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Class 11 Math Practice Test Online

Let's push your mathematical boundaries past simple arithmetic. We will challenge you to evaluate sets, compute circular combinations, track trigonometric variables, and calculate complex coordinates. Each question contains detailed steps to build your procedural speed.

Class 11MathAI practice test
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About this Class 11 Math practice test

Entering Class 11 Math introduces you to the rigorous language of formal mathematical proofs, set theories, pre-calculus, and trigonometric identities. This specialized workspace helps you drill complex formulas and prepare for competitive engineering entrance papers.

Class 11 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. 1. If Set A contains elements 1, 2, 3 and Set B contains elements 3, 4, 5, find the union of Set A and Set B.

  2. 2. Calculate the additive inverse of the complex number 3 - 4i.

  3. 3. Find the multiplicative inverse of the complex number 4 + 3i.

  4. 4. Solve the linear inequality for the variable x: 3x - 5 less than 16.

  5. 5. Find the sum of the first 10 terms of the arithmetic progression: 3, 7, 11, 15...

  6. 6. Find the number of proper subsets of a set that has 6 elements.

  7. 7. In a class, 20 students play cricket, 28 students play football, and 36 students play at least one of the two games. Find the number of students who play both games.

  8. 8. Find the modulus of the complex number z = 5 - 12i.

  9. 9. Solve the quadratic equation x² - 4x + 13 = 0 and express the roots in the form a + bi.

  10. 10. Find the sum to infinity of the geometric series 12 + 4 + 4/3 + 4/9 + ...

  11. 11. Solve the inequality -3 < 2x - 1 ≤ 7 and write the solution in interval notation.

  12. 12. In a race with 8 runners, in how many different ways can the first, second, and third place positions be awarded?

  13. 13. How many distinct arrangements can be made using all the letters of the word SUCCESS?

  14. 14. A school wants to form a committee of 4 students from a group of 10 students. In how many ways can this committee be chosen?

  15. 15. From a group of 6 men and 5 women, a committee of 3 men and 2 women is to be formed. In how many ways can this be done?

  16. 16. Convert an angle of 150 degrees into radian measure.

  17. 17. Find the value of tan 30°.

  18. 18. If sinθ = 3/5 and θ lies between 0° and 90°, find the value of cosθ.

  19. 19. Using the sine addition formula, find the value of sin 75°, given that 75° = 45° + 30°.

  20. 20. Find the coefficient of x³y² in the binomial expansion of (x + y)^5.

  21. 21. Find the slope of the line passing through the points (2, 3) and (6, 11).

  22. 22. Find the equation of the line that passes through the point (3, -2) and has a slope of 4.

  23. 23. Find the distance between the points (1, 2) and (4, 6).

  24. 24. Find the equation of a circle with center (2, -3) and radius 5 units.

  25. 25. Evaluate the limit: lim(x→3) of (x² - 9)/(x - 3).

  26. 26. The first term of a geometric progression is 3 and the common ratio is 2. Find the 6th term.

  27. 27. A die is rolled once. What is the probability of getting a number greater than 4?

  28. 28. A bag contains 5 red balls and 3 blue balls. If 2 balls are drawn at random without replacement, what is the probability that both balls are red?

  29. 29. Find the mean deviation about the mean for the data set: 4, 6, 8, 10, 12.

  30. 30. Using the digits 1, 2, 3, 4, and 5 without repetition, how many 3-digit numbers can be formed?

Syllabus & Core Topics

Sets operations, union intersection subsets, and Venn diagramsRelations and functions, domain range mapping, and functionsComplex numbers, imaginary numbers, and complex plane representationsLinear inequalities, interval notations, and graphing regionsPermutations, combinations, progressions, and coordinates

Senior secondary math underpins modern physics, quantitative trade, and AI algorithms. Building standard procedural logic and accurate analytical habits now sets you up for absolute success in advanced calculus and coordinate geometry.

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Why this practice page is useful

  • Solving functional indices, quadratic inequalities, and sequence terms now builds the pre-calculus foundation senior board calculus depends on.

  • Step-by-step guides for sets, permutations, and complex numbers build both calculation speed and accuracy.

  • Guided practice with coordinate geometry, angle formulas, and progressions catches the setup mistakes that most often cost marks on tests.

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. 1. If Set A contains elements 1, 2, 3 and Set B contains elements 3, 4, 5, find the union of Set A and Set B.

    Set with elements 1, 2, 3, 4, 5

    The union of two sets combines all unique elements present across both sets. Common elements like 3 are listed only once, resulting in the set containing 1, 2, 3, 4, 5.

  2. 2. Calculate the additive inverse of the complex number 3 - 4i.

    -3 + 4i

    The additive inverse of a complex number z = a + bi is -z = -a - bi. Thus, the additive inverse of 3 - 4i is found by changing the signs of both parts, yielding -3 + 4i.

  3. 3. Find the multiplicative inverse of the complex number 4 + 3i.

    4/25 - 3/25i

    The multiplicative inverse is 1/z. Multiplying the numerator and denominator by the conjugate 4 - 3i yields conjugate/magnitude-squared = (4 - 3i)/(4^2 + 3^2) = (4 - 3i)/25 = 4/25 - 3/25i.

  4. 4. Solve the linear inequality for the variable x: 3x - 5 less than 16.

    x less than 7

    Add 5 to both sides to balance the inequality: 3x less than 16 + 5 -> 3x less than 21. Dividing both sides by the positive number 3 gives x less than 7, which in interval form is (negative infinity, 7).

  5. 5. Find the sum of the first 10 terms of the arithmetic progression: 3, 7, 11, 15...

    210

    Here, first term a = 3 and common difference d = 4. The sum formula is S_n = (n/2) × (2a + (n - 1)d). For n = 10: S_10 = 5 × (2(3) + 9(4)) = 5 × (6 + 36) = 5 × 42 = 210.

  6. 6. Find the number of proper subsets of a set that has 6 elements.

    63

    A set with n elements has 2^n total subsets; excluding the set itself leaves 2^n - 1 proper subsets, so 2^6 - 1 = 63.

  7. 7. In a class, 20 students play cricket, 28 students play football, and 36 students play at least one of the two games. Find the number of students who play both games.

    12

    By the formula n(A∪B) = n(A) + n(B) − n(A∩B), rearranging gives n(A∩B) = 20 + 28 − 36 = 12 students who play both games.

  8. 8. Find the modulus of the complex number z = 5 - 12i.

    13

    The modulus of a complex number a + bi is √(a² + b²); here √(5² + (-12)²) = √(25 + 144) = √169 = 13.

  9. 9. Solve the quadratic equation x² - 4x + 13 = 0 and express the roots in the form a + bi.

    x = 2 + 3i or x = 2 - 3i

    Using the quadratic formula, x = [4 ± √(16 - 52)]/2 = [4 ± √(-36)]/2 = [4 ± 6i]/2 = 2 ± 3i, since the discriminant is negative the roots are complex conjugates.

  10. 10. Find the sum to infinity of the geometric series 12 + 4 + 4/3 + 4/9 + ...

    18

    This is an infinite GP with first term a = 12 and common ratio r = 1/3 (|r| < 1), so the sum to infinity is a/(1-r) = 12/(1 - 1/3) = 12/(2/3) = 18.

  11. 11. Solve the inequality -3 < 2x - 1 ≤ 7 and write the solution in interval notation.

    (-1, 4]

    Adding 1 to all three parts gives -2 < 2x ≤ 8, then dividing by 2 gives -1 < x ≤ 4, which in interval notation is (-1, 4].

  12. 12. In a race with 8 runners, in how many different ways can the first, second, and third place positions be awarded?

    336

    This is a permutation of 8 runners taken 3 at a time: P(8,3) = 8 × 7 × 6 = 336, since the order of finishing matters.

  13. 13. How many distinct arrangements can be made using all the letters of the word SUCCESS?

    420

    SUCCESS has 7 letters where S repeats 3 times and C repeats 2 times, so the number of distinct arrangements is 7!/(3!×2!) = 5040/12 = 420.

  14. 14. A school wants to form a committee of 4 students from a group of 10 students. In how many ways can this committee be chosen?

    210

    Since the order of selection does not matter, the number of ways is C(10,4) = 10!/(4!×6!) = 210.

  15. 15. From a group of 6 men and 5 women, a committee of 3 men and 2 women is to be formed. In how many ways can this be done?

    200

    Choose 3 men from 6 in C(6,3) = 20 ways and 2 women from 5 in C(5,2) = 10 ways; by the multiplication principle the total number of committees is 20 × 10 = 200.

  16. 16. Convert an angle of 150 degrees into radian measure.

    5π/6 radians

    To convert degrees to radians, multiply by π/180: 150 × π/180 = 150π/180 = 5π/6.

  17. 17. Find the value of tan 30°.

    1/√3 (equivalently √3/3)

    tan 30° is a standard trigonometric ratio equal to 1/√3, which can be rationalized to √3/3.

  18. 18. If sinθ = 3/5 and θ lies between 0° and 90°, find the value of cosθ.

    4/5

    Using sin²θ + cos²θ = 1, cos²θ = 1 - 9/25 = 16/25, so cosθ = 4/5 (positive since θ is in the first quadrant).

  19. 19. Using the sine addition formula, find the value of sin 75°, given that 75° = 45° + 30°.

    (√6 + √2)/4

    sin(A+B) = sinA cosB + cosA sinB, so sin75° = sin45°cos30° + cos45°sin30° = (√2/2)(√3/2) + (√2/2)(1/2) = (√6 + √2)/4.

  20. 20. Find the coefficient of x³y² in the binomial expansion of (x + y)^5.

    10

    The general term in the expansion of (x+y)^5 is C(5,r) x^(5-r) y^r; for x³y² we need r = 2, giving coefficient C(5,2) = 10.

  21. 21. Find the slope of the line passing through the points (2, 3) and (6, 11).

    2

    Slope = (y2 - y1)/(x2 - x1) = (11 - 3)/(6 - 2) = 8/4 = 2.

  22. 22. Find the equation of the line that passes through the point (3, -2) and has a slope of 4.

    4x - y - 14 = 0 (equivalently y = 4x - 14)

    Using point-slope form y - y1 = m(x - x1): y - (-2) = 4(x - 3), which simplifies to y + 2 = 4x - 12, i.e., 4x - y - 14 = 0.

  23. 23. Find the distance between the points (1, 2) and (4, 6).

    5 units

    Using the distance formula, d = √((4-1)² + (6-2)²) = √(9 + 16) = √25 = 5.

  24. 24. Find the equation of a circle with center (2, -3) and radius 5 units.

    (x - 2)² + (y + 3)² = 25

    The standard equation of a circle with center (h,k) and radius r is (x-h)² + (y-k)² = r²; substituting h=2, k=-3, r=5 gives (x-2)² + (y+3)² = 25.

  25. 25. Evaluate the limit: lim(x→3) of (x² - 9)/(x - 3).

    6

    Factor the numerator as (x-3)(x+3), cancel the common (x-3) factor since x ≠ 3 in the limit, and substitute x=3 into (x+3) to get 6.

  26. 26. The first term of a geometric progression is 3 and the common ratio is 2. Find the 6th term.

    96

    The nth term of a GP is a·r^(n-1); the 6th term is 3 × 2^5 = 3 × 32 = 96.

  27. 27. A die is rolled once. What is the probability of getting a number greater than 4?

    1/3

    Numbers greater than 4 on a die are 5 and 6, so there are 2 favorable outcomes out of 6 total, giving a probability of 2/6 = 1/3.

  28. 28. A bag contains 5 red balls and 3 blue balls. If 2 balls are drawn at random without replacement, what is the probability that both balls are red?

    5/14

    The total ways to choose 2 balls from 8 is C(8,2) = 28, and the ways to choose 2 red balls from 5 is C(5,2) = 10, so the probability is 10/28 = 5/14.

  29. 29. Find the mean deviation about the mean for the data set: 4, 6, 8, 10, 12.

    2.4

    The mean is (4+6+8+10+12)/5 = 8; the absolute deviations are 4, 2, 0, 2, 4 which sum to 12, and dividing by 5 gives a mean deviation of 2.4.

  30. 30. Using the digits 1, 2, 3, 4, and 5 without repetition, how many 3-digit numbers can be formed?

    60

    This is a permutation problem: choosing and arranging 3 digits out of 5 without repetition gives P(5,3) = 5 × 4 × 3 = 60 distinct 3-digit numbers.

Curriculum Mapping & Learning Guide

Use this breakdown to identify which skills each question tests and guide post-test review.

Sets, Sequences & Complex Numbers (Questions 1-10)

Tests set operations and subset counts, complex number modulus and quadratic roots, linear inequalities, and arithmetic/geometric progression sums.

Permutations, Combinations & Trigonometry (Questions 11-20)

Measures permutation and combination word problems, and trigonometric conversions, identities, and standard angle values.

Coordinate Geometry, Limits & Probability (Questions 21-30)

Reviews straight-line slope and equations, circle equations, an introductory limit, geometric progression terms, probability, and mean deviation.

Class 11 Math chapters covered

  1. Chapter 1: Sets: Understanding unions, intersections, subsets, and subset counting.
  2. Chapter 2: Complex Numbers & Quadratic Equations: Modulus, additive/multiplicative inverses, and complex roots.
  3. Chapter 3: Linear Inequalities: Solving single and compound inequalities in interval notation.
  4. Chapter 4: Sequences and Series: Applying arithmetic and geometric progression formulas.
  5. Chapter 5: Permutations and Combinations: Counting arrangements and selections in real scenarios.
  6. Chapter 6: Trigonometric Functions: Degree-radian conversion, standard angle values, and identities.
  7. Chapter 7: Straight Lines, Circles, Limits & Probability: Coordinate geometry, an intro to limits, and probability.

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