CIC Mathematics Curriculum Documentation

IB Math 2 Higher Level

COURSE OVERVIEW

This course is designed for twelfth grade students who are likely to make extensive use of mathematics in their college studies, or who enjoy the pursuit of mathematics for its own sake.

The course extends calculus techniques and examines more rigorously the theoretical foundations that lead to the fundamental theorem of the calculus.

The course also treats probability through to probability density functions, and the vector geometry of point, line and plane. There is an optional topic that is usually either abstract algebra or analysis and approximation.

COURSE SKILLS

Students will be able to

1. evaluate simple definite integrals as the limit of a sum.
2. differentiate functions defined by an integral
3. solve differential equations using an integrating factor.
4. solve problems of point, line and plane using vector methods.
5. solve problems in the elementary theory of finite groups.
6. interpret problems of linear systems in the context of abstract algebra.
7. solve statistical problems using binomial and normal models, and other density functions.

COURSE CONTENT

1. Rieman sums and the existence of the integral
2. The fundamental theorem of the calculus
3. Further integration techniques; reduction formulae
4. Solution of first order differential equations by an integrating factor
5. Simple homogeneous differential equations
6. Further volumes of revolution
7. Algebra of matrices with applications to the solution of linear systems
8. Algebra of vectors including scalar and vector product
9. Forms of the equations of lines and planes
10. Intersections of lines, lines and planes and planes
11. Distances in three dimensions between points, lines and planes.
12. Basic theory of binary operations and mappings between abstract sets
13. The group axioms and uniqueness of identity and inverse
14. Finite and cyclic groups
15. Lagrange’s theorem and corollary
16. Isomorphism and its consequences
17. Expectation , mean and variance in discrete and continuous variable
18. The binomial and normal models

ASSESSMENT TECHNIQUES AND TEACHING METHODOLOGIES

For this course, assessment and teaching method are determined by the rigor of the final external examination. Students are encouraged to expect difficult questions and trained to deploy rigorous analytical skills. Whilst group work is used as appropriate, assessment is based on individual testing.

KEY RESOURCES

1. Pure Mathematics 1 and 2, Bostock and Chandler (ST(P) 1994)
2. Calculus, Larson and Hostetler (Alt. 4th. Ed, D.C. Heath 1990)
3. Advanced Mathematics 2, Perkins and Perkins (1990)

ESL STRATEGIES AND CONSIDERATIONS

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

FUTURE NEEDS AND CHANGES

1. For the 1999 — 2000 school year:
   1. Course content summary and skills overview should be modified so as to be appropriate for the level of the new IB higher level mathematics syllabus
   2. Assessment techniques and teaching methodologies must be revised to reflect the required IB coursework component.
2. For the 2000 — 2001 school year, the content summary and skills overview should be modified to complete the two-year sequence begun by IB Higher Level Math 1, a new course for the 1999 — 2000 school year.