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Engineering Mathematics I

Industrial Control and Installation · Level 6  ·  5 Chapters

Can I download Engineering Mathematics I notes as a PDF?

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What Engineering Mathematics I covers

In this unit, you will be able to confidently tackle a wide range of engineering mathematics problems, from solving complex equations and working with logarithms to mastering trigonometric and hyperbolic functions. You’ll skillfully use scientific calculators and visualize complex numbers and polar equations, empowering you to apply these essential mathematical tools with precision and confidence in real-world engineering tasks. By the end, you’ll have a solid foundation to solve practical problems and support your success in the engineering field.

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Careers after Engineering Mathematics I

Engineering Mathematics I gives you powerful tools to solve real-world problems—tools that Kenyan industries and businesses rely on every day. These skills go far beyond the classroom, opening doors to exciting opportunities across our country.

  • Construction Sites & County Works: Calculating measurements, angles, and material quantities using trigonometry and indices is essential for site supervisors, quantity surveyors, and masons. Accurate maths ensures safe, cost-effective structures.
  • KenGen & Power Sector: Engineers and technicians use logarithms, simultaneous equations, and complex numbers to analyse electrical circuits, troubleshoot faults, and optimise power generation.
  • Jua Kali Workshops: Artisans apply arithmetic progressions and quadratic equations to price jobs, cut materials, and design products—making their work more efficient and profitable.
  • Matatu Industry: Fleet managers and mechanics use progressions to schedule maintenance, calculate fuel efficiency, and manage finances—keeping vehicles running and businesses thriving.
  • Agribusiness & KTDA: Farm managers and agronomists apply maths to estimate yields, plan planting cycles, and analyse market trends. Accurate calculations mean better profits and sustainable growth.
  • Hospitality & Entrepreneurship: Chefs, event planners, and hoteliers use maths to budget, price menus, and manage inventories—skills vital for running successful businesses.
  • Self-Employment: Whether you’re designing, building, or innovating, strong maths skills help you quote accurately, solve technical challenges, and earn trust from clients.

Mastering Engineering Mathematics I is your ticket to a future where your skills are respected, your opportunities are limitless, and your confidence to solve real problems sets you apart—so embrace it, and see yourself building Kenya’s tomorrow!

Chapters

1
Apply Algebra
11 topics
Open chapter →
2
Apply Trigonometry and hyperbolic functions
16 topics
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3
Apply complex numbers
7 topics
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4
Apply Coordinate Geometry
7 topics
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5
Carry out Binomial Expansion
4 topics
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What Engineering Mathematics I covers: 45 main topics in 5 chapters

1. Apply Algebra

  1. 1.1 Base and Index
  2. 1.2 Law of indices
  3. 1.3 Indicial equations
  4. 1.4 Laws of logarithm
  5. 1.5 Logarithmic equations
  6. 1.6 Conversion of bases
  7. 1.7 Use of calculator
  8. 1.8 Reduction of equations
  9. 1.9 Solution of equations reduced to quadratic form
  10. 1.10 Solutions of simultaneous linear equations in three unknowns
  11. 1.11 Solutions of problems involving AP and GP

2. Apply Trigonometry and hyperbolic functions

  1. 2.1 Half -angle formula
  2. 2.2 Factor formula
  3. 2.3 Trigonometric functions
  4. 2.4 Parametric equations
  5. 2.5 Relative and absolute measures
  6. 2.6 Measures calculation
  7. 2.7 Meaning of hyperbolic equations
  8. 2.8 Properties of hyperbolic functions
  9. 2.9 Evaluations of hyperbolic functions Hyperbolic identities
  10. 2.10 Osborne's Rule
  11. 2.11 Ashx+bshx=C equation
  12. 2.12 One-to-one relationship in functions
  13. 2.13 Inverse functions for one- to-one relationship
  14. 2.14 Inverse functions for trigonometric functions
  15. 2.15 Graph of inverse functions
  16. 2.16 Inverse hyperbolic functions

3. Apply complex numbers

  1. 3.1 Meaning of complex numbers
  2. 3.2 Stating complex numbers in
  3. 3.3 Modulus
  4. 3.4 Representation of complex numbers on the Argand diagram
  5. 3.5 Arithmetic operation of complex numbers
  6. 3.6 Application of De Moivre's theorem
  7. 3.7 Application of complex numbers to engineering

4. Apply Coordinate Geometry

  1. 4.1 Polar equations
  2. 4.2 Cartesian equation
  3. 4.3 Graphs of polar equations
  4. 4.4 Normal and tangents
  5. 4.5 Definition of a point
  6. 4.6 Locus of a point in relation to a circle
  7. 4.7 Loci of points for given mechanism

5. Carry out Binomial Expansion

  1. 5.1 Binomial theorem in determination of Roots of numbers
  2. 5.2 Estimation of errors of small changes using binomial theorem
  3. 5.3 Binomial Expansion in
  4. 5.4 deriving power series S/No. Description/ Specifications Quantity Recommended Ratio (Item: Trainee) A

Revise this unit

Exam-style questions 70 Written to CDACC standard, with answers Test yourself 200 Multiple-choice, one at a time Practise questions 147 Quick recall — check you know the facts
3 more for this unit
Oral exam preparation 48 What the assessor asks, and how to answer out loud Worked calculations 36 Step-by-step maths with the common mistakes Quick cards 916 Myth busters, skill tips and scenarios

Beyond the syllabus

Decision simulator 5 On site, what would you do? Workplace scenarios 101 Real site situations — what would you do? Turn this into income 60 Where this skill earns — what to charge, how to find clients

Other units in Module II