ISC 2018 Mathematics Solved Paper for Class 12

About this paper

This is the ISC Class 12 Mathematics paper from the 2018 CISCE board examination, with a worked solution printed after the questions. It runs for three hours plus fifteen minutes of reading time. Section A is worth 80 marks and is all compulsory: Question 1 has ten two-mark parts, and the rest are four-mark and six-mark questions, with an internal choice in three four-mark questions and two six-mark questions. Candidates then attempt either Section B or Section C, each worth 20 marks, with an internal choice in two four-mark questions. Section B is vectors, lines, planes and area; Section C is cost, correlation, regression and a linear programming problem on teaching aids. Mathematical tables and graph paper are provided.

Exam

ISC Class 12

Subject

Mathematics

Year

2018

Maximum marks

100

Time allowed

3 hours + 15 min reading

Questions

22

Pages

30

Answers included

Yes

Paper pattern

• Section A

  80 marks

  Questions 1–14, all compulsory. Question 1 has ten parts of two marks each; the other questions are of four or six marks, with an internal choice in three four-mark questions and two six-mark questions

• Section B or Section C

  20 marks

  Attempt every question in one section only. Section B (Questions 15–18) is vectors, lines, planes and area; Section C (Questions 19–22) is cost, correlation, regression and linear programming. Each has an internal choice in two four-mark questions

Topics covered

• Relations, binary operations and inverse functions
• Inverse trigonometric functions
• Matrices and determinants
• Continuity, differentiability and Rolle's theorem
• Applications of derivatives
• Indefinite and definite integrals
• Differential equations
• Probability and probability distributions
• Vectors and three-dimensional geometry
• Area under curves
• Cost, correlation and regression
• Linear programming

Questions from this paper

1. The binary operation * on real numbers is defined by a * b = 2a + b. Find (2 * 3) * 4.
2. If f(x) = √(2x − 3) is invertible, find its inverse and prove that (f ∘ f⁻¹)(x) = x.
3. If tan⁻¹a + tan⁻¹b + tan⁻¹c = π, prove that a + b + c = abc.
4. A speaks the truth in 60% of cases and B in 40% of cases. In what percentage of cases are they likely to contradict each other in stating the same fact?
5. A cone is inscribed in a sphere of radius 12 cm. If the volume of the cone is maximum, find its height.
6. The population of a town grows at 10% per year. Using a differential equation, find how long it will take for the population to become four times.