Group 5 - Mathematics
Overview
Mathematics is a tool we use to understand and interpret our world. It is the language used to describe patterns and solve quantitative problems in fields ranging from art and graphic design to science and engineering. It also develops creativity and higher order thinking skills. Because the level of mathematical thinking and problem solving needed in the workplace and in the world continues to increase, those who understand mathematics will have opportunities others do not.
At BISC we have developed Mathematics courses aligned with the IB Mathematics subject requirements, which aim for the best preparation for the IB examinations as well as the acquisition of a well-balanced Mathematics Learner profile.
Key Skills Developed in the Mathematics IB Courses
- Know and use mathematical concepts and principles.
- Read, interpret and solve a given problem using appropriate mathematical terms.
- Organise and present information and data in tabular, graphical and/or diagrammatic forms.
- Know and use appropriate notation and terminology.
- Formulate a mathematical argument and communicate it clearly.
- Select and use appropriate mathematical strategies and techniques.
- Demonstrate an understanding of both the significance and the reasonableness of results.
- Recognise patterns and structures in a variety of situations, and make generalisations.
- Recognise and demonstrate an understanding of the practical applications of mathematics.
- Use appropriate technological devices as mathematical tools.
- Demonstrate an understanding of and the use of mathematical modelling.
There are two Mathematics courses at IB and each can be studied at Standard Level or Higher Level:
- Mathematics: Applications and Interpretation (SL & HL)
- Mathematics: Analysis and Approaches (SL & HL)
Group 5:
Mathematics: Applications and Interpretation (SL & HL)
Why study Mathematics: Applications and Interpretation?
This course is designed for students who enjoy describing the real world and solving practical problems using mathematics, those who are interested in harnessing the power of technology alongside exploring mathematical models and enjoy the more practical side of mathematics.
The difference between the SL (150 hours) and HL (240 hours) courses are given in detail below in the Contents of each course. Essentially, the SL course is a subset of the HL course - students studying HL study 90 more hours of more challenging content. The emphasis for both courses is on the use of mathematics, rather than its theoretical underpinning.
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Content - Mathematics: Applications and Interpretation - SL |
% of total grade |
|
|
Paper 1: 1 hour and 30 minutes (Calculator) |
Number and Algebra: Scientific notation; arithmetic and geometric sequences; simple treatment of logarithms and exponentials; simple proof; approximations and errors. Functions: Models with linear, exponential, natural logarithm, cubic and simple trigonometric functions. Geometry and Trigonometry: Volume and surface area of 3d solids; right-angled and non-right-angled trigonometry including bearings; Voronoi diagrams. Statistics and Probability: Sampling techniques; presentation of data; measures of central tendency and spread; correlation; regression; calculating probabilities; probability diagrams; the normal distribution; Chi-squared test. Calculus: Differentiation and optimisation; simple integration and the trapezium/trapezoidal rule to calculate areas of irregular shapes. |
40% |
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Paper 2: 1 hour and 30 minute (Calculator) |
40% |
|
|
Internal assessment |
This is a piece of written work that involves investigating an area of mathematics. Independent work Criteria-based assessment |
20% |
Pupils who wish to apply to universities in Germany, must study an additional Vectors module. You must make the Head of Mathematics aware so that this can be organised for you.
Entry Requirement: Applications and Interpretation - SL
Grade 4 at IGCSE Mathematics
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Content - Mathematics: Applications and Interpretation - HL |
% of total grade |
|
|
Paper 1: 2 hours (Calculator) |
In additional to the content of the SL course, HL also includes: Number and Algebra: Logarithms; complex numbers; matrices and their applications for solving systems of equations, for geometric transformations, and their applications to probability. Functions: Use of log-log graphs; graph transformations; creating, fitting and using models with further trigonometric, logarithmic, rational, logistic and piecewise functions. Geometry and Trigonometry: Vector concepts and their applications in kinematics; applications of adjacency matrices, and tree and cycle algorithms. Statistics and Probability: Binomial and Poisson distributions; designing data collection methods; tests for reliability and validity; hypothesis testing and confidence intervals. Calculus: Kinematics and practical problems involving rates of change; volumes of revolution; setting up and solving models involving differential equations using numerical and analytic methods; slope field;, coupled and second-order differential equations in context. |
30% |
|
Paper 2: 2 hours (Calculator) |
30% |
|
|
Paper 3: 1 hour and 15 mins (Calculator) |
20% |
|
|
Internal assessment |
This is a piece of written work that involves investigating an area of mathematics. Independent work Criteria-based assessment |
20% |
Entry Requirement: Applications and Interpretation - HL
Grade 8 at IGCSE Mathematics
Group 5:
Mathematics: Analysis and Approaches (SL & HL)
Why study Mathematics: Analysis and Approaches?
This course is intended for students who wish to pursue studies in mathematics at university or subjects that have a large mathematical content; it is for students who enjoy developing mathematical arguments, problem solving and exploring real and abstract applications, with and without technology.
The difference between the SL (150 hours) and HL (240 hours) courses are given in detail below in the Contents of each course. Essentially, the SL course is a subset of the HL course - students studying HL study 90 more hours of more challenging content. The emphasis for both courses is on the theoretical underpinnings of Mathematics as well as the use of Mathematics in the wider world.
|
Content - Mathematics: Analysis and Approaches - SL |
% of total grade |
|
|
Paper 1: 1 hour and 30 minutes (Non-calculator) |
Number and Algebra: Scientific notation; arithmetic and geometric sequences and series; logarithms and exponentials; simple proof; approximations and errors; the binomial theorem. Functions: Equations of straight lines; functions and their graphs, including composite, inverse, the identity, rational, exponential, logarithmic and quadratic functions. Solving equations both analytically and graphically; transformation of graphs. Geometry and Trigonometry: Volume and surface area of 3d solids; right-angled and non-right-angled trigonometry including bearings and angles of elevation and depression; radian measure; trigonometric identities and equations; composite trigonometric functions. Statistics and Probability: Sampling techniques; presentation of data; measures of central tendency and spread; correlation, regression; calculating probabilities; probability diagrams; the normal distribution; the binomial distribution Calculus: Limits and convergence; differentiation including analysing graphical behaviour of functions; normals and tangents; optimisation; kinematics involving displacement, velocity, acceleration and total distance travelled; the chain, product and quotient rules; definite and indefinite integration. |
40% |
|
Paper 2: 1 hour and 30 minutes (Calculator) |
40% |
|
|
Internal assessment |
This is a piece of written work that involves investigating an area of mathematics. Independent work Criteria-based assessment |
20% |
Pupils who wish to apply to universities in Germany, must study an additional Vectors module. You must make the Head of Mathematics aware so that this can be organised for you.
Entry Requirement: Analysis and Approaches - SL
Grade 7 at IGCSE Mathematics
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Content - Mathematics: Analysis and Approaches - HL |
% of total grade |
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Paper 1: 2 hours (Non-calculator) |
In additional to the content of the SL course, HL also includes: Number and Algebra: Permutations and combinations; partial fractions; complex numbers; proof by induction, contradiction and counter-example; solution of systems of linear equations. Functions: Factor and remainder theorems; sums and products of roots of polynomials; rational functions; odd and even functions; self-inverse functions; solving function inequalities and the modulus function. Geometry and Trigonometry: Reciprocal trigonometric ratios; inverse trigonometric functions; compound angle identities, double angle identity for tangent; symmetry properties of trigonometric graph; vector theory, applications with lines and planes, and vector algebra. Statistics and Probability: Bayes theorem; probability distributions; probability density functions; expectation algebra. Calculus: Continuity and differentiability; convergence and divergence; differentiation from first principles; limits and L’Hopital’s rule; implicit differentiation; derivatives of inverse and reciprocal trigonometric functions; integration by substitution and parts; volumes of revolution; solution of first order differential equations using Euler’s method, by separating variables and using the integrating factor; Maclaurin series. |
30% |
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Paper 2: 2 hours (Calculator) |
30% |
|
|
Paper 3: 1 hour and 15 mins (Calculator) |
20% |
|
|
Internal assessment |
This is a piece of written work that involves investigating an area of mathematics.
|
20% |
Entry Requirement: Analysis and Approaches - HL
Grade 7 in IGCSE Further Pure Maths.