SUBJECT: Mathematics HL
YEAR GROUP: IB 2
Week Learning objectives
Implicit differentiation
1
Implicit differentiaion
2
3
4
Related rates of change
Derivatives of inverse trigonometric
functions
Application of differentiation;
Related rates of change.
5
Anti-differentiation
6
Definite integrals;
Rules of integration
7
Applications of integration
8
10
Application of integration;
Rules of integration
Practice in techniques of integration;
Miscellaneous calculus problems
Vectors
11
Vector geometry
9
TEACHER: Anna Tokarz
Activities (in brief)
Introduction and practice of implicit differentiation
Application in finding equations of tangents and normals to curves;
Second derivative;
Using chain rule in solving problems involving related rates of change;
Deriving and applying formulas for inverse trig functions
Motion in a straight line; definitions of displacement, velocity and acceleration
functions;
interpretation of signs; application in problem solving;
Related rates of change in problem solving with application of differentiation of
various functions.
Introduction to indefinite integration as anti-differentiation;
interpretation of indefinite integral as a family of curves;
establishing rules for indefinite integrals for xn, sin x, cos x, and ex;
Integration with a boundary condition to determine the constant of integration.
Introduction to definite integrals and the Fundamental Theorem of Calculus;
Analyzing properties of definite integrals;
Effective use of GDC in evaluating definite integrals;
Integration by substitution
Finding areas of regions bounded by curves;
Application in motion problems.
Finding volumes of solids of revolution about the x-axis or the y-axis;
Integration by parts.
Application of miscellaneous rules for integration –intensive practice;
Practice in solving compound calculus problems
Vectors in 2D and 3D and various forms of representing vectors.
Operations with vectors.
Scalar product and vector product of vectors.
Describing lines and planes using vector equations.
12
13
Vector geometry
Complex numbers as 2D vectors
14
Complex numbers as 2D vectors
15
Complex numbers and de Moivre’s Theorem
Analyzing relationships between lines and planes.
Finding angles between lines and planes.
Solving miscellaneous problems.
Illustrating complex numbers in Argand plane. Finding modulus and argument of
a complex number. Writing complex numbers in polar form and Euler form.
Discovering properties of modulus and arguments of complex numbers.
Manipulating complex numbers in polar and Euler form.
Establishing de Moivre’s theorem for complex numbers. Application of the
theorem to solve equations and find roots of complex numbers.
*Please note that the curriculum summary is a long-term plan, which may be altered according to the needs and/or curiosity of the
students. If topics are changed they will still be in line with the prescribed IGCSE or IB syllabi respectively.