Download IB Mathematics - A Programme of Study

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.