IB Diploma Programme course outlines: Mathematical Studies

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1 IB Diploma Programme course outlines: Mathematical Studies Course Description This course caters for students with varied backgrounds and abilities. More specifically, it is designed to build confidence and encourage an appreciation of mathematics in students who do not anticipate a need for mathematics in their future studies. Students taking this course need to be already equipped with fundamental skills and a rudimentary knowledge of basic processes. The course concentrates on mathematics that can be applied to contexts related as far as possible to other subjects being studied, to common real-world occurrences and to topics that relate to home, work and leisure situations. The course includes project work, a feature unique within this group of courses: students must produce a project, a piece of written work based on personal research, guided and supervised by the teacher. The project provides an opportunity for students to carry out a mathematical investigation in the context of another course being studied, a hobby or interest of their choice using skills learned before and during the course. This process allows students to ask their own questions about mathematics and to take responsibility for a part of their own course of studies in mathematics. The students most likely to select this course are those whose main interests lie outside the field of mathematics, and for many students this course will be their final experience of being taught formal mathematics. The students will use text books which emphasize the international nature of mathematics. The history of mathematics is of course multi national, rich and diverse and the origins of some of these discoveries will be discussed. When appropriate items from the current news and/or discoveries in other countries will also be used to see the necessity of maths around the world. Also teaching in an international school the students will naturally have a different notation to others which will be commented on and accepted. The specific purposes of the project are to develop students' personal insight into the nature of mathematics and to develop their ability to ask their own questions about mathematics, encourage students to initiate and sustain a piece of work in mathematics, enable students to acquire confidence in developing strategies for dealing with new situations and problems, provide opportunities for students to develop individual skills and techniques and to allow, students with varying abilities, interests and experiences to achieve a sense of personal, satisfaction in studying mathematics, enable students to experience mathematics as an integrated organic discipline rather than, fragmented and compartmentalized skills and knowledge, enable students to see connections and applications of mathematics to other areas of interest, provide opportunities for students to show, with confidence, what they know and what they can do. The regular topics tests, end of year test and mock exam are set to identify the misunderstandings of the students and get them use to a timed exam, which they will be facing at the end of the 2 years which carries a high percentage of their overall mark. Topics The course content is based on the IB Mathematical Studies guide. All of the IB syllabus topics have been covered in my two year plan detailed below.

2 The course starts off by covering topics they should have already met in previous years, so they won t feel daunted by the upcoming work. At the end of every couple of topics the students will face past exam questions on the topics they have studied, giving them an insight as to what awaits them at the end of their two IB DP years. Algebra is taught to them relatively early in the course even though it is not specifically mentioned in the syllabus but it is necessary in all areas of mathematics. The statistical work is introduced at an early stage because most of the work they will have met before, it is also provides them with a good grounding in some of the skills they will require in order to do their main project. With each mini project they will be taught the necessary skills and shown how to use certain software to enhance their own projects. When they come do to their own project they will hopefully have sufficient knowledge in order to carry out their projects. Statistical work is generally the area of Mathematics which lends itself to the student who will be undertaking Mathematical Studies. It is also very difficult for students to get below a certain mark or above a certain mark for their project. In their second year they will be under enormous pressure from all subjects to hand in projects and demand on their time will be considerable. In doing the project in their first year they won t have to stress over possible time management issues with other subjects if we were to wait until their second year. Connections to TOK Proof: Axioms, rules of inference; mathematical deduction (and induction); is there more to maths than manipulation of symbols according to given rules; if not, then why is maths interesting? What is intelligence? Can a machine think? Alan Turing s test. Godel Logic: Limitations of logic; Russell s set paradox and ancient Greek paradoxes; mention of Godel. Truth: universal truths; is maths discovered or invented; could God make 2+2=5? Nature of infinity: irrational numbers and Euclid s proof; one-one mappings and counting; Cantor s diagonal arguments. Beauty and creativity: What makes a proof beautiful? Is the result or the proof more interesting? Ways of proving Pythagoras Theorem. Computers: Can we use computers to see things which were not otherwise possible eg fractals? Influences of computers and calculating devices on the development of maths. History: The story of mathematics; important turning points and significant mathematicians. Map of mathematics: Who is doing maths today? Where are the main centres? What are the main research areas? Who funds mathematics? Cryptography.

3 Course outline Maths Studies SL weekly topic guide Start of year 1 of 33 weeks Week Topics Notes 1 Number sets and properties 2.1: Sets of natural numbers, integers, rational numbers, real numbers, exponential notation, factors, multiples 2-3 Measurement : Standard form, rounding, approximation, error, percentage error, conversion of units 4-5 Sets and Venn diagrams : Basic concepts of set theory, subsets, intersection, union, complement, Venn diagrams and simple applications 6 Pythagoras Theorem 5.3 2d, 3d, finding a and b in addition to c 7-10 Descriptive Statistics Classification of data, discrete, continuous, frq tables, frq polygons, mid interval values, upper and lower boundaries, frq histograms, stem and leaf plots, box and whisker plots, percentiles, quartiles, Central Tendency, mean, approx mean, median. Mode, modal group, range, interquartile range, standard deviation Throughout 2 years students will be continually be using their GDC so no particular lesson has been allocated to 1.1 as it will be in progress throughout the 2 years. Assessment on first 2 topics work. Mini project given over 4 weeks to gather data and address the statistical course all tools will be given and they have to apply them in their project. 11 Revision on all terms topics Test on all of the term s topics Linear and exponential algebra Not in syllabus content but necessary skills: algebraic, substitution, linear and fractional equations, problem solving, formula substitution and rearrangement, simultaneous equations (2.7), index notation and laws, negative bases, exponential equations Coordinate Geometry Coordinates in two dimensions: points, lines, midpoints, equation of a line in 2d: y=mx+c, ax+by+d=0, gradients, intercepts, points of

4 intersection of lines, parallel lines, perpendicular lines Two variable statistics, Scatter diagrams, line of best fit passing through mean, bivariate data the concept of correlation, positive, negative and zero correlation, Pearson s product-moment correlation coefficient, Regression line for y on x use of formula, use of regression line for prediction, the chi squared test for independence, null and alternative hypothesis, degrees of freedom Quadratic Algebra 2.7 Solutions of quadratic equations by factorising and use of GDC Sequences and series 2.5,2.6,8.3 Arithmetic and geometric series and their applications, nth term and sum of n terms, compound interest, growth and decay Function notation and quadratic function Concept of a function as a mapping, domain and range, mapping diagrams, linear functions and their graphs, graph of the quadratic function, properties of symmetry, vertex and intercepts Financial Mathematics Simple interest, currency conversion, compound interest, depreciation, construction and use of tables, loan and repayment schemes, investment and saving schemes, inflation Revision Revision on whole years work 33 End of year exam End of year 1 for end of year exam Assessment on last 2 topics 3 weeks work assessment mini project, also includes time in IT lab looking at software to use for Spearman s coefficient, least squares regressions, graphs etc. Project given students 2 weeks to come up with a suitable idea and action plan on how to tackle the project. When project plan and idea are suitable, 1 week to write the official intro of the project. 2 weeks to collect raw data for project Test on last 2 topics Organise data, represent it carry out mathematical tests (3 weeks) Time will need to be spent teaching how the graphics calculator can be utilised to help them. 1 week to draw conclusions for project and hand it in, final deadline end of week 28. Test on last 2 topics

5 Maths Studies SL weekly topic guide Start of year 2 of 26 weeks Week No. Topic Notes 1-3 Numerical Trigonometry Right angled trigonometry, sine cosine, tangent, sine and cosine rule, 3d problems, vertices, mid points, size of angles between 2 lines and 2 planes 4 5 Perimeter, Area and 2.4,5.5 Converting units, Volume surface area, perimeter, volume 6 7 Probability probability of an event and a complementary event, Venn diagrams, tree diagrams, with and without replacement, laws of probability, combined events, mutually exclusive events, independent events, conditional probability 8 11 Exponential and Trig Functions Exponential expression, graph and functions of exponential functions, growth and decay, graphs and properties of sine and cosine functions, amplitude and period, accurate graph drawing Test on 1 st two topics of the year Revision for mocks Past paper questions on all topics covered 14 Mocks 15 More functions: cubic polynomials, quartic polynomials, rectangular hyperbola, using GDC to draw and analyse unfamiliar functions Introductory Differential Calculus gradient of a line through two points, behaviour of a gradient of the line through 2 points, tangent to a curve, derivative of functions, gradients of curves, equation of a tangent at a given point, increasing and decreasing functions, values where the gradient of a curve is zero, max and min points Logic Symbolic logic, propositions, compound statements, implication, equivalence, negation, Test on final 3 topics

6 conjunction, disjunction, exclusive disjunction, translate verbal statements into symbolic forms and Venn diagrams, truth tables to prove connectives, concepts of logical contradiction and tautology, definition of implication, converse, inverse, contrapositive, logical equivalence Study leave 27 IBDP exams in year 2 28 IBDP exams in year 2 29 IBDP exams in year 2 30 IBDP exams in year 2