Kang Chiao International SchoolEast China Campus

IBDP Math SL Syllabus

Grade: 11

Level: SL

Room: 1344

Teacher’s Name: Christopher Strobel

Email: christopher_strobel@kcisec.com

Website: www.christopherstrobel.cmswiki.wikispaces.net

IBDP Syllabus

IBDP Class Essential Agreement s

We agree that: We will be principled and academically honest in all of our IB-related work (including

written and oral assignments as well as examinations). We will actively seek for relevant information and cite all sources used in our

assignments (i.e. inquirers) We will complete our homework and submit our assignments in a timely manner. We will foster an open-minded learning environment, where all opinions will be

recognized and respected. We will bring, take care of and take away all of our required lesson materials. We will be punctual and prepared to learn for every class we attend in a balanced

manner. We will participate as thinkers - and contribute to the class at every opportunity -

cooperatively and proactively – to become more knowledgeable. We will be mutually respectful and caring by choosing appropriate language, effective

non-verbal communication and tolerance of differences in gender, culture, religion and ethnicity.

We will use electronic devices appropriately (including iPads, translators, laptops, tablets and smart watches).

We will follow the regulations and safety procedures of laboratories.

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IBDP Syllabus

Group 5:Mathematics

Group 5 aimsThe aims of all mathematics courses in group 5 are to enable students to:1. Enjoy mathematics, and develop an appreciation of the elegance and power of mathematics2. Develop an understanding of the principles and nature of mathematics3. Communicate clearly and confidently in a variety of contexts4. Develop logical, critical and creative thinking, and patience and persistence in problem-solving5. Employ and refine their powers of abstraction and generalization6. Apply and transfer skills to alternative situations, to other areas of knowledge and to future developments7. Appreciate how developments in technology and mathematics have influenced each other8. Appreciate the moral, social and ethical implications arising from the work of mathematicians and the applications of mathematics9. Appreciate the international dimension in mathematics through an awareness of the universality of mathematics and its multicultural and historical perspectives10. Appreciate the contribution of mathematics to other disciplines, and as a particular “area of knowledge” in the TOK course.

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Contents

I. INTRODUCTION........................................................................................1

II. COURSE PRE-REQUISITE....................................................................2

III. COURSE AIMS.........................................................................................5

IV. SYLLABUS DETAILS.................................................................................6

V. ITGS AND THE INTERNATIONAL DIMENSION............................11

VI. POSSIBLE LINKS TO THE CORE......................................................12

7.1. LINK TO THEORY OF KNOWLEDGE........................................................12

VII. ASSESSMENT.........................................................................................13

8.1 ASSESSMENT OBJECTIVES........................................................................138.2 ASSESSMENT DETAILS..............................................................................138.3 IN-SCHOOL ASSESSMENT.........................................................................148.4 IB ASSESSMENT...................................................................................14-15

VII. RESOURCES...........................................................................................16

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IBDP Syllabus

I. Introduction

The nature of mathematics can be summarized in a number of ways: for example, it can be seen as a well defined body of knowledge, as an abstract system of ideas, or as a useful tool. For many people it is probably a combination of these, but there is no doubt that mathematical knowledge provides an important key to understanding the world in which we live. Mathematics can enter our lives in a number of ways: we buy produce in the market, consult a timetable, read a newspaper, time a process or estimate a length. Mathematics, for most of us, also extends into our chosen profession: visual artists need to learn about perspective; musicians need to appreciate the mathematical relationships within and between different rhythms; economists need to recognize trends in financial dealings; and engineers need to take account of stress patterns in physical materials. Scientists view mathematics as a language that is central to our understanding of events that occur in the natural world. Some people enjoy the challenges offered by the logical methods of mathematics and the adventure in reason that mathematical proof has to offer. Others appreciate mathematics as an aesthetic experience or even as a cornerstone of philosophy. This prevalence of mathematics in our lives, with all its interdisciplinary connections, provides a clear and sufficient rationale for making the study of this subject compulsory for students studying the full diploma.

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IBDP Syllabus

II. Course Pre-requisite

Mathematics is a linear subject, and it is expected that most students embarking on a Diploma Programme (DP) mathematics course will have studied mathematics for at least 10 years. There will be a great variety of topics studied, and differing approaches to teaching and learning. Thus students will have a wide variety of skills and knowledge when they start the mathematics SL course. Most will have some background in arithmetic, algebra, geometry, trigonometry, probability and statistics. Some will be familiar with an inquiry approach, and may have had an opportunity to complete an extended piece of work in mathematics.

At the beginning of the syllabus section there is a list of topics that are considered to be prior learning for the mathematics SL course. It is recognized that this may contain topics that are unfamiliar to some students, but it is anticipated that there may be other topics in the syllabus itself that these students have already encountered.

Number Routine use of addition, subtraction, multiplication and division, using integers,

decimals and fractions, including order of operations. Simple positive exponents. Simplification of expressions involving roots (surds or radicals). Prime numbers and factors, including greatest common divisors and least common

multiples. Simple applications of ratio, percentage and proportion, linked to similarity. Definition and elementary treatment of absolute value (modulus). Rounding, decimal approximations and significant figures, including appreciation of

errors. Expression of numbers in standard form (scientific notation).

Sets and numbers Concept and notation of sets, elements, universal (reference) set, empty (null) set,

complement, subset, equality of sets, disjoint sets. Operations on sets: union and intersection. Commutative, associative and distributive properties. Venn diagrams. Number systems: natural numbers; integers, rationales, and irrationals; real numbers Intervals on the real number line using set notation and using inequalities. Expressing

the solution set of a linear inequality on the number line and in set notation.

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IBDP Syllabus

Mappings of the elements of one set to another. Illustration by means of sets of ordered pairs, tables, diagrams and graphs.

Algebra Manipulation of simple algebraic expressions involving factorization and expansion,

including quadratic expressions. Rearrangement, evaluation and combination of simple formulae. Examples from other

subject areas, particularly the sciences, should be included. The linear function and its graph, gradient and y-intercept. Addition and subtraction of algebraic fractions. The properties of order relations: <, ≤, >, ≥ . Solution of equations and inequalities in one variable, including cases with rational

coefficients. Solution of simultaneous equations in two variables.

Trigonometry Angle measurement in degrees. Compass directions and three figure bearings. Right-angle trigonometry. Simple applications for solving triangles. Pythagoras’ theorem and its converse.

Geometry Simple geometric transformations: translation, reflection, rotation, enlargement. Congruence and similarity, including the concept of scale factor of an enlargement. The circle, its centre and radius, area and circumference. The terms “arc”, “sector”,

“chord”, “tangent” and “segment”. Perimeter and area of plane figures. Properties of triangles and quadrilaterals,

including parallelograms, rhombuses, rectangles, squares, kites and trapeziums (trapezoids); compound shapes.

Volumes of prisms, pyramids, spheres, cylinders and cones.

Coordinate geometry Elementary geometry of the plane, including the concepts of dimension for point, line,

plane and space. The equation of a line in the form y = mx + c Parallel and perpendicular lines. Geometry of simple plane figures. The Cartesian plane: ordered pairs (x, y), origin, and axes.

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IBDP Syllabus

Mid-point of a line segment and distance between two points in the Cartesian plane and in three dimensions.

Statistics and probability Descriptive statistics: collection of raw data; display of data in pictorial and

diagrammatic forms, including pie charts, pictograms, stem and leaf diagrams, bar graphs and line graphs.

Obtaining simple statistics from discrete and continuous data, including mean, median, mode, quartiles, range, and inter-quartile range.

Calculating probabilities of simple events.

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IBDP Syllabus

III. Course Aims

The course focuses on introducing important mathematical concepts through the development of mathematical techniques. The intention is to introduce students to these concepts in a comprehensible and coherent way, rather than insisting on the mathematical rigor required for mathematics HL. Students should, wherever possible, apply the mathematical knowledge they have acquired to solve realistic problems set in an appropriate context.

The internally assessed component, the exploration, offers students the opportunity for developing independence in their mathematical learning. Students are encouraged to take a considered approach to various mathematical activities and to explore different mathematical ideas. The exploration also allows students to work without the time constraints of a written examination and to develop the skills they need for communicating mathematical ideas.

This course does not have the depth found in the mathematics HL courses. Students wishing to study subjects with a high degree of mathematical content should therefore opt for a mathematics HL course rather than a mathematics SL course.

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IBDP Syllabus

IV. Syllabus Details

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IBDP Syllabus

Year 1/ Grade 11

Semester 1

For SL only

Week Dates Topic/ Unit ContentSchool

Assessment

1 09.06 Course and

assessment overview

Go over syllabus

Introductions from teacher and students

Questionnaire

2 09.07 – 09.11 Unit 1: Algebra 1.1- Arithmetic and geometric sequences and series

1.3 - The binomial theorem, expansion, and Pascal’s Triangle

(This units material can be found in chapter 6 of your textbook)

Quiz

Unit 1 test3 09.14 – 09.18

4 09.21 – 09.25

5 09.28 – 09.30 Unit 2: Functions

and Equations

2.1 Functions- Composite, Identity, Inverse, and other basic functions.

(This can be found in chapter 1 of your textbook)

10.01 – 10.07 Golden Week

6 10.08 – 10.10 Unit 2: Functions

and Equations

2.3 Transformations of graphs

2.4 The quadratic function and its graph

2.7 Solving equations using different methods

2.8 Application of graphing skills related to real life

(2.3 can be found in chapter 1 of your textbook; 2.4, 2.7, 2.8 can be found in chapter 2 of your

textbook)

Quizzes

Mid unit test7 10.12 – 10.16

8 10.19 – 10.23

9 10.26 – 10.30

10 11.02 – 11.06

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IBDP Syllabus

Week Dates Topic/ Unit ContentSchool

Assessment

11 11.09 – 11.13 MID-TERM EXAMINATIONS

12 11.16 – 11.20 Unit 2: Functions

and Equations

2.5 Reciprocal and rational functions

(2.5 can be found in chapter 5 of your textbook)

Project

13 11.23 – 11.27 Unit 3: Logarithmic

and Exponential

Functions

1.2 Laws of exponents and logarithms

2.6 Exponential and logarithmic functions and their graphs

2.7 Solving exponential equations

(This unit can be found in chapter 4 of your textbook)

Quiz

Unit Test14 11.30 – 12.04

15 12.07 – 12.11

16 12.14 – 12.18

17 12.21 – 12.25 Unit 4: Statistics 5.1 Concepts and presentation of data

5.2Statistical measures and their interpretations

5.3 Cumulative frequency

(5.1 – 5.3 can be found in chapter 8 of your textbook

Project

Quiz

Mid Unit Test

18 12.28 – 01.01

19 01.04 – 01.08

20 01.11 – 01.15

21 01.18 – 01.22 FINAL EXAMINATION (TBC)

01.25 – 01.29

02.01 – 02.05

SCHOOL HOLIDAY02.08 – 02.12

02.15 – 02.19

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IBDP Syllabus

Year 1/ Grade 11

Semester 2

For SL only

Week Dates Topic/ Unit ContentSchool

Assessment

1 02.22 – 02.26 Unit 4: Statistics 5.4 Linear correlation of bivariate data

(5.4 can be found in chapter 10 of your textbook)

Quiz

Unit Test2 02.29 – 03.04

3 03.07 – 03.11 Unit 5: Probability 5.5 Concepts of trial, outcome, sample space, and event

5.6 Events, conditional probability, and probabilities without

replacement

5.7 Discrete random variables and their distributions, expected

value, and application

5.8 Binomial distribution with its mean and variance

5.9 Normal distributions, properties, curves, and the z-scores5.

(5.5 – 5.6 can be found in chapter 3 of your textbook)

(5.7 – 5.9 can be found in chapter 15 of your textbook)

Project

Quiz

Unit Test

4 03.14 – 03.18

5 03.21 – 03.25

6 03.28 – 04.01

7 04.04 – 04.08

8 04.11 – 04.15

9 04.18 – 04.22

10 04.25 – 04.29 MID-TERM EXAMINATION (TBC)

11 05.02 – 05.06 Unit 6: Circular

Functions and

Trigonometry

3.1 Unit circle

3.2 Trigonometry and the unit circle

3.3 Special trigonometric identities

Project

Quiz

Unit Test

12 05.09 – 05.13

13 05.16 – 05.20

14 05.23 – 05.27

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IBDP Syllabus

Week Dates Topic/ Unit ContentSchool

Assessment

3.4 Trigonometric functions and their graphs

3.5 Solving trigonometric equations graphically and analytically

3.6 Trigonometry and triangles

(3.2 – 3.5 can be found in chapter 13 of your textbook; 3.1 – 3.3, 3.6

can be found in chapter 11 of your textbook)

15 05.30 – 06.03

16 06.06 – 06. 10

17 06.13 – 06.17

18 06.20 – 06.24 Review Review for Final Examination

19 06.27 – 07.01 FINAL EXAMINATION (TBC)

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IBDP Syllabus

V. Math SL and the International Dimension

Mathematics is in a sense an international language, and, apart from slightly differing notation, mathematicians from around the world can communicate within their field. Mathematics transcends politics, religion and nationality, yet throughout history great civilizations owe their success in part to their mathematicians being able to create and maintain complex social and architectural structures.

Despite recent advances in the development of information and communication technologies, the global exchange of mathematical information and ideas is not a new phenomenon and has been essential to the progress of mathematics. Indeed, many of the foundations of modern mathematics were laid many centuries ago by Arabic, Greek, Indian and Chinese civilizations, among others. Teachers could use timeline websites to show the contributions of different civilizations to mathematics, but not just for their mathematical content. Illustrating the characters and personalities of the mathematicians concerned and the historical context in which they worked brings home the human and cultural dimension of mathematics.

The importance of science and technology in the everyday world is clear, but the vital role of mathematics is not so well recognized. It is the language of science, and underpins most developments in science and technology. A good example of this is the digital revolution, which is transforming the world, as it is all based on the binary number system in mathematics.

Many international bodies now exist to promote mathematics. Students are encouraged to access the extensive websites of international mathematical organizations to enhance their appreciation of the international dimension and to engage in the global issues surrounding the subject.

Examples of global issues relating to international-mindedness (Int) are given in the “Links” column of the syllabus.

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IBDP Syllabus

VI. Possible Links to the Core

7.1. Link to Theory of Knowledge

The Theory of knowledge guide (March 2006) identifies four ways of knowing, and it could be claimed that these all have some role in the acquisition of mathematical knowledge. While perhaps initially inspired by data from sense perception, mathematics is dominated by reason, and some mathematicians argue that their subject is a language, that it is, in some sense, universal. However, there is also no doubt that mathematicians perceive beauty in mathematics, and that emotion can be a strong driver in the search for mathematical knowledge.

As an area of knowledge, mathematics seems to supply a certainty perhaps missing in other disciplines. This may be related to the “purity” of the subject that makes it sometimes seem divorced from reality. However, mathematics has also provided important knowledge about the world, and the use of mathematics in science and technology has been one of the driving forces for scientific advances.

Despite all its undoubted power for understanding and change, mathematics is in the end a puzzling phenomenon. A fundamental question for all knowers is whether mathematical knowledge really exists independently of our thinking about it. Is it there “waiting to be discovered” or is it a human creation?

7.2. Link to Extended Essay

All students will be expected to perform writing assignments throughout the two years in this course. This includes class assignment and the internal assessment (IA). Within the students writing assignments, authentic use of citation, grammar, and standard English conventions will be expected to prepare students for the rigor of the Extended Essay paper.

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IBDP Syllabus

VII. Assessment

8.1 Assessment Objectives

Problem-solving is central to learning mathematics and involves the acquisition of mathematical skills and concepts in a wide range of situations, including non-routine, open-ended and real-world problems. Having followed a DP mathematics SL course, students will be expected to demonstrate the following.

1. Knowledge and understanding: recall, select and use their knowledge of mathematical facts, concepts and techniques in a variety of familiar and unfamiliar contexts.2. Problem-solving: recall, select and use their knowledge of mathematical skills, results and models in both real and abstract contexts to solve problems.3. Communication and interpretation: transform common realistic contexts into mathematics; comment on the context; sketch or draw mathematical diagrams, graphs or constructions both on paper and using technology; record methods, solutions and conclusions using standardized notation.4. Technology: use technology, accurately, appropriately and efficiently both to explore new ideas and to solve problems.5. Reasoning: construct mathematical arguments through use of precise statements, logical deduction and inference, and by the manipulation of mathematical expressions.6. Inquiry approaches: investigate unfamiliar situations, both abstract and real-world, involving organizing and analyzing information, making conjectures, drawing conclusions and testing their validity.

8.2 Assessment Details

There will be in class quizzes and tests. These assessments will be comprised of recent material as well as any materials covered in the past. Midterms and Finals will be given each semester as well which will be cumulative.

There will also an Internal Assessment and an External Assessment in your second year of this course.

8.3 In-School Assessment

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IBDP Syllabus

The following table illustrates in-school assessment. All works are assessed against the IB criteria in the Math SL course.

Assessment Category Weighting

Practice problems 5%Projects/ presentations 5%Quizzes 5%Tests 15%Midterm 30%Final 40%

Grade breakdown for KCIS:

Semester 1, Year 1 (40% of total year grade)

In class assessments – 30% of semester grade

Midterm – 30% of semester grade

Final – 40% of semester grade

Semester 2, Year 1 (60% of total year grade)

In class assessments – 30% of semester grade

Midterm – 30% of semester grade

Final – 40% of semester grade

Grade breakdown for IB:

Internal Assessment – 20%

External Assessment – 80%

8.4 IB Assessment

The IB assessment is as follows.

Assessment Outline – SL

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IBDP Syllabus

Assessment Component Weighting

External assessment (3 hours) 80%Paper 1 (1 hour 30 minutes) No calculator allowed. (90 marks)

Section ACompulsory short response questions based on the whole syllabus

Section B Compulsory extended response questions based on the whole syllabus

40%

Paper 2 (1 hour and 30 minutes)Graphic display calculator required. (90 marks)

Section A Compulsory short response questions based on the whole syllabus

Section B Compulsory extended response questions based on the whole syllabus

40%

Internal assessmentThis component is internally assessed by the teacher and externally moderated by the IB at the end of the course

Mathematical explorationInternal assessment in mathematics SL is an individual exploration. This is a piece of written work that involves investigating an area of mathematics. (20 marks)

20%

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IBDP Syllabus

VIII. Resources

Required for Students

Course Companion

Pencils

Notebook

Graphing Calculator (TI-84 Plus C Silver)

Erasers

I Pad/ laptop

For Reference

My website will have my in class notes and assignments for your reference:

www.christopherstrobel.cmswiki.wikispaces.net

Work Cited

Buchanan, L., Fensom, J., Kemp, E., Rondie, P.L., Stevens, J. (2012). Mathematics Standard Level Course Companion. Oxford: Oxford University Press.

International Baccalaureate Diploma Programme. (2012). Mathematics SL guide. United Kingdom: International Baccalaureate Organization.

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