Higher Maths 1 Extended Notes

HIGHER SECONDARY CERTIFICATE 2028 Science Group • English Version • Dhaka Education Board Higher Mathematics First Paper Subject Code 265 Complete Chapter Notes Full syllabus • Labelled diagrams • Board style questions Prepared by Md Ahbab Hamid Khan ahbab.dev September 6, 2026

HSC 2028 • Higher Mathematics First Paper • Code 265 1 Contents 1 Matrix and Determinant 5 1.1 What this chapter is about . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Syllabus map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Every definition you need . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Every formula, derived . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.5 Methods for each problem type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.6 Worked board questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.7 Practice set with answers only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.8 Common mistakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.9 Board tips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.10 Chapter 1 cheat sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2 Vector 24 2.1 What this chapter is about . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2 Syllabus m

HSC 2028 • Higher Mathematics First Paper • Code 265 2 3.9 Board tips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.10 Chapter 3 cheat sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4 Circle 59 4.1 What this chapter is about . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.2 Syllabus map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.3 Every definition you need . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.4 Every formula, derived . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.5 Methods for each problem type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.6 Worked board questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.7 Practice set with answers only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.8 Common mistakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.9 Board tips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.10 Chapter 4 cheat sheet . . . . . . . .