HSC EV Higher Math 1st Paper Textbook & Guide (Previous year questions) PDF - এইচএসসি (ইংরেজি ভার্সন) উচ্চতর গণিত ১ম পত্র পাঠ্যবই এবং গাইড পিডিএফ 2026

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HSC English Version Higher Math 1st Paper Book & Guide PDF 2026 | Previous Year Questions & Solutions Download - ইচএসসি ইংরেজি ভার্সন উচ্চতর গণিত ১ম পত্র বই ও গাইড পিডিএফ ২০২৬ | বিগত বছরের প্রশ্ন ও সমাধান

Complete English Medium HSC Higher Mathematics 1st Paper Book, Notes, and Previous Year Question Collection (PDF Download)

ভূমিকা (Introduction)

এইচএসসি (ইংরেজি ভার্সন) শিক্ষার্থীদের জন্য উচ্চতর গণিত একটি গুরুত্বপূর্ণ ও চ্যালেঞ্জিং বিষয়। ২০২৬ শিক্ষাবর্ষের নতুন পাঠ্যসূচি অনুযায়ী প্রস্তুতি নিতে হলে শুধু মূল পাঠ্যবই পড়লেই যথেষ্ট নয়— এর পাশাপাশি প্রয়োজন অধ্যায়ভিত্তিক গাইড, বিশ্লেষণ, এবং বিগত বছরের বোর্ড প্রশ্নের অনুশীলন। এই PDF সংকলনে একসাথে দেওয়া হয়েছে — NCTB অনুমোদিত ইংরেজি ভার্সন Higher Math 1st Paper Textbook, চ্যাপ্টারওয়াইজ গাইড ও গুরুত্বপূর্ণ সূত্রসমূহ, এবং২০১৫–২০২৫ সালের বোর্ড প্রশ্ন ও সমাধান। এটি শিক্ষার্থীদের জন্য একটি পূর্ণাঙ্গ প্রস্তুতি প্যাকেজ, যেখানে মূল বই, সহায়ক নোটস, এবং পূর্ববর্তী প্রশ্নসমূহের বিশ্লেষণ সবই অন্তর্ভুক্ত। এই রিসোর্সটি ব্যবহার করে শিক্ষার্থীরা সহজেই অধ্যায়ভিত্তিক প্রস্তুতি নিতে পারবে, বোর্ড পরীক্ষার ধরন বুঝতে পারবে, এবং ২০২৬ সালের এইচএসসি পরীক্ষায় উচ্চতর গণিতে ভালো ফল অর্জন করতে পারবে।

Syllabus

Chapter One: Matrices and Determinants (12 Periods)

Matrices and various types of matrices; equality, addition, subtraction and multiplication of matrices (of sizes at most 3 x 3) determinants; evaluation of determinants (of sizes 2 x 2 and 3 x 3); minor and cofactor of determinants; properties of determinants; singular and non-singular matrix; inverse matrix of a square matrix; solution of systems of linear equation (Cramer's Rule).

Chapter Two: Vector (12 Periods)

Vector as representation of directed quantity; support of a geometric vector; equality of vectors, opposite vector; addition, subtraction of geometric vectors, scalar multiples of vector and their properties; resolved parts of a vector in the plane; representation of vectors in Cartesian coordinates; unit vectors i, j; position vector; application of vectors in two-dimensional geometric problems; resolved parts of a vector in three dimensions; unit vectors i, j, k in three dimensions; expression of vectors in terms of î, j, k; expression of sum and scalar multiple of vectors in terms of i, j, k; vector equation of straight line; scalar product of vectors; properties of scalar product; expression of scalar product in terms of components of the vectors; vector product of vectors; properties of vector product; expression of vector product in terms of components of the vectors.

Chapter Three: Straight Lines (16 Periods)

Cartesian and polar coordinates in a plane; relation between Cartesian and polar coordinates; distance between two points; coordinates of points of division of a line-segment; area of a triangle; locus; slope of a straight line; slope of the line joining two points, equations of straight lines parallel to the axes; equations of straight lines in the forms: (i) y = mx + c, (ii) y - y₁ = m(x - x), (iii) y - y = x-x, (x-x), (iv)+= 1, (v) x cos a + y sin a = p; the equation ax + by + c = 0 represents a straight line; graphical representation of straight lines; the point of intersection of two straight lines; angle between two straight lines; condition for two straight lines to be parallel or perpendicular; equations of straight lines under various conditions; perpendicular distance of a point from a straight line; equation of bisectors of angle between two straight lines. Practical: Coordinates of division point of a line-segment; area of a triangle in terms of the coordinates of its vertices; graph of equation of a straight line; determination of equation of a straight line from graph; image of a point and a line-segment with respect to an axis; image of a point and a line-segment with respect to a given straight line.

Chapter Four: The Circle (10 Periods)

Equations of a circle with centre at the origin; drawing a circle with centre at the origin and determination of points of intersection with the axes; equation of a circle with given centre and radius; equation of a circle in polar coordinates; equations of tangent and normal of a circle; length of tangent; determination of the equation of common chord of two circles; Practical: drawing the graph (freehand on graph paper) of the equation (xa)² + (yb)² = c2.

Chapter Five: Permutations and Combinations (10 periods)

Addition and multiplication laws of counting; n!; various formula for determination of number of permutations; combinations; number of combinations; complementary combination; the formula: "C+"C+C; conditional combination.

Chapter Six: Trigonometric Ratios (14 Periods)

Trigonometric angle; the degree and radian measure of angles; formula for arc length and area of a sector of circle in radian measure; trigonometric ratios; signs of trigonometric ratios according to quadrant; relations between various trigonometric ratios; change in values of trigonometric ratios; periods of trigonometric functions.

Chapter Seven: Trigonometric Ratios of Associated Angles (16 Periods)

Trigonometric ratios of associated angles; trigonometric ratios of compound angles; sine law of triangles; cosine law of triangles; Practical: determination of desired angle when the lengths of the sides are given; determination of the ratios of the lengths of sides. When the angles are given; given measures of two angles and length of one side of a triangle to find the length of a desired side; given the lengths of two sides and measure of one angle of a triangle to find the measure of a desired angle.

Chapter Eight: Functions and Graph of Functions (18 Periods)

Relation and function; domain and range of a relation or function; types of function; one-one function; onto function; identity function; constant function; inverse function; elementary functions; sketch of functions: quadratic functions, exponential functions, logarithmic functions; trigonometric functions, absolute value functions; sketching of functions and transformed functions; sketching of a function and inverse function; determination of periods of trigonometric functions; Practical : drawing of graphs of functions and transformed functions; drawing graph of a function and its inverse function on the same graph paper; graphs of quadratic functions, exponential functions, logarithmic functions, trigonometric functions, absolute value functions.

Chapter Nine: Differentiation (18 Periods)

x-0 x0 X Limit; slope; limits of functions (with examples and graphs); one-sided limit; limit at infinity; infinite limit; lim sinx, lim e-l and similar limits; derivative as a limit; derivative of x"; differentiation of polynomial functions, trigonometric functions, exponential functions and logarithmic functions; derivative as slope of tangent; use of the symbols f'(x), dy, dy dx dx, f(x), etc. for derivative; derivatives of sum, product and quotient of functions; derivative of composite function and inverse function; differential of independent and dependent variables; increasing and decreasing functions; extreme point; maxima and minima of functions; Practical: representing the graph of a function locally in the neighbourhood of a given point by the tangent at that point; representing the graph of a function approximately by a combination of small line-segments; relation between differential of independent and dependent variables and its application.

Chapter Ten: Integration (12 Periods)

The definite integral as area; the definite integral as limit; anti-derivative and indefinite integral; the fundamental theorem of integral calculus; various techniques of finding indefinite integrals: substitution, integration by parts; use of partial fractions; determination of areas using definite integrals; Practical: approximate determination of the area bounded by the graph of a function, the x-axis and two given ordinates.

এই বইয়ে বিগত বছরের যে সকল বোর্ডের প্রশ্ন অন্তর্ভুক্ত করা হয়েছে

• ঢাকা বোর্ড - ২০২৫
• রাজশাহী বোর্ড - ২০২৫
• কুমিল্লা বোর্ড - ২০২৫
• যশোর বোর্ড - ২০২৫
• চট্টগ্রাম বোর্ড - ২০২৫
• বরিশাল বোর্ড - ২০২৫
• সিলেট বোর্ড - ২০২৫
• দিনাজপুর বোর্ড - ২০২৫
• ময়মনসিংহ বোর্ড - ২০২৫

প্রতিটি Chapter শেষে রয়েছে।

• Exercise
• A - Multiple Choice Questions
• B - Multiple Choice Questions From Board Exams
• C - Multiple Choice Questions From Admission Tests
• D - Creative Questions
• E - Creative Questions from Board Exams
• Answers - Multiple Choice Questions

Table of Contents

                                

Chapter	Title	Page
***	Detailed Contents	5
***	Necessary Formulae at a Glance	5-8
Chapter : 01	Matrices and Determinants	9-84
Chapter : 02	Vector	85-134
Chapter : 03	Straight Lines	135-238
Chapter : 04	The Circle	239-302
Chapter : 05	Permutations and Combinations	303-344
Chapter : 06	Trigonometric Ratios	345-384
Chapter : 07	Trigonometric Ratios of Associated Angles	385-460
Chapter : 08	Functions and Graph of Functions	461-510
Chapter : 19	Differentiation	511-616
Chapter : 10	Integration	617-704
01	Appendix	705-784
02	Combined Chapter Questions	705
03	Fun Math: Brain Teasers	712
04	Questions of University Admission Test	713
05	Board Exam Questions	731

Marks Distribution HSC EV Higher Math 1st Paper "Full Marks : 100"

ক্র.	HSC EV Higher Math 1st Paper Textbook Chapter Name	পিডিএফ
**	Necessary formulae At A Glance
১	Chapter One: Matrices and Determinants (12 Periods)
২	Chapter Two: Vector (12 Periods)
৩	Chapter Three: Straight Lines (16 Periods)
৪	Chapter Four: The Circle (10 Periods)
৫	Chapter Five: Permutations and Combinations (10 periods)
৬	Chapter Six: Trigonometric Ratios (14 Periods)
৭	Chapter Seven: Trigonometric Ratios of Associated Angles (16 Periods)
৮	Chapter Eight: Functions and Graph of Functions (18 Periods)
৯	Chapter Nine: Differentiation (18 Periods)
১০	Chapter Ten: Integration (12 Periods)
১১	Fun Math Brain Teasers
১২	Board Exam Questions

উপসংহার (Conclusion):

এইচএসসি ইংরেজি ভার্সনের শিক্ষার্থীদের জন্য এই Higher Math 1st Paper বই ও গাইড ২০২৬ সংস্করণটি একটি পূর্ণাঙ্গ রিসোর্স। এতে রয়েছে মূল পাঠ্যবই, অধ্যায়ভিত্তিক গাইড, এবং বিগত বছরের প্রশ্নসহ সমাধান — যা পরীক্ষার প্রস্তুতিতে সহায়ক ভূমিকা রাখবে।

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