Class notes Technical Mathematics

Western Cape Education Department
Directorate: Curriculum FET




TECHNICAL MATHEMATICS
REVISION BOOKLET
2025 TERM 2


Grade 10

This revision program is designed to assist you in revising the critical content and skills that
you have covered during the 2nd 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.



The revision program covers the following topics:

1. Algebraic expressions
2. Equations and Inequalities
3. Trigonometry

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Technical mathematics revision booklet 2025 Grade 10 Term 2

PRODUCTS
Multiplying a monomial and a binomial:


Example 1

Simplify: 𝟐𝒂(𝒂 − 𝟏)– 𝟑(𝒂2 − 𝟏)

Solution: 𝟐𝒂² − 𝟐𝒂 − 𝟑𝒂𝟐 + 𝟑
= −𝒂𝟐 − 𝟐𝒂 + 𝟑

Try this:
3𝑥(𝑥 − 4) − (𝑥 2 + 2)

Multiplying two binomials:




Example 2

Simplify: (𝟐𝒙 − 𝟑)(𝟒𝒙 − 𝟓)

Solution : 𝟖𝒙² − 𝟏𝟎𝒙 − 𝟏𝟐𝒙 + 𝟏𝟓
= 𝟖𝒙² − 𝟐𝟐𝒙 + 𝟏𝟓

Try this
(3𝑥 − 4)(𝑥 + 2)

Example 3

Simplify: (𝟐𝒙 − 𝟑)(𝟐𝒙 + 𝟑)

Solution : 𝟒𝒙² − 𝟔𝒙 − 𝟔𝒙 − 𝟗
= 𝟒𝒙² − 𝟗

Try this:
(3𝑥 − 4)(3𝑥 + 4)

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Technical mathematics revision booklet 2025 Grade 10 Term 2

Example 4.1

Simplify: (𝟐𝒙 − 𝟑)²
OR
Solution: (𝟐𝒙 − 𝟑)(𝟐𝒙 − 𝟑) (𝟐𝒙 − 𝟑)²
= 𝟒𝒙² − 𝟔𝒙 − 𝟔𝒙 + 𝟗
= 𝟒𝒙² − 𝟏𝟐𝒙 + 𝟗 −𝟔𝒙 x2

= 𝟒𝒙² − 𝟏𝟐𝒙 +𝟗



Example 4.2

Simplify: −𝟏(𝟐𝒙 + 𝟓)²
OR
Solution: −𝟏(𝟐𝒙 + 𝟓)(𝟐𝒙 + 𝟓) (𝟐𝒙 + 𝟓)²

= −𝟏(𝟒𝒙² + 𝟏𝟎𝒙 + 𝟏𝟎𝒙 + 𝟐𝟓) +𝟏𝟎𝒙 x2
= −𝟏(𝟒𝒙𝟐 + 𝟐𝟎𝒙 + 𝟐𝟓)
= −𝟒𝒙𝟐 − 𝟐𝟎𝒙 − 𝟐𝟓 = 𝟒𝒙² + 𝟐𝟎𝒙 + 𝟐𝟓

Try this:
(3𝑥 + 4)² −2(2𝑦 − 5)²