1 Changes and clarifications to the Higher Level Syllabus

Changes to the IB Higher Level Mathematics SyllabusFirst Examinations 2014Big overall changes are that matrices (12 hours of teaching time) have been removed. The two portfolio pieces have been replaced by a more open-ended mathematical exploration. Applications are mentioned much more than previously.

Prior LearningIn Out or officially excluded

Rationalising denominator Solution of non-linear simultaneous equations

Rational exponents

Completing the square

Quadratic formula

Solution of quadratic inequalities

Properties of triangles and quadrilaterals, including parallelograms, rhombuses, rectangles, squares, kites and trapeziums (trapezoids)

Volumes of cuboids, pyramids, spheres, cylinders and cones

Classification of prisms and pyramids, including tetrahedra

Obtaining statistics from continuous data

Median, mode, quartiles, range, interquartile range and percentiles

Calculating probabilities of simple events

Frequency histograms

Cumulative frequency graphs

Topic 1 – AlgebraIncreased from 20 hours to 30 hours of teaching time.

In Out or officially excluded

nPr notation Permutations where some objects are identical, circular arrangements

Describe reiθ as Euler’s form Proof of the Binomial Theorem

Solutions of simultaneous equations in three unknowns, including no solution and infinity of solutions. (Now without matrix terminology, but “linked to vectors” for geometrical interpretation)

Prior learning includes rational indices

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2 Changes and clarifications to the Higher Level Syllabus

Topic 2 – Functions and EquationsDecreased from 26 hours to 22 hours of teaching time.

In Out or officially excluded

Odd and even functions No longer explicitly mentions absolute value sign in inequalities

Self inverse functions – now not only for reciprocal function

Completing the square and factorizing quadratics moved to prior learning

The fundamental theorem of algebra

Sums and products of roots

Inequalities in polynomials up to degree 3 rather than 2

Rational functions (linear over linear)

Topic 3 – Circular Functions and TrigonometryStays at 22 hours.

In Out or officially excluded

Definition of tan θ in terms of the unit circle Proof of compound angle formula removed

Angles of elevation and depression

Topic 4 – VectorsIncreased from 22 to 24 hours.

In Out or officially excluded

Proofs of geometrical properties using vectors

Simple applications to kinematics

Algebraic properties of the vector product

Component form of vector product now in the formula book

Topic 5 – Statistics and ProbabilityDecreased from 40 to 36 hours.

In Out or officially excluded

Bayes’ theorem now for up to three events Estimating population parameters from a sample

Box plots

Histograms and cumulative frequency diagrams moved to Prior Learning

Median, mode, range, interquartile range and quartiles and percentiles moved to Prior Learning

Use of statistical tables

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3 Changes and clarifications to the Higher Level Syllabus

Topic 6 – CalculusStays at 48 hours.

In Out or officially excluded

All required derivatives can now be reversed as integrals

Differential equations

Total distance travelled Differentiation from first principles only applied to polynomials

Informal idea of continuity Oblique asymptotes no longer explicitly mentioned

Volume of revolution

Indefinite integrals using the results of everything that can be differentiated e.g. sec x

Relationships between the graphs of f, f ′ and f ″

Topic 7 – Option: Statistics and ProbabilityIncreased from 40 to 48 hours.

In Out or officially excluded

Expectation of product of independent random variables

Hypergeometric, Bernouilli, exponential or uniform distributions

General unbiased estimators, including efficiency of estimators

Hypothesis testing and confidence intervals for proportions

Bivariate distributions Chi-squared

Covariance Approximate normal distribution of sample proportion

Pearson’s product moment correlation coefficient – it’s population definition and sample estimate

Proof that ρ = 0 when independent and ±1 when in a linear relationship

Testing the null hypothesis ρ = 0 using the

statistic R nR

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21 2

Probability generating functions

Cumulative distribution function now explicitly for both discrete and continuous distributions

x and sn-12 as unbiased estimators now introduced

for the first time

Higher Level Syllabus_New.indd 3 1/3/2012 9:23:49 PM

4 Changes and clarifications to the Higher Level Syllabus

Topic 8 – Option: Sets, Relations and GroupsIncreased from 40 to 48 hours.

In Out or officially excluded

The operation table of a group is a Latin square but the converse is false

No matrix examples in groups

Symmetries of plane figures beyond triangles and rectangles are now included

Cycle notation for permutations; Every permutation can be written as a composition of disjoint cycles

The order of a combination of cycles

Left and right cosets

Definition of a group homomorphism

Definition of the kernel

Proof that the kernel and range of a homomorphism are subgroups

The order of an element is unchanged by an isomorphism (rather than properties for identities and inverses under isomorphisms)

Topic 9 – Option: CalculusIncreased from 40 to 48 hours.

In Out or officially excluded

Only an informal treatment of limits of sums, products etc

Formal limit theorems for sequences (i.e. - δ proofs are out)

Continuity and differentiability Partial fractions

Fundamental theorem of calculus Telescoping series

Differential Equations are introduced – no longer in the core

Only the Lagrange form of the error term is required

Slope fields include identifications of isoclines.

Rolle’s theorem

Mean value theorem

Taylor series developed from differential equations

Higher Level Syllabus_New.indd 4 1/3/2012 9:23:51 PM

5 Changes and clarifications to the Higher Level Syllabus

Topic 10 – Option: Discrete MathematicsIncreased from 40 to 48 hours.

In Out or officially excluded

Strong induction Graph isomorphisms

Pigeonhole principle Adjacency matrices

Degree sequence Prim’s algorithms

Handshaking lemma

Tabular representation of graphs

Solution of 1st and 2nd degree linear homogenous recurrence relations with constant coefficients

The first degree linear recurrence relation

Modelling with recurrence relations

Adjacency tables

Chinese postman problem with four odd vertices

Higher Level Syllabus_New.indd 5 1/3/2012 9:23:52 PM