ISC 2015 Mathematics Question Paper for Class 12

About this paper

This is the ISC Class 12 Mathematics paper, code 860, from the 2015 CISCE board examination. It runs for three hours, with fifteen minutes extra for reading only. Question 1 is compulsory and has ten parts of three marks each; any five of Questions 2 to 9 are then taken, at ten marks each, and two further ten-mark questions come from either Section B or Section C, so the attempted work totals 100 marks. Section B is vectors, planes, lines and probability. Section C is compound interest, a vitamin-mix linear programming problem, a discounted bill, cost functions, index numbers and quarterly moving averages. Mathematical tables and graph paper are provided, and a slide rule may be used. This copy has the questions only.

Exam

ISC Class 12

Subject

Mathematics

Year

2015

Paper code

860

Maximum marks

100

Time allowed

3 hours + 15 min reading

Questions

15

Pages

6

Answers included

No, questions only

Paper pattern

• Section A

  80 marks

  Question 1, compulsory, ten parts of three marks each, and any five of Questions 2–9, ten marks each (five plus five)

• Section B or Section C

  20 marks

  Any two questions from either Section B (Questions 10–12: vectors, planes, lines and probability) or Section C (Questions 13–15: interest, linear programming, bills, cost, index numbers and moving averages), ten marks each

Topics covered

• Matrices and determinants
• Inverse trigonometric functions
• Ellipse and hyperbola
• Limits and L'Hospital's rule
• Definite integrals
• Differential equations
• Maxima and minima
• Boolean algebra and switching circuits
• Correlation, regression and rank correlation
• Probability
• Vectors and three-dimensional geometry
• Linear programming, index numbers and bills of exchange

Questions from this paper

1. Find the equation of an ellipse whose latus rectum is 8 and whose eccentricity is 1/3.
2. Using L'Hospital's rule, evaluate lim (x → 0) (x − sin x)/(x² sin x).
3. The lines of regression are 4x + 2y − 3 = 0 and 3x + 6y + 5 = 0. Find the correlation coefficient between x and y.
4. A card is drawn from a well-shuffled pack. What is the probability that it is either a spade or an ace or both?
5. Using vectors, prove that the angle in a semicircle is a right angle.
6. Show that the rectangle of maximum perimeter which can be inscribed in a circle of radius 10 cm is a square of side 10√2 cm.