CBSE Class 10 · Mathematics · board exam 2027 · pre-board season

CBSE Class 10 Maths important questions 2027, chapter-wise

140 original questions across all 14 chapters, in the five question types of the board paper, each with a step-marked worked answer. Below they are grouped by unit and ordered by the CBSE unit weightage, so you revise Algebra (20 marks) and Geometry (15 marks) first. Then sit a full sample paper written to the same blueprint.

140 questions, 14 chapters
Ordered by the 80-mark weightage
70 worked answers open; the rest with a free account

Start with the heaviest unit Sit a full sample paper Start the free 7-day trial

Important questions, not leaked questions

Nobody outside CBSE knows the 2027 paper. These questions are written by CBSE Math Revision, not taken from NCERT, NCERT Exemplar or CBSE papers, and every answer was re-solved independently. Our prediction is only the weighting: the units that carry the most marks come first. Always sit CBSE's own 2026-27 sample question paper too, linked from our Class 10 question papers page.

Chapter-wise important questions, by unit weightage

Units in order of their marks in the 80-mark theory paper (the other 20 marks are internal assessment). Across the 14 chapters: 28 1-mark MCQ, 14 assertion–reason, 28 2-mark short answer, 28 3-mark short answer, 28 5-mark long answer, 14 4-mark case study questions.

Algebra · 20 of 80 marks

Chapter 2: Polynomials 10 questions on Relationship between zeroes and coefficients; Zeroes of a polynomial; Forming a quadratic polynomial; Geometrical meaning of the zeroes.
Chapter 3: Pair of Linear Equations in Two Variables 10 questions on Consistency and number of solutions; Elimination method; Substitution method; Situational problems; Graphical method of solution.
Chapter 4: Quadratic Equations 10 questions on Standard form of a quadratic equation; Nature of roots; Solution by factorisation; Solution by quadratic formula; Situational problems.
Chapter 5: Arithmetic Progressions 10 questions on nth term of an AP; Sum of first n terms of an AP; Arithmetic progressions and common difference; Situational problems.

Geometry · 15 of 80 marks

Chapter 6: Triangles 10 questions on Basic Proportionality Theorem and its converse; Similar figures; Criteria for similarity of triangles; Applications of similarity.
Chapter 10: Circles 10 questions on Length of tangent; Tangents from an external point; Tangent perpendicular to radius.

Trigonometry · 12 of 80 marks

Chapter 8: Introduction to Trigonometry 10 questions on Trigonometric ratios; Ratios of specific angles; Trigonometric identities.
Chapter 9: Some Applications of Trigonometry 10 questions on Angle of elevation; Angle of depression; Two-triangle problems.

Statistics and Probability · 11 of 80 marks

Chapter 13: Statistics 10 questions on Median of grouped data; Mode of grouped data; Mean of grouped data.
Chapter 14: Probability 10 questions on Coins and dice; Playing cards; Classical probability.

Mensuration · 10 of 80 marks

Chapter 11: Areas Related to Circles 10 questions on Area of a sector; Length of an arc; Area of a segment.
Chapter 12: Surface Areas and Volumes 10 questions on Volume of combined solids; Surface area of combined solids.

Number Systems · 6 of 80 marks

Chapter 1: Real Numbers 10 questions on HCF and LCM by prime factorisation; Irrational numbers; Fundamental Theorem of Arithmetic; Applications of HCF and LCM.

Coordinate Geometry · 6 of 80 marks

Chapter 7: Coordinate Geometry 10 questions on Distance formula; Mid-point formula; Section formula; Applications to geometric shapes.

Try one from each unit

One short-answer question from each unit, with its worked answer. Try it first, then open the answer and check every step mark.

Ch 2·3 marks·Short answerPolynomials: Relationship between zeroes and coefficients

$α$ and $β$ are the zeroes of $2 x^{2} - 3 x - 6$ . Without finding the zeroes, find $\frac{1}{α} + \frac{1}{β}$ and $α^{2} β + α β^{2}$ .

Show worked answer

Answer:

- \frac{1}{2}

and

- \frac{9}{2}

$α + β = \frac{3}{2}$ and $α β = - 3$ A1
$\begin{aligned} \frac{1}{α} + \frac{1}{β} & = \frac{α + β}{α β} \\ = \frac{3 / 2}{- 3} \\ = - \frac{1}{2} \end{aligned}$ A1
$\begin{aligned} α^{2} β + α β^{2} & = α β (α + β) \\ = - 3 \times \frac{3}{2} \\ = - \frac{9}{2} \end{aligned}$ A1

Ch 6·3 marks·Short answerTriangles: Basic Proportionality Theorem and its converse

$D$ and $E$ are points on the sides $A B$ and $A C$ of $△ A B C$ with $A D = 2$ cm, $D B = 3$ cm, $A E = 3$ cm and $E C = 4.5$ cm. Show that $D E ∥ B C$ .

Triangle ABC with D on AB and E on AC, joined by the line DE. AD is marked 2 cm, DB 3 cm, AE 3 cm and EC 4.5 cm. — AD = 2 cm, DB = 3 cm, AE = 3 cm, EC = 4.5 cm

Show worked answer

Answer:

D E ∥ B C

$\frac{A D}{D B} = \frac{2}{3}$ and $\begin{aligned} \frac{A E}{E C} & = \frac{3}{4.5} \\ = \frac{2}{3} \end{aligned}$ M1
So $\frac{A D}{D B} = \frac{A E}{E C}$ A1
By the converse of the Basic Proportionality Theorem, $D E ∥ B C$ R1

Ch 8·3 marks·Short answerIntroduction to Trigonometry: Trigonometric identities

Prove that $\sec^{4} θ - \sec^{2} θ = \tan^{4} θ + \tan^{2} θ$ .

Show worked answer

Answer: Proved

LHS $= \sec^{2} θ (\sec^{2} θ - 1)$ M1
$= (1 + \tan^{2} θ) \tan^{2} θ$ , using $\sec^{2} θ - 1 = \tan^{2} θ$ A1
$= \tan^{2} θ + \tan^{4} θ =$ RHS A1

Ch 13·3 marks·Short answerStatistics: Median of grouped data

Find the median of the distribution: $0$ – $10$ : $5$ , $10$ – $20$ : $8$ , $20$ – $30$ : $12$ , $30$ – $40$ : $10$ , $40$ – $50$ : $5$ .

Show worked answer

Answer:

\frac{155}{6} \approx 25.83

$n = 40$ , $\frac{n}{2} = 20$ ; cumulative frequencies $5, 13, 25, 35, 40$ , so the median class is $20$ – $30$ M1
Median $= l + \frac{\frac{n}{2} - c f}{f} \times h = 20 + \frac{20 - 13}{12} \times 10$ A1
$= 20 + \frac{35}{6} = \frac{155}{6} \approx 25.83$ A1

Ch 11·3 marks·Short answerAreas Related to Circles: Area of a segment

A chord of a circle of radius $6$ cm subtends an angle of $60^{\circ}$ at the centre. Find the area of the minor segment, leaving $π$ and surds in your answer.

Show worked answer

Answer:

(6 π - 9 \sqrt{3}) {cm}^{2}

Area of the sector $= \frac{60}{360} \times π \times 36 = 6 π {cm}^{2}$ A1
The triangle formed by the chord and the radii is equilateral with side $6$ cm: area $= \frac{\sqrt{3}}{4} \times 36 = 9 \sqrt{3} {cm}^{2}$ M1
Minor segment $= (6 π - 9 \sqrt{3}) {cm}^{2}$ A1

Ch 1·3 marks·Short answerReal Numbers: Applications of HCF and LCM

Two tankers hold $850$ litres and $680$ litres of milk. Find the greatest capacity of a container that can measure out the milk of each tanker an exact number of times. How many times in all is the container filled?

Show worked answer

Answer:

170

litres;

9

times

$850 = 2 \times 5^{2} \times 17$ and $680 = 2^{3} \times 5 \times 17$ M1
Greatest capacity $=$ HCF $= 2 \times 5 \times 17 = 170$ litres A1
Number of fillings $\begin{aligned} = \frac{850}{170} + \frac{680}{170} & = 5 + 4 \\ = 9 \end{aligned}$ A1

Ch 7·3 marks·Short answerCoordinate Geometry: Applications to geometric shapes

Prove that the points $A (- 1, 0)$ , $B (3, 3)$ , $C (6, - 1)$ and $D (2, - 4)$ , taken in order, form a square.

Coordinate grid with A(−1, 0), B(3, 3), C(6, −1) and D(2, −4) plotted and joined in order. — A(−1, 0), B(3, 3), C(6, −1), D(2, −4)

Show worked answer

Answer:

A B C D

is a square

$A B = \sqrt{16 + 9} = 5$ , $B C = \sqrt{9 + 16} = 5$ , $C D = \sqrt{16 + 9} = 5$ , $D A = \sqrt{9 + 16} = 5$ M1
All four sides are equal A1
Diagonals: $A C = \sqrt{49 + 1} = \sqrt{50}$ and $B D = \sqrt{1 + 49} = \sqrt{50}$ are equal, so $A B C D$ is a square A1

Final 6 Weeks: your final prediction set

Dates confirmed when CBSE publishes

A free six-week plan counted back from your first paper, ending with a final set of timed papers. Each paper opens only once it is checked.

Start the free plan

Then sit a full paper

The honest "predicted paper". Our Class 10 sample papers follow the 2026-27 blueprint exactly: 80 marks, 38 questions, sections A to E, each unit at its weightage, with a 3-hour timer and a step-marking scheme.
Pre-boards coming up? The Class 10 pre-board revision plan sets the days out for you, and the free four-week pre-board plan counts back from the day your pre-boards start.
Section A drill. MCQ and case study questions and assertion–reason questions for every chapter.
No formula sheet in the exam. Learn them first from the Class 10 formula sheet (free PDF).

Questions

Are these the questions that will come in the CBSE Class 10 Maths board exam 2027?

No. Nobody outside CBSE knows the 2027 questions, and we do not claim to. These are original questions written by CBSE Math Revision in the board paper's question types. What we can do honestly is weight your revision: the board's unit weightage says where the 80 marks are, so the chapters here are ordered by it.

How were the important questions chosen?

Each chapter has 10 questions covering its main topics in the five question types of the board paper, from 1-mark MCQs and assertion–reason to 5-mark long answers and a 4-mark case study. On this page the chapters are grouped by unit and the units are ordered by their marks out of 80, heaviest first, so you know where to start.

Are they free?

Yes. 70 of the 140 worked answers are open on the chapter pages to everyone. The other 70 open with a free account (no card).

Is there a predicted paper for CBSE Class 10 Maths 2027?

Not a leaked or official one: any site that says it has the real paper is guessing. Our sample papers are the honest version: full 80-mark papers written to the 2026-27 blueprint, with each unit at its exact weightage, a 3-hour timer and a step-marking scheme.

When is the CBSE Class 10 Maths board exam in 2027?

CBSE has not published the 2027 date sheet yet. For reference, in 2026 Class 10 Mathematics was on Tuesday 17 February 2026 (main exam). Our exam dates page adds the 2027 date once CBSE publishes it.

How should I use them in pre-board season?

Start with the heaviest units, do a chapter's 10 questions in one sitting, mark them against the worked answers and redo what you dropped two days later. Then sit a full sample paper against the 3-hour timer. If your school's pre-boards are in December or January, the pre-board revision plan sets this out day by day.

Free account, no card: 5 more practice questions on every chapter with instant feedback, full worked answers on free questions, and marking schemes for our sample papers. Join free

Original questions and worked answers written by CBSE Math Revision; not taken from NCERT, NCERT Exemplar or CBSE papers. CBSE Math Revision is independent and not affiliated with CBSE or NCERT.