Kang Chiao International School

Kang Chiao International School

East China Campus

IBDP Math SL Syllabus

Grade: 11

Level: SL

Room: 1344

Teacher’s Name: Christopher Strobel

Email:

Website: www.christopherstrobel.cmswiki.wikispaces.net

IBDP Syllabus

IBDP Class Essential Agreements

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.

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.

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 13

8.1 Assessment Objectives 13

8.2 Assessment Details 13

8.3 In-School Assessment 14

8.4 IB Assessment 14-15

VII. Resources 16

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.

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.

· 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.

· 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.

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.

IBDP Syllabus

IV. Syllabus Details

IBDP Syllabus

Year 1/ Grade 11

Semester 1

For SL only

Week / Dates / Topic/ Unit / Content / School
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 test
3 / 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 test
7 / 10.12 – 10.16
8 / 10.19 – 10.23
9 / 10.26 – 10.30
10 / 11.02 – 11.06
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 Test
14 / 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 HOLIDAY
02.08 – 02.12
02.15 – 02.19

Year 1/ Grade 11

Semester 2

For SL only

Week / Dates / Topic/ Unit / Content / School
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 Test
2 / 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
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) / Project
Quiz
Unit Test
12 / 05.09 – 05.13
13 / 05.16 – 05.20
14 / 05.23 – 05.27
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)