would like to know more about… | |
One thing that You still have a question about… | |
455
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IGCSE
0606
TERMS & VOCABULARY
Required for this topic...
456
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