ABC Mathematical Concepts
Grade 9
C Nel & Dr T Jordaan
1
Page
2025 © C Nel, Dr T Jordaan
, Foreword
Mathematics is a language with unique terms, concepts, processes and procedures
which must be understood and deliberately learnt to be successful in Mathematics.
Mathematics learners do not always realize the importance of knowing this language
and the ability to use the language effectively and correctly.
This booklet is the brainchild of Ms Charmaine Nel who is a well-qualified and
experienced mathematics teacher and tutor. She noticed that learners struggle with
the subject since they do not know what to do and how to do it. It is a timely and
useful resource to assist Grade 9, and other learners, to master the language of
Mathematics to become successful and improve their performance.
I am convinced that this booklet will make a difference in the lives of many learners
in future. Over the past years, universities have experienced a decline in Grade 12
learners who qualify for tertiary education where Mathematics and Physical
Education are prerequisites for admission. I trust that this booklet will also help to
address this challenge.
Dr Tertia Jordaan
Senior Lecturer Mathematics Education
North-West University – Potchefstroom Campus
2
Page
2025 © C Nel, Dr T Jordaan
, A Mathematics: Concepts
Acute angle An angle greater than 0° and smaller than 90°.
(0°< angle < 90°)
Acute-angled Based on its angles: A triangle in which all 3 of the angles are acute.
triangle Acute-angled (more than 0° and less than 90 °):
See a triangle in which all 3 angles are acute. (0°< angle < 90°)
Obtuse-angled
Right-angled
Right-angled (an angle exactly = 90 °):
a triangle in which one of the angles is a right angle.
Obtuse-angled (more than 90° and less than 180 °):
a triangle in which one of the angles is obtuse.
Addition The process in mathematics of combining two or
See 2+6 = 8 more numbers.
Algebraic expression
addition
Decimal addition
Fraction Addition
Sum
Additive inverse 4 −𝟒 = 0 The number that is added to another and yields an
answer of 0.
Additive property 4 +𝟎 = 4 Adding zero to a number leaves it unchanged.
See Identity element (0 is the identity element for addition).
3
Page
2025 © C Nel, Dr T Jordaan
, Adjacent angles Adjacent angles have a common vertex and a
common side (The side right next to the point or
angle being looked at).
Common vertex O and a common side OD.
Adjacent angles are next to each other.
Algebra Algebra is where symbols, usually letters of the
2 2 3 alphabet and numbers are used to represent
2𝑥 − 4𝑥 − 5𝑥 − 6 − 5𝑥
numbers and to express general relationships.
Algebraic Algebraic equation means it contains variables, constants
equation 2𝑥 + 2 = 10 and an equal sign.
Algebraic Distributive law says that multiplying a number by a
equation group of numbers added together is the same as doing
Brackets each multiplication separately.
See Distributive 3(2 + 4) = 3 × 2 + 3 × 4
property
BODMAS
First multiply the bracket out before using any
other method.
4 Page
2025 © C Nel, Dr T Jordaan
Grade 9
C Nel & Dr T Jordaan
1
Page
2025 © C Nel, Dr T Jordaan
, Foreword
Mathematics is a language with unique terms, concepts, processes and procedures
which must be understood and deliberately learnt to be successful in Mathematics.
Mathematics learners do not always realize the importance of knowing this language
and the ability to use the language effectively and correctly.
This booklet is the brainchild of Ms Charmaine Nel who is a well-qualified and
experienced mathematics teacher and tutor. She noticed that learners struggle with
the subject since they do not know what to do and how to do it. It is a timely and
useful resource to assist Grade 9, and other learners, to master the language of
Mathematics to become successful and improve their performance.
I am convinced that this booklet will make a difference in the lives of many learners
in future. Over the past years, universities have experienced a decline in Grade 12
learners who qualify for tertiary education where Mathematics and Physical
Education are prerequisites for admission. I trust that this booklet will also help to
address this challenge.
Dr Tertia Jordaan
Senior Lecturer Mathematics Education
North-West University – Potchefstroom Campus
2
Page
2025 © C Nel, Dr T Jordaan
, A Mathematics: Concepts
Acute angle An angle greater than 0° and smaller than 90°.
(0°< angle < 90°)
Acute-angled Based on its angles: A triangle in which all 3 of the angles are acute.
triangle Acute-angled (more than 0° and less than 90 °):
See a triangle in which all 3 angles are acute. (0°< angle < 90°)
Obtuse-angled
Right-angled
Right-angled (an angle exactly = 90 °):
a triangle in which one of the angles is a right angle.
Obtuse-angled (more than 90° and less than 180 °):
a triangle in which one of the angles is obtuse.
Addition The process in mathematics of combining two or
See 2+6 = 8 more numbers.
Algebraic expression
addition
Decimal addition
Fraction Addition
Sum
Additive inverse 4 −𝟒 = 0 The number that is added to another and yields an
answer of 0.
Additive property 4 +𝟎 = 4 Adding zero to a number leaves it unchanged.
See Identity element (0 is the identity element for addition).
3
Page
2025 © C Nel, Dr T Jordaan
, Adjacent angles Adjacent angles have a common vertex and a
common side (The side right next to the point or
angle being looked at).
Common vertex O and a common side OD.
Adjacent angles are next to each other.
Algebra Algebra is where symbols, usually letters of the
2 2 3 alphabet and numbers are used to represent
2𝑥 − 4𝑥 − 5𝑥 − 6 − 5𝑥
numbers and to express general relationships.
Algebraic Algebraic equation means it contains variables, constants
equation 2𝑥 + 2 = 10 and an equal sign.
Algebraic Distributive law says that multiplying a number by a
equation group of numbers added together is the same as doing
Brackets each multiplication separately.
See Distributive 3(2 + 4) = 3 × 2 + 3 × 4
property
BODMAS
First multiply the bracket out before using any
other method.
4 Page
2025 © C Nel, Dr T Jordaan
