CBSE Math RevisionCBSE Class 12 Maths Board Paper 2023
The CBSE Class 12 Mathematics board exam paper from March 2023, 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
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.
Relations and Functions · 2 marks
An equivalence relation \(R\) on \(A = \{1, 2, 3, 4, 5\}\) has exactly the two equivalence classes \(\{1, 4\}\) and \(\{2, 3, 5\}\). Write \(R\) as a set of ordered pairs and state how many ordered pairs it has.
Worked answer
\(R = \{(1,1),(1,4),(4,1),(4,4)\} \cup \{(a, b) : a, b \in \{2, 3, 5\}\}\), i.e. also \((2,2),(2,3),(2,5),(3,2),(3,3),(3,5),(5,2),(5,3),(5,5)\) M1
Number of pairs \(= 2^2 + 3^2 = 13\) A1Continuity and Differentiability · 4 marks
Bacterial culture. In a laboratory, the number of bacteria in a culture \(t\) hours after observation begins is modelled by \(N(t) = 2000e^{t/5}\).
Find \(N'(t)\). [1 mark]
Show that the relative growth rate \(\dfrac{N'(t)}{N(t)}\) is constant and state its value. [1 mark]
Find the time at which the culture is growing at \(800\) bacteria per hour. [2 marks]
Worked answer
\(N'(t) = 2000\cdot\dfrac15e^{t/5} = 400e^{t/5}\) A1
\(\dfrac{400e^{t/5}}{2000e^{t/5}} = \dfrac15 = 0.2\) per hour, independent of \(t\) A1
\(400e^{t/5} = 800 \Rightarrow e^{t/5} = 2\) M1
\(t = 5\log_e 2\) hours A1
Differential Equations · 3 marks
Find the general solution of \(\dfrac{dy}{dx} = \dfrac{2y}{x}\) \((x \gt 0)\). Find the particular solution whose tangent at the point where \(x = 2\) has slope \(12\), and the point on this particular solution curve at which the slope of the tangent is \(6\).
Worked answer
\(\dfrac{dy}{y} = \dfrac{2\,dx}{x} \Rightarrow \ln|y| = 2\ln x + c \Rightarrow y = Cx^2\) A1
\(\dfrac{dy}{dx} = 2Cx\); at \(x = 2\): \(4C = 12 \Rightarrow C = 3\), so \(y = 3x^2\) A1
\(6x = 6 \Rightarrow x = 1\): the point \((1, 3)\) A1
More on these topics: Relations and Functions · Continuity and Differentiability · Differential Equations
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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. 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 2023?
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.