ISC Class 12 Project Work in Maths

MATHEMATICS (860)

CLASS XII
PAPER II – PROJECT WORK – 20 Marks same graphically. Give its geometrical
interpretation.
Candidates will be expected to have completed
two projects, one from Section A and one from 8. For a dependent system (non-homogeneous) of
either Section B or Section C. three linear equations of three variables, identify
infinite number of solutions.
The project work will be assessed by the
9. For a given function, give the geometrical
subject teacher and a Visiting Examiner interpretation of Mean Value theorems. Explain
appointed locally and approved by the the significance of closed and open intervals for
Council. continuity and differentiability properties of the
Mark allocation for each Project [10 marks]: theorems.
Overall format 1 mark 10. Explain the concepts of increasing and
decreasing functions, using geometrical
Content 4 marks significance of dy/dx. Illustrate with proper
Findings 2 marks examples.

Viva-voce based on the Project 3 marks 11. Explain the geometrical significance of point of
inflexion with examples and illustrate it using
Total 10 marks graphs.
12. Explain and illustrate (with suitable examples)
List of suggested assignments for Project the concept of local maxima and local minima
Work: using graph.
Section A 13. Explain and illustrate (with suitable examples)
1. Using a graph, demonstrate a function which is the concept of absolute maxima and absolute
one-one but not onto. minima using graph.
2. Using a graph demonstrate a function which is 14. Illustrate the concept of definite integral
invertible. , expressing as the limit of a sum and
3. Construct a composition table using a binary verify it by actual integration.
function addition/multiplication modulo upto 5 15. Demonstrate application of differential equations
and verify the existence of the properties of to solve a given problem (example, population
binary operation. increase or decrease, bacteria count in a culture,
4. Draw the graph of y = sin-1 x (or any other inverse etc.).
trigonometric function), using the graph of 16. Explain the conditional probability, the theorem
y = sin x (or any other relevant trigonometric of total probability and the concept of Bayes’
function). Demonstrate the concept of mirror line theorem with suitable examples.
(about y = x) and find its domain and range.
17. Explain the types of probability distributions and
5. Explore the principal value of the function derive mean and variance of binomial probability
sin-1 x (or any other inverse trigonometric distribution for a given function.
function) using a unit circle.
Section B
6. Find the derivatives of a determinant of the order
of 3 x 3 and verify the same by other methods. 18. Using vector algebra, find the area of a
parallelogram/triangle. Also, derive the area
7. Verify the consistency of the system of three analytically and verify the same.
linear equations of two variables and verify the

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19. Using Vector algebra, prove the formulae of Section C
properties of triangles (sine/cosine rule, etc.)
31. Draw a rough sketch of Cost (C), Average Cost
20. Using Vector algebra, prove the formulae of (AC) and Marginal Cost (MC)
compound angles, e.g. sin (A + B) = Sin A Cos B
Or
+ Sin B Cos A, etc.
Revenue (R), Average Revenue (AR) and
21. Describe the geometrical interpretation of scalar
Marginal Revenue (MR).
triple product and for a given data, find the scalar
triple product. Give their mathematical interpretation using the
concept of increasing - decreasing functions and
22. Find the image of a line with respect to a given
maxima-minima.
plane.
32. For a given data, find regression equations by the
23. Find the distance of a point from a given plane
method of least squares. Also find angles
measured parallel to a given line.
between regression lines.
24. Find the distance of a point from a line measured
33. Draw the scatter diagram for a given data. Use it
parallel to a given plane.
to draw the lines of best fit and estimate the value
25. Find the area bounded by a parabola and an of Y when X is given and vice-versa.
oblique line.
34. Using any suitable data, find the minimum cost
26. Find the area bounded by a circle and an oblique by applying the concept of Transportation
line. problem.
27. Find the area bounded by an ellipse and an 35. Using any suitable data, find the minimum cost
oblique line. and maximum nutritional value by applying the
concept of Diet problem.
28. Find the area bounded by a circle and a circle.
36. Using any suitable data, find the Optimum cost in
29. Find the area bounded by a parabola and a
the manufacturing problem by formulating a
parabola.
linear programming problem (LPP).
30. Find the area bounded by a circle and a parabola.
(Any other pair of curves which are specified in NOTE: No question paper for Project Work will be
the syllabus may also be taken.) set by the Council.

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SAMPLE TABLE FOR PROJECT WORK
S. No. Unique PROJECT 1 PROJECT 2 TOTAL
Identification MARKS
Number A B C D E F G H I J
(Unique ID) Teacher Visiting Average Viva-Voce Total Teacher Visiting Average Viva-Voce Total (E + J)
of the Examiner Marks by Visiting Marks Examiner Marks by Marks
candidate (A + B ÷ Examiner (C + D) (F + G ÷ Visiting (H + I)
2) 2) Examiner
7 Marks* 7 Marks* 7 Marks 3 Marks 10 Marks 7 Marks* 7 Marks* 7 Marks 3 Marks 10 Marks 20 Marks

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2
3
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5
6
7
8
9
10

*Breakup of 7 Marks to be awarded separately by
Name of Teacher:
the Teacher and the Visiting Examiner is as follows:
Signature: Date
Overall Format 1 Mark
Content 4 Marks Name of Visiting Examiner
Findings 2 Marks
Signature: Date
NOTE: VIVA-VOCE (3 Marks) for each Project is to be conducted only by the Visiting Examiner, and should be based on the Project only

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