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Educart has designed Class 10 Maths important questions with solutions for the academic year 2026-27 through closely studying and monitoring previous years' question papers. This page includes topics like Arithmetic Progressions (AP), Quadratic Equations, Trigonometry and Applications, and so on. All answers are also explained clearly to help with preparation.
Below are a few questions that are very common as well as important and thus mentioned for further discussion.
CBSE Class 10 Maths Important Questions: Chapter-wise PDFs
CBSE differentiates Maths into two different categories: Mathematics Basics and Standard. Students can choose any one of the papers, as the only difference between the two papers is their difficulty level.
To make the study easier, the below links will help you find the chapter-wise PDF of all the important questions of mathematics. These questions are based on the newly designed CBSE Syllabus Class 10 Maths, but also have some influence from the common questions asked in previous years’ papers.
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
CBSE Class 10 Maths Exam Pattern: At a Glance
According to the updated CBSE exam pattern of the year 2026, the math paper consists of a total of 100 marks. The theory paper carries 80 marks, and the remaining marks can be gained through internal assessments. The table below will help you understand the exam pattern of mathematics.
Unit-Wise Weightage & Important Topics of Maths
CBSE has been allotting a unit-wise marking system for the last few years. Thus, it is important to understand the weightage system for better preparation for the upcoming CBSE Class 10 Maths Board examination 2026-27.
Understanding the important topics from each chapter is important to score a good mark in the examination. The following table allows you to go through all the important topics of the chapters in the CBSE Class 10 Maths textbook. After practicing chapter-wise important questions, test your preparation with full-length pattern papers using the CBSE Class 10 Sample Papers 2026-27.
Class 10 Maths Important Questions for 2026-27 With Solutions
Here are a few important Class 10 CBSE Maths questions with solutions for the 2026-27 academic year. This will help students understand the types of questions they may face in the exam. Also, understand how questions are answered in the Class 10 CBSE important questions with solutions PDFs above.
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 their 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 into 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, the ratio of areas = the square of the ratio of corresponding sides.
Q4. Two similar triangles have areas 49 cm² and 81 cm². Find the ratio of sides. (HOTS)
Answer:
Ratio of sides = √(49/81) = 7:9.
7. Coordinate Geometry
Q1. Find the 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 the 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 the coordinates dividing (2,3) and (8,9) in the ratio 1:2. (HOTS)
Answer:
Using the 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 the unit circle triangle,
op² + adj² = hyp².
Dividing by hyp² gives the 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 the line of sight and the horizontal when the object is above the observer.
Q2. A tower casts a 20 m shadow at 45°. Find the height. (Medium)
Answer:
tan 45° = height/20
1 = h/20 ⇒ h = 20 m.
Q3. A kite string makes a 60° angle, length 40 m. Find the 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 the 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 a 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 and PB be tangents drawn to a circle with center O.
Join OA, OB, and OP.
In triangles OAP and OBP:
OA = OB (radii of the 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 a radius and PT is a tangent, find angle OTP. (Medium)
Answer:
Radius OP is perpendicular to tangent PT at point P.
So angle OPT = 90°.
Since OTP is the angle formed at point T between OT and TP, we consider triangle OPT where OP ⟂ PT.
Thus, the angle at P is 90°, and OTP depends on the configuration, but the key result is that OP ⟂ PT, so the angle between the radius and the tangent at the point of contact is 90°.
Q4. If two tangents from a point are 8 cm each, find the 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 the area of a circle. (Easy)
Answer:
πr²
Q2. Find the area of a semicircle of radius 7 cm. (Medium)
Answer:
(1/2)πr² = (1/2) × 22/7 × 49 = 77 cm².
Q3. Find the circumference of a circle with a radius of 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 a cube formula. (Easy)
Answer:
a³
Q2. Find the TSA of a cube with side 4 cm. (Medium)
Answer:
6a² = 6 × 16 = 96 cm².
Q3. Volume of a cylinder with radius 7 cm and height 10 cm. (Medium)
Answer:
πr²h = 22/7 × 49 × 10 = 1540 cm³.
Q4. HOTS: Find the radius of a sphere with a volume of 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 the 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, outliers change the total significantly.
14. Probability
Q1. Formula of probability. (Easy)
Answer:
P(E) = favourable outcomes / total outcomes.
Q2. Probability of getting a head in a coin toss. (Easy)
Answer:
1/2
Q3. Probability of getting an even number on a die. (Medium)
Answer:
3/6 = 1/2
Q4. HOTS: Probability of getting a prime number on a die. (HOTS)
Answer:
Primes = 2,3,5 = 3/6 = ½
Which Books Should You Use to Practice Class 10 Maths Important Questions?
To get all the important and frequently asked questions for preparation for the CBSE Board exam of 2026-27, students can have a good question bank.
Students can go for the newly published Educart CBSE Class 10 Maths Question Banks (Question Banks and One-Shot Question Banks) to prepare themselves before the Board examination 2026-27. It features various benefits, such as:
- Updated as per CBSE syllabus: Educart’s question banks are updated as per the new CBSE syllabus. It helps students stay up-to-date with newly constructed questions, especially in subjects like math.
- Topic-wise Notes: The question banks are made, and explanations are covered based on different topic-wise notes. This helps students learn to solve problems step-by-step.
- Error Finding Test: These books have a dedicated section with a 30-minute Error Finding challenge after each chapter. It helps the students to test and correct themselves before going to a new chapter.
- Unit-test Worksheets: The Educarts question bank offers 1 hour of pull-out paper for each chapter.
- Objective Questions: Question banks for math offer various important assertion-reason and MCQ-based questions. Dealing with these objective questions helps to speed up and make smarter calculations in the exam hall.
- Subjective Questions: The question banks also provide questions such as Short Answers (SA), Long Answers (LA), and case-based questions. These types of questions carry high marks in the paper.
How to Practice CBSE Class 10 Maths Important Questions for Boards 2026-27
Preparation for subjects like Math requires a disciplined approach, because it has many formulas, chapters, and concepts. Covering all of them is necessary to get good marks on the paper. Below are some steps students should follow to effectively prepare for the examination:
- Follow NCERT: For the CBSE Class 10 Board Exam, the NCERT textbook plays the most important role. Thus, clearing all concepts is necessary.
- Prepare formula notes: Students need to keep a formula sheet for all the chapters. It makes remembering and revising easier.
- Use of Materials: Students can use different materials. Educart’s Class 10 Maths Exemplar, Educart’s Question Banks, and One Shot Question Banks are recommended for it.
- PYQs and Sample Papers: Especially in Maths, solving PYQs and sample papers helps you understand the marking pattern. Students should solve official CBSE sample papers and at least 5 years of PYQs.
- Simulate the exam conditions: Try solving the Sample papers and PYQs in one go, like the environment given in the exams. It helps you to understand time management and analyse mistakes.
Recommended Books For Class 10 Board Exams
You can also explore Educart CBSE Class 10 Books for all subjects to better prepare for the 2026-27 Board Exam.
Frequently Asked Questions
Q1. Which is the most important chapter in the CBSE Class 10 Maths?
Ans: The unit "Algebra" carries the highest weightage, but it doesn’t make other units less important. So, clearing every concept of each chapter is necessary.
Q2. How can I download important questions for the Class 10 Board exam?
Ans: You can go to www.educart.co and look for the Free Study Materials to download necessary materials, along with the CBSE 10 Maths Important Questions with Solutions chapter-wise PDF.
Q3. What is the difference between Mathematics Basics and Mathematics Standard?
Ans: In both papers, the syllabus and exam pattern are the same. The main difference is the difficulty level. Mathematics Standard can be chosen by students who are interested in opting for math after Class 10. Mathematics Basics is less difficult than the standard.
Q4. How can I download the other materials for the CBSE Class 10 Maths Board exam?
Ans: You can visit the official CBSE Academics website or download the DIKSHA app to get access to all types of materials for the preparation of the CBSE Class 10 Maths Board exam. For free additional materials, you can also visit www.educart.co.
Q5. What is the best time to use CBSE Class 10 maths important questions?
Ans: After completing each chapter, you can use the CBSE Class 10 Maths Important Questions: Chapter-wise PDFs. It will help you understand the types of questions that can arise in every chapter.
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