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IB Mathematics - A Programme of Study 2011 Time recommended by IB to complete the courses HL: 240 hours SL: 150 hours (below shows 160 hours) At The International School of Toulouse the allocation of time is as follows: Weeks Hours per week Y12 SL 36 3 Y13 SL 28 3 Y12 HL 36 4 Y13 HL 28 4 Suggested Programme by Richard Wade: Higher Level Standard Level YEAR 12 Module 1 – Number & Algebra Module 1 – Number & Algebra (20 hours) (12 hours) Arithmetic Sequences and Series Geometric Sequences and Series ,Sigma Notation and Infinite Series Indices and Surds Graphs of Exponential Functions Investigating e Arithmetic Sequences and Series Geometric Sequences and Series Sigma Notation and Infinite Series Indices and Surds Graphs of Exponential Functions Investigating e Logarithms & the Logarithmic Function Counting Principles – Arrangements, Permutations & Combinations The Binomial Expansion Proof by Induction Investigation task – Series & Induction (2 hours) Logarithms & the Logarithmic Function The Binomial Expansion TEST on module 1 Possible Internal Assessment – Investigation Type - Lacsap’s Fractions (2 hours) TEST on module 1 (1 hour) Module 2 – Functions Module 2 – Functions (16 hours) ( 20 hours) Introduction to Function Notation, domain Introduction to Function Notation, domain & range & range Composite Functions Composite Functions The Inverse Function Investigation Task – Absolute Value Investigation Task – Investigating the Graphs (1 hour) Quadratic Function (1 hour) IB Mathematics - A Programme of Study 2011 The Absolute Function The Inverse Function Transforming Functions Graph of y=1/f(x) Quadratic Functions & The Discriminant Solving Inequalities Polynomials – Factor & Remainder Theorem Transforming Functions Quadratic Functions & The Discriminant TEST on module 2 (1 hour) TEST on module 2 (1 hour) Module 3 – Circular Functions & Trigonometry Module 3 – Circular Functions & Trigonometry (20 hours) The circle: radian measure of angles; length of an arc; area of a sector. The Solution of Triangles – recap Sine, Cosine Rule, area of triangle Unit Circle Pythagorean Identities Compound Angle Formulae Double Angle Formulae Transforming Trig Functions Solving Trig Equations Modelling using Trig Functions Inverse Trig Functions (14 hours) The circle: radian measure of angles; length of an arc; area of a sector. The Solution of Triangles – recap Sine, Cosine Rule, area of triangle Unit Circle Pythagorean Identities Double Angle Formulae Transforming Trig Functions Modelling using Trig Functions Solving Trig Equations TEST on module 3 (1 hour) TEST on module 3 (1 hour) Internal Assessment – Investigation Type – Circles (3 hours) Module 4 – Differentiation (28 hours) Introducing Rates of Change Differentiation from 1st Principles Differentiating Polynomials Equations of Tangents and Normals Module 4 – Differentiation (24 hours) Introducing Rates of Change Differentiation from 1st Principles Differentiating Polynomials Equations of Tangents and Normals Practice Internal Assessment -Zeros of Cubic Functions (2 hours) Stationary Points Non-stationary points of inflexion Oblique Asymptotes Small Angle Approximations Differentiating Trig Function Chain Rule Differentiating Exponential & Log Functions Product & Quotient Rule Implicit Differentiation Stationary Points Non-stationary points of inflexion Small Angle Approximations Differentiating Trig Function Chain Rule Differentiating Exponential & Log Functions Product & Quotient Rule Optimisation IB Mathematics - A Programme of Study 2011 Differentiating Inverse Trig Functions Connected Rates of Change Optimisation Differentiating & Proof by Induction TEST on module 4 (1 hour) TEST on module 4 (1 hour) Module 5 – Statistics & Probability (28 hours) Module 5 – Statistics & Probability (26 hours) Manipulation and Presentation of statistical Data Standard Deviation Experimental & theoretical Probability Independent & dependent Events & Probability trees Venn Diagrams Laws of Probability Conditional Probability Bayes’ Theorem Probability & Combinations & Permutations Discrete Random Variables Binomial Distribution Poisson Distribution Normal Distribution Manipulation and Presentation of statistical Data Standard Deviation Experimental & theoretical Probability Independent & dependent Events & Probability trees Venn Diagrams TEST on module 5 (1 hour) Revision for End of Year 12 Examinations (2 hours) End of Year Examinations IB Mathematics - A Programme of Study 2011 Higher Level Standard Level YEAR 13 Module 6 – Matrices (12 hours) Properties of Matrices Addition, Multiplication, Identity, Inverse Proof By Induction with Matrices The Determinant Inverse 3by3 Matrix Solving Simultaneous Equations using Matrices 2by2 & 3by3 Zero, unique & infinite solutions Module 5 – Statistics & Probability (continued) Recap Y12 probability Laws of Probability Conditional Probability Discrete Random Variables Binomial Distribution Normal Distribution TEST on module 6 (1 hour) TEST on module 5 (1 hour) Internal Assessment – Investigation Type Module 6 – Matrices – Systems of Linear Equations (8 hours) (2 hours) Module 7 – Integration Properties of Matrices (24 hours) Addition, Multiplication, Identity, Inverse Proof By Induction with Matrices The Determinant Inverse 3by3 Matrix Solving Simultaneous Equations using Matrices 2by2 & 3by3 (unique soln only) Recap Differentiation Area under a Graph investigation Antidifferentiation Finding C Definite Integrals Areas under Graphs Volumes of Revolution Integration by Recognition Integration by Substitution Integration by Parts Differential Equations Kinematics Continuous Probability Distributions TEST on module 7 (1 hour) Internal Assessment – Modelling Type – Modelling a Functional Building (2 hours) TEST on module 6 (1 hour) IB Mathematics - A Programme of Study 2011 Module 8 – Vectors Module 7 – Integration (18 hours) (16 hours) Notation, Scalar Multiple , adding & subtracting Length of a Vector, midpoints, distances, position vectors & 3D Vectors Angle between 2 vectors, Scalar (Dot) Product The Vector Equation of a Straight Line 2D & 3D Applications - The Velocity Vector of a Moving Object Vector Product Intersecting lines and planes Recap Differentiation Area under a Graph investigation Antidifferentiation Finding C Definite Integrals Areas under Graphs Volumes of Revolution Integration by Recognition Kinematics TEST on module 8 (1 hour) Internal Assessment – Modelling Type – Fish Production (2 hours) Module 9 – Complex Numbers Module 8 – Vectors (8 hours) (14 hours) Introducing i Notation, Scalar Multiple , adding & subtracting Length of a Vector, midpoints, distances, position vectors & 3D Vectors Angle between 2 vectors, Scalar (Dot) Product The Vector Equation of a Straight Line 2D & 3D Applications - The Velocity Vector of a Moving Object Lines – intersecting, coincident & parallel TEST on module 8 (1 hour) Internal Assessment – Modelling Type – Population Trends in China (2 hours) Modulus, Argument, Polar Form and Euler Form De Moivre’s Theorem TEST on module 9 (1 hour) Reserve Internal Assessment – Investigation Type – Patterns from Complex Numbers (2 hours) Module 10 – Statistic Option (35 hours) Expectation algebra. Linear transformation of a single random variable. Mean and variance of linear combinations of TEST on module 7 (1 hour) Revision (6 hours) IB Mathematics - A Programme of Study 2011 two independent random variables. Extension to linear combinations of n independent random variables. Cumulative distribution functions. Discrete distributions: uniform, Bernoulli, binomial, negative binomial, Poisson, geometric, hypergeometric. Continuous distributions: uniform, exponential,normal. Distribution of the sample mean. The distribution of linear combinations of independent normal random variables. The central limit theorem. The approximate normality of the proportion of successes in a large sample. Finding confidence intervals for the mean of a population. Finding confidence intervals for the proportionof successes in a population. Significance testing for a mean. Significance testing for a proportion. Type I and Type II errors. Chi Squared test – goodness of fit & Independence TEST on module 10 (1 hour) Reserve Internal Assessment – Modelling Type – The Dice Game Revision (6 hours) EXAM The above times are approximate and do not include homework assignments, end of year and mock examinations. IB provides their own approximate times for covering each of the topics which are not necessarily consistent with these timings. This programme of study does not give the full details of the course. For full details of the course content refer to the IB syllabus.