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Class 12 Math Practice Test Online

This Class 12 Math practice test page helps students generate a quick math exam from sample questions. It works well for arithmetic, word problems, formulas, and chapter-wise revision.

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About this Class 12 Math practice test

This Class 12 Maths practice test targets the heaviest-weightage chapters of the CBSE Class 12 board syllabus — Calculus (Continuity, Differentiability, Application of Derivatives, Integrals, Differential Equations), Vectors and 3D Geometry, Matrices and Determinants, Probability, and Linear Programming. The starter set leans toward the 4-mark and 6-mark patterns of the board paper so revision feels close to actual exam conditions. It is also useful as a JEE Main / NDA foundation drill since the same chapters carry the bulk of those papers. Paste your own previous-year questions to regenerate a fresh paper of the same difficulty mix.

Class 12 Math Practice Test sample questions

These starter questions help you launch a math mock test quickly. Swap them with your own worksheet, notebook, or textbook questions any time.

1. Differentiate w.r.t. x: y = sin(x² + 1).
2. Find dy/dx if y = e^x · cos x.
3. Evaluate: ∫ (2x + 3) cos x dx.
4. Evaluate: ∫₀^(π/2) sin²x dx.
5. Find the area bounded by y = x² and y = x in the first quadrant.
6. Solve the differential equation: dy/dx + 2y = e^x.
7. If A = [[1, 2],[3, 4]], find A⁻¹.
8. Find the determinant of [[2, -1, 3],[0, 4, 5],[1, 2, -2]].
9. Find the angle between the vectors a = i + j + k and b = i - j + k.
10. Find the projection of the vector i + 3j + 7k on the vector 7i - j + 8k.
11. Find the equation of the line passing through (1, 2, 3) and parallel to the vector 2i + 3j + 4k.
12. Find the shortest distance between the lines (x-1)/2 = (y-2)/3 = (z-3)/4 and (x-2)/3 = (y-4)/4 = (z-5)/5.
13. A bag contains 4 red and 6 black balls. Two balls are drawn at random without replacement. Find the probability that both are red.
14. The probabilities that A and B will solve a problem are 1/2 and 1/3 respectively. Find the probability that the problem is solved.
15. Maximize Z = 4x + 5y subject to x + y ≤ 10, 2x + y ≤ 12, x, y ≥ 0.

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This page is built for students looking for class 12 math practice test, chapter practice, and quick school exam revision.

Why this practice page is useful

Use this Class 12 math practice test page to start with a ready-made sample instead of typing everything from scratch.

The generated paper mirrors the tone of a Class 12 math exam and works well for school revision, homework support, and quick mock tests.

You can replace the starter questions with your own textbook or worksheet content for more targeted math practice.

Answer key & quick explanations

Short answers for the sample questions above. Use this to self-check before generating a fresh AI-built mock test.

  1. d/dx sin(x²+1): cos(x²+1) · 2x = 2x cos(x²+1).
  2. d/dx (e^x cosx): e^x(cos x - sin x).
  3. ∫(2x+3)cosx dx: Use integration by parts → (2x+3) sin x + 2 cos x + C.
  4. ∫₀^(π/2) sin²x dx: Using sin²x = (1-cos2x)/2 → π/4.
  5. Area between y=x² and y=x: ∫₀¹(x - x²)dx = 1/2 - 1/3 = 1/6 sq units.
  6. dy/dx + 2y = e^x: IF = e^(2x); y·e^(2x) = ∫e^(3x)dx → y = (1/3)e^x + C·e^(−2x).
  7. Inverse of [[1,2],[3,4]]: det = -2; A⁻¹ = (−1/2)[[4,-2],[-3,1]] = [[-2,1],[1.5,-0.5]].
  8. 3x3 determinant: Expand along R1: 2(-8-10) -(-1)(0-5) + 3(0-4) = -36 -5 -12 = -53.
  9. Angle between a, b: cosθ = (1-1+1)/(√3·√3) = 1/3 → θ = cos⁻¹(1/3).
  10. Projection of a on b: (a·b)/|b| = (7-3+56)/√114 = 60/√114.
  11. Line equation: r = (i+2j+3k) + λ(2i+3j+4k); cartesian: (x-1)/2 = (y-2)/3 = (z-3)/4.
  12. Shortest distance: Use formula |(a₂-a₁)·(b₁×b₂)| / |b₁×b₂| → 1/√6 units.
  13. Both red probability: (4/10)×(3/9) = 12/90 = 2/15.
  14. Problem solved by A or B: 1 - P(not A)P(not B) = 1 - (1/2)(2/3) = 2/3.
  15. LP maximum: Corner points: (0,0), (6,0), (2,8), (0,10) → Z values 0, 24, 48, 50 → max Z = 50 at (0,10).

Class 12 Math chapters covered

Typical NCERT / board-syllabus chapters this practice test draws from. Paste questions from any chapter below to generate a focused chapter-wise mock test.

  • Relations and Functions
  • Inverse Trigonometric Functions
  • Matrices
  • Determinants
  • Continuity and Differentiability
  • Application of Derivatives
  • Integrals
  • Application of Integrals
  • Differential Equations
  • Vector Algebra
  • Three Dimensional Geometry
  • Linear Programming
  • Probability

How to use this class 12 math practice test page

1. Open the ready-made starter and generate the test.

2. Review the output as a quick Class 12 math mock test.

3. Replace the starter with your own chapter questions for more accurate revision.

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