Test for Calculus - Mathematics (Maths) Class 11

To assess the knowledge and understanding of calculus concepts in Class 11 Mathematics, a comprehensive test can be designed. This test will cover various topics related to calculus, including limits, derivatives, and applications of derivatives. Here is a suggested structure for the test:

Section 1: Limits (50 marks)
1. Define the concept of a limit and explain its importance in calculus.
2. Evaluate the following limits:
a) lim(x→2) (x^2 + 3x - 2)
b) lim(x→∞) (3x^2 - 2x + 1)/(x^2 + 5)
c) lim(x→0) (sinx/x)
3. Determine the continuity of the following functions at the given points:
a) f(x) = 2x^2 - 5x + 3 at x = 1
b) g(x) = √(x - 1) at x = 1

Section 2: Derivatives (50 marks)
1. Define the derivative of a function and explain its significance.
2. Find the derivative of the following functions:
a) f(x) = 3x^2 + 2x - 1
b) g(x) = (x^3 - 4x^2 + 2)/(2x - 1)
c) h(x) = √x + 1/x
3. Determine the points of maxima and minima for the function f(x) = 2x^3 - 9x^2 + 12x - 3.

Section 3: Applications of Derivatives (50 marks)
1. A rectangular box with an open top is to be constructed from a 36 square meter cardboard. Find the dimensions of the box that minimize the amount of cardboard used.
2. A ladder is leaning against a wall. The bottom of the ladder is sliding away from the wall at a rate of 2 m/s. When the bottom of the ladder is 6 meters from the wall, it is 8 meters long. How fast is the top of the ladder sliding down the wall at that instant?
3. A particle is moving along a straight line such that its position at time t is given by s(t) = 3t^2 - 2t + 5. Find the velocity and acceleration of the particle at t = 2 seconds.

This test will provide a comprehensive assessment of the students' understanding of calculus concepts in Class 11 Mathematics. It covers topics such as limits, derivatives, continuity, and applications of derivatives. Remember to allocate appropriate marks for each question and provide clear instructions for students to follow.