GROUP FIVE
Math Studies | Math SL| Math HL
Group 5 : MATHEMATICAL STUDIES Standard Level
Grade 11
AIMS:
The course is aimed at students who are going to university or college, but to pursue a subject that does not involve mathematics or is not mathematically based. In this course, the skills needed to cope with the mathematical demands of a technological society are developed. Emphasis is placed on the application of mathematics to real-life situations and a research project is a requirement.
OBJECTIVES
To enable students to:
• know and use essential notation and terminology;
• know and use mathematical concepts and principles;
• represent a given situation in mathematical terms;
• select and use mathematical techniques that are appropriate to a given problem;
• develop and use mathematical arguments and reasoning at an appropriate level of sophistication;
• express arguments in a clear, logical manner, both orally and in writing;
• organise, interpret and present information/data accurately in written symbolic, tabular, graphical and diagrammatic forms;
• present and communicate information processed and analysed by appropriate mathematical tools;
• interpret derived results in the correct context;
• demonstrate good mathematical practice in formulating and presenting answers to written questions;
• demonstrate a sensible approach to numerical and graphical accuracy;
• recognize patterns and structures in a variety of situations and draw inductive generalisations;
• make logical deductions from given data;
• demonstrate knowledge of the applications of mathematics to life in a technological society.
CONTENT
1. Use of standard index form
2. Use of decimal places and significant figures
3. Use of graphic display calculator
4. Revision of basic algebra
5. Number theory
6. Linear equations and inequalities; graphing of linear functions
7. Introduction to functions
8. Quadratic functions
9. Exponential graphs
10. Sets and probability
11. Trigonometry: Right angle trigonometry; Pythagoras; sine rule; cosine rule
12. Statistics: Basic concepts; chi-square test; cumulative frequency; Pearson’s Correlation coefficient
ASSESSMENT
Internal assessment
Term grades will be based on:
Continuous assessment 25%
Tests 75%
A final exam will be given in June.
External Assessment (at the end of grade 12)
Final assessment will be based on:
Project 20%
Examination 80%
The project is a piece of written work based on personal research involving the collection, analysis and evaluation of data.
Grades will be assigned using the scales:
7 90 - 100%
6 75 - 89%
5 60 - 74%
4 45 - 59%
3 30 - 44%
2 15 - 29%
1 0 - 14%
GRADE 12
OBJECTIVES
To enable students to:
• know and use essential notation and terminology;
• know and use mathematical concepts and principles;
• represent a given situation in mathematical terms;
• select and use mathematical techniques that are appropriate to a given problem;
• develop and use mathematical arguments and reasoning at an appropriate level of sophistication;
• express arguments in a clear, logical manner, both orally and in writing;
• organise, interpret and present information/data accurately in written symbolic, tabular, graphical and diagrammatic forms;
• present and communicate information processed and analysed by appropriate mathematical tools;
• interpret derived results in the correct context;
• demonstrate good mathematical practice in formulating and presenting answers to written questions;
• demonstrate a sensible approach to numerical and graphical accuracy;
• recognize patterns and structures in a variety of situations and draw inductive generalisations;
• make logical deductions from given data;
• demonstrate knowledge of the applications of mathematics to life in a technological society.
CONTENT
1. Arithmetic and geometric sequences and series
2. Logic
3. Introduction to differential calculus
4. Functions: Trigonometric
5. Geometry and trigonometry: Coordinates in two and three dimensions; distances and midpoints; three dimensional trigonometry
6. Financial math: Currency and interest
ASSESSMENT
Internal assessment
Term grades will be based on:
Continuous assessment 25%
Tests and quizzes 75%
A mock exam will be given in February.
External Assessment
Final assessment will be based on:
Project 20%
Examination 80%
The project is a piece of written work based on personal research involving the collection, analysis and evaluation of data.
Grades will be assigned using the scales:
7 90 - 100%
6 75 - 89%
5 60 - 74%
4 45 - 59%
3 30 - 44%
2 15 - 29%
1 0 - 14%
Group 5 : MATHEMATICS Standard Level
Grade 11
AIMS:
This is a demanding program containing a wide variety of mathematical topics aiming to provide a sound mathematical basis for those students who plan to study perhaps chemistry, economics, geography or business administration in the future.
OBJECTIVES
To enable students to:
• know and use essential notation and terminology;
• know and use mathematical concepts and principles;
• represent a given situation in mathematical terms;
• select and use mathematical techniques that are appropriate to a given problem;
• develop and use mathematical arguments and reasoning at an appropriate level of sophistication;
• express arguments in a clear, logical manner, both orally and in writing;
• organise, interpret and present information/data accurately in written symbolic, tabular, graphical and diagrammatic forms;
• present and communicate information processed and analysed by appropriate mathematical tools;
• interpret derived results in the correct context;
• demonstrate good mathematical practice in formulating and presenting answers to written questions;
• demonstrate a sensible approach to numerical and graphical accuracy;
• recognize patterns and structures in a variety of situations and draw inductive generalisations;
• make logical deductions from given data;
• demonstrate knowledge of the applications of mathematics to life in a technological society.
CONTENT
1. Number systems and algebra
2. Linear functions
3. Quadratic functions; solving quadratic equations
4. Functions: The graph of a function; transformations of graphs; the concept of a function; the reciprocal function
5. Exponential and logarithmic functions
6. The binomial theorem
7. Arithmetic and geometric sequences and series
8. Circular functions and trigonometry: Solution of triangles; the circle; unit circle and trigonometric identities; circular functions; solutions of trigonometric equations; double angle formulae
9. Calculus: Limits and derivatives; further differentiation; applications of the first derivative; graphical behaviour of functions
10. Matrices: Basic concepts; algebra of matrices; determinants and inverses; solutions to systems
ASSESSMENT
Internal assessment
Term grades will be based on:
Continuous assessment 25%
Tests and portfolio 75%
A final exam will be given in June.
External Assessment (at the end of grade 12)
Final assessment will be based on:
Portfolio 20%
Examination 80%
The portfolio consists of 2 assignments, one involving mathematical investigation and the other mathematical modelling.
Grades will be assigned using the scales:
7 90 - 100%
6 75 - 89%
5 60 - 74%
4 45 - 59%
3 30 - 44%
2 15 - 29%
1 0 - 14%
GRADE 12
OBJECTIVES
To enable students to:
• know and use essential notation and terminology;
• know and use mathematical concepts and principles;
• represent a given situation in mathematical terms;
• select and use mathematical techniques that are appropriate to a given problem;
• develop and use mathematical arguments and reasoning at an appropriate level of sophistication;
• express arguments in a clear, logical manner, both orally and in writing;
• organise, interpret and present information/data accurately in written symbolic, tabular, graphical and diagrammatic forms;
• present and communicate information processed and analysed by appropriate mathematical tools;
• interpret derived results in the correct context;
• demonstrate good mathematical practice in formulating and presenting answers to written questions;
• demonstrate a sensible approach to numerical and graphical accuracy;
• recognize patterns and structures in a variety of situations and draw inductive generalisations;
• make logical deductions from given data;
• demonstrate knowledge of the applications of mathematics to life in a technological society.
CONTENT
1. Statistics: Basic concepts; presentation of data; measures of central tendency and dispersion; cumulative frequency
2. Vector geometry: Basic concepts; scalar product; representation of a line in a plane; systems of lines
3. Calculus: Indefinite and definite integrals; kinematics; volumes of revolution
4. Probability: Basic concepts; combined events; conditional probability; applications
5. Statistics and probability: Discrete random variables; binomial distributions; normal distributions
ASSESSMENT
Internal assessment
Term grades will be based on:
Continuous assessment 25%
Tests and portfolio 75%
A mock exam will be given in February.
External Assessment
Final assessment will be based on:
Portfolio 20%
Examination 80%
The portfolio consists of 2 assignments, one involving mathematical investigation and the other mathematical modelling.
Grades will be assigned using the scales:
7 90 - 100%
6 75 - 89%
5 60 - 74%
4 45 - 59%
3 30 - 44%
2 15 - 29%
1 0 - 14%
Group 5 : MATHEMATICS Higher Level
Grade 11
AIMS:
This course aims to provide stimulation and challenge for those with a genuine interest in the subject and to fulfil the mathematical need for future studies in physics, engineering, technology, and mathematics.
OBJECTIVES
To enable students to:
• know and use essential notation and terminology;
• know and use mathematical concepts and principles;
• represent a given situation in mathematical terms;
• select and use mathematical techniques that are appropriate to a given problem;
• develop and use mathematical arguments and reasoning at an appropriate level of sophistication;
• express arguments in a clear, logical manner, both orally and in writing;
• organise, interpret and present information/data accurately in written symbolic, tabular, graphical and diagrammatic forms;
• present and communicate information processed and analysed by appropriate mathematical tools;
• interpret derived results in the correct context;
• demonstrate good mathematical practice in formulating and presenting answers to written questions;
• demonstrate a sensible approach to numerical and graphical accuracy;
• recognize patterns and structures in a variety of situations and draw inductive generalisations;
• make logical deductions from given data;
• demonstrate knowledge of the applications of mathematics to life in a technological society.
CONTENT
1. Number and algebra: Basic algebraic techniques; exponents and logarithms
2. Arithmetic and geometric sequences and series
3. Complex numbers
4. Counting principles; permutations and combinations; the binomial theorem
5. Proof by mathematical induction
6. Functions: Concept of a function; the graph of a function; transformations of graphs; linear, quadratic, reciprocal, polynomial, exponential and logarithmic functions; solution of quadratic equations; inequalities; remainder and factor theorems
7. Circular functions and trigonometry: Solution of triangles; arc length; area of sector; the unit circle; trigonometric identities, including Pythagorean, compound and double angle; circular and inverse circular functions; solutions of trigonometric equations
8. Matrices: Basic concepts; algebra of matrices; determinants and inverses; solution to systems
9. Calculus: Limits and derivatives; including derivatives of circular, reciprocal circular, inverse circular, exponential and logarithmic functions; product rule; quotient rule; chain rule; applications of the first derivative and second derivative; graphical behaviour of functions; implicit differentiation; related rates
10. Calculus: Indefinite and definite integrals; integration by substitution and parts; circular function integration; applications; kinematics; area; differential equations; volumes of revolution
ASSESSMENT
Internal assessment
Term grades will be based on:
Continuous assessment 25%
Tests and portfolio 75%
A final exam will be given in June.
External Assessment (at the end of grade 12)
Final assessment will be based on:
Portfolio 20%
Examination 80%
The portfolio consists of 2 assignments, one involving mathematical investigation and the other mathematical modelling.
Grades will be assigned using the scales:
7 90 - 100%
6 75 - 89%
5 60 - 74%
4 45 - 59%
3 30 - 44%
2 15 - 29%
1 0 - 14%
GRADE 12
OBJECTIVES
To enable students to:
• know and use essential notation and terminology;
• know and use mathematical concepts and principles;
• represent a given situation in mathematical terms;
• select and use mathematical techniques that are appropriate to a given problem;
• develop and use mathematical arguments and reasoning at an appropriate level of sophistication;
• express arguments in a clear, logical manner, both orally and in writing;
• organise, interpret and present information/data accurately in written symbolic, tabular, graphical and diagrammatic forms;
• present and communicate information processed and analysed by appropriate mathematical tools;
• interpret derived results in the correct context;
• demonstrate good mathematical practice in formulating and presenting answers to written questions;
• demonstrate a sensible approach to numerical and graphical accuracy;
• recognize patterns and structures in a variety of situations and draw inductive generalisations;
• make logical deductions from given data;
• demonstrate knowledge of the applications of mathematics to life in a technological society.
CONTENT
1. Complex numbers: DeMoivre’s Theorem; conjugate roots of polynomial equations
2. Vector geometry: Basic concepts; scalar product; vector equations of lines; systems of lines; vector product; vector equation of a plane; intersections and angles between lines and planes
3. Statistics: Basic concepts; presentation of data; measures of central tendency and dispersion; cumulative frequency
4. Probability: Basic concepts; combined events; conditional probability; applications
5. Statistics and probability: Discrete and continuous random variables; probability density functions; binomial distributions; normal distributions; Poisson Distributions
6. Sets: Finite and infinite sets; subsets; operations on sets; DeMorgan’s laws; distributive, associate and commutative laws
7. Relations: Cartesian products; equivalence relations; equivalence classes; partitions
8. Functions: Injections; surjections; bijections; compositions
9. Group theory: Binary operations; operation tables; axioms of a group; finite and infinite groups; cyclic groups; subgroups; Lagrange’s theorem; isomorphisms
ASSESSMENT
Internal assessment
Term grades will be based on:
Continuous assessment 25%
Tests and portfolio 75%
A mock exam will be given in February.
External Assessment
Final assessment will be based on:
Portfolio 20%
Examination 80%
The portfolio consists of 2 assignments, one involving mathematical investigation and the other mathematical modelling.
Grades will be assigned using the scales:
7 90 - 100%
6 75 - 89%
5 60 - 74%
4 45 - 59%
3 30 - 44%
2 15 - 29%
1 0 - 14%
