Chapter-wise mathematics examples, short solutions, and uploaded PDF material for stronger independent practice.
Class 12th Mathematics
Math examples, practice flow, and uploaded PDFs in one place.
This page gives students a clearer Class 12th mathematics path with chapter-wise NCERT-style example practice, quick answers, and downloadable PDFs uploaded by SSP.
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Mathematics notes and PDF resources
These items are pulled from SSP uploaded study materials that match Class 12th mathematics topics.
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Practice Zone
Chapter-wise NCERT-style mathematics examples
These are original practice examples inspired by Class 12th NCERT mathematics chapters, written for guided revision rather than copied textbook content.
Relations and Functions
Example 1
If f(x) = 2x + 3, find f(4) and state whether the function is linear.
Answer:
f(4) = 2(4) + 3 = 11. Since the highest power of x is 1, it is a linear function.
Inverse Trigonometric Functions
Example 1
Find the principal value of sin^-1(1/2).
Answer:
The principal value of sin^-1(1/2) is pi/6.
Matrices
Example 1
If A = [[1, 2], [3, 4]] and B = [[2, 0], [1, 5]], find A + B.
Answer:
A + B = [[3, 2], [4, 9]]. Add corresponding entries of the two matrices.
Determinants
Example 1
Find the determinant of [[3, 1], [2, 5]].
Answer:
Determinant = (3 x 5) - (1 x 2) = 15 - 2 = 13.
Continuity and Differentiability
Example 1
Differentiate f(x) = x^3 + 2x^2 - 5x.
Answer:
Using the power rule, f'(x) = 3x^2 + 4x - 5.
Applications of Derivatives
Example 1
For f(x) = x^2 - 4x + 1, find the x-coordinate of the turning point.
Answer:
Set f'(x) = 2x - 4 = 0, so x = 2. The turning point occurs at x = 2.
Integrals
Example 1
Evaluate integral of (2x + 1) dx.
Answer:
Integral of (2x + 1) dx = x^2 + x + C.
Differential Equations
Example 1
Solve dy/dx = 3x^2.
Answer:
Integrating both sides gives y = x^3 + C.
Vector Algebra
Example 1
Find the magnitude of vector 3i + 4j.
Answer:
Magnitude = sqrt(3^2 + 4^2) = sqrt(25) = 5.
Three Dimensional Geometry
Example 1
Find the distance between points A(1, 2, 3) and B(4, 6, 3).
Answer:
Distance = sqrt((4-1)^2 + (6-2)^2 + (3-3)^2) = sqrt(9 + 16) = 5.
Linear Programming
Example 1
What is the first step in solving a linear programming problem graphically?
Answer:
The first step is to define the decision variables and write the objective function and constraints clearly.
Probability
Example 1
If P(A) = 0.6 and P(B|A) = 0.5, find P(A and B).
Answer:
P(A and B) = P(A) x P(B|A) = 0.6 x 0.5 = 0.3.