CBSE Math RevisionCBSE Class 10 Maths Official Sample Paper 2021-22 (Standard and Basic)
CBSE's official sample question paper and marking scheme for the 2021-22 session, linked straight to CBSE. Time yourself, mark it against the scheme, then practise the weakest units.
The official sample paper and marking scheme
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Class 10 Mathematics Standard: sample question paper (Term 1) 041 Specimen
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Class 10 Mathematics Standard: sample question paper (Term 2) 041 Specimen
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Class 10 Mathematics Basic: sample question paper (Term 1) 041 Specimen
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Class 10 Mathematics Basic: sample question paper (Term 2) 041 Specimen
2021-22 had two terms, each with its own sample paper. Term 1 was multiple choice (90 minutes, 40 marks). 2021-22 had two terms, each with its own sample paper. Term 2 was a written paper (2 hours, 40 marks).
Sit it under exam conditions: open the paper, press Start timer, press Finish when time is up, then mark it against the mark scheme.
Try 3 Class 10 questions like these
Written and checked by us, not taken from the CBSE paper. Tap "Worked answer" to see every step.
Pair of Linear Equations in Two Variables · 3 marks
Rohan invested a total of ₹50,000 in two schemes. Scheme A pays simple interest at \(6\%\) per annum and scheme B at \(8\%\) per annum. His total interest at the end of one year was ₹3,560. Form a pair of linear equations and find the amount invested in each scheme.
Worked answer
Let the amounts be ₹\(x\) (A) and ₹\(y\) (B): \(x + y = 50000,\ \dfrac{6x}{100} + \dfrac{8y}{100} = 3560\), i.e. \(3x + 4y = 178000\) M1
Substituting \(y = 50000 - x\): \(3x + 200000 - 4x = 178000 \Rightarrow x = 22000\) A1
\(y = 28000\): ₹22,000 in scheme A and ₹28,000 in scheme B (check: \(1320 + 2240 = 3560\)) A1Surface Areas and Volumes · 3 marks
A wooden cuboid measuring \(10\ \text{cm}\times10\ \text{cm}\times5\ \text{cm}\) has a cylindrical hole of diameter 4 cm drilled straight through from the centre of the square top face to the bottom face. Find the total surface area of the remaining solid. \((\pi=3.14)\)
Worked answer
Cuboid SA \(=2(100+50+50)=400\ \text{cm}^2\) M1
Remove two circles \(2\pi r^2=8\pi\) and add the inner curved surface \(2\pi rh=2\pi(2)(5)=20\pi\) M1
SA \(=400+12\pi=400+37.68=437.68\ \text{cm}^2\) A1
Statistics · 2 marks
For a grouped distribution of the heights (in cm) of students, \(a = 150\), \(h = 5\), \(\sum f_iu_i = 12\) and \(\sum f_i = 40\). Find the mean height.
Worked answer
\(\bar x=150+5\times\dfrac{12}{40}\) M1
\(=150+1.5=151.5\) cm A1
More on these topics: Pair of Linear Equations in Two Variables · Surface Areas and Volumes · Statistics
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What the paper covers
Class 10 has two levels: Mathematics Standard (041) and Mathematics Basic (241). Both are a 3-hour, 80-mark theory paper plus 20 marks of internal assessment. This sample paper is different: 1 h 30 min, 40 marks (see the note above). Unit weightage in the CBSE curriculum:
| Unit | Marks (of 80) |
|---|---|
| Number Systems | 6 |
| Algebra | 20 |
| Coordinate Geometry | 6 |
| Geometry | 15 |
| Trigonometry | 12 |
| Mensuration | 10 |
| Statistics and Probability | 11 |
Chapter links will appear once the CBSE course pages are live. We haven't mapped this paper question by question yet.
More practice: our 5 sample papers on the same pattern
Original Class 10 Maths papers written to the CBSE 2026-27 pattern by us (not official CBSE papers): 80 marks, 38 questions, sections A to E, a 3-hour timer, an A4 print view and a step-marking scheme with where toppers lose marks.
Formula booklet
CBSE Mathematics (Class 10 and Class 12) · CBSE · No official formula booklet
CBSE does not publish a formula booklet and none is given in the exam: formulas must be learnt. Use our one-page sheets to revise them.
More Class 10 papers
Questions students ask
Where do I download the Class 10 Maths official sample paper 2021-22?
The buttons above open CBSE's own copy on cbseacademic.nic.in. We link to CBSE rather than host the file, so you always get the current version.
Is there a marking scheme?
Yes: the marking scheme button opens CBSE's own copy (a dashed button opens CBSE's page where it is listed). Mark your answers against it, then enter your mark.
How is the Class 10 Maths paper marked?
Class 10 has two levels: Mathematics Standard (041) and Mathematics Basic (241). Both are a 3-hour, 80-mark theory paper plus 20 marks of internal assessment. The unit weightage is in the table on this page.