Grade 10 Mathematics: Algebraic Expressions
A comprehensive study guide covering the real number system, multiplication and factorisation of algebraic expressions,
simplification of algebraic fractions, and fully worked practice exercises. Designed for Grade 10 learners preparing for
mathematics assessments.
© E-Loné Scheepers 2026
,What's Inside This Guide
This study guide is structured to take you step by step through the key topics in algebraic expressions. Each section builds
on the previous, so work through them in order for best results.
01 02 03
The Real Number System Multiplication of Algebraic Factorisation
Understand the classification of all Expressions Learn to reverse multiplication using
numbers — natural, whole, integer, Master the distributive law, FOIL HCF, difference of two squares,
rational, and irrational. method, and special products including trinomials, grouping, and
difference of two squares and squaring sum/difference of cubes.
a binomial.
04 05
Algebraic Fractions Practice Exercises
Simplify expressions involving algebraic fractions using Three timed exercise sets with fully worked solutions to
factorisation, cancellation, and the LCD method. build exam confidence and reinforce all key methods.
© E-Loné Scheepers 2026
, CHAPTER 1
The Real Number System
The real number system includes every number that can be placed on a
continuous number line. Understanding how numbers are classified is
essential for algebra, and exam questions frequently ask you to identify
whether a given number is rational or irrational, real or non-real. The
system is built in layers, with each set of numbers contained within a
larger set.
© E-Loné Scheepers 2026
, The Hierarchy of Real Numbers
Every set of numbers is a subset of the one above it. Natural numbers sit at the core, and each layer expands the set by
including additional types of numbers. Irrational numbers sit alongside the rational numbers — both together make up the
full set of real numbers.
© E-Loné Scheepers 2026
A comprehensive study guide covering the real number system, multiplication and factorisation of algebraic expressions,
simplification of algebraic fractions, and fully worked practice exercises. Designed for Grade 10 learners preparing for
mathematics assessments.
© E-Loné Scheepers 2026
,What's Inside This Guide
This study guide is structured to take you step by step through the key topics in algebraic expressions. Each section builds
on the previous, so work through them in order for best results.
01 02 03
The Real Number System Multiplication of Algebraic Factorisation
Understand the classification of all Expressions Learn to reverse multiplication using
numbers — natural, whole, integer, Master the distributive law, FOIL HCF, difference of two squares,
rational, and irrational. method, and special products including trinomials, grouping, and
difference of two squares and squaring sum/difference of cubes.
a binomial.
04 05
Algebraic Fractions Practice Exercises
Simplify expressions involving algebraic fractions using Three timed exercise sets with fully worked solutions to
factorisation, cancellation, and the LCD method. build exam confidence and reinforce all key methods.
© E-Loné Scheepers 2026
, CHAPTER 1
The Real Number System
The real number system includes every number that can be placed on a
continuous number line. Understanding how numbers are classified is
essential for algebra, and exam questions frequently ask you to identify
whether a given number is rational or irrational, real or non-real. The
system is built in layers, with each set of numbers contained within a
larger set.
© E-Loné Scheepers 2026
, The Hierarchy of Real Numbers
Every set of numbers is a subset of the one above it. Natural numbers sit at the core, and each layer expands the set by
including additional types of numbers. Irrational numbers sit alongside the rational numbers — both together make up the
full set of real numbers.
© E-Loné Scheepers 2026
