Higher Mathematics 1

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.tech November 7, 2026

HSC 2028 • Higher Mathematics First Paper • Code 265 1 Contents 1 Matrix and Determinant 2 1.1 What this chapter is about . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Syllabus map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Every definition you need . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 Every formula, derived . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.5 Methods for each problem type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.6 Worked board questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.7 Practice set with answers only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.8 Common mistakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.9 Board tips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.10 Chapter 1 cheat sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2 Vector 21 2.1 What this chapter is about . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2 Syllabus map

HSC 2028 • Higher Mathematics First Paper • Code 265 2 3.9 Board tips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.10 Chapter 3 cheat sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4 Circle 56 4.1 What this chapter is about . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.2 Syllabus map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.3 Every definition you need . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.4 Every formula, derived . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.5 Methods for each problem type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.6 Worked board questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.7 Practice set with answers only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.8 Common mistakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.9 Board tips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.10 Chapter 4 cheat sheet . . . . . . . .