2
Functions and
Equations
Assessment statements
2.1 Concept of function f : x f (x); domain, range, image (value).
Composite functions (f g); identity function. Inverse function f21.
2.2 The graph of a function; its equation y5f(x).
Function graphing
6
Trigonometric Functions
and Equations
Assessment statements
3.1 The circle: radian measure of angles; length of an arc; area of a sector.
3.2 Definition of cos u and sin u in terms of the unit circle.
Definition of tan u as _
sin u
.
cos u
p , _
THEORY OF KNOWLEDGE
18 Theory of Knowledge
What is TOK?
Theory of knowledge is concerned with how we know what we claim to
know. As an IB diploma student you take classes in a number of areas of
knowledge corresponding to the IB hexagon. While we call wha
Fundamentals
1
Introduction
Mathematics is an exciting field of study, concerned with structure,
patterns and ideas. To fully appreciate and understand these core aspects
of mathematics, you need to be confident and skilled in the rules and
language of al
Sequences and
Series
3
Assessment statements
1.1 Arithmetic sequences and series; sum of finite arithmetic sequences;
geometric sequences and series; sum of finite and infinite geometric series.
Sigma notation.
1.3 The binomial theorem: expansion of (
4
Exponential and
Logarithmic Functions
Assessment statements
1.2 Exponents and logarithms.
Laws of exponents; laws of logarithms.
Change of base.
2.6 Exponential functions and their graphs.
x a x, a > 0; x e x.
Logarithmic functions and their g
13
Differential
Calculus -I-I : Further
Techniques and
Applications
Assessment statements
6.2
Derivative of xn, sin x, cos x, tan x, ex and ln x.
Differentiation of a sum and a real multiple of these functions.
The chain rule for composite functions.
8
Vectors -I
Assessment statements
4.1
Vectors as displacements in the plane.
Components of a vector; column representation.
v 1
v 5 v
2 5 v1i 1 v2 j 1 v3k
v3
Algebraic and geometric approaches to the following topics:
the sum and difference of two
16
The Mathematical
Exploration Internal
Assessment
If digressions can bring knowledge of new truths, why should they
trouble us? how do we know that we shall not discover curious
things that are more interesting than the answers we originally sought?
Gal
17
Sample Examination
Papers
Paper 1 Non-GDC paper
Full marks are not necessarily awarded for a correct answer with no
working. Answers must be supported by working and/or explanations.
Where an answer is incorrect, some marks may be given for a correct
m