CIC Mathematics Curriculum Documentation

IB Mathematics 1.

COURSE OVERVIEW

This course is designed for eleventh grade students who need a calculus-based course as a preparation for the IB examinations at higher level and at standard level (math methods).

The course is an introduction to differential and integral calculus. The course also extends the students’ knowledge of the properties and applications of the elementary functions and of algebraic topics in the context of a calculus oriented approach. Extensive use of graphics calculators is a feature of the course, as is the appropriate use of software. Project work is an integral part of the course.

COURSE SKILLS

Students will be able to:

1. sketch and identify the main features of the graphs of the elementary functions*.
2. solve problems in practical and theoretical situations by choosing and using appropriate elementary functions.
3. solve problems of point, line and circle using the method of coordinate geometry.
4. differentiate simple polynomials from first principles.
5. differentiate elementary functions by appropriate use of rules.
6. apply differentiation to solve standard problems of tangent, normal, velocity, acceleration, stationary values, and approximation.
7. find indefinite and definite integrals by recognition, substitution and by parts.
8. use integation to find areas and volumes, and solve differential equations.
9. solve problems using complex numbers interpreted algebraically and geometrically.

COURSE CONTENT

1. Basic Algebra
   1. Forms of the line
   2. Quadratics and completing the square; symmetry relations; the discriminant inequalities.
   3. Line and quadratic intersection.
   4. Remainder and factor theorem
   5. Partial fractions
   6. Graphs of polynomials
   7. Asymptote of rational functions; curve sketching; limits
2. Trigonometry
   1. Definitions and properties of trigonometric functions; radians; circle mensuration
   2. Solution of trigonometric equations
   3. Fundamental Identities
   4. Inverse functions
   5. Small angle formulae
   6. Models of waves
3. Exponential and logarithmic functions
   1. Definitions and properties; graphs; half-life
   2. Inverse properties and change of base; nature of e
4. Differential Calculus
   1. Definition of the derivative and graphical interpretation
   2. Differentiation of sum, product, quotient and composite functions
   3. Second order derivatives; implicit and parametric differentiation
   4. Applications to stationary values, tangents and normals, rates of change, velocity and acceleration, approximation
5. Integral Calculus
   1. Indefinite and definite integrals; the fundamental theorem
   2. Techniques of integration including substitution and parts
   3. Applications to area, volume and distance-time
   4. Solution of differential equations by recognition and separation of variables
6. Complex numbers
   1. Algebra and geometry of complex numbers
   2. DeMoivre’s theorem; roots of unity

ASSESSMENT TECHNIQUES AND TEACHING METHODOLOGIES

1. Assessment Techniques
   1. Coursework (20% per quarter): meets the coursework requirement to build a portfolio for IB Math Methods or Higher Level. This may consist of open-ended problems, projects and investigations.
   2. Quizzes and tests (70%): at least 4 tests per quarter
   3. Homework/classwork:(10%).
2. Teaching Methodologies
   1. Direct instruction: usually in the form of a dialogue or discussion
   2. Student presentations
   3. Investigations with small group discussion or individual work
   4. Critical reading of set text and other reference sources

KEY RESOURCES

1. Texts
   1. Pure Mathematics 1 and 2, Bostock and Chandler (ST(P) 1994)
   2. Calculus, Larson and Hostetler ( Alt. 4th Ed. D.C. Heath 1990)
2. Technology
   1. Graphics Calculator
   2. Spreadsheets

ESL STRATEGIES AND CONSIDERATIONS

At this level, CIC students are required to be proficient in English at grade level.

FUTURE NEEDS AND CHANGES

For the 1999 — 2000 school year, this class has been replaced by two first year IB mathematics courses. New course content summaries and skills overviews must be created for the new courses.