Central Board of Secondary Education
Practice Question Paper — not an official CBSE document
Subject Code 041 · Set 3 of 3
Practice questions aligned to NCERT topics used in CBSE classrooms. These are original exam-oriented questions for revision — not official CBSE board papers and not a guarantee of any exam question. Always match the textbook issued by your school and the latest PDFs on ncert.nic.in and cbseacademic.nic.in.
Objective type (MCQ and Assertion–Reason) · Q1–20 · 1 mark each · 20 marks
B. Circumference = 2πr
NoteCircumference = 2πr. The other options mix ideas from nearby topics or reverse the textbook fact.
D. Graph of a quadratic is a parabola
NoteGraph of a quadratic is a parabola. The other options mix ideas from nearby topics or reverse the textbook fact.
D. Every chapter ends with keywords or a summary that is useful for one-mark answers
NoteEvery chapter ends with keywords or a summary that is useful for one-mark answers. The other options mix ideas from nearby topics or reverse the textbook fact.
A. Write three points from Surface Areas and Volumes in your own words; that is enough for a short-answer start
NoteWrite three points from Surface Areas and Volumes in your own words; that is enough for a short-answer start. The other options mix ideas from nearby topics or reverse the textbook fact.
A. Consistent pair: unique or infinitely many solutions
NoteConsistent pair: unique or infinitely many solutions. The other options mix ideas from nearby topics or reverse the textbook fact.
A. Standard angles 0°, 30°, 45°, 60°, 90°
NoteStandard angles 0°, 30°, 45°, 60°, 90°. The other options mix ideas from nearby topics or reverse the textbook fact.
D. Read the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions
NoteRead the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions. The other options mix ideas from nearby topics or reverse the textbook fact.
A. If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures
NoteIf the chapter has a diagram, practise labelling it — many school tests ask for labelled figures. The other options mix ideas from nearby topics or reverse the textbook fact.
D. Mix MCQs with short answers so you remember both facts and explanations from Some Applications of Trigonometry
NoteMix MCQs with short answers so you remember both facts and explanations from Some Applications of Trigonometry. The other options mix ideas from nearby topics or reverse the textbook fact.
D. P(not E) = 1 − P(E)
NoteP(not E) = 1 − P(E). The other options mix ideas from nearby topics or reverse the textbook fact.
A. Arithmetic Progressions is an NCERT chapter taught in CBSE Class 10 Mathematics
NoteArithmetic Progressions is an NCERT chapter taught in CBSE Class 10 Mathematics. The other options mix ideas from nearby topics or reverse the textbook fact.
B. CBSE often tests a concept by asking a daily-life example from the same chapter
NoteCBSE often tests a concept by asking a daily-life example from the same chapter. The other options mix ideas from nearby topics or reverse the textbook fact.
D. √2, √3, √5 are irrational
Note√2, √3, √5 are irrational. The other options mix ideas from nearby topics or reverse the textbook fact.
A. Basic Proportionality Theorem (Thales) — statement and application
NoteBasic Proportionality Theorem (Thales) — statement and application. The other options mix ideas from nearby topics or reverse the textbook fact.
D. Length of arc = (θ/360)×2πr
NoteLength of arc = (θ/360)×2πr. The other options mix ideas from nearby topics or reverse the textbook fact.
A. Every chapter ends with keywords or a summary that is useful for one-mark answers
NoteEvery chapter ends with keywords or a summary that is useful for one-mark answers. The other options mix ideas from nearby topics or reverse the textbook fact.
B. Write three points from Coordinate Geometry in your own words; that is enough for a short-answer start
NoteWrite three points from Coordinate Geometry in your own words; that is enough for a short-answer start. The other options mix ideas from nearby topics or reverse the textbook fact.
C. CSA, TSA, volume of cone, sphere, cylinder, frustum if included
NoteCSA, TSA, volume of cone, sphere, cylinder, frustum if included. The other options mix ideas from nearby topics or reverse the textbook fact.
A. Both A and R are true, and R is the correct explanation of A.
NoteRead Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
A. Both A and R are true, and R is the correct explanation of A.
NoteRead Assertion and Reason separately first. Here both match the textbook idea, and R explains why A is taught in this chapter.
Very Short Answer · Q21–25 · 2 marks each · internal choice in 2 questions · 10 marks
1. If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
1. Mix MCQs with short answers so you remember both facts and explanations from Quadratic Equations.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
1. A right triangle model.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
OR
1. Probability is an NCERT chapter taught in CBSE Class 10 Mathematics.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
OR — marking points1. Use the terms used in the NCERT book; do not replace them with unofficial names.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
OR
1. CBSE often tests a concept by asking a daily-life example from the same chapter.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Two-mark answers work best as two numbered points. One definition plus one example is usually enough.
OR — marking points1. sin²θ+cos²θ=1.
2. Keep the NCERT wording and add one daily-life example from the same chapter.
Short Answer · Q26–31 · 3 marks each · internal choice in 2 questions · 18 marks
Use the terms used in the NCERT book; do not replace them with unofficial names. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
NoteThree-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
For two positive integers, HCF × LCM equals the product of the numbers. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
NoteThree-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
Converse of Pythagoras. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
NoteThree-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
Every chapter ends with keywords or a summary that is useful for one-mark answers. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
NoteThree-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
OR
Write three points from Polynomials in your own words; that is enough for a short-answer start. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
NoteThree-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
OR — marking pointsd can be negative. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
OR
Distance formula. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
NoteThree-mark questions want a short explanation, not a full essay. Link the idea to a figure or an activity.
OR — marking pointsRead the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions. Example: Use a situation from the NCERT activity or a labelled diagram in this chapter.
Long Answer · Q32–35 · 5 marks each · internal choice in 2 questions · 20 marks
Surface Areas and Volumes — Melted and recast problems keep volume constant. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
NoteLong answers are marked for structure. Use headings or numbered steps so the examiner can see each part.
Textbook first — Read the definitions, diagrams and solved examples in the NCERT textbook before practising extra questions. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
NoteLong answers are marked for structure. Use headings or numbered steps so the examiner can see each part.
OR
Diagrams — If the chapter has a diagram, practise labelling it — many school tests ask for labelled figures. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
NoteLong answers are marked for structure. Use headings or numbered steps so the examiner can see each part.
OR — marking pointsAreas Related to Circles — Sector area = (θ/360)×πr². Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
OR
Practice — Mix MCQs with short answers so you remember both facts and explanations from Statistics. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
NoteLong answers are marked for structure. Use headings or numbered steps so the examiner can see each part.
OR — marking pointsPolynomials — Polynomials is an NCERT chapter taught in CBSE Class 10 Mathematics. Explain the idea in order (definition → working → result). End with one application from daily life or a numerical/diagram if the chapter has one.
Case-study based · Q36–38 · 4 marks each (1 + 1 + 2) · 12 marks
(i) Quadratic Equations.
(ii) D>0 two distinct real roots.
(iii) Apply it in a school experiment, a labelled diagram, or a situation described in the NCERT chapter.
Case-based items recycle a short story. Pull the fact out first, then apply it. This is original practice in CBSE case style — not a copied board paper.
(i) Some Applications of Trigonometry.
(ii) Some Applications of Trigonometry is an NCERT chapter taught in CBSE Class 10 Mathematics.
(iii) Apply it in a school experiment, a labelled diagram, or a situation described in the NCERT chapter.
Case-based items recycle a short story. Pull the fact out first, then apply it. This is original practice in CBSE case style — not a copied board paper.
(i) Examples.
(ii) CBSE often tests a concept by asking a daily-life example from the same chapter.
(iii) Apply it in a school experiment, a labelled diagram, or a situation described in the NCERT chapter.
Case-based items recycle a short story. Pull the fact out first, then apply it. This is original practice in CBSE case style — not a copied board paper.
*** End of paper ***
No. The layout (sections, question numbers, marks and time) follows the 2025-26 sample paper. The questions are original GKSchools practice.
MCQ, assertion–reason and reading MCQ parts are auto-scored when you submit. Written answers are for self-check against the key.
Download it from CBSE Academic: https://cbseacademic.nic.in/web_material/SQP/ClassX_2025_26/MathsStandard-SQP.pdf
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