IB Mathematics Standard Level ... 2. Develop an understanding of the principles
and nature of mathematics. 3. .... (IBO Mathematics SL Guide 2012) ....
assessments (examination) will be over two separate examinations (Paper 1 &
Paper 2),.
IB Mathematics Standard Level Introduction This course caters for motivated students who already possess a robust knowledge of a wide range of mathematical concepts, and who are equipped with the skills needed to apply mathematical techniques correctly. These students will need a significant mathematical background as they prepare for future studies in subjects such as Chemistry, Biomedicine, Economics, Psychology, Technology and Business Administration. Students will need to be aware of the pathways for which this subject is a prerequisite. 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. The course covers Algebra, Functions, Equations, Circular Functions, Trigonometry, Vectors, Statistics, Probability and Calculus. 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. Aims The aims of all mathematics courses 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. Zhuhai International School IB-DP Math SL Course outline
Objectives What should you be able to do and understand when you have successfully completed the Maths SL course? 1. Read, interpret and solve a given problem using appropriate mathematical terms 2. Organize and present information and data in tabular, graphical and/or diagrammatic forms 3. Know and use appropriate notation and terminology 4. Formulate a mathematical argument and communicate it clearly 5. Select and use appropriate mathematical strategies and techniques 6. Demonstrate an understanding of both the significance and the reasonableness of results 7. Recognize patterns and structures in a variety of situations, and make generalizations 8. Recognize and demonstrate an understanding of the practical applications of mathematics 9. Use appropriate technological devices as mathematical tools 10. Demonstrate an understanding of and the appropriate use of mathematical modeling. Language policy The language of delivery is English. It is understood that many students have a first language other than English. The majority of first language in the class will be Chinese. Students are permitted to use Chinese to help relate ideas and clarify meaning. However, they are encouraged to master the English terms as most of the biological terms have not direct analogue in Chinese. In addition, the use of Chinese excludes other students who do not understand the language, so it is to be used minimally. Plagiarism and malpractice Academic honesty is expected of all students at ZIS. You are responsible for making sure that the work you produce is your own and that you do not offer other people’s work as your own. In addition we expect that as an individual you will not help another pupil to cheat in any way. Your teachers are here to help make sure that you know what this means. Your teachers are responsible for fostering intellectual honesty as well as your intellectual development. To this end they will apply methods of teaching, examination, and assignments that discourage student dishonesty. If necessary, your teachers will explain clearly any specialized meanings of cheating and plagiarism as they apply to the subjects you study. For details about what academic malpractice and plagiarism look like, and the processes involved, please see the Secondary School Handbook.
Zhuhai International School IB-DP Math SL Course outline
Expectations aches to Following on from the DP Orientation Camp, Mathematics students are expected to: the teaching and learning Fully engage with the course and their own success in it1 thematics SL Communicate openly, frequently and respectfully with their teacher Develop and follow a study schedule that sees them keep up with the particular demands of the course, as well as the broader reading and learning activity demands too '")(*+(,-'"),-'./0(12(/$%#0)3(0'%4)5'0(0"$%64(7)()5/$%#-&)4('$(4)8)6$9('").#(%54)#0'-54.5&( Develop comprehensive class notes 4$6$&;(-54(9#-/'./)($:('")(4.0/.96.5)($:(,-'"),-'./07#@%7&(%7"47$,3#@%B3%7&4%&##>#3%>4%39$%7"(($73>"4C% )604=C%"'=&4>A&3>"4%&4+%&4&(8#>#%"6%+&3&@%47'$&#$%39$%#7",$%"6%39$%,'"-($.%#>3?&3>"4#%39&3% &'$%&77$##>-($%3"%#3?+$43#@%#>"4#@
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Course pre‐requisites General: Students are not required to be familiar with all the topics listed as presumed knowledge (PK) before they start this course. However, they should be familiar with these topics before they take the examinations, because questions assume knowledge of them.
This list of topics is not designed to represent the outline of a course that might lead to the mathematics SL course. Instead, it lists the knowledge, together with the syllabus content, that is essential to successful completion of the mathematics SL course.
Zhuhai International School IB-DP Math SL Course outline
The subject and TOK TOK identifies 8 ways of knowing, and most, if not all, can be argued to have some role in the acquisition of mathematical knowledge. On the surface, Mathematical knowledge would appear to have been driven by reason and informed by sensory perception, but what role is there for emotion, intuition and uniquely in Mathematics, language. Certainty and predictability are central in Mathematics but ‘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?’. (IBO Mathematics SL Guide 2012) As well as deepening students’ knowledge, thinking and perspectives in Mathematics, incorporating the TOK framework into this course is aimed at supporting students with the TOK course.
Zhuhai International School IB-DP Math SL Course outline
Contents and skills Syllabus outline: The course consists of the study of seven topics – for a total of 150 hrs Syllabus content is 140 hrs and the Exploration is 10 hrs. All topics are compulsory. Students must study all the sub‐topics in each of the topics in the syllabus as listed in this guide. The topics, and the suggested time for them, are Topic 1—Algebra
9 hrs
Topic 2—Functions and equations
24 hrs
Topic 3—Circular functions and trigonometry
16 hrs
Topic 4—Vectors
16 hrs
Topic 5—Statistics and probability
35 hrs
Topic 6—Calculus
40 hrs
Investigation
10 hrs
A Mathematics Exploration of an area of mathematics. In Year 1… The aim in Year 1 is to complete the first 5 units: 1. Algebra 2. Functions and equations 3. Circular functions and trigonometry 4. Vectors …however we will likely break the Calculus topic in 2, starting it within Year 1. In Year 2… You will have already completed the first year of the Mathematics SL course, and you have covered 5 of the 7 topics. You will look at the last two topics – Statistics and Probability, and Differential Calculus – as well as revising content from last year. There will be internal and external assessments. Both of these are either marked or moderated by IB teachers from other schools than ours.
Zhuhai International School IB-DP Math SL Course outline
Year 1 Semester I Content 1.1 Arithmetic sequences and series, Sigma notation. 1.2 Elementary treatment of exponents and logarithms. Laws of exponents; laws of logarithms. Algebra Change of base. 1.3 The binomial theorem, expansion, calculation of binomial coefficients using Pascal’s triangle and !! 2.1 Concept of function, Composite, Identity. Inverse functions 2.2 Function graphing skills 2.3 Transformation of graphs 2.4 Quadratic function Functions & 2.5 Reciprocal function equations 2.6 Exponential functions and graphs 2.7 Solving equations graphically and analytically 2.8 Applications of graphing skills and solving equations that relate to real‐life situations. 3.1 The circle: radian measure of angles; length of an arc; area of a sector. 3.2 Cos, sin, tan and the unit circle. Exact trigonometric ratio values in Circular radians and pi functions & 3.3 Identities trigonometry 3.4 Circular functions and their graphs 3.5 Solving trigonometric equations in a finite interval, both graphically and analytically. 3.6 Solution of triangles (sine, cosine, area rules) Semester exam Everything covered to date Semester II 4.1 Vectors as displacements in the plane and in three dimensions. 4.2 The scalar product of two vectors. Perpendicular vectors; parallel vectors. The angle between two vectors. Vectors 4.3 Vector equations of a line, angles between lines 4.4 Distinguishing between coincident and parallel lines. Finding the point of intersection of two lines. Determining whether two lines intersect. Differential 6.1 Limits, gradient of functions, differentiating from first principles calculus – 6.2 Derivatives, chain rule, product rule, quotient rule, second derivative part 2 Semester Everything covered to date exam Unit Theme
Zhuhai International School IB-DP Math SL Course outline
Hours
9
24
16
16
12
Year 2
Statistics & probability
IA Investigation Differential calculus – part 2 Semester Exam Differential calculus – part 3
Semester III 5.1 Concepts of population, sample, random sample, discrete and continuous data. Presentation of data: frequency distributions (tables); frequency histograms with equal class intervals 5.2 Statistical measures and their interpretations. 5.3 Cumulative frequency 5.4 Linear correlation of bivariate data. 5.5 Concepts of trial, outcome, equally likely outcomes, sample space 35 (U) and event. 5.6 Probability – Combined mutually exclusive events, conditional and independent 5.7 Concept of discrete random variables and their probability distributions. 5.8 Binomial distribution. Mean and variance of the binomial distribution. 5.9 Normal distributions and curves.
10
6.3 Local max and min points, points of inflection, 6.4 Anti‐differentiation
10
Everything covered to date Semester IV 6.5 Anti‐differentiation with a boundary condition to determine the constant term. 6.6 Kinematics Revision Mock exams
Scheme Of Work (SOW) – descriptive planner Hyperlink Course materials and textbooks Main: Mathematics for the international student – Haese & Harris (3rd edition, 2012) Mathematics SL WORKED SOLUTIONS – Haese & Harris (3rd edition, 2012) Supporting: Mathematics HL & SL ‐ Peter Smythe (2nd Edition) (Mathematics Publishing) Further texts TBA Periodicals: Websites/blogs/forums: TBA TBA Zhuhai International School IB-DP Math SL Course outline
18 12
Assessment Overview: See the Secondary School Handbook full details of assessment practices and expectations in the Diploma Programme. There are three types to the assessment of this course 1. Summative assessment: These are assessments set at the end of the grading period to determine a student’s performance in that reporting period. 2. Formative assessments: These are a variety of tests and assignments set by the subject teacher as part of the teaching and learning process. 3. Final assessment: These are the assessments determined by the IB for this course. Summative Assessments: Semester grades are determined using the following criteria: The semester grade is derived by evaluating the student’s current standard at the time of grading. Regardless of which stage of the course the grading is done, students are held against the expected knowledge, understanding and skills required for the entire course. These grades are based on: End of semester exams (Paper 1 and Paper 2) In‐class Summative tasks, including tests, projects, reports etc Predicted Grades are determined as follows based on portfolio work and mock exam performance. Final Assessment External assessments (examination) will be over two separate examinations (Paper 1 & Paper 2), each 90 minutes long, for a total exam time of 3 hours. They will make up 80% of your subject mark. Paper 1: 1 hr 30 min, 40% of subject mark No calculator allowed Section A: Q1 – 7: Compulsory short‐response questions based on the whole syllabus Section B: Q8 – 10: Compulsory extended‐response questions based on the whole syllabus Zhuhai International School IB-DP Math SL Course outline
Paper 2: 1 hr 30 min 40% of subject mark Graphic display calculator (GDC) required Section A: Q1 – 7: Compulsory short‐response questions based on the whole syllabus Section B: Q8 – 10: Compulsory extended‐response questions based on the whole syllabus Internal Assessment 20% of subject mark The IA is a Mathematical Exploration of in area of mathematics. It is an individual exploration. This is a piece of written work that involves investigating an area of mathematics. ‘This is a short report written by the student based on a topic chosen by him or her, and it should focus on the mathematics of that particular area. The emphasis is on mathematical communication (including formulae, diagrams, graphs and so on), with accompanying commentary, good mathematical writing and thoughtful reflection….[in the project students] develop area(s) of interest to them without a time constraint as in an examination, and allow all students to experience a feeling of success. The final report should be approximately 6 to 12 pages long... Students should be able to explain all stages of their work in such a way that demonstrates clear understanding. While there is no requirement that students present their work in class, it should be written in such a way that their peers would be able to follow it fairly easily’ (IBO Mathematics Guide 2012) The exploration is intended to provide students with opportunities to increase their understanding of mathematical concepts and processes, and to develop a wider appreciation of mathematics. These are noted in the aims of the course, in particular, aims 6–9 (applications, technology, moral, social and ethical implications, and the international dimension). It is intended that, by doing the exploration, students benefit from the mathematical activities undertaken and find them both stimulating and rewarding. It will enable students to acquire the attributes of the IB learner profile. Teachers can give advice to students on a first draft of the exploration, but this first draft must not be heavily annotated or edited by the teacher. The next version handed to the teacher after the first draft must be the final one. It is expected that a total of approximately 10 teaching hours should be allocated to the work. This should include: time for the teacher to explain to students the requirements of the exploration class time for students to work on the exploration time for consultation between the teacher and each student time to review and monitor progress, and to check authenticity.
Zhuhai International School IB-DP Math SL Course outline
This will be marked by me, and externally moderated by other IB‐DP teachers from around the world. Each exploration is assessed against the following five criteria. The final mark for each exploration is the sum of the scores for each criterion. The maximum possible final mark is 20. Criterion A Communication Criterion B Mathematical presentation Criterion C Personal engagement Criterion D Reflection Criterion E Use of mathematics Students can choose from a wide variety of activities, for example, modelling, investigations and applications of mathematics. The specific purposes of the exploration are to: Develop students’ personal insight into the nature of mathematics and to develop their ability to ask their own questions about mathematics Provide opportunities for students to complete a piece of mathematical work over an extended period of time Enable students to experience the satisfaction of applying mathematical processes independently Provide students with the opportunity to experience for themselves the beauty, power and usefulness of mathematics Encourage students, where appropriate, to discover, use and appreciate the power of technology as a mathematical tool Enable students to develop the qualities of patience and persistence, and to reflect on the significance of their work Provide opportunities for students to show, with confidence, how they have developed mathematically. Key Dates: Semester 1, Year 2 (Before Easter End of Semester 1 Year 2 Holidays) Hand in final internal assessment
Start internal assessment
draft
End of Semester 2, Year 1
st
Exam on everything from 1 year Summer break between Year 1 and 2
Semester 3 Year 2
Semester 4, Year 2
Develop mock exploration/s
Mock Exams
Zhuhai International School IB-DP Math SL Course outline
Mock Exam
May 2014
Exams
