Western Cape Education Department
Directorate: Curriculum FET
MATHEMATICS
REVISION BOOKLET
2025 TERM 1
Grade 10
This revision program is designed to assist you in revising the critical
content and skills that you have covered during the 1st term. The
purpose is to prepare you to understand the key concepts and to
provide you with an opportunity to establish the required standard and
the application of the knowledge necessary to succeed in the
examination.
, 2
Mathematics revision booklet 2025 Grade 10 Term 1
The revision program covers the following topics:
A. PRODUCT AND FACTORIZATION
B. SIMPLIFICATION OF
EXPRESSIONS
I. Simplification Algebraic Fractions
II. Simplification Of Exponential Fractions:
C. SOLVING EQUATIONS
I. Linear Equations
II. Quadratic Equations
III. Exponential Equations
D. INEQUALITIES
E. SIMULTANEOUS EQUATIONS
F. TRIGONOMETRY
, 3
Mathematics revision booklet 2025 Grade 10 Term 1
ALGEBRA
A. PRODUCT and FACTORIZATION
Terminology:
A monomial is an expression with one term.
A binomial is an expression with two terms.
A trinomial is an expression with three terms.
Product Monomial & Binomial Factorization Common Factor
𝒂𝒂(𝒃𝒃𝒃𝒃 + 𝒄𝒄) 1. 𝒂𝒂𝒃𝒃𝒃𝒃 + 𝒂𝒂𝒂𝒂
= 𝒂𝒂𝒂𝒂𝒂𝒂 + 𝒂𝒂𝒂𝒂 = 𝒂𝒂(𝒃𝒃𝒃𝒃 + 𝒄𝒄)
2. 𝒂𝒂(𝒃𝒃𝒃𝒃 + 𝒄𝒄) − 𝒅𝒅 (𝒃𝒃𝒃𝒃 + 𝒄𝒄)
= (𝒃𝒃𝒃𝒃 + 𝒄𝒄)(𝒂𝒂 − 𝒅𝒅 )
Factorization by Grouping
𝟔𝟔𝒙𝒙𝟐𝟐 𝒚𝒚 − 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 + 𝟏𝟏𝟏𝟏𝟏𝟏 − 𝟐𝟐𝟐𝟐
= �𝟔𝟔𝒙𝒙𝟐𝟐 𝒚𝒚 − 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏� + (𝟏𝟏𝟏𝟏𝟏𝟏 − 𝟐𝟐𝟐𝟐)
= 𝟐𝟐𝟐𝟐𝟐𝟐(𝟑𝟑𝟑𝟑 − 𝟓𝟓) + 𝟓𝟓(𝟑𝟑𝟑𝟑 − 𝟓𝟓)
= (𝟑𝟑𝟑𝟑 − 𝟓𝟓)(𝟐𝟐𝟐𝟐𝟐𝟐 + 𝟓𝟓)
Product of binomials Factorize Difference of Squares
(𝒂𝒂 + 𝒃𝒃)(𝒂𝒂 − 𝒃𝒃) 𝒂𝒂𝟐𝟐 − 𝒃𝒃𝟐𝟐
= 𝒂𝒂𝟐𝟐 − 𝒃𝒃𝟐𝟐 = (𝒂𝒂 + 𝒃𝒃)(𝒂𝒂 − 𝒃𝒃)
Factorize Quadratic Trinomial
(𝒂𝒂 + 𝒃𝒃)𝟐𝟐 𝒂𝒂𝟐𝟐 + 𝟐𝟐𝟐𝟐𝟐𝟐 + 𝒃𝒃𝟐𝟐
= (𝒂𝒂 + 𝒃𝒃)(𝒂𝒂 + 𝒃𝒃) = (𝒂𝒂 + 𝒃𝒃)(𝒂𝒂 + 𝒃𝒃)
= 𝒂𝒂𝟐𝟐 + 𝟐𝟐𝟐𝟐𝟐𝟐 + 𝒃𝒃𝟐𝟐
(𝒂𝒂 − 𝒃𝒃)𝟐𝟐 𝒂𝒂𝟐𝟐 − 𝟐𝟐𝟐𝟐𝟐𝟐 + 𝒃𝒃𝟐𝟐
= (𝒂𝒂 − 𝒃𝒃)(𝒂𝒂 − 𝒃𝒃) = (𝒂𝒂 − 𝒃𝒃)(𝒂𝒂 − 𝒃𝒃)
= 𝒂𝒂𝟐𝟐 − 𝟐𝟐𝟐𝟐𝟐𝟐 + 𝒃𝒃𝟐𝟐
Product of Binomial and Trinomial Factorize Sum & Difference of Cubes
(𝒂𝒂 + 𝒃𝒃)�𝒂𝒂𝟐𝟐 − 𝒂𝒂𝒂𝒂 + 𝒃𝒃𝟐𝟐 � 𝒂𝒂𝟑𝟑 + 𝒃𝒃𝟑𝟑
= 𝒂𝒂𝟑𝟑 + 𝒃𝒃𝟑𝟑 = (𝒂𝒂 + 𝒃𝒃)�𝒂𝒂𝟐𝟐 − 𝒂𝒂𝒂𝒂 + 𝒃𝒃𝟐𝟐 �
(𝒂𝒂 − 𝒃𝒃)�𝒂𝒂𝟐𝟐 + 𝒂𝒂𝒂𝒂 + 𝒃𝒃𝟐𝟐 � 𝒂𝒂𝟑𝟑 − 𝒃𝒃𝟑𝟑
= 𝒂𝒂𝟑𝟑 − 𝒃𝒃𝟑𝟑 = (𝒂𝒂 − 𝒃𝒃)�𝒂𝒂𝟐𝟐 + 𝒂𝒂𝒂𝒂 + 𝒃𝒃𝟐𝟐 �
Determine the product and simplify where possible:
Directorate: Curriculum FET
MATHEMATICS
REVISION BOOKLET
2025 TERM 1
Grade 10
This revision program is designed to assist you in revising the critical
content and skills that you have covered during the 1st term. The
purpose is to prepare you to understand the key concepts and to
provide you with an opportunity to establish the required standard and
the application of the knowledge necessary to succeed in the
examination.
, 2
Mathematics revision booklet 2025 Grade 10 Term 1
The revision program covers the following topics:
A. PRODUCT AND FACTORIZATION
B. SIMPLIFICATION OF
EXPRESSIONS
I. Simplification Algebraic Fractions
II. Simplification Of Exponential Fractions:
C. SOLVING EQUATIONS
I. Linear Equations
II. Quadratic Equations
III. Exponential Equations
D. INEQUALITIES
E. SIMULTANEOUS EQUATIONS
F. TRIGONOMETRY
, 3
Mathematics revision booklet 2025 Grade 10 Term 1
ALGEBRA
A. PRODUCT and FACTORIZATION
Terminology:
A monomial is an expression with one term.
A binomial is an expression with two terms.
A trinomial is an expression with three terms.
Product Monomial & Binomial Factorization Common Factor
𝒂𝒂(𝒃𝒃𝒃𝒃 + 𝒄𝒄) 1. 𝒂𝒂𝒃𝒃𝒃𝒃 + 𝒂𝒂𝒂𝒂
= 𝒂𝒂𝒂𝒂𝒂𝒂 + 𝒂𝒂𝒂𝒂 = 𝒂𝒂(𝒃𝒃𝒃𝒃 + 𝒄𝒄)
2. 𝒂𝒂(𝒃𝒃𝒃𝒃 + 𝒄𝒄) − 𝒅𝒅 (𝒃𝒃𝒃𝒃 + 𝒄𝒄)
= (𝒃𝒃𝒃𝒃 + 𝒄𝒄)(𝒂𝒂 − 𝒅𝒅 )
Factorization by Grouping
𝟔𝟔𝒙𝒙𝟐𝟐 𝒚𝒚 − 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 + 𝟏𝟏𝟏𝟏𝟏𝟏 − 𝟐𝟐𝟐𝟐
= �𝟔𝟔𝒙𝒙𝟐𝟐 𝒚𝒚 − 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏� + (𝟏𝟏𝟏𝟏𝟏𝟏 − 𝟐𝟐𝟐𝟐)
= 𝟐𝟐𝟐𝟐𝟐𝟐(𝟑𝟑𝟑𝟑 − 𝟓𝟓) + 𝟓𝟓(𝟑𝟑𝟑𝟑 − 𝟓𝟓)
= (𝟑𝟑𝟑𝟑 − 𝟓𝟓)(𝟐𝟐𝟐𝟐𝟐𝟐 + 𝟓𝟓)
Product of binomials Factorize Difference of Squares
(𝒂𝒂 + 𝒃𝒃)(𝒂𝒂 − 𝒃𝒃) 𝒂𝒂𝟐𝟐 − 𝒃𝒃𝟐𝟐
= 𝒂𝒂𝟐𝟐 − 𝒃𝒃𝟐𝟐 = (𝒂𝒂 + 𝒃𝒃)(𝒂𝒂 − 𝒃𝒃)
Factorize Quadratic Trinomial
(𝒂𝒂 + 𝒃𝒃)𝟐𝟐 𝒂𝒂𝟐𝟐 + 𝟐𝟐𝟐𝟐𝟐𝟐 + 𝒃𝒃𝟐𝟐
= (𝒂𝒂 + 𝒃𝒃)(𝒂𝒂 + 𝒃𝒃) = (𝒂𝒂 + 𝒃𝒃)(𝒂𝒂 + 𝒃𝒃)
= 𝒂𝒂𝟐𝟐 + 𝟐𝟐𝟐𝟐𝟐𝟐 + 𝒃𝒃𝟐𝟐
(𝒂𝒂 − 𝒃𝒃)𝟐𝟐 𝒂𝒂𝟐𝟐 − 𝟐𝟐𝟐𝟐𝟐𝟐 + 𝒃𝒃𝟐𝟐
= (𝒂𝒂 − 𝒃𝒃)(𝒂𝒂 − 𝒃𝒃) = (𝒂𝒂 − 𝒃𝒃)(𝒂𝒂 − 𝒃𝒃)
= 𝒂𝒂𝟐𝟐 − 𝟐𝟐𝟐𝟐𝟐𝟐 + 𝒃𝒃𝟐𝟐
Product of Binomial and Trinomial Factorize Sum & Difference of Cubes
(𝒂𝒂 + 𝒃𝒃)�𝒂𝒂𝟐𝟐 − 𝒂𝒂𝒂𝒂 + 𝒃𝒃𝟐𝟐 � 𝒂𝒂𝟑𝟑 + 𝒃𝒃𝟑𝟑
= 𝒂𝒂𝟑𝟑 + 𝒃𝒃𝟑𝟑 = (𝒂𝒂 + 𝒃𝒃)�𝒂𝒂𝟐𝟐 − 𝒂𝒂𝒂𝒂 + 𝒃𝒃𝟐𝟐 �
(𝒂𝒂 − 𝒃𝒃)�𝒂𝒂𝟐𝟐 + 𝒂𝒂𝒂𝒂 + 𝒃𝒃𝟐𝟐 � 𝒂𝒂𝟑𝟑 − 𝒃𝒃𝟑𝟑
= 𝒂𝒂𝟑𝟑 − 𝒃𝒃𝟑𝟑 = (𝒂𝒂 − 𝒃𝒃)�𝒂𝒂𝟐𝟐 + 𝒂𝒂𝒂𝒂 + 𝒃𝒃𝟐𝟐 �
Determine the product and simplify where possible:
