Assessment: Mini IA PowerPoint, Mathematical Modelling (10%) Rational/ Exponenti al and Logarithm ic functions
4.1 4.2 4.3
Jan 23rd (2 weeks)
Toolkit Test and Review Feb 6th
Mid Term Break Feb 13th – 17th
Feb 20th (4 weeks)
Calculus – Differenti ation and its Applicatio n (Focus only on polynomi als)
5.1 5.2 5.3 5.4 5.5
2.8 The reciprocal function f(x)=1x,x≠0: its graph and self-inverse nature. Rational functions of the form f(x)=(ax+b)/(cx+d) and their graphs. Equations of vertical and horizontal asymptotes. 2.9 Exponential functions and their graphs: Logarithmic functions and their graphs: 2.10 Solving equations, both graphically and analytically. Use of technology to solve a variety of equations, including those where there is no appropriate analytic approach. Applications of graphing skills and solving equations that relate to real-life situations. Assessment: Functions (Cumulative)
TOK: 1. What role do “models” play in mathematics? Do they play a different role in mathematics compared to their role in other areas of knowledge?
5.1 Introduction to the concept of a limit. Derivative interpreted as gradient function and as rate of change. 5.2 Increasing and decreasing functions. Graphical interpretation of fʹ(x)>0,fʹ(x)=0,fʹ(x)<0.
IM: Attempts by Indian mathematicians (5001000 CE) to explain division by zero. TOK: 1. What value does the knowledge of limits have? Is infinitesimal behaviour applicable to real life? Is intuition a valid way of knowing in mathematics? 2. The seemingly abstract concept of calculus allows us to create mathematical models that permit human feats such as
5.3 Derivative of f(x)=axn is fʹ(x)=anxn−1, n∈ℤ The derivative of functions of the form f(x)=axn+bxn−1+... where all exponents are integers. 5.4 Tangents and normals at a given point, and their equations. 5.6 Differentiation of a sum and a multiple of these functions.
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2. What assumptions do mathematicians make when they apply mathematics to real-life situations?
