Important Questions for Class 10 Maths – Chapter-Wise Guide with Formulas
CBSE Class 10 Maths Important Questions, Concepts & Formula Tables | MyClass24
Class 10 Maths is one of the most scoring subjects in the CBSE board exam, provided students practice the right set of questions from every chapter. This page brings together important questions for Class 10 Maths chapter-wise, along with the key concepts and formulas that are frequently tested in board exams and school assessments. Whether you are revising Real Numbers, Trigonometry, or Statistics, working through these curated important questions for Class 10 Maths will help you recognise question patterns, strengthen your basics, and manage exam time better. Each important question of the chapter below includes a short concept recap, a few important questions to attempt on your own, and an easy-to-scan formula table you can revise anytime, even on your phone, right before an exam. Use this guide alongside your NCERT textbook to build genuine problem-solving speed rather than rote memorisation.
1. Real Numbers
Euclid's division lemma, finding HCF and LCM using prime factorisation, and proving the irrationality of numbers are the most important questions for Class 10 Maths from this chapter.
Important Questions to Practice:
Prove that √5 is an irrational number.
Find the HCF and LCM of 96 and 404 using the prime factorisation method.
Show that any positive odd integer is of the form 6q + 1, 6q + 3, or 6q + 5.
Key Formulas – Real Numbers
Concept | Formula |
Euclid's Division Lemma | a = bq + r, where 0 ≤ r < b |
Relation between HCF and LCM | HCF(a, b) × LCM(a, b) = a × b |
Fundamental Theorem of Arithmetic | Every composite number can be expressed as a product of primes in a unique way |
2. Polynomials
The relationship between zeroes and coefficients, along with the division algorithm for polynomials, forms the core of important questions for Class 10 Maths in this chapter.
Important Questions to Practice:
Find the zeroes of 2x² − 5x − 3 and verify the relationship between the zeroes and coefficients.
If α and β are the zeroes of x² − 5x + 6, find the value of α² + β².
Divide the polynomial p(x) by g(x) and verify the division algorithm.
Key Formulas – Polynomials
Concept | Formula |
Quadratic polynomial ax² + bx + c | Sum of zeroes = −b/a; Product of zeroes = c/a |
Cubic polynomial ax³ + bx² + cx + d | Sum = −b/a; Sum of products (two at a time) = c/a; Product = −d/a |
Division Algorithm | p(x) = g(x) × q(x) + r(x) |
3. Pair of Linear Equations in Two Variables
Questions on checking consistency of a pair of equations, and solving them by substitution, elimination, or cross-multiplication, are common important questions for Class 10 Maths from this unit.
Important Questions to Practice:
Solve by elimination method: 2x + 3y = 11 and 2x − 4y = −24.
Find the value of k for which the system kx + 3y = k − 3, 12x + ky = k has no solution.
Solve a word problem based on ages, speed, or cost using a pair of linear equations.
Key Formulas – Pair of Linear Equations in Two Variables
Concept | Formula |
a1/a2 ≠ b1/b2 | Unique solution (lines intersect at one point) |
a1/a2 = b1/b2 ≠ c1/c2 | No solution (lines are parallel) |
a1/a2 = b1/b2 = c1/c2 | Infinitely many solutions (coincident lines) |
4. Quadratic Equations
Finding the nature of roots using the discriminant and solving word problems using the quadratic formula are high-weightage important questions for Class 10 Maths.
Important Questions to Practice:
Find the discriminant of 2x² − 4x + 3 = 0 and comment on the nature of its roots.
Solve x² − 3x − 10 = 0 by the method of factorisation.
A train travels a certain distance at a uniform speed; form and solve the quadratic equation based on the given conditions.
Key Formulas – Quadratic Equations
Concept | Formula |
Quadratic Formula | x = [−b ± √(b² − 4ac)] / 2a |
Discriminant | D = b² − 4ac |
Nature of Roots | D > 0: real & distinct; D = 0: real & equal; D < 0: no real roots |
5. Arithmetic Progressions
Calculating the nth term and the sum of n terms, along with real-life applications, make this chapter a regular source of important questions for Class 10 Maths.
Important Questions to Practice:
Find the 20th term of the AP 2, 7, 12, 17, ...
How many terms of the AP 9, 17, 25, ... must be taken to give a sum of 636?
Find the sum of the first 40 positive integers divisible by 6.
Key Formulas – Arithmetic Progressions
Concept | Formula |
nth term | an = a + (n − 1)d |
Sum of n terms | Sn = n/2 [2a + (n − 1)d] |
Sum of n terms (using last term) | Sn = n/2 (a + l) |
6. Triangles
Proof-based important questions for Class 10 Maths from this chapter usually cover the Basic Proportionality Theorem, similarity of triangles, and the Pythagoras theorem.
Important Questions to Practice:
State and prove the Basic Proportionality Theorem (Thales' Theorem).
Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Prove the Pythagoras theorem for a right-angled triangle.
Key Formulas – Triangles
Concept | Formula |
Basic Proportionality Theorem | If DE ∥ BC in △ABC, then AD/DB = AE/EC |
Pythagoras Theorem | (Hypotenuse)² = (Base)² + (Height)² |
Area ratio of similar triangles | = (ratio of corresponding sides)² |
7. Coordinate Geometry
The distance formula, section formula, and area of a triangle using coordinates are frequently asked as important questions for Class 10 Maths.
Important Questions to Practice:
Find the distance between the points (3, −5) and (−2, 7).
Find the point which divides the line segment joining (−1, 7) and (4, −3) in the ratio 2:3.
Find the area of the triangle whose vertices are (1, −1), (−4, 6), and (−3, −5).
Key Formulas – Coordinate Geometry
Concept | Formula |
Distance Formula | d = √[(x2 − x1)² + (y2 − y1)²] |
Section Formula | x = (m1x2 + m2x1)/(m1 + m2), y = (m1y2 + m2y1)/(m1 + m2) |
Area of Triangle | ½ |x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)| |
8. Introduction to Trigonometry
Trigonometric ratios, standard angle values, and identities are the building blocks for many important questions for Class 10 Maths in this chapter and the next.
Important Questions to Practice:
If sin A = 3/4, calculate cos A and tan A.
Prove that (1 + tan²A) = sec²A using the definitions of trigonometric ratios.
Evaluate sin 60° cos 30° + sin 30° cos 60°.
Key Formulas – Introduction to Trigonometry
Concept | Formula |
sin θ (0°,30°,45°,60°,90°) | 0, 1/2, 1/√2, √3/2, 1 |
cos θ (0°,30°,45°,60°,90°) | 1, √3/2, 1/√2, 1/2, 0 |
tan θ (0°,30°,45°,60°,90°) | 0, 1/√3, 1, √3, not defined |
Key Identities | sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ |
9. Some Applications of Trigonometry (Heights and Distances)
Word problems based on the angle of elevation and angle of depression are classic important questions for Class 10 Maths that combine trigonometry with real-life scenarios.
Important Questions to Practice:
A tower stands vertically on the ground. From a point 20 m away, the angle of elevation is 60°; find the height of the tower.
Two poles of equal height stand on either side of a road; find the height of the poles and the distances of the point from each pole.
From the top of a building, the angle of depression to a car on the road is 30°; find the distance of the car from the building.
Key Formulas – Some Applications of Trigonometry (Heights and Distances)
Concept | Formula |
Core relation used | tan θ = Opposite side / Adjacent side |
Angle of elevation | Angle formed above the horizontal line while looking up at an object |
Angle of depression | Angle formed below the horizontal line while looking down at an object (equal to the angle of elevation by alternate angles) |
10. Circles
Tangent properties and their proofs are the most commonly asked important questions for Class 10 Maths under this chapter.
Important Questions to Practice:
Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
Prove that the lengths of tangents drawn from an external point to a circle are equal.
Find the length of a tangent drawn from a point 25 cm away from the centre of a circle of radius 7 cm.
Key Formulas – Circles
Concept | Formula |
Tangent and radius | Tangent is perpendicular to the radius at the point of contact |
Length of tangent from an external point | √(d² − r²), where d is the distance from the centre |
Tangents from an external point | Equal in length |
11. Areas Related to Circles
Calculating the area of sectors, segments, and combinations of circles are standard important questions for Class 10 Maths from this chapter.
Important Questions to Practice:
Find the area of a sector of a circle with radius 21 cm and a central angle of 60°.
Find the area of a circular ring formed by two concentric circles of given radii.
A chord subtends an angle of 90° at the centre; find the area of the minor segment.
Key Formulas – Areas Related to Circles
Concept | Formula |
Circumference of a circle | 2πr |
Area of a circle | πr² |
Area of a sector | (θ/360) × πr² |
Area of a segment | Area of sector − Area of triangle |
12. Surface Areas and Volumes
Problems involving the combination of two or more solids, and conversion of one solid into another, are high-scoring important questions for Class 10 Maths.
Important Questions to Practice:
A cone is mounted on a hemisphere of the same radius; find the total surface area of the combined solid.
Find the volume of a frustum of a cone given its two radii and height.
A solid metallic cylinder is melted and recast into small spheres; find the number of spheres formed.
Key Formulas – Surface Areas and Volumes
Concept | Formula |
Cylinder | CSA = 2πrh; TSA = 2πr(r + h); Volume = πr²h |
Cone | CSA = πrl; TSA = πr(l + r); Volume = ⅓πr²h |
Sphere / Hemisphere | Sphere Volume = 4/3 πr³; Hemisphere Volume = 2/3 πr³ |
Frustum of a Cone | Volume = ⅓πh(r1² + r2² + r1r2) |
13. Statistics
Calculating the mean, median, and mode of grouped data using their respective formulas is a regular feature among important questions for Class 10 Maths.
Important Questions to Practice:
Find the mean of a grouped frequency distribution using the step-deviation method.
Find the median of a given grouped frequency distribution.
Find the mode of the data presented in a frequency distribution table.
Key Formulas – Statistics
Concept | Formula |
Mean (Direct Method) | Mean = Σfixi / Σfi |
Median | l + [(n/2 − cf) / f] × h |
Mode | l + [(f1 − f0) / (2f1 − f0 − f2)] × h |
14. Probability
Simple experiments involving coins, dice, and cards are the usual source of important questions for Class 10 Maths in this chapter.
Important Questions to Practice:
A bag contains 5 red, 8 white, and 4 green balls; find the probability of not drawing a red ball.
Two dice are thrown together; find the probability of getting a sum of 8.
A card is drawn from a well-shuffled deck of 52 cards; find the probability of getting a face card.
Key Formulas – Probability
Concept | Formula |
Probability of an event | P(E) = Number of favourable outcomes / Total number of outcomes |
Complementary event | P(E) + P(not E) = 1 |
Range of probability | 0 ≤ P(E) ≤ 1 |
Tips to Solve Important Questions for Class 10 Maths Effectively
Scoring well in Class 10 Maths is less about memorising answers and more about building a consistent problem-solving habit. Start by solving every NCERT example and exercise before moving to extra important questions, since board papers draw heavily from the textbook pattern. Keep the formula tables from each chapter handy and revise them daily for five minutes rather than cramming everything the night before an exam.
Attempt important questions chapter-wise first, then mix questions from different chapters to simulate the actual board exam.
Always write the formula before substituting values; this secures step-marking even if the final answer goes wrong.
Time yourself while solving a set of important questions to improve speed and accuracy under exam conditions.
Maintain a separate notebook of mistakes from important questions and revise it a week before the exam.
Practice previous years' board question papers and sample papers alongside these important questions for complete preparation.
Final Thoughts
Going through these important questions for Class 10 Maths, chapter by chapter, gives you a clear map of what to expect in your board exam and where your preparation needs more attention. Pair this practice with regular revision of the formula tables, and you will notice steady improvement in both speed and accuracy. Keep visiting MyClass24 for more chapter-wise important questions, formula sheets, and practice resources designed to help Class 10 Maths students prepare with confidence and score higher in their board exams.