School Programmes, Syllabi & Academic Information.

MATHEMATICS AND STATISTICS

MATHEMATICS AND STATISTICS (81 Hours)

Course Description: This course caters for students who already possess knowledge of basic mathematical concepts, and who are equipped with the skills needed to apply simple mathematical techniques correctly. The majority of these students will expect to need a sound mathematical background as they prepare for future studies in subjects such as chemistry, economics, psychology and business administration.

Aim of the Course: The course focuses on introducing important mathematical concepts through the development of mathematical techniques. The intention is to introduce students to these concepts in a comprehensible and coherent way, rather than insisting on the mathematical rigour required for mathematics HL. Students should, wherever possible, apply the mathematical knowledge they have acquired to solve realistic problems set in an appropriate context. The internally assessed component, the exploration, offers students the opportunity for developing independence in their mathematical learning. Students are encouraged to take a considered approach to various mathematical activities and to explore different mathematical ideas. The exploration also allows students to work without the time constraints of a written examination and to develop the skills they need for communicating mathematical ideas. 

Learning Outcomes:

  1. Enjoy mathematics, and develop an appreciation of the elegance and power of mathematics
  2. Develop an understanding of the principles and nature of mathematics.
  3. Communicate clearly and confidently in a variety of contexts
  4. Develop logical, critical and creative thinking, and patience and persistence in problem-solving
  5. Employ and refine their powers of abstraction and generalisation
  6. Apply and transfer skills to alternative situations, to other areas of knowledge and to future developments
  7. Appreciate how developments in technology and mathematics have influenced each other
  8. Appreciate the moral, social and ethical implications arising from the work of mathematicians and the applications of mathematics
  9. Appreciate the international dimension in mathematics through an awareness of the universality of mathematics and its multicultural and historical perspectives

Syllabus

MATHEMATICS Algebra: Sets of Real Numbers, Properties of Real Numbers, Operations With Algebraic Expressions, Equations, Inequalities and Applications, Algebraic Operations on Polynomials, Partial Fractions, Quadratic Equation theory, Quadratic Inequalities, Applications.

Exponential and Logarithmic functions and Equations, Cartesian Coordinates, Straight Line Equations, Equations of Parabolas and Hyperbolas.

Basic Trigonometric Functions, Trigonometric Equations and Identities. Sequences Of Numbers: Arithmetic Sequences, Geometric Sequences, Series.

Calculus: The Derivative Function, Simple Rules of Differentiation, The Chain Rule, Product And Quotient Rules. Tangents And Normals, Rates of Change. Integration: Antidifferentiation and Antiderivative,

The Fundamental Theorem of Calculus, Rules for Integration, The Definite Integral and Areas Under Curves, Volumes of Revolution, Mean Values, Further Applications of Differentiation and Integration.

Curve Properties (e.g. Maxima-Minima) and Sketching. Transformations, Matrices, Determinants. Differential Equations: First Order, Separable, Integrating Factor, Second order With Constant coefficients. Numerical Methods. Linear Algebra: Matrix Theory, Linear System Solutions, Linear Programming Methods. Advanced topics: Binomial expansion, Taylor series, numerical methods of finding roots of equations, the Trapezium rule, Simpson’s rule

Descriptive Statistics: Key Statistical Concepts, Sampling, Frequency Distributions, Graphical Representation of Statistical Data, Measures of Centre: Mean, Median, Mode, Cumulative Frequency, Cumulative Frequency Polygon, Measures of Spread: Quartiles, Percentiles, Standard Deviation, Standard Deviation and The Normal Curve (informal)

Inferential Statistics: Estimation, confidence Intervals, Hypothesis Testing. Statistical Modelling: Regression Analysis. Correlation Analysis.

Probability: Key Concepts, Experimental Probability, Theoretical Probability, Sample Space: Definition, Representations. Probability of Events, Compound Events and their Probability: Introduction, Sampling With and Without Replacement, Binomial Probabilities, Combination Counting. Laws of Probability: Sets And Venn Diagrams, The Addition Law, Mutually Exclusive Events, Conditional Probability, Independent Events, Dependent Events. Probabilities Using Permutations And Combinations. Bayes’ Theorem.

Discrete Random Variables: Mass Function, Common Distributions, Measures of Discrete Random Variables.

Continuous Random Variables: Probability Density, Measures of Continuous Random Variables. Nor- mal Distribution, Standard Normal Distribution, Standardizing any Normal Distribution, Applications of the Normal Distribution.

Resources and booklist suggestions:

  1. Introductory Mathematical Analysis, E. Haeussler, R. Paul, Prentice Hall International Editions
  2. A-Level Mathematics Longman Revise Guides.
  3. A Concise Course in A-Level Statistics (3rd ed.), J, Crawshaw, J. Chambers, Stanley Thornes (Publishers) Ltd.
  4. Mathematics, The core course for A-Level, L. Bostock and S. Chandler, Stanley Thornes (Publishers) Ltd.
  5. Further Pure Mathematics, L. Bostock, S. Chandler, C. Rourke, Stanley Thornes (Publishers) Ltd.
  6. Mathematics A-Level Course Companion Letts (Educational) Ltd.