Chapter 1
Exercise 1.1Exercise 1.2Exercise 1.3Miscellaneous Exercise 1Complex Numbers
Learn about complex numbers, their properties, conjugations, modulus, and algebraic operations on complex numbers.
FBISE • Class 10 • Mathematics
10th Class Mathematics Notes Federal Board (FBISE)
Access complete chapter-wise solved notes, conceptual MCQs, short and long exercise questions, and free PDF downloads aligned with the National Book Foundation (NBF) 2026-2027 syllabus and Student Learning Outcomes (SLO).
Federal BoardClass 10SSC-IIMathematicsEnglish MediumSession 2026-2027SLO BasedSNC AlignedNBF TextbookChapter-Wise Notes
Quick Answer
This page provides comprehensive solved notes for 10th Class Mathematics under the Federal Board (FBISE) curriculum. It includes SLO-based conceptual MCQs, step-by-step solved algebraic and geometric exercises, short-answer questions, and detailed proofs of theorems. You can read these notes online or download the free PDF notes for chapters 1 to 12 offline.
Chapter-Wise Mathematics Notes
Select any chapter to read online or download the PDF notes for exam preparation.
Chapter 2
Exercise 2.1Exercise 2.2Exercise 2.3Exercise 2.4Exercise 2.5Exercise 2.6Miscellaneous Exercise 2Quadratic Equations
Learn how to solve quadratic equations using factorization, completing the square, and quadratic formula, along with the theory of quadratic equations.
Chapter 3
Exercise 3.1Exercise 3.2Exercise 3.3Exercise 3.4Miscellaneous Exercise 3Matrices and Determinants
Explore matrices, types of matrices, addition, subtraction, multiplication, determinants, and solving linear equations using Cramer's rule.
Chapter 4
Exercise 4.1Exercise 4.2Exercise 4.3Exercise 4.4Miscellaneous Exercise 4Linear and Quadratic Inequalities
Understand linear inequalities, quadratic inequalities, their graphs, and solving inequality problems in real-world contexts.
Chapter 5
Exercise 5.1Exercise 5.2Exercise 5.3Miscellaneous Exercise 5Algebraic Functions
Learn about algebraic functions, polynomial functions, rational functions, partial fractions, and their properties.
Chapter 6
Exercise 6.1Exercise 6.2Exercise 6.3Miscellaneous Exercise 6Functions and Graphs
Study domain and range of functions, algebraic operations on functions, mapping, composition of functions, and drawing graphs of linear and quadratic functions.
Chapter 7
Exercise 7.1Exercise 7.2Miscellaneous Exercise 7Vectors in Plane
Learn about vectors, their representations, magnitude, direction, vector addition, subtraction, scalar multiplication, and applications in a plane.
Chapter 8
Exercise 8.1Exercise 8.2Exercise 8.3Exercise 8.4Exercise 8.5Exercise 8.6Miscellaneous Exercise 8Application of Trigonometry
Understand trigonometric ratios, identities, angles of elevation and depression, and solving right-angled triangles in practical situations.
Chapter 9
Exercise 9.1Exercise 9.2Exercise 9.3Exercise 9.4Miscellaneous Exercise 9Chord and Arcs of a Circle
Study theorems on chords, perpendicular bisectors, central angles, circular arcs, and congruent segments of a circle.
Chapter 10
Exercise 10.1Exercise 10.2Miscellaneous Exercise 10Tangents and Angles of a Circle
Explore tangents to circles, angles in circular segments, secants, and important geometric theorems related to tangent lines.
Chapter 11
Exercise 11.1Exercise 11.2Miscellaneous Exercise 11Practical Geometry of Circles
Learn geometric constructions involving circles, tangents, circumscribed and inscribed circles, and common tangents to two circles.
Chapter 12
Exercise 12.1Exercise 12.2Exercise 12.3Exercise 12.4Miscellaneous Exercise 12Basic Statistics
Understand frequency distributions, cumulative frequency, measures of central tendency (mean, median, mode), and measures of dispersion.
Overview of 10th Class Mathematics Notes FBISE
Class 10 Mathematics for Federal Board (FBISE) is a key subject that bridges fundamental algebraic calculations with advanced geometric proofs. The syllabus is split into two primary components: algebra and geometry, both of which are designed to enhance logical reasoning and analytical skills. These solved notes provide a detailed breakdown of each chapter, ensuring that matric students can grasp complex mathematical concepts easily.
Following the latest Student Learning Outcomes (SLO) guidelines by the Federal Board, exams now test students' conceptual understanding rather than rote memorization. These notes are specifically designed to address this change. They include a wide variety of conceptual MCQs, tricky short questions, and step-by-step solutions to textbook exercises from the National Book Foundation (NBF) textbook. Complex mathematical derivations are simplified with detailed step-by-step calculations.
Additionally, circular geometry and practical construction play a major role in the SSC-II Mathematics paper. Chapters 9 to 11 cover crucial circle theorems and geometric construction techniques. Our solved notes include neat, labeled diagrams and detailed geometric justifications to help students score maximum marks in the geometry portion of the board exam.
What Are These Mathematics Notes?
These Class 10 Mathematics solved notes are a comprehensive study resource built specifically for FBISE English medium students. They are designed to act as a complete exam preparation companion, providing clear explanations for every topic in the NBF syllabus.
Whether you are trying to understand complex numbers, solved matrices, or searching for the geometric proof of tangents to circles, these notes cover it all. Every formula is highlighted, and algebraic steps are structured logically to help you follow along without needing an external tutor.
By using these solved notes, students can ensure a thorough revision of the entire syllabus. The notes cover the following essential components:
- Chapter summaries
- Important terms
- Key concepts and explanations
- Solved textbook exercises
- Conceptual MCQs
- Short-answer questions
- Detailed long-answer questions
- Important comparisons
- Diagrams and labeling
- SLO-based practice questions
- Exam-focused revision points
What Is Included in the Notes?
Students can use the chapter-wise material to access the following learning resources:
✓
Solved Exercises
Detailed step-by-step solutions to all textbook exercise problems for algebra, statistics, and geometry.
A
MCQs
Conceptual and calculation-based multiple-choice questions with verified keys and explanatory notes.
Q
Short Questions
Focused short-answer questions highlighting algebraic formulas, key definitions, and quick theorem applications.
L
Long Questions
Detailed long-answer questions covering complex algebraic simplifications and formal geometric theorem proofs.
D
Definitions
Clear and precise definitions of mathematical terms, sets, statistical measures, and geometric concepts.
◎
Diagrams
Accurate, neat, and labeled geometric diagrams for circle theorems and practical construction exercises.
★
SLO-based Questions
Analytical and application-based questions designed to prepare students for the latest FBISE SLO exam model.
↓
PDF Download
Free downloadable PDF files for each chapter, allowing students to study offline at their own convenience.
SNC and National Curriculum Alignment
These notes are 100% aligned with the Single National Curriculum (SNC) and the latest National Curriculum guidelines. They strictly follow the Student Learning Outcomes (SLO) framework introduced by the Federal Board (FBISE) for the 2026-2027 academic session, utilizing the official National Book Foundation (NBF) textbook.
How to Prepare Class 10 Mathematics from These Notes
Follow this simple preparation method to get better results in Mathematics.
1
Read the textbook chapter first
Start by reading the explanations and solved examples in the official NBF textbook to build a baseline understanding.
2
Revise key concepts
Go through the formulas and summaries in these notes to reinforce what you have read in the textbook.
3
Solve MCQs
Practice the objective questions to test your speed and accuracy in basic calculations and conceptual queries.
4
Prepare short questions
Focus on the short-answer questions to learn how to apply algebraic identities and formulas concisely.
5
Prepare long questions
Practice the detailed exercise questions and derivations to master logical steps and algebraic formatting.
6
Practice diagrams
Draw geometric figures and write out the steps of construction and theorem proofs repeatedly to ensure accuracy.
7
Revise before tests and board exams
Use the summarized sheets and PDF downloads for quick revisions before your school assessments and final board exams.
Related Resources
Use these resources to complete your Mathematics preparation and other subjects.
Frequently Asked Questions
Are these Class 10 Mathematics notes updated for the 2026-2027 session?
Yes, these solved notes are fully updated for the 2026-2027 academic session according to the National Book Foundation (NBF) textbook prescribed by FBISE.
Do these notes cover the latest SLO guidelines?
Yes, these notes are structured around the Student Learning Outcomes (SLO) framework, helping students solve conceptual and application-based exam questions.
Is the circular geometry portion included in these notes?
Absolutely. All circular geometry chapters (from Chapter 9 to Chapter 11), including circle theorems, cyclic quadrilaterals, and practical constructions, are fully solved.
How do the chapter numbers work in Class 10 Mathematics?
In the FBISE SSC curriculum, Class 9 covers Chapters 1 to 9 (old syllabus) or relevant math subjects, while Class 10 Mathematics starts from Chapter 1 (Complex Numbers) and goes up to Chapter 12 (Basic Statistics) under the new NBF curriculum.
Are step-by-step proofs of mathematical theorems included?
Yes, all circle theorems in Chapters 9 and 10 are proven formally with "Given", "To Prove", "Construction", and "Statements & Reasons" tables along with labeled diagrams.
Can I download these Class 10 Mathematics notes as PDF files?
Yes, chapter-wise PDF download links are available so you can download and study the notes offline.
Do the notes contain solved MCQs?
Yes, each chapter features conceptual and computational MCQs with explanatory hints to prepare you for the objective section of the paper.
Are these notes based on the National Book Foundation (NBF) textbook?
Yes, the solutions and chapter order strictly follow the official textbook published by the National Book Foundation for Federal Board.
How can weak students prepare for math exams using these notes?
The notes break down complex algebraic simplifications and proofs into simple, logical steps, making it easy for students of all learning levels to follow.
Is there any fee to read these notes online?
No, all matric math notes and solutions on StudyPlusPlus are 100% free to read online for all students.
Are these notes aligned with the Single National Curriculum (SNC)?
Yes, the textbook and these solved notes comply fully with the Single National Curriculum guidelines approved by the government.
Can Punjab Board students use these notes for prep?
While these notes are tailored to the NBF book for FBISE, the core algebraic concepts (like matrices, inequalities, and functions) and geometry principles are useful for Punjab Board students as well.
What is the best way to practice circle theorems?
We recommend drawing the figure first, memorizing the key geometric properties, and writing out the statements and reasons multiple times to build memory.
Does the website offer online tests for Class 10 Mathematics?
Currently, we offer solved MCQs for self-assessment, with interactive practice tests planned in our upcoming platform updates.