Everything Maths Grade 10

1 Algebraic expressions

1.1 Introduction EMA

Over human history, all peoples and cultures have contributed to the field of Mathematics. Topics like algebra
may seem obvious now, but for many centuries mathematicians had to make do without it. Over the next three
grades, you will explore more advanced and abstract mathematics. It may not be obvious how this applies to
everyday life, but the truth is, mathematics is required for nearly everything you will do one day. Enjoy your
mathematical journey. Remember, there is no such thing as a “maths person” or “not a maths person”. We can
all do mathematics, it just takes practice.

Figure 1.1:Some examples of early tally sticks. These were used to help people count things such as the number of days
between events or the number of livestock they had.

In this chapter, we will begin by revising the real number system and then learn about estimating surds and
rounding real numbers. We will also be expanding on prior knowledge of factorisation and delve into more
complex calculations involving binomial and trinomial expressions.

1.2 The real number system EMA

RealR

RationalQ

IntegerZ

WholeN 0

NaturalN

IrrationalQ’

We use the following definitions:

• N: natural numbers aref1; 2; 3;: : :g


• N 0 : whole numbers aref0; 1; 2; 3;: : :g


• Z: integers aref: : :;3;2;1; 0; 1; 2; 3;: : :g

6 1.1. Introduction