CBSE Important Questions Maths Class 10 | PDF  Download 2026-27

CBSE Class 10 Maths Important Questions for 2026-27 are a blend of the different questions from the CBSE Class 10 syllabus. The important questions cover all the chapters in Mathematics with questions different from what is given in the NCERT textbook for Class 10 Maths. 

In this collection of important questions, questions are arranged chapter-wise covering MCQs, short and long answers, case-based questions and HOTS. These questions often appear in the CBSE Class 10 Maths board exam. Some of those questions are mentioned here. Follow along to know how to put these questions to best use. 

Chapter-wise Important Questions for Maths class 10th 

Chapter 1: Real Numbers Important Questions 

Chapter 2: Polynomials Important Questions 

Chapter 3: Pair of Linear Equations in Two Variables Important Questions 

Chapter 4: Quadratic Equations Important Questions 

Chapter 5: Arithmetic Progressions Important Questions 

Chapter 6: Triangles Important Questions 

Chapter 7: Coordinate Geometry Important Questions 

Chapter 8: Introduction to Trigonometry Important Questions 

Chapter 9: Some Applications of Trigonometry Important Questions 

Chapter 10: Circles Important Questions 

Chapter 11: Areas Related to Circles Important Questions 

Chapter 12: Surface Areas and Volumes Important Questions 

Chapter 13: Statistics Important Questions 

Chapter 14: Probability Important Questions 

Maths Class 10 Assessment Pattern: At a Glance

Let us see what is inside Class 10 2026-27 Maths CBSE Maths Syllabus:

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Important Questions Maths Class 10 With Solutions 2026-27

Here chapter-wise important questions are listed for Maths Class 10. These questions are based on the CBSE Syllabus for Maths 2026-27. The questions given are provided with solutions for understanding. 

1. Real Numbers

Q1. Find the HCF of 135 and 225 using Euclid's Division Algorithm. (Easy)

Answer: 225 = 135 × 1 + 90
135 = 90 × 1 + 45
90 = 45 × 2 + 0
Hence, the HCF of 135 and 225 is 45.

Q2. Show that √7 is irrational. (Medium)

Answer: Assume √7 = p/q where p and q are coprime integers. Squaring both sides gives 7q² = p². Thus p is divisible by 7. Let p = 7k. Substituting back shows q is also divisible by 7, contradicting that p and q are coprime. Therefore, √7 is irrational.

Q3. Determine whether 17/1600 has a terminating decimal expansion. (Medium)

Answer: 1600 = 2⁶ × 5². Since the denominator contains only prime factors 2 and 5, the decimal expansion terminates. Hence, 17/1600 has a terminating decimal expansion.

Q4. Two numbers have HCF 18 and LCM 540. If one number is 90, find the other. (HOTS)

Answer:  Product of two numbers = HCF × LCM
= 18 × 540 = 9720
Other number = 9720 ÷ 90 = 108.

2. Polynomials 

Q1. Find the zeroes of x² − 9. (Easy)

Answer: x² − 9 = (x − 3)(x + 3)
Therefore, the zeroes are 3 and −3.

Q2. Verify the relationship between zeroes and coefficients of x² − 8x + 15. (Medium)

Answer: The zeroes are 3 and 5. Their sum is 8 and product is 15. Since −b/a = 8 and c/a = 15, the relationship between zeroes and coefficients is verified.

Q3. Form a quadratic polynomial whose zeroes are 4 and −2. (Medium)

Answer: Polynomial = (x − 4)(x + 2)
= x² − 2x − 8.
Hence, the required polynomial is x² − 2x − 8.

Q4. If one zero of 3x² − 11x + k is 2, find k. (HOTS)

Answer: Substitute x = 2:
3(4) − 22 + k = 0
12 − 22 + k = 0
k = 10.

3. Pair of Linear Equations in Two Variables 

Q1. Solve: x + y = 7 and x − y = 3. (Easy)

Answer: Adding the equations:
2x = 10 ⇒ x = 5
Substituting in x + y = 7 gives y = 2.
Therefore, the solution is (5, 2).

Q2. Solve 2x + 3y = 13 and x − y = 1. (Medium)

Answer: From x − y = 1, x = y + 1.
Substituting into the first equation gives 2(y + 1) + 3y = 13.
Thus y = 11/5 and x = 16/5.

Q3. Determine the nature of solutions of 2x + 3y = 5 and 4x + 6y = 10. (Medium)

Answer: a₁/a₂ = 2/4 = 1/2 and b₁/b₂ = 3/6 = 1/2 and c₁/c₂ = 5/10 = 1/2.
All ratios are equal. Therefore, the equations have infinitely many solutions.

Q4. A notebook costs ₹20 and a pen costs ₹10. A student buys 8 items for ₹110. Find the number of notebooks and pens. (HOTS)

Answer: Let notebooks = x and pens = y.
x + y = 8 and 20x + 10y = 110.
Solving gives x = 3 and y = 5.
Hence, the student bought 3 notebooks and 5 pens.

4. Quadratic Equations 

Q1. Solve x² − 16 = 0. (Easy)

Answer:
x² = 16
x = ±4
Hence, the roots are 4 and −4.

Q2. Solve x² − 7x + 12 = 0. (Medium)

Answer:
x² − 7x + 12 = (x − 3)(x − 4)
Therefore, x = 3 or x = 4.

Q3. Find the discriminant of 2x² + x − 6 = 0. (Medium)

Answer:
D = b² − 4ac
= 1² − 4(2)(−6)
= 49.
Since D > 0, the roots are real and distinct.

Q4. The area of a rectangle is 120 m² and its length exceeds its breadth by 4 m. Find its dimensions. (HOTS)

Answer:
Let breadth = x m.
Then x(x + 4) = 120.
Solving x² + 4x − 120 = 0 gives x = 10.
Dimensions are 10 m and 14 m.

5. Arithmetic Progressions

Q1. Find the 15th term of the AP: 3, 7, 11, 15, ... (Easy)

Answer:
a = 3, d = 4
a₁₅ = a + (15 − 1)d
= 3 + 14(4) = 59.
Therefore, the 15th term is 59.

Q2. Find the sum of the first 20 natural numbers. (Medium)

Answer: Using Sₙ = n(n + 1)/2
S₂₀ = 20 × 21 / 2 = 210.
Hence, the sum is 210.

Q3. Determine the common difference of the AP: 11, 8, 5, 2, ... (Easy)

Answer:
d = second term − first term
= 8 − 11
= −3.
Thus, the common difference is −3.

Q4. The sum of the first n terms of an AP is 3n² + 2n. Find its nth term. (HOTS)

Answer:
aₙ = Sₙ − Sₙ₋₁
= (3n² + 2n) − [3(n − 1)² + 2(n − 1)]
= 6n − 1.
Hence, the nth term is 6n − 1.

6. Triangles

Q1. State the Basic Proportionality Theorem. (Easy)

Answer: If a line is drawn parallel to one side of a triangle and intersects the other two sides, then it divides those two sides in the same ratio.

Q2. If DE ∥ BC in ΔABC, AD = 4 cm, DB = 6 cm, AE = 5 cm, find EC. (Medium)

Answer:
By BPT: AD/DB = AE/EC
4/6 = 5/EC
EC = 7.5 cm.

Q3. Prove that areas of similar triangles are proportional to the square of corresponding sides. (Medium)

Answer:
For similar triangles, corresponding sides are proportional.
Area depends on base × height.
Thus, ratio of areas = square of ratio of corresponding sides.

Q4. Two similar triangles have areas 49 cm² and 81 cm². Find ratio of sides. (HOTS)

Answer:
Ratio of sides = √(49/81) = 7:9.

7. Coordinate Geometry

Q1. Find distance between (3, 4) and (0, 0). (Easy)

Answer:
Distance = √(3² + 4²) = √25 = 5 units.

Q2. Find the midpoint of (2, 6) and (8, 4). (Easy)

Answer:
Midpoint = ((2+8)/2, (6+4)/2) = (5, 5).

Q3. Find an area of a triangle with vertices (0,0), (4,0), (0,3). (Medium)

Answer:
Area = 1/2 × base × height
= 1/2 × 4 × 3 = 6 sq units.

Q4. Find coordinates dividing (2,3) and (8,9) in ratio 1:2. (HOTS)

Answer:
Using section formula:
x = (1×8 + 2×2)/3 = 4
y = (1×9 + 2×3)/3 = 5
Point = (4,5).

8. Introduction to Trigonometry

Q1. Find sin 45°. (Easy)

Answer:
sin 45° = 1/√2.

Q2. If tan θ = 1, find θ. (Easy)

Answer:
tan θ = 1 ⇒ θ = 45°.

Q3. Prove: sin²θ + cos²θ = 1. (Medium)

Answer:
From Pythagoras theorem in unit circle triangle,
op² + adj² = hyp².
Dividing by hyp² gives identity.

Q4. If sin θ = 12/13, find cos θ and tan θ. (HOTS)

Answer:
os θ = 5/13, tan θ = 12/5.

9. Some Applications of Trigonometry

Q1. Angle of elevation definition. (Easy)

Answer:
Angle between line of sight and horizontal when the object is above the observer.

Q2. A tower casts a 20 m shadow at 45°. Find height. (Medium)

Answer:
tan 45° = height/20
1 = h/20 ⇒ h = 20 m.

Q3. A kite string makes 60° angle, length 40 m. Find height. (Medium)

Answer:
height = 40 sin 60° = 40 × √3/2 = 20√3 m.

Q4. From the top of a 50 m tall tower, the angles of depression of two cars on the same straight road are 30° and 60°. If both cars are on the same side of the tower, find the distance between the two cars. (HOTS)

Answer:
Let the height of the tower be 50 m.
Let the distance of the nearer car (60° angle) from the base be x and the farther car (30° angle) be y.

For 60° angle:
tan 60° = 50 / x
√3 = 50 / x
x = 50 / √3

For 30° angle:
tan 30° = 50 / y
1/√3 = 50 / y
y = 50√3

Distance between cars = y - x
= 50√3 - 50/√3
= 50( (3 - 1) / √3 )
= 100 / √3
= 57.7 m

Final Answer:
100 / √3 m = 57.7 m

10. Circles

Q1. State tangent theorem. (Easy)

Answer:
The tangent to a circle at any point is perpendicular to the radius drawn to the point of contact.
So, if a line PT is tangent at point P and OP is radius, then OP ⟂ PT, meaning the angle between them is 90°.

Q2. Prove tangents from an external point are equal. (Medium)

Answer:
Let P be an external point and PA, PB be tangents drawn to a circle with center O.
Join OA, OB and OP.
In triangles OAP and OBP:
OA = OB (radii of same circle)
OP = OP (common side)
∠OAP = ∠OBP = 90° (radius ⟂ tangent)
So both triangles are congruent by RHS criterion.
Therefore, PA = PB, hence tangents from an external point are equal.

Q3. If OP is radius and PT is tangent, find angle OTP. (Medium)

Answer:
Radius OP is perpendicular to tangent PT at point P.
So angle OPT = 90°.
Since OTP is angle formed at point T between OT and TP, we consider triangle OPT where OP ⟂ PT.
Thus, angle at P is 90° and OTP depends on configuration but the key result is that OP ⟂ PT, so the angle involving radius and tangent at point of contact is 90°.

Q4. If two tangents from a point are 8 cm each, find property used. (HOTS)

Answer:
From a common external point, the lengths of tangents drawn to a circle are equal.
So if two tangents from the same point are 8 cm each, it confirms this property.
Hence both tangents are equal in length, meaning PA = PB = 8 cm.

11. Areas Related to Circles

Q1. Formula for area of circle. (Easy)

Answer:
πr²

Q2. Find area of semicircle of radius 7 cm. (Medium)

Answer:
(1/2)πr² = (1/2) × 22/7 × 49 = 77 cm².

Q3. Find circumference of circle radius 14 cm. (Medium)

Answer:
2πr = 2 × 22/7 × 14 = 88 cm.

Q4. Find the area of the ring with radii 10 cm and 5 cm. (HOTS)

Answer:
π(10² − 5²) = π(100 − 25) = 75π cm².

12. Surface Areas and Volumes

Q1. Volume of cube formula. (Easy)

Answer:
a³

Q2. Find TSA of cube side 4 cm. (Medium)

Answer:
6a² = 6 × 16 = 96 cm².

Q3. Volume of cylinder radius 7 cm, height 10 cm. (Medium)

Answer:
πr²h = 22/7 × 49 × 10 = 1540 cm³.

Q4. HOTS: Find radius of sphere with volume 36π cm³. (HOTS)

Answer:
(4/3)πr³ = 36π
r³ = 27 ⇒ r = 3 cm.

13. Statistics

Q1. Mean formula. (Easy)

Answer:
Sum of observations ÷ number of observations.

Q2. Find mean of 2, 4, 6, 8. (Easy) 

Answer:
(20 ÷ 4) = 5.

Q3. Find the median of 3, 5, 7, 9, 11. (Medium)

Answer:
Middle value = 7.

Q4. HOTS: Why is the mean affected by extreme values? (HOTS)

Answer:
Because it uses all values, so outliers change total significantly.

14. Probability

Q1. Formula of probability. (Easy)

Answer:
P(E) = favourable outcomes / total outcomes.

Q2. Probability of getting head in coin toss. (Easy)

Answer:
1/2

Q3. Probability of getting an even number on dice. (Medium)

Answer:
3/6 = 1/2

Q4. HOTS: Probability of getting prime number on dice. (HOTS)

Answer:
Primes = 2,3,5 = 3/6 = ½

Chapter-wise Marks Weightage Analysis - Class 10 Maths 2026-27

This section explains how marks are distributed across different units in Class 10 Maths 2026-27. This weightage helps students prioritise high-scoring chapters and plan their preparation effectively.

Unit-wise Marks Distribution

The CBSE Class 10 Maths paper is divided into major units based on concepts and difficulty levels. Each unit carries a fixed weightage that reflects its importance in the final board exam.

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List of Important Chapters Based on Frequency - Maths Class 10 

Here is a list of important chapters based on their weightage and chances of coming in Class 10 Maths exam.  

• Real Numbers: Almost comes every year with 1-2 questions. It mainly covers Euclid’s algorithm, irrationality proofs, and decimal expansion.
• Polynomials: Very frequent with at least 1-2 questions. Zeroes, relationship between coefficients and factor theorem.
• Quadratic Equations: High occurrence every year with 1 long answer & 1 MCQ/case-based question.
• Arithmetic Progressions (AP): Very consistent with case-based or application-based questions in most papers. Often linked to real-life patterns.
• Triangles: One of the most important Geometry chapters. Appears every year with a theorem or proof-based question.
• Circles: Frequent appearance with 1 proof or theorem-based question almost every year.
• Trigonometry (Intro & Heights & Distances): Very high frequency. At least 1-2 questions appear every year often in application format.
• Statistics & Probability: Very predictable. Comes in data-based and probability questions every year.
• Coordinate Geometry: Moderate but consistent presence of distance, midpoint, area-based questions. 

Expected Question Types for 2026-27

These are the kind of questions one can expect in Class 10 board exam 2026-27:

• Case-Based Questions (CBQs):
  
  • AP (real-life patterns, savings, seating arrangements)
  • Statistics (data tables and interpretation)
  • Trigonometry (height & distance real-world scenarios)
• Long Answer Questions (5 marks):
  
  • Quadratic Equations (word problems)
  • Triangles (similarity proofs)
  • Surface Areas & Volumes (combined solids)
• Short Answer Questions (2-3 marks):
  
  • Polynomials (zeroes, verification)
  • Coordinate Geometry (distance, midpoint)
  • Circles (tangent properties)
• MCQs (1 mark):
  
  • Real Numbers, Probability, Trigonometric identities

Here is the final scoring strategy for Class 10 Maths exam 2026-27: 

• Prioritise Algebra, Geometry and Trigonometry as they together carry 60-65% exam weightage. 
• Don’t ignore Statistics, Probability and Real Numbers, as they fetch marks easily with less efforts
• Focus more on application and case-based questions, as with the shift in exam pattern, there  is a shift towards competency and concept clarity. 

How to Score High in Class 10 Maths Using Important Questions

To score good marks in Class 10 CBSE Board exams, it is necessary to know how to put the important questions to use. Here is a step-by-step approach. 

Step 1: Complete NCERT First - NCERT sets the foundation for Class 10 so it is important to complete the chapter understanding from it, thoroughly. 

Step 2: Prioritise High-weightage Chapters - Chapters carrying the highest marks (Algebra, Geometry  and Trigonometry) in the exam should be practiced first. 

Step 3: Practice Different Question Types - To get familiar with the exam pattern format, solve different types of questions for complete preparation. 

Step 4: Learn from Mistakes - Answers having mistakes should be  marked so that one can come back to these questions for revision and understand what mistakes to avoid.  

Important Tips for Answer Writing: CBSE Class 10 Maths 

Some of the tips to write structured answers for CBSE Class 10 Maths board exam are given here. These tips can lead to improved scores, as the answers are written clearly. 

• Always show full working steps in every solution 
• Practice diagrams whenever required, especially for Geometry
• Write answers in a structured format - Given - To Find - Solution - Final Answer

• Focus more on NCERT examples and solved problems

Why Solving Class 10 Maths Important Questions Helps

These are some reasons so as to why solving class 10 Maths Important Questions actually helps for exam preparation.

• Better problem-solving speed - Regular practice through important questions helps solve problems faster with more accuracy. 
• Exam pattern familiarity - Important questions cover topics frequently asked in the CBSE Class 10 board examination. So, by practicing them, students will get comfortable with the style of questions asked in the exam and get familiar with the exam pattern.
• Improved time management - Important questions are challenging and solving them in time makes one comfortable with solving the easy ones. This leads to better time management.  
• Confidence before the board exam - Solving  important questions builds confidence and reduces the stress of exam difficulty level. 

FAQs

Q1. What types of questions are asked in Class 10 Maths 2026-27?

Ans. Class 10 Maths 2026-27 includes MCQs, short answer questions, long answer questions, case-based questions and competency-based HOTS questions. The paper focuses more on application-based and stepwise problem-solving rather than direct formula-based questions.

Q2. Which chapters carry the highest marks in Class 10 Maths?

Ans. Algebra, Geometry and Trigonometry carry the highest weightage in the Class 10 Maths paper. Chapters like Quadratic Equations, Triangles, Circles and Trigonometry are frequently repeated in board exams.

Q3. Is NCERT enough for Class 10 Maths or should I solve extra questions?

Ans. NCERT is absolutely essential and forms the base of the entire board exam. However, solving important questions and previous year papers is necessary to handle different question variations and improve speed.

Q4. How many important questions should I practise per chapter?

Ans. You should practise at least 10-15 important questions per high-weightage chapter and 5-8 questions for lower-weightage chapters. This ensures balanced coverage of MCQs, short answers and HOTS.

Q5. What are HOTS questions in Class 10 Maths?

Ans. HOTS (Higher Order Thinking Skills) questions require multi-step reasoning and application of concepts rather than direct formulas. These questions test logical thinking, especially in Algebra, Geometry and Trigonometry.

Q6. How do I improve my speed in the Class 10 Maths exam?

Ans. Speed improves through timed practice of mixed question sets daily. Solving at least one full-length section under a 45-60 minute timer helps reduce calculation time and improves accuracy.

Q7. Are case-based questions included in Class 10 Maths 2026-27?

Ans. Yes, case-based questions are an important part of the latest CBSE pattern. They usually appear in Statistics, Arithmetic Progressions and Trigonometry-based real-life applications.

Q8. How can I download the Class 10 Maths important questions PDF for 2027?

Ans. You can download the Class 10 Maths Important Questions PDF from educational study portals that provide chapter-wise practice sets. These PDFs are usually free and do not require login access.

Q9. Will geometry questions be asked in Class 10 board exam 2027?

Ans. Yes, Geometry is one of the most important units and regularly appears in board exams. Questions from Triangles, Circles and constructions are expected every year with both proof-based and application-based formats.

Q10. What is the best time to start solving important questions for boards?

Ans. You should start solving important questions immediately after completing each chapter from NCERT. Early practice helps in better revision cycles and reduces last-minute exam stress.