IB Group 5 subjects
Encyclopedia
The Group 5 subjects of the IB Diploma Programme
consist of four different mathematics
courses and two computer science
courses. To earn an IB Diploma, a candidate must pass one of the following four mathematics courses: Mathematical Studies SL (Standard Level), Mathematics SL, Mathematics HL (Higher Level), or Further Mathematics SL. The Group 5 electives are Further Mathematics SL (if taken in addition to Mathematics HL), Computer science SL, and Computer science HL. Although Computer Science is in Group 5, this is only an administrative convenience - a Computer Science course does not fulfill the Group 5 requirement for an IB Diploma.
Students are provided a minimum of 130 hours of instruction on these topics.
The details for the external assessment exams, both of which evaluate a student's knowledge of the entire curriculum, are outlined in the table below.
of the Mathematics HL curriculum. Topics from the following areas form the common "Core curriculum" for both courses:
In Mathematics SL, students are provided a minimum of 140 instructional hours on the topics from the Core.
The table below outlines the external assessment requirements for both courses:
In both courses, the Paper 1 and Paper 2 exams test students only on their knowledge of topics from the Core. In Mathematics HL, the Paper 3 exam tests students specifically on their knowledge of the material from the Option selected by the school. As of the May 2008 examinations, schools are required to register students for a specific Option in advance and the school is now provided only the examination paper for the registered Option. In order for a student to be awarded full marks for an answer on any of the Mathematics SL or HL exams, accurate work must be shown.
, for which 30 hours of instruction are allotted. There are no optional topics in Further Mathematics SL.
An internal assessment component, consisting of a program dossier which is designed to address a single problem counts for 35% of the final grade in both courses. In Computer Science SL, the Dossier should have 25 teaching hours dedicated to it, while in Computer Science HL, this should be 35 teaching hours.
on some or all of their IB mathematics exams, depending on which course the student takes. Noting again that calculators are not permitted on the Paper 1 exam for both Mathematics SL and HL, the IB offers the following guidance with regards to required GDC functionality on mathematics exams:
All other types of calculators (such as those found on phones, watches
, or PDA
s, or those equipped with a Computer Algebra System (CAS)
) are prohibited on all IB exams. To be approved for use on IB exams, a GDC must have its memory cleared and all user-written/downloaded programs and applications must be removed (except for a limited number of specifically approved applications). The list of approved applications primarily consists of native language support for users who are not English speakers, along with a small number of additional applications.
Recommended models include the TI-83 Plus/TI-84 Plus families and 11 different non-CAS Casio GDCs, as well as the non-CAS TI-Nspire either with TI-84 faceplate or with the Nspire faceplate configured as described below.
While the TI-Nspire with Nspire faceplate was initially prohibited, it was later authorized, provided the (non-CAS) GDC is equipped with version 1.3 of the operating software, has the "Press-to-Test" mode enabled (with "limit geometry functions" enabled), and has the green LED flashing. (A notice that reflected this change was posted on the IB Online Curriculum Center on 15 Sep 2008.)
IB Diploma Programme
The International Baccalaureate Diploma Programme is a two-year educational programme for students aged 16–19that provides an internationally accepted qualification for entry into higher education, and is recognised by universities worldwide. It was developed in the early to mid-1960s in Geneva by...
consist of four different mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
courses and two computer science
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
courses. To earn an IB Diploma, a candidate must pass one of the following four mathematics courses: Mathematical Studies SL (Standard Level), Mathematics SL, Mathematics HL (Higher Level), or Further Mathematics SL. The Group 5 electives are Further Mathematics SL (if taken in addition to Mathematics HL), Computer science SL, and Computer science HL. Although Computer Science is in Group 5, this is only an administrative convenience - a Computer Science course does not fulfill the Group 5 requirement for an IB Diploma.
Curriculum
The Mathematical Studies SL course "is designed to build confidence and encourage an appreciation of mathematics in students" who do not expect mathematics to be a major component of their university studies. Its curriculum consists of the following topics:- NumberNumberA number is a mathematical object used to count and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers....
and algebraAlgebraAlgebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures... - Sets, logicLogicIn philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
, and probabilityProbabilityProbability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The... - FunctionsFunction (mathematics)In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...
- GeometryGeometryGeometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
and trigonometryTrigonometryTrigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves... - StatisticsStatisticsStatistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
- Introductory differential calculusDifferential calculusIn mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus....
- Financial mathematics
Students are provided a minimum of 130 hours of instruction on these topics.
Assessment
The internal assessment for this course comprises 20% of the final mark and consists of a project that is "an individual piece of work involving the collection of information or the generation of measurement." The project is intended to make up 20 hours of the overall classroom time for the course.The details for the external assessment exams, both of which evaluate a student's knowledge of the entire curriculum, are outlined in the table below.
| Exam | Time limit | # and type of questions | % of final mark |
|---|---|---|---|
| Paper 1 (GDC required) | 1 hour, 30 minutes | 15 short response questions | 40% |
| Paper 2 (GDC required) | 1 hour, 30 minutes | 5 extended response questions | 40% |
Core curriculum for Mathematics SL and HL
Mathematics SL is primarily intended for students who "expect to need a sound mathematical background as they prepare for future studies in subjects such as chemistry, economics, psychology and business administration," and its curriculum is a proper subsetSubset
In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment...
of the Mathematics HL curriculum. Topics from the following areas form the common "Core curriculum" for both courses:
- AlgebraAlgebraAlgebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
- FunctionsFunction (mathematics)In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...
and equations - Circular functions and trigonometryTrigonometryTrigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
- MatricesMatrix (mathematics)In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
- Vectors
- StatisticsStatisticsStatistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
and probabilityProbabilityProbability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The... - CalculusCalculusCalculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
In Mathematics SL, students are provided a minimum of 140 instructional hours on the topics from the Core.
Additional requirements for Mathematics HL
Mathematics HL is primarily intended for students "with a good background in mathematics who are competent in a range of analytical and technical skills," and who anticipate that mathematics will be "a major component of their university studies, either as a subject in its own right or within courses such as physics, engineering and technology." Therefore HL students study the Core topics in greater depth for a minimum of 190 instructional hours and study at least one of the following optional topics ("Options"), for a minimum of 40 additional instructional hours:- Further statisticsStatisticsStatistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
and probabilityProbabilityProbability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The... - Sets, relationsRelation (mathematics)In set theory and logic, a relation is a property that assigns truth values to k-tuples of individuals. Typically, the property describes a possible connection between the components of a k-tuple...
, and groupsGroup (mathematics)In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. To qualify as a group, the set and the operation must satisfy a few conditions called group axioms, namely closure, associativity, identity... - SeriesSeries (mathematics)A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely....
and differential equationDifferential equationA differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
s - Discrete mathematicsDiscrete mathematicsDiscrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not...
Assessment
In both courses, there is an internal assessment composed of two portfolio projects, each of which is worth 10% of the student's final mark (thus together they form 20% of the final mark). The portfolio projects are intended to comprise a combined total of 10 hours of the overall classroom time for both courses. A description of the two types of required portfolio projects follows below:- Mathematical investigation: the student identifies and investigates some sort of pattern, formulates a formal conjectureConjectureA conjecture is a proposition that is unproven but is thought to be true and has not been disproven. Karl Popper pioneered the use of the term "conjecture" in scientific philosophy. Conjecture is contrasted by hypothesis , which is a testable statement based on accepted grounds...
to describe the pattern, and provides a formal mathematical proofMathematical proofIn mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning, rather than from inductive or empirical arguments. That is, a proof must demonstrate that a statement is true in all cases, without a single...
of the conjecture. - Mathematical modelling: the student is given a scenario, is provided with or generates a set of data relating to the scenario, and develops a mathematical modelMathematical modelA mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...
to accurately describe the data and make predictions about future data.
The table below outlines the external assessment requirements for both courses:
| Course | Exam | Time limit | Description | # and type of questions | % of final mark |
|---|---|---|---|---|---|
| Mathematics SL | Paper 1 (no calculator) | 1 hour, 30 minutes | Section A | ~7 short response questions | |
| Section B | ~3 extended response questions | 40% | |||
| Paper 2 (GDC required) | 1 hour, 30 minutes | Section A | ~7 short response questions | ||
| Section B | ~3 extended response questions | 40% | |||
| Mathematics HL | Paper 1 (no calculator) | 2 hours | Section A | ~10 short response questions | |
| Section B | ~5 extended response questions | 30% | |||
| Paper 2 (GDC required) | 2 hours | Section A | ~10 short response questions | ||
| Section B | ~5 extended response questions | 30% | |||
| Paper 3 (GDC required) | 1 hour | ~5 extended response questions | 20% |
In both courses, the Paper 1 and Paper 2 exams test students only on their knowledge of topics from the Core. In Mathematics HL, the Paper 3 exam tests students specifically on their knowledge of the material from the Option selected by the school. As of the May 2008 examinations, schools are required to register students for a specific Option in advance and the school is now provided only the examination paper for the registered Option. In order for a student to be awarded full marks for an answer on any of the Mathematics SL or HL exams, accurate work must be shown.
Curriculum
The Further Mathematics SL course is designed for students with a high degree of competence and interest in mathematics, and who "intend to study mathematics at university, either as a subject in its own right or as a major component of a related subject." Students who take this course most often also take Mathematics HL and knowledge of all material from the Core curriculum of Mathematics HL is necessary and presumed, as well as knowledge of at least one of the four Options offered in Mathematics HL. The curriculum for Further Mathematics SL includes all of the topics from all four of these Options, for which 120 hours of instruction are allotted, and additional topics from geometryGeometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, for which 30 hours of instruction are allotted. There are no optional topics in Further Mathematics SL.
Assessment
There is no internal assessment for this course. A summary of the required external assessment exams, both of which evaluate the student's knowledge of the entire curriculum, is provided in the table below.| Exam | Time limit | # and type of questions | % of final mark |
|---|---|---|---|
| Paper 1 (GDC required) | 1 hour | 4–6 short response questions | 35% |
| Paper 2 (GDC required) | 2 hours | 4–6 extended response questions | 65% |
Further Mathematics HL
Further Mathematics SL will become a Higher Level course for 2014 exams onwards.Curriculum for Computer science SL
Computer Science SL and HL students are required to study a common core of 3 topics, for a total of 125 teaching hours.- Systems lifecycle and software development
- Program construction in Java
- Computing system fundamentals
Additional Requirements for Computer science HL
Computer Science HL students are also required to study 4 additional topics, for a total of 80 teaching hours.- Computer mathematics and logic
- Abstract data structures and algorithms
- Further system fundamentals
- File organisation
Assessment
The external assessment component of the course is summarised in the table below:| Course | Exam | Time limit | Description | # and type of questions | % of final mark |
|---|---|---|---|---|---|
| Computer Science SL | Paper 1 | 1 hour, 30 minutes | Section A | Several compulsory short answer questions | |
| Section B | 4 compulsory structured questions | 32.5% | |||
| Paper 2 | 1 hour, 30 minutes | Section A | 2 compulsory extended-response questions including the construction of an algorithm |
||
| Section B | 1 compulsory structured question based on the case study |
32.5% | |||
| Computer Science HL | Paper 1 | 2 hours 15 mins | Section A | Several compulsory short answer questions | |
| Section B | 6 compulsory structured questions | 32.5% | |||
| Paper 2 | 2 hours 15 mins | Section A | 3 compulsory extended-response questions including the construction of an algorithm |
||
| Section B | 1 compulsory structured question based on the case study | 32.5% | |||
An internal assessment component, consisting of a program dossier which is designed to address a single problem counts for 35% of the final grade in both courses. In Computer Science SL, the Dossier should have 25 teaching hours dedicated to it, while in Computer Science HL, this should be 35 teaching hours.
Use of calculators on IB mathematics external assessments
Students are permitted and expected to use a graphic display calculator (GDC)Graphing calculator
A graphing calculator typically refers to a class of handheld calculators that are capable of plotting graphs, solving simultaneous equations, and performing numerous other tasks with variables...
on some or all of their IB mathematics exams, depending on which course the student takes. Noting again that calculators are not permitted on the Paper 1 exam for both Mathematics SL and HL, the IB offers the following guidance with regards to required GDC functionality on mathematics exams:
"A GDC with the following minimum functionalities is required on all other papers:
- draw graphs with any viewing window
- solve equations numerically
- add and multiply and find inverse matrices
- find a numerical derivative at a point
- find a numerical definite integral
- find p values (not required for mathematics SL).
Examiners will set questions assuming that all candidates have a GDC with the minimum functionalities listed here. Candidates using only four-function or scientific calculators, or a less able GDC will be at a disadvantage."
All other types of calculators (such as those found on phones, watches
Calculator watch
A calculator watch is a watch with a calculator built into it.- History :Calculator watches first appeared in the Mid 1970s introduced by Pulsar and Hewlett Packard. Several watch manufacturers have made calculator watches over the years, but the Japanese electronics company Casio produced the...
, or PDA
PDA
A PDA is most commonly a Personal digital assistant, also known as a Personal data assistant, a mobile electronic device.PDA may also refer to:In science, medicine and technology:...
s, or those equipped with a Computer Algebra System (CAS)
Computer algebra system
A computer algebra system is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form.-Symbolic manipulations:...
) are prohibited on all IB exams. To be approved for use on IB exams, a GDC must have its memory cleared and all user-written/downloaded programs and applications must be removed (except for a limited number of specifically approved applications). The list of approved applications primarily consists of native language support for users who are not English speakers, along with a small number of additional applications.
Recommended models include the TI-83 Plus/TI-84 Plus families and 11 different non-CAS Casio GDCs, as well as the non-CAS TI-Nspire either with TI-84 faceplate or with the Nspire faceplate configured as described below.
While the TI-Nspire with Nspire faceplate was initially prohibited, it was later authorized, provided the (non-CAS) GDC is equipped with version 1.3 of the operating software, has the "Press-to-Test" mode enabled (with "limit geometry functions" enabled), and has the green LED flashing. (A notice that reflected this change was posted on the IB Online Curriculum Center on 15 Sep 2008.)