Kang Chiao International School
East China Campus
IBDP Math SL Syllabus
Grade: 11
Level: SL
Room: 1344
Teacher’s Name: Christopher Strobel
Email: [email protected]
Website: www.christopherstrobel.cmswiki.wikispaces.net
IBDP Syllabus
IBDP Class Essential Agreements
We agree that:
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We will be principled and academically honest in all of our IB-related work (including
written and oral assignments as well as examinations).
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We will actively seek for relevant information and cite all sources used in our
assignments (i.e. inquirers)
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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.
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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.
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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 aims
The 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 mathematics
2. Develop an understanding of the principles and nature of mathematics
3. Communicate clearly and confidently in a variety of contexts
4. Develop logical, critical and creative thinking, and patience and persistence in
problem-solving
5. Employ and refine their powers of abstraction and generalization
6. Apply and transfer skills to alternative situations, to other areas of knowledge and to future
developments
7. Appreciate how developments in technology and mathematics have influenced each other
8. Appreciate the moral, social and ethical implications arising from the work of
mathematicians and the applications of mathematics
9. Appreciate the international dimension in mathematics through an awareness of the
universality of mathematics and its multicultural and historical perspectives
10. Appreciate the contribution of mathematics to other disciplines, and as a particular “area of
knowledge” in the TOK course.
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IBDP Syllabus
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 ....................................................................................... 113
8.1 ASSESSMENT OBJECTIVES ....................................................................... 113
8.2 ASSESSMENT DETAILS.............................................................................. 113
8.3 IN-SCHOOL ASSESSMENT ........................................................................... 14
8.4 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
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Routine use of addition, subtraction, multiplication and division, using integers,
decimals and fractions, including order of operations.
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Simple positive exponents.
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Simplification of expressions involving roots (surds or radicals).
Prime numbers and factors, including greatest common divisors and least common
multiples.
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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.
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Expression of numbers in standard form (scientific notation).
Sets and numbers
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Concept and notation of sets, elements, universal (reference) set, empty (null) set,
complement, subset, equality of sets, disjoint sets.
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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
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Mappings of the elements of one set to another. Illustration by means of sets of ordered
pairs, tables, diagrams and graphs.
Algebra
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Manipulation of simple algebraic expressions involving factorization and expansion,
including quadratic expressions.
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Rearrangement, evaluation and combination of simple formulae. Examples from other
subject areas, particularly the sciences, should be included.
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The linear function and its graph, gradient and y-intercept.
Addition and subtraction of algebraic fractions.
The properties of order relations: <, ≤, >, ≥ .
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Solution of equations and inequalities in one variable, including cases with rational
coefficients.
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Solution of simultaneous equations in two variables.
Trigonometry
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Angle measurement in degrees.
Compass directions and three figure bearings.
Right-angle trigonometry.
Simple applications for solving triangles.
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Pythagoras’ theorem and its converse.
Geometry
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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”.
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Perimeter and area of plane figures. Properties of triangles and quadrilaterals, including
parallelograms, rhombuses, rectangles, squares, kites and trapeziums (trapezoids);
compound shapes.
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Volumes of prisms, pyramids, spheres, cylinders and cones.
Coordinate geometry
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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
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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
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Mid-point of a line segment and distance between two points in the Cartesian plane and
in three dimensions.
Statistics and probability
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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.
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Obtaining simple statistics from discrete and continuous data, including mean, median,
mode, quartiles, range, and inter-quartile range.
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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
Content
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
3
09.14 – 09.18
4
09.21 – 09.25
1.3 - The binomial theorem, expansion, and Pascal’s Triangle
School
Assessment
Quiz
Unit 1 test
(This units material can be found in chapter 6 of your textbook)
5
09.28 – 09.30
Unit 2: Functions
and Equations
(This can be found in chapter 1 of your textbook)
Golden Week
10.01 – 10.07
6
10.08 – 10.10
7
10.12 – 10.16
8
10.19 – 10.23
9
10.26 – 10.30
10
11.02 – 11.06
2.1 Functions- Composite, Identity, Inverse, and other basic functions.
Unit 2: Functions
and Equations
Quizzes
Mid unit test
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)
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11.09 – 11.13
MID-TERM EXAMINATIONS
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IBDP Syllabus
12
11.16 – 11.20
Unit 2: Functions
and Equations
13
11.23 – 11.27
14
11.30 – 12.04
15
12.07 – 12.11
Unit 3: Logarithmic
and Exponential
Functions
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12.14 – 12.18
Project
2.5 Reciprocal and rational functions
(2.5 can be found in chapter 5 of your textbook)
1.2 Laws of exponents and logarithms
Quiz
Unit Test
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)
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12.21 – 12.25
18
12.28 – 01.01
19
01.04 – 01.08
20
01.11 – 01.15
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
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01.18 – 01.22
FINAL EXAMINATION (TBC)
01.25 – 01.29
02.01 – 02.05
02.08 – 02.12
SCHOOL HOLIDAY
02.15 – 02.19
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Project
Quiz
Mid Unit Test
IBDP Syllabus
Year 1/ Grade 11
Semester 2
For SL only
Week
Dates
Topic/ Unit
Content
1
02.22 – 02.26
2
02.29 – 03.04
3
03.07 – 03.11
4
03.14 – 03.18
5.6 Events, conditional probability, and probabilities without
5
03.21 – 03.25
replacement
6
03.28 – 04.01
7
04.04 – 04.08
8
04.11 – 04.15
9
04.18 – 04.22
Unit 4: Statistics
5.4 Linear correlation of bivariate data
(5.4 can be found in chapter 10 of your textbook)
Unit 5: Probability
5.5 Concepts of trial, outcome, sample space, and event
School
Assessment
Quiz
Unit Test
Project
Quiz
Unit Test
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)
10
04.25 – 04.29
11
05.02 – 05.06
12
05.09 – 05.13
13
05.16 – 05.20
14
05.23 – 05.27
15
05.30 – 06.03
MID-TERM EXAMINATION (TBC)
Unit 6: Circular
Functions and
Trigonometry
3.1 Unit circle
3.2 Trigonometry and the unit circle
3.3 Special trigonometric identities
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Project
Quiz
Unit Test
IBDP Syllabus
Topic/ Unit
School
Assessment
Week
Dates
Content
16
06.06 – 06. 10
3.4 Trigonometric functions and their graphs
17
06.13 – 06.17
3.5 Solving trigonometric equations graphically and analytically
3.6 Trigonometry and triangles
18
06.20 – 06.24
19
06.27 – 07.01
Review
(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)
Review for Final Examination
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.
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IBDP Syllabus
8.3 In-School Assessment
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
Projects/ presentations
Quizzes
Tests
Midterm
Final
5%
5%
5%
15%
30%
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:
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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)
Paper 1 (1 hour 30 minutes)
No calculator allowed. (90 marks)
80%
40%
Section A
Compulsory short response questions based on the whole syllabus
Section B
Compulsory extended response questions based on the whole syllabus
Paper 2 (1 hour and 30 minutes)
Graphic display calculator required. (90 marks)
40%
Section A
Compulsory short response questions based on the whole syllabus
Section B
Compulsory extended response questions based on the whole syllabus
Internal assessment
This component is internally assessed by the teacher and externally moderated by
the IB at the end of the course
Mathematical exploration
Internal assessment in mathematics SL is an individual exploration. This is a piece
of written work that involves investigating an area of mathematics. (20 marks)
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20%
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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