CBSE Math RevisionCBSE Class 12 Maths Board Paper 2022
The CBSE Class 12 Mathematics board exam paper from 2022 (Term 2), linked straight to CBSE. Time yourself, mark it against the scheme, then practise the weakest units.
The official paper and marking scheme
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Class 12 Mathematics (all sets) 041
2021-22 had two terms; this is the Term 2 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 12 questions like these
Written and checked by us, not taken from the CBSE paper. Tap "Worked answer" to see every step.
Continuity and Differentiability · 3 marks
Let \(g(x) = [x]^2 - [x^2]\) for \(0 \le x \lt 2\), where \([\,\cdot\,]\) is the greatest integer function. Write \(g\) as a piecewise function, and hence find all points of \((0, 2)\) at which \(g\) is discontinuous. Is \(g\) continuous at \(x = 1\), where both \([x]^2\) and \([x^2]\) jump?
Worked answer
\([x^2]\) changes value at \(x = 1, \sqrt2, \sqrt3\) and \([x]\) at \(x = 1\): \(g(x) = 0 - 0 = 0\) on \([0, 1)\); \(1 - 1 = 0\) on \([1, \sqrt2)\); \(1 - 2 = -1\) on \([\sqrt2, \sqrt3)\); \(1 - 3 = -2\) on \([\sqrt3, 2)\) A1
At \(x = 1\): LHL \(= 0\), RHL \(= 0\), \(g(1) = 0\), so \(g\) is continuous at \(1\) (the two jumps cancel) R1
At \(\sqrt2\): LHL \(= 0 \ne -1 = \) RHL; at \(\sqrt3\): LHL \(= -1 \ne -2 = \) RHL. \(g\) is discontinuous exactly at \(x = \sqrt2\) and \(x = \sqrt3\) in \((0, 2)\) A1Application of Derivatives · 2 marks
The height of a closed cylindrical container is always twice its radius. If the radius is increasing at \(0.1\) cm/s, find the rate at which its volume is increasing when the radius is \(3\) cm.
Worked answer
\(V = \pi r^2(2r) = 2\pi r^3 \Rightarrow \dfrac{dV}{dt} = 6\pi r^2\dfrac{dr}{dt}\) M1
\(= 6\pi(9)(0.1) = 5.4\pi\ \text{cm}^3/\text{s}\) A1Probability · 2 marks
A family has three children. Assuming each child is equally likely to be a boy or a girl, find the probability that at least two of the children are girls, given that the eldest child is a girl.
Worked answer
Given eldest is a girl: \(GBB, GBG, GGB, GGG\) (4 equally likely) M1
At least two girls: \(GBG, GGB, GGG\); probability \(\dfrac34\) A1
More on these topics: Continuity and Differentiability · Application of Derivatives · Probability
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What the paper covers
Class 12 Mathematics (041) is a 3-hour, 80-mark theory paper plus 20 marks of internal assessment. This paper is different: 2 h, 40 marks (see the note above). Unit weightage in the CBSE curriculum:
| Unit | Marks (of 80) |
|---|---|
| Relations and Functions | 8 |
| Algebra | 10 |
| Calculus | 35 |
| Vectors and Three-Dimensional Geometry | 14 |
| Linear Programming | 5 |
| Probability | 8 |
Chapter links will appear once the CBSE course pages are live. We haven't mapped this paper question by question yet.
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.
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Questions students ask
Where do I download the Class 12 Maths board paper 2022?
The buttons above open CBSE's own copy on cbse.gov.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 12 Maths paper marked?
Class 12 Mathematics (041) is a 3-hour, 80-mark theory paper plus 20 marks of internal assessment. The unit weightage is in the table on this page.