TN 10th Maths Unit-Wise Important 2-Mark & 5-Mark Questions with Step-by-Step Solutions PDF

Securing a centum (100/100) in the Tamil Nadu Class 10 (SSLC) Mathematics examination requires consistent step-by-step algebraic accuracy, geometric theorem proof mastery, and thorough conceptual practice across all eight prescribed chapters. To build high-scoring confidence across all state board subjects, students should practice systematically with curated study guides for Tamil (பொதுத்தமிழ்), English, Mathematics (கணிதம்), Science (அறிவியல்), and Social Science (சமூக அறிவியல்) via our master 10th SSLC Study Materials Hub.

Unlike other subjects, the Class 10 Mathematics paper carries 100 full theory marks with no internal practical deductions, making every single formula, substitution step, and concluding statement critical. Scoring top marks demands targeted mastery over 2-mark definitions, 5-mark comprehensive problems, and the 8-mark Practical Geometry and Graph constructions. Students can revise core textbook examples from our Samacheer Kalvi 10th Standard Textbooks, review upcoming exam schedules on the TN 10th Public Exam Time Table 2027, test problem solving with the 10th SSLC Question Papers Archive and 10th PTA Question Bank (6 Sets), and cross-reference with our 10th Science Important Questions Guide. This comprehensive guide provides unit-wise high-yield 2-mark and 5-mark solved problems for Tamil Medium and English Medium students.

தமிழ்நாடு 10-ஆம் வகுப்பு கணிதம் (SSLC Mathematics) பாடம் — 8 அலகுகளுக்கான மிக முக்கியமான 2 மதிப்பெண், 5 மதிப்பெண் மற்றும் கட்டாயக் கணக்குகள் (Compulsory Questions) படிமுறை தீர்வுகள் PDF தொகுப்பு கீழே கொடுக்கப்பட்டுள்ளது.

Overview

TN 10th Maths Question Paper Pattern & Marks Allocation

The Tamil Nadu SSLC Mathematics examination carries 100 marks and is structured into four distinct sections designed to test calculation speed, theorem proofs, and geometric visualization:

Passing Requirement: Minimum 35 marks out of 100. However, scoring 16/16 in Part IV (Geometry & Graph) combined with textbook 1-mark MCQs guarantees a first-class pass with minimal effort.

Top Unit-Wise 2-Mark Important Questions & Concepts

Part II requires answering 10 out of 14 questions (each carrying 2 marks). Below are the high-probability recurring problems across the 8 chapters:

• Unit 1 (Relations and Functions): If A × B = {(3,2), (3,4), (5,2), (5,4)}, find A and B. Check whether a relation represents a function using vertical line test. Find f ο g and g ο f when f(x) = 2x + 1 and g(x) = x² − 2.
• Unit 2 (Numbers and Sequences): Use Euclid’s Division Algorithm to find the HCF of two positive integers (e.g., 340 and 412). Find the 19th term of an AP: −11, −15, −19, … Find the sum of first 28 terms of an AP or sum of special series: 1 + 2 + 3 + … + 45.
• Unit 3 (Algebra): Find the GCD of polynomials (e.g., 16x³y², 24xy²). Find the square root of expressions like 256(x − a)⁸(x − b)⁴. Solve quadratic equations by factorization method. Determine the nature of roots using discriminant Δ = b² − 4ac. Matrix addition, transpose, and scalar multiplication.
• Unit 4 (Geometry): State Basic Proportionality Theorem (Thales Theorem). State Angle Bisector Theorem (ABT). In ΔABC, D and E are points on sides AB and AC such that DE || BC; find the missing segment.
• Unit 5 (Coordinate Geometry): Find the area of the triangle whose vertices are (−3, 5), (5, 6), and (5, −2). Find the slope of a line passing through given points. Show that three given points are collinear. Find the intercepts made by a straight line on the coordinate axes.
• Unit 6 (Trigonometry): Prove basic trigonometric identities: e.g., prove that √[(1 + cos θ) / (1 − cos θ)] = cosec θ + cot θ. Find the angle of elevation of the top of a tower from a point on the ground.
• Unit 7 (Mensuration): If the total surface area of a cone of radius 7 cm is 704 cm², find its slant height. Find the volume of a sphere whose radius is 5 cm. Differentiate curved surface area and total surface area of a hollow cylinder.
• Unit 8 (Statistics and Probability): Find the range and coefficient of range of the given data. Find the standard deviation of first 21 natural numbers. If P(A) = 0.37, P(B) = 0.42, and P(A ∩ B) = 0.09, find P(A ∪ B). A die is rolled; find the probability of getting an odd prime number.

Top Unit-Wise 5-Mark Golden Problems (SSLC Centum Targets)

Part III carries 50 total marks (10 questions × 5 marks). Mastering these standardized 5-mark models is mandatory for high scores:

• Unit 1 (Relations and Functions): Given A = {x ∈ ℕ | 1 < x < 4}, B = {x ∈ ℤ | 0 ≤ x < 2}, and C = {x ∈ ℕ | x < 3}, verify that A × (B ∩ C) = (A × B) ∩ (A × C). Composition of three functions: verify (f ο g) ο h = f ο (g ο h).
• Unit 2 (Numbers and Sequences): Find the sum to n terms of the series: 5 + 55 + 555 + … to n terms. In an AP, sum of four consecutive terms is 28 and their sum of squares is 276; find the four numbers. Special series summation: 1² + 2² + 3² + … + 19² or 1³ + 2³ + … + k³.
• Unit 3 (Algebra): Solve the system of linear equations in three variables: x + y + z = 5, 2x − y + z = 9, x − 2y + 3z = 16. Find the square root of polynomial 64x⁴ − 16x³ + 17x² − 2x + 1 by division method. Matrix multiplication: if A, B, and C are given matrices, verify that A(BC) = (AB)C and A(B + C) = AB + AC.
• Unit 4 (Geometry): State and prove Basic Proportionality Theorem (Thales Theorem) with complete hypothesis, construction, and proof. State and prove Angle Bisector Theorem. State and prove Pythagoras Theorem.
• Unit 5 (Coordinate Geometry): Find the area of the quadrilateral formed by vertices (−9, −2), (−8, −4), (2, 2), and (1, −3) using shoelace formula. Find the equation of a straight line passing through the intersection of two lines and perpendicular to another given line.
• Unit 6 (Trigonometry): From the top of a 60 m high building, the angles of depression of the top and bottom of a vertical lamp post are observed to be 38° and 60° respectively; find the height of the lamp post. Two ships are sailing in the sea on either side of a lighthouse; calculate the distance between the two ships.
• Unit 7 (Mensuration): A solid metallic cylinder of base radius 3 cm and height 5 cm is melted to form a cone of height 1 cm; find the base radius of the cone. The internal and external radii of a hollow hemispherical shell are 3 m and 5 m respectively; find its TSA and CSA.
• Unit 8 (Statistics and Probability): Calculate the standard deviation and coefficient of variation for ungrouped and grouped frequency distributions. State and prove Addition Theorem of Probability: P(A ∪ B) = P(A) + P(B) − P(A ∩ B). Probability of drawing cards from a well-shuffled pack of 52 cards.

Part IV: Practical Geometry & Linear Graph (16 Guaranteed Marks)

Part IV contains two compulsory questions with internal “Either / Or” choice carrying 8 marks each (16 marks total). Every student must master these constructions:

How to Solve Compulsory Questions (Q.28 and Q.42)

The compulsory questions in the SSLC board examination are specifically designed to test analytical application rather than routine textbook memorization:

• Compulsory Q.No. 28 (Part II • 2 Marks): Typically drawn from Chapter 3 (Algebra), Chapter 5 (Coordinate Geometry), or Chapter 7 (Mensuration). Common patterns include finding the value of unknown constant k when roots are equal (Δ = 0), proving three points collinear using slope formula, or computing ratio of volumes.
• Compulsory Q.No. 42 (Part III • 5 Marks): Frequently chosen from Chapter 2 (AP/GP series summation like 7 + 77 + 777 + …), Chapter 6 (Trigonometric heights & distances involving two right-angled triangles), or Chapter 7 (Conversion of solids melting & recasting).
• Mark-Retention Formula: (1) Write “Given Data” with symbols. (2) State the standard mathematical formula. (3) Show substitution steps clearly without jumping. (4) Box the final answer and append correct units (e.g., cm², cm³, or units).

Download 10th Maths Solved Important Questions PDF

Free downloadable PDF files prepared by Tamil Nadu state mathematics experts and PTA master teachers are provided below for both Tamil Medium and English Medium students:

Frequently asked questions

Which chapters carry the highest marks in 10th Maths?

Chapter 3 (Algebra) carries the maximum marks (around 28 to 32 marks across parts including Graph), followed by Chapter 4 (Geometry, around 16 to 18 marks including Practical Geometry), Chapter 5 (Coordinate Geometry, around 14 marks), and Chapter 2 (Numbers & Sequences, around 12 to 14 marks).

What are the compulsory question numbers in the SSLC Maths board exam?

Question No. 28 in Part II (2-mark question) and Question No. 42 in Part III (5-mark question) are compulsory. Students cannot skip these questions and must solve them to attain a centum score.

How can average students easily score passing marks (35+) in 10th Maths?

Students can easily clear the exam by focusing on Part IV (Practical Geometry & Graph: 16 marks), textbook-back Multiple Choice Questions (14 marks), and mastering simple 2-mark models from Chapter 1 (Relations) and Chapter 8 (Probability), guaranteeing over 45 marks.

What scale should be written for Graph questions in 10th Maths?

Students must write the scale on the top-right corner of the graph sheet clearly specifying units for both axes (e.g., On X-axis: 1 cm = 1 unit; On Y-axis: 1 cm = 2 units). Omitting the scale results in a 1-mark deduction.

Where can students download 10th Maths PTA question bank with answer keys?

Students and teachers can download the complete 6 sets of PTA model question papers with step-by-step verified solutions directly from KalviMani’s dedicated SSLC study materials portal.

Related pages on KalviMani

10th Maths Study Materials Hub · 10th SSLC Study Materials Portal · Samacheer Kalvi 10th Textbooks PDF · TN 10th Public Exam Time Table 2027 · 10th Science Important Questions PDF · 10th PTA Question Bank (6 Sets) · SSLC Question Papers Archive