Chapter 1 : Numbers and sets

1. Numbers and sets

1.1 Real numbers

1.2 Exponents and logarithms

1.3 Complex numbers

1.4 Sets


Explanatory notes

Candidates should be able to

(a) understand the real number system;

(b) carry out elementary operations on real numbers;

(c) use the properties of real numbers;

(d) use the notation for intervals of real numbers;

(e) use the notation |x| and its properties;

(f) understand integral and rational exponents;

(g) understand the relationship between logarithms and exponents;

(h) carry out change of base for logarithms;

(i) use the laws of exponents and laws of logarithms;

(j) use the results: for a1, and and,,and

(k) solve equations and inequality of involving exponents and logarithms;

(l) understand the meaning of the real part, imaginary part, and conjugate of a complex number;

(m) find the modulus and argument of a complex number;

(n) represent complex numbers geometrically by means of an Argand diagram;

(o) use the condition for the equality of two complex numbers;

(p) carry out elementary operations on complex numbers expressed in Cartesian form;

(q) understand the concept of a set and set notation;

(r) carry out operations on sets;

(s) use the laws of the algebra of sets;