CBSE Class 10 Maths — 30 Most Expected Questions Board Exam 2027
30 most expected questions for CBSE Class 10 Maths board exam 2027. Based on SQP analysis, PYQ trends (2024-2026), and chapter-wise weightage. Algebra, Geometry, Trigonometry, Mensuration, Statistics — question type, marks, and where to practice each.
In short: These 30 questions cover 75+ marks out of the 80-mark CBSE Class 10 Maths Standard paper. They are not random guesses — each one is derived from the official 2027 SQP pattern, previous year paper trends (2024-2026), and the CBSE unit-wise marks allocation. For each question: what it asks, which chapter it comes from, expected marks, and the section it will likely appear in. Print this list. Practice every question. Walk into the exam hall knowing you have already seen 80% of the paper. Also see our Science expected questions for Class 10.
How This List Was Built
Source
What We Analysed
CBSE Official SQP 2027
Released Sep 21, 2026. 38 questions across 5 sections. Same pattern as 2025-26.
Previous Year Papers (2024-2026)
3 years of actual board papers. Identified questions repeated across years.
CBSE Unit-Wise Weightage
Algebra: 20 marks, Geometry: 15, Trigonometry: 12, Mensuration: 10, Statistics & Probability: 11, Number Systems: 6, Coordinate Geometry: 6. See the full chapter-wise weightage breakdown.
Polynomials, Linear Equations, Quadratic Equations, AP
20
#3-10
Coordinate Geometry
Coordinate Geometry
6
#11-13
Geometry
Triangles, Circles
15
#14-18
Trigonometry
Intro to Trigonometry, Applications
12
#19-22
Mensuration
Areas Related to Circles, Surface Areas and Volumes
10
#23-26
Statistics and Probability
Statistics, Probability
11
#27-30
Total
14 chapters
80
30 questions
Number Systems — Real Numbers (6 Marks)
#
Expected Question
Type
Marks
Section
1
Find the HCF and LCM of two or three numbers using prime factorisation. Verify that HCF × LCM = product of the two numbers.
VSA / SA
2-3
B / C
2
Prove that √2, √3, or √5 is irrational. (Asked every single year from 2024-2026.)
SA
3
C
What the examiner wants
Q1: Step-by-step prime factorisation shown clearly. HCF = product of lowest powers. LCM = product of highest powers. Verification step mandatory for full marks.
Q2: Start by assuming the number is rational (p/q form, coprime). Arrive at a contradiction. Conclude it is irrational. Each logical step = 1 mark.
PYQ track record
Year
Q1 (HCF/LCM) appeared?
Q2 (Irrationality proof) appeared?
2024
Yes (3 marks)
Yes (3 marks)
2025
Yes (2 marks)
Yes (3 marks)
2026
Yes (2 marks)
Yes (3 marks)
2027 SQP
Yes
Yes
Verdict: Both questions are virtually guaranteed. Practice until you can write them in under 4 minutes each.
Algebra — Polynomials (4 Marks)
#
Expected Question
Type
Marks
Section
3
Find the zeroes of a quadratic polynomial (e.g., x² - 3x - 10) and verify the relationship between zeroes and coefficients (sum = -b/a, product = c/a).
SA
3
C
4
If α and β are zeroes of a polynomial, find the value of an expression involving α and β (e.g., α² + β², 1/α + 1/β).
MCQ
1
A
What the examiner wants
Q3: Factorise → find zeroes → verify sum = -b/a and product = c/a. All three steps needed. Missing verification = lose 1 mark.
Q4: Use identities: α² + β² = (α+β)² - 2αβ. Pure formula application.
Algebra — Pair of Linear Equations (5 Marks)
#
Expected Question
Type
Marks
Section
5
Solve a pair of linear equations using substitution or elimination method. (Often given as a word problem — age, speed-distance, or fraction problem.)
SA / LA
3-5
C / D
6
Determine whether a pair of linear equations is consistent, inconsistent, or has infinitely many solutions using the ratio test (a₁/a₂, b₁/b₂, c₁/c₂).
MCQ / VSA
1-2
A / B
What the examiner wants
Q5: Word problems require you to SET UP the equations first (1-2 marks for forming equations correctly), then SOLVE them (2-3 marks). Even if your answer is wrong, correct equation formation scores marks.
Q6: Compare ratios. If a₁/a₂ ≠ b₁/b₂ → unique solution (consistent). If a₁/a₂ = b₁/b₂ = c₁/c₂ → infinite solutions. If a₁/a₂ = b₁/b₂ ≠ c₁/c₂ → no solution (inconsistent).
Algebra — Quadratic Equations (6 Marks)
#
Expected Question
Type
Marks
Section
7
Solve a quadratic equation using the quadratic formula. Determine the nature of roots using the discriminant (D = b² - 4ac).
LA
5
D
8
Word problem on quadratic equations — typically involves: area of a rectangle, product of consecutive numbers, speed of a train/boat, or age problem.
LA
5
D
What the examiner wants
Q7: Write the quadratic formula. Substitute values. Calculate discriminant. State nature of roots. Find both roots. 5 clear steps = 5 marks.
Q8: Form the quadratic equation from the word problem (2 marks). Solve it (2 marks). Reject the invalid root with reasoning (1 mark). The "reject negative root" step is often forgotten — it costs 1 mark.
PYQ pattern
Quadratic word problems have appeared in EVERY board paper from 2024-2026 as a 5-mark question in Section D. The themes rotate between:
Area of a rectangle given perimeter and area relationship
Two consecutive numbers whose product is given
Speed-time-distance problem (upstream/downstream boat, or two trains)
Algebra — Arithmetic Progressions (6 Marks)
#
Expected Question
Type
Marks
Section
9
Find the nth term or the sum of first n terms of an AP. Given 2-3 conditions (like a₃ = 12, a₇ = 24, find S₂₀).
SA / Case-Based
3-4
C / E
10
Determine how many terms of an AP are needed for the sum to reach a given value. OR find whether a given number is a term of the AP.
MCQ / VSA
1-2
A / B
Key formulas to memorize cold
Formula
Expression
When to use
nth term
aₙ = a + (n-1)d
Find any specific term
Sum of n terms
Sₙ = n/2 [2a + (n-1)d]
When first term and CD are known
Sum (alt)
Sₙ = n/2 [a + l]
When first and last term are known
Middle term
If n is odd, middle term = a₍ₙ₊₁₎/₂
Finding the median of AP
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Find the distance between two points using the distance formula. Show that given points form a specific shape (right triangle, isosceles triangle, parallelogram).
VSA / SA
2-3
B / C
12
Find the coordinates of a point dividing a line segment in a given ratio using the section formula.
VSA
2
B
13
Find the area of a triangle given the coordinates of its three vertices. OR show that three points are collinear.
SA / Case-Based
3-4
C / E
What the examiner wants
Q11: Apply formula correctly. If the question says "show it is a right triangle" — calculate all 3 sides, then verify Pythagoras theorem. Do NOT just calculate 2 sides.
Q13: For collinearity, show that the area of the triangle = 0. Use the determinant formula: Area = ½|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)|.
Case study pattern
Coordinate geometry appears in Section E almost every year. Typical scenario: a park, garden, or town plan with landmarks at given coordinates. Sub-questions ask for distance, midpoint, section formula, and area.
Geometry — Triangles (8 Marks)
#
Expected Question
Type
Marks
Section
14
Prove the Basic Proportionality Theorem (Thales Theorem): If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.
LA
5
D
15
Application of BPT or similarity — find the length of a side using proportionality in similar triangles.
SA / MCQ
2-3
B / C
16
Prove that the ratio of areas of two similar triangles equals the square of the ratio of their corresponding sides.
SA
3
C
PYQ track record for BPT
Year
BPT proof appeared?
Marks
2024
Yes
5
2025
Yes
5
2026
Yes (with application)
5
2027 SQP
Yes
5
This is the most predictable 5-mark question in the entire paper. Memorize the proof with the diagram. Practice it until you can write it in 8 minutes flat.
Geometry — Circles (7 Marks)
#
Expected Question
Type
Marks
Section
17
Prove that the tangent at any point of a circle is perpendicular to the radius at the point of contact.
LA / SA
3-5
C / D
18
From an external point, two tangents are drawn to a circle. Prove that they are equal in length. Then find the angle between them or the length of a tangent given specific measurements.
SA / LA
3-5
C / D
What the examiner wants
Q17: Draw the diagram FIRST (1 mark for diagram in the marking scheme). Use proof by contradiction or Pythagoras. Step-by-step logical flow.
Q18: Prove PA = PB using congruent triangles (RHS congruence). Then apply the specific numerical part. Diagram is worth 1 mark.
Trigonometry — Introduction (8 Marks)
#
Expected Question
Type
Marks
Section
19
Prove a trigonometric identity. Common forms: (sinA + cosA)² + (sinA - cosA)² = 2, or (1 + tan²A)/(1 + cot²A) = tan²A, or expressions involving sec and cosec.
SA
3
C
20
Evaluate a trigonometric expression using standard angle values (0°, 30°, 45°, 60°, 90°). Example: (sin60° × cos30° + sin30° × cos60°).
MCQ / VSA
1-2
A / B
21
If sinA = 3/5, find cosA, tanA, and all other ratios. OR given one ratio, find an expression involving multiple ratios.
VSA / MCQ
1-2
A / B
Identity proof strategy
Take the more complex side (LHS usually).
Convert everything to sinθ and cosθ.
Simplify step by step until you reach the other side.
Never work on both sides simultaneously — always simplify one side to match the other.
Trigonometry — Applications: Heights and Distances (4 Marks)
#
Expected Question
Type
Marks
Section
22
A word problem involving angle of elevation or depression. Typical: height of a tower/building/cliff, distance of a boat/car from the base, shadow length problem.
LA / Case-Based
4-5
D / E
What the examiner wants
DRAW THE DIAGRAM (1 mark). Label everything: height, distance, angles.
Set up the trigonometric equation using tan (for height/distance), sin, or cos as needed.
Solve step by step. Leave the answer in surd form if required (do not force decimals unless asked).
Common values you must know: tan30° = 1/√3, tan45° = 1, tan60° = √3.
Case study pattern
Heights and distances problems appear in Section E almost every year. Typical scenario: two people observing the same tower from different points, or a lighthouse and a boat.
Mensuration — Areas Related to Circles (4 Marks)
#
Expected Question
Type
Marks
Section
23
Find the area of a shaded region involving combinations of circles, semicircles, and quadrants inscribed in or circumscribing squares/rectangles.
SA
3
C
24
Find the area of a sector or segment of a circle given the radius and angle.
MCQ / VSA
1-2
A / B
Key formulas
Formula
Expression
Area of circle
πr²
Circumference
2πr
Area of sector
(θ/360) × πr²
Length of arc
(θ/360) × 2πr
Area of segment
Area of sector - Area of triangle
Mensuration — Surface Areas and Volumes (6 Marks)
#
Expected Question
Type
Marks
Section
25
Combined solid problem: A solid is formed by combining two shapes (cone + cylinder, hemisphere + cylinder, cone + hemisphere). Find the total surface area or volume.
LA
5
D
26
Conversion problem: A solid is melted and recast into another shape. Find the number of new objects or dimensions of the new shape.
SA / LA
3-5
C / D
What the examiner wants
Q25: Draw or label the combined solid. Calculate each part's contribution separately. Add them correctly. Common mistake: including the flat circular face that joins the two solids in "total surface area" — that face is NOT exposed and should NOT be included.
Q26: Set up: Volume of original = n × Volume of each new object. Solve for n or the unknown dimension.
PYQ pattern
Combined solid and melting/recasting problems have appeared in Section D in every year from 2024-2026. Practice at least 10 problems of each type.
Statistics (8 Marks)
#
Expected Question
Type
Marks
Section
27
Find the mean of grouped data using the step-deviation method or assumed mean method.
LA
5
D
28
Find the median of grouped data from a cumulative frequency table. OR draw an ogive and find the median graphically.
SA / LA
3-5
C / D
29
Find the mode of grouped data using the mode formula.
MCQ / VSA
1-2
A / B
Key formulas
Measure
Formula
Mean (Direct)
x̄ = Σfᵢxᵢ / Σfᵢ
Mean (Assumed)
x̄ = a + (Σfᵢdᵢ / Σfᵢ)
Mean (Step-deviation)
x̄ = a + (Σfᵢuᵢ / Σfᵢ) × h
Median
M = l + [(n/2 - cf) / f] × h
Mode
Mo = l + [(f₁ - f₀) / (2f₁ - f₀ - f₂)] × h
What the examiner wants
Q27: The step-deviation method is preferred by CBSE (shown in SQP). Show the full table: class intervals, frequencies, class marks, deviations, uᵢ, fᵢuᵢ. The TABLE itself carries 2 marks out of 5.
Q28: Write the cumulative frequency column. Identify the median class. Apply the formula. Each step = 1 mark.
Probability (3 Marks)
#
Expected Question
Type
Marks
Section
30
A probability problem involving cards, dice, or a real-life scenario. Example: "A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (i) a red king, (ii) a face card, (iii) a card which is neither a jack nor a king."
VSA / SA
2-3
B / C
Standard probability values to memorize
Scenario
Total Outcomes
One die
6
Two dice
36
One card from deck
52
Face cards in deck
12 (4J + 4Q + 4K)
Red cards
26
Black cards
26
Aces
4
30-Day Practice Plan Using This List
Week
Focus
Questions from This List
Week 1
Algebra + Number Systems
#1-10 (practice each question type 3 times)
Week 2
Geometry + Coordinate Geometry
#11-18 (focus on proofs — BPT, tangent theorem)
Week 3
Trigonometry + Mensuration
#19-26 (identity proofs + combined solids)
Week 4
Statistics + Probability + Full Papers
#27-30 + solve 3 full mock papers under timed conditions
Section-Wise Time Strategy on Exam Day
Section
Questions
Marks
Time
Strategy
A (MCQ + A-R)
20
20
30 min
Quick and confident. Skip tough MCQs, come back later.
B (VSA)
5
10
15 min
Direct formulas. Show working for 2 marks per question.
E (Case-Based)
3
12
20 min
Do BEFORE Section D. Easier marks per minute. Read the case fully first.
C (SA)
6
18
30 min
Medium difficulty. Step-wise working essential.
D (LA)
4
20
40 min
Hardest. BPT proof, quadratic word problem, statistics, combined solid.
Review
—
—
15 min
Re-check MCQs, verify calculations in D.
Key insight: Do Section E before Section D. Case-based questions are typically easier than long answers but carry similar marks. Secure those 12 marks early.
Frequently Asked Questions
Q1. Are these 30 questions enough for the full 80-mark paper?
These 30 questions cover every question TYPE that will appear. The actual paper has 38 questions — but many MCQs are variations of the same concepts. If you can solve all 30 question types confidently, you are prepared for 75+ marks.
Q2. How were these questions selected?
From three sources: the official CBSE SQP 2027 (released Sep 21), previous year board papers (2024-2026), and the CBSE unit-wise marks allocation. Questions that appeared in 2+ years AND appear in the SQP pattern are included.
Q3. Should I practice Maths Standard or Maths Basic questions?
If you are appearing for Maths Standard, practice Standard-level questions. Basic questions are simpler and will not prepare you for the harder Section D questions. This list is designed for Maths Standard.
Q4. What if a question comes that is not on this list?
Unlikely — but possible for 5-8 marks worth of MCQs that test minor concepts. The 30 questions here cover the high-weightage, high-probability topics. The remaining marks come from straightforward MCQs that test basic formula application.
Q5. Is NCERT enough or do I need extra books?
NCERT textbook + NCERT Exemplar + this expected questions list is sufficient for 75+ marks. If you want 90+, add 3-4 previous year papers and the official SQP. Also keep our all formulas cheat sheet for Maths, Science, and SST handy during revision.
Q6. How much time should I spend on this list?
Follow the 30-day plan above. If you have less time, focus on the starred high-priority sections: Algebra (#3-10), Geometry proofs (#14, #17-18), Statistics (#27-28), and Combined Solids (#25). For exam day, make sure your time management strategy for the 3-hour paper is locked in. And before you sit down to write, review our guide on how to write answers for maximum marks — presentation alone can add 10-15 marks.
