Class 12 maths is the foundation for engineering and science entrance exams as well as the board itself, and the syllabus is heavy on calculus. Students who practise a steady mix of problems from every chapter through the year handle the board paper and the JEE-style questions that build on it with far less stress. Maths Daily Helper gives you unlimited fresh Class 12 questions, matched to the NCERT chapters, each with a full worked solution so you learn the method the board expects, not just the answer.
Chapters covered
- Relations and Functions
- Inverse Trigonometric Functions
- Matrices and Determinants
- Continuity and Differentiability
- Application of Derivatives (maxima, minima, rate of change)
- Integrals (indefinite and definite)
- Application of Integrals (area under curves)
- Differential Equations
- Vector Algebra
- Three-Dimensional Geometry
- Linear Programming
- Probability
Try a few Class 12 problems
Work each one out first, then check your steps.
Evaluate ∫ (2x + 3) dx.
1. Integrate term by term: ∫ 2x dx = x², and ∫ 3 dx = 3x.
2. Add the constant of integration.
Answer: x² + 3x + C.
Differentiate y = sin(x²) with respect to x.
1. Use the chain rule: dy/dx = cos(x²) × d/dx(x²).
2. d/dx(x²) = 2x.
Answer: 2x·cos(x²).
Find the determinant of the 2×2 matrix [[3, 4], [1, 2]].
1. For [[a, b], [c, d]], the determinant is ad − bc.
2. = (3)(2) − (4)(1) = 6 − 4.
Answer: 2.
Find the principal value of sin⁻¹(1/2).
1. We need the angle θ in [−π/2, π/2] with sin θ = 1/2.
2. sin(π/6) = 1/2, and π/6 lies in the principal range.
Answer: π/6.
Find the slope of the tangent to y = x³ at x = 2.
1. The slope of the tangent is dy/dx = 3x².
2. At x = 2: 3(2)² = 3 × 4 = 12.
Answer: 12.
Evaluate ∫₀¹ x² dx.
1. ∫ x² dx = x³/3.
2. Evaluate from 0 to 1: (1³/3) − (0³/3) = 1/3 − 0.
Answer: 1/3.
Find the magnitude of the vector a = 3i + 4j.
1. Magnitude = √(x² + y²) = √(3² + 4²).
2. = √(9 + 16) = √25.
Answer: 5.
If P(A) = 0.6 and P(B) = 0.5 with A and B independent, find P(A ∩ B).
1. For independent events, P(A ∩ B) = P(A) × P(B).
2. = 0.6 × 0.5 = 0.30.
Answer: 0.3.
Practise every chapter, unlimited
Choose Class 12 and any chapter. Get a fresh question each time, with hints and full solutions.
Open Maths Daily Helper →A simple daily routine for the board exam
Aim for ten to fifteen questions a day across two or three chapters, weighting calculus most heavily since it carries the largest share of marks. Do the ones you find hardest first, while you are fresh. Use hints before solutions so you build the habit of finding the next step yourself, which is exactly what the three-hour board paper tests. Closer to the exam, switch to generating full sample papers and time yourself, so pace and presentation become automatic.