## Topic 1 - Algebra (9 hours)

The aim of this topic is to introduce students to some basic algebraic concepts and applications

## PowerPoints covering all of the syllabus content for topic 1 can be found below.

sl_2014_arithmetic_sequences_and_series.pptx | |

File Size: | 6667 kb |

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sigma_notation.pptx | |

File Size: | 1779 kb |

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reviewing_the_exponent_laws_powerpoint.pptx | |

File Size: | 1433 kb |

File Type: | pptx |

logarithms_powerpoint.pptx | |

File Size: | 2464 kb |

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the_binomial_theorem_powerpoint.pptx | |

File Size: | 28951 kb |

File Type: | pptx |

## Arithmetic sequences and series

sl_2014_arithmetic_sequences_and_series.pptx | |

File Size: | 5716 kb |

File Type: | pptx |

sigma_notation.pptx | |

File Size: | 1779 kb |

File Type: | pptx |

**History of Mathematics**

The School of Athens is a depiction of philosophy. The scene takes place in classical times, as both the architecture and the garments indicate. Figures representing each subject that must be mastered in order to hold a true philosophic debate - astronomy, geometry, arithmetic, and solid geometry - are depicted in concrete form. The arbiters of this rule, the main figures, Plato and Aristotle, are shown in the centre, engaged in such a dialogue.

## TOK: What is Zeno's dichotomy paradox?

First let's start with "Zeno's dilemma".

**Zeno's dilemma**

Once upon a time (about 450 BC), a Greek named Zeno made up several word problems that became known as Zeno's paradoxes. This problem is not a paradox, but was inspired by one of Zeno's problems. Consider a race between Achilles and a tortoise. The tortoise has a 100-metre head start. Achilles runs at a rate of 10 metres per second, whereas the tortoise runs 1 metre per second (it is an extraordinarily swift tortoise). How long does it take Achilles to catch up with the tortoise?

Now let's take a look at Zeno's paradox.

## The Limit: Zeno's Paradox

Zeno was a Greek philosopher known primarily for his famous paradoxes. One of those concerns a race between Achilles, a legendary Greek hero, and a tortoise. When the race begins, the (slower) tortoise is given a head start, as shown in the figure above. Is it possible for Achilles to overtake the tortoise? Zeno pointed out that by the time Achilles reaches the tortoise's starting point, the tortoise will have moved ahead to a new point. When Achilles gets to this next point, the tortoise will be at a new point. The tortoise, even though much slower than Achilles, keeps moving forward. Although the distance between Achilles and the tortoise is getting smaller and smaller, the tortoise will apparently always be ahead.

Of course, common sense tells us that Achilles will overtake the slow tortoise, but where is the error in reasoning in the previous paragraph that always gives the tortoise the lead? The error is in the assumption that an infinite amount of time is required to cover a distance divided into an infinite number of segments. This discussion is getting at an essential idea in calculus--namely, the notion of a limit.

Of course, common sense tells us that Achilles will overtake the slow tortoise, but where is the error in reasoning in the previous paragraph that always gives the tortoise the lead? The error is in the assumption that an infinite amount of time is required to cover a distance divided into an infinite number of segments. This discussion is getting at an essential idea in calculus--namely, the notion of a limit.

## Arithmetic Sequences

Perhaps the simplest pattern is the counting numbers themselves: 1, 2, 3, 4, 5, 6, .... A list of numbers having a first number, a second number, a third number, and so on is called a

The numbers in a sequence are called the

**sequence**.The numbers in a sequence are called the

**terms**of the sequence. Sequences obtained by adding the same number to each term to obtain the next term are called**arithmetic sequences**or**arithmetic progressions**. Source: "Mathematics Standard Level" Oxford University Press 2012.

## Sequences

sequences_worksheet_a.pdf | |

File Size: | 102 kb |

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sequences_worksheet_a_soln.pdf | |

File Size: | 96 kb |

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## Arithmetic Series

arithmetic_series_worksheet_b.pdf | |

File Size: | 97 kb |

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arithmetic_series_worksheet_b_soln.pdf | |

File Size: | 98 kb |

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## Arithmetic Series - Further Questions

arithmetic_series_-_further_questions_worksheet_c.pdf | |

File Size: | 99 kb |

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arithmetic_series_-_further_questions_worksheet_c_soln.pdf | |

File Size: | 99 kb |

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## Sigma Notes & Examples

Students have been experiencing difficulty with Sigma notation can review the following document and practice the example questions.

sigma_notes__examples.pdf | |

File Size: | 84 kb |

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## Geometric Series

geometric_series_worksheet_a.pdf | |

File Size: | 98 kb |

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geometric_series_worksheet_a_soln.pdf | |

File Size: | 100 kb |

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## Geometric Series - Further Questions

geometric_series_-_further_questions_worksheet_b.pdf | |

File Size: | 99 kb |

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geometric_series_-_further_questions_worksheet_b_soln.pdf | |

File Size: | 100 kb |

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## SUMMARY NOTES: SEQUENCES & SEREIS (with practice questions & answers) STUDY REVIEW

topic_1_-_algebra_sequences_and_series_study_review.pdf | |

File Size: | 1161 kb |

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__Remember__:

*It is easy to remember what your truly understand.*

**Don't memorize - seek to understand**-Students wanting to practice more challenging sequences and series problems, are encouraged to download "CHALLENGING SEQUENCE & SERIES PRACTICE QUESTIONS (WITH ANSWERS).

__Extension:__ Challenging Sequences & Series Practice Questions (with Answers)

dp_sl_11_sequences_and_series_practice_questions.pdf | |

File Size: | 1190 kb |

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## Pascal's Triangle & Binomial Expansion

Source: "Mathematics Standard Level" Oxford University Press 2012. Source: http://mathforum.org/

## Binomial Expansions

binomial_expansions_worksheet_c.pdf | |

File Size: | 85 kb |

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binomial_expansions_worksheet_c_soln.pdf | |

File Size: | 97 kb |

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Source: "Mathematics Standard Level" Oxford University Press 2012.

## Binomial Expansions - Further Questions

binomial_expansions_-_further_questions_worksheet_d.pdf | |

File Size: | 106 kb |

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binomial_expansions_-_further_questions_worksheet_d_soln.pdf | |

File Size: | 117 kb |

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## Mixed Exam-Style Questions on Sequences and Series

mixed_exam-style_questions_on_sequences_and_series_worksheet_d.pdf | |

File Size: | 103 kb |

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mixed_exam-style_questions_on_sequences_and_series_worksheet_d_soln.pdf | |

File Size: | 100 kb |

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## Mixed Exam-Style Questions on Sequences and Series & Binomial Expansions

mixed_exam-style_questions_on_sequences_and_series_worksheet_e.pdf | |

File Size: | 103 kb |

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mixed_exam-style_questions_on_sequences_and_series_worksheet_e_soln.pdf | |

File Size: | 103 kb |

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mixed_exam-style_questions_on_sequences_and_series_worksheet_f.pdf | |

File Size: | 103 kb |

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mixed_exam-style_questions_on_sequences_and_series_worksheet_f_soln.pdf | |

File Size: | 110 kb |

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## Patterns, Sequences & Series Summary Sheet

Please be sure to download the document below as a study reference. It will be useful when your are studying for tests and your final exam.

patterns_sequences__series_summary_sheet.pdf | |

File Size: | 193 kb |

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Go through the PowerPoint "the_binomial _theorem_powerpoint" below and try all of the examples. In addition, be sure to independently go through the binomial expansion chapter in the textbook (excluding the review sets at the end).

the_binomial_theorem_powerpoint.pptx | |

File Size: | 28951 kb |

File Type: | pptx |

## "I GOT SKILLS"

Regardless of what domain of life, "perfect practice makes perfect". All students should be reviewing and practicing their mathematical skills daily. Below the photos are practice algebra exercises that will help you on your journey of mastering skills and developing a deeper understanding of concepts.

algebra_exercises.pdf | |

File Size: | 603 kb |

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algebra_exercises_soln.pdf | |

File Size: | 255 kb |

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## Combined DP Mathematics Standard Level Classes

During the week that Ms. MacDonald was away in Vietnam with the grade 10 excursion (we missed you Ms. MacDonald, but we hope you had fun), Year 1 students experienced a variety of instructional strategies and activities, including 'under pressure' timed learning stations, and a simulated university lecture in the school's auditorium.

## Algebra Exam Type Questions

year_1_exam_type_questions.pdf | |

File Size: | 845 kb |

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year_1_exam_type_questions_soln.pdf | |

File Size: | 1184 kb |

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## Sequences & Series and Binomial Theorem Test (Reflection)

Students have received their assessed tests back on Topic 1 - Algebra. As IB Learners, each student will independently reflect on their test, make the necessary corrections and get their tests signed by their parents.

**Post Test Reflection Questions**:- How did you prepare for the test? (Be specific)
- How long did you study? (Include how many days in advance)
- Did you re-write and review your notes?
- Did you change your answers?
- Were you distracted during the test?
- Did you eat breakfast the morning of the test?
- Did you get enough sleep the night before?
- Did you study with friends or parents?
- Did you attend to tutorial/help sessions to ask questions? Did you go into the test with unanswered questions? (Be specific)
- Is there anything that you would have done differently to prepare? Is there anything that worked well to help you prepare that you want to do again before the next test?

## Exponential and Logarithmic Functions

Exponential and logarithmic functions are used to model several real-life situations. Some of them include: Radioactive decay, compound interest, continuous compound interest, population growth, pH of a solution, decibel voltage gain, intensity of earthquakes measured on Richter Scale, Weber-Fechner Law, and depreciation.

## Laws of Logarithms

laws_of_logarithms_worksheet_a.pdf | |

File Size: | 88 kb |

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laws_of_logarithms_worksheet_a_soln.pdf | |

File Size: | 92 kb |

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## Laws of Logarithms - Further Questions

laws_of_logarithms_-_further_questions_worksheet_b.pdf | |

File Size: | 87 kb |

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laws_of_logarithms_-_further_questions_worksheet_b_soln.pdf | |

File Size: | 99 kb |

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## Uses of Exponential and Logarithmic Functions - Workbook Notes & Exercises

topic_1_-_algebra_-_uses_of_exponential_and_logarithmic_functions_workbook.pdf | |

File Size: | 1228 kb |

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## Exponential Graphs and Using Logarithms to Solve Equations

exponential_graphs_and_using_logarithms_to_solve_equations_worksheet_c.pdf | |

File Size: | 93 kb |

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exponential_graphs_and_using_logarithms_to_solve_equations_worksheet_c_soln.pdf | |

File Size: | 133 kb |

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## Exponential and Logarithmic Exercises

topic_1_-_algebra_exponentials_and_logarithms_workbook_with_answers.pdf | |

File Size: | 1697 kb |

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topic_1_-_algebra_laws_of_exponents_and_logarithms_study_review.pdf | |

File Size: | 2475 kb |

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