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Class 10 Math Practice Test Online

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Class 10MathAI practice test
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About this Class 10 Math practice test

Class 10 Math is a pivotal bridge for senior secondary science and commerce streams. Getting comfortable with quadratic roots, arithmetic sequences, trigonometric ratios, and circle theorems is essential for securing high boards outcomes. This interactive test provides step-by-step methods.

Class 10 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. Calculate the additive inverse of the rational number negative 8/13.

  2. 2. State the multiplicative inverse of the rational number negative 17/25.

  3. 3. Solve the linear balance for the variable x: 4x - 11 = 25.

  4. 4. Determine the sum of all interior angles of a regular heptagon (7 sides).

  5. 5. In a parallelogram, two adjacent angles are in the ratio 4:5. Find the degree measure of the smaller angle.

  6. 6. Find the square root of the number 1600 using prime factorization.

  7. 7. What is the smallest natural number by which 18 must be multiplied to make it a perfect square?

  8. 8. Calculate the cube root of the integer 729.

  9. 9. Express the percentage 28% in its simplest fraction terms.

  10. 10. If an article priced at 150 rupees is sold for 120 rupees, what is the discount percentage?

  11. 11. Solve the algebraic simplification: (3x + 4) × (2x - 3).

  12. 12. Find the value of 6 raised to the power of 3 × 6 raised to the power of negative 1.

  13. 13. If 12 workers can build a stone wall in 30 hours, how many workers are needed to do the same work in 20 hours?

  14. 14. Factorize the algebraic expression: x square - 25.

  15. 15. Calculate the area of a trapezium whose parallel sides measure 15 cm and 25 cm, and the perpendicular height is 10 cm.

  16. 16. Find the volume of a cylinder with a base radius of 7 cm and a height of 15 cm. Take the value of pi as 22/7.

  17. 17. What is the value of the expression: (3 raised to the power of 0 + 4 raised to the power of 0) × 6 raised to the power of 1?

  18. 18. Find the coordinates of the central origin on a cartesian grid.

  19. 19. Factorize the expression: p square - 14p + 49.

  20. 20. Solve for y: 3y/4 - 5 = 10.

  21. 21. What is the sum of the exterior angles of any convex polygon in degrees?

  22. 22. If the printed price of an article is 400 rupees with an additional GST of 18%, calculate the final bill total including tax.

  23. 23. Calculate the square of the decimal number 3.5.

  24. 24. A bag contains 7 red balls and 5 blue balls. If a ball is drawn at random, what is the probability of getting a red ball?

  25. 25. Find the value of x when 2 raised to the power of 5x = 128.

  26. 26. Express the small number 0.000072 in standard scientific notation.

  27. 27. Calculate the total surface area of a cube whose side edge length measures 5 cm.

  28. 28. Find the product of the monomials: negative 3p and 8pq.

  29. 29. If x and y are in inverse proportion, and x = 6 when y = 8, find the value of y when x = 12.

  30. 30. State the coefficient of the variable term x square in the algebraic expression: 8 - 9x square + 12x.

Syllabus & Core Topics

Real numbers, rational decimal expansions, and prime factorizationQuadratic equations, factoring trinomials, and the quadratic formulaArithmetic progressions, common differences, and sum formulasCoordinate geometry, midpoints, and distance formulas on a Cartesian gridSurface areas and volumes of composite solid cylinders and cones

Consistent problem-solving is the single most effective way to eliminate math anxiety. By linking algebra systems with spatial calculations, you cultivate the technical confidence and speed required to excel under timed board exam pressures.

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Why this practice page is useful

  • Practicing quadratic formulas, arithmetic progression sequences, and trigonometric identities builds the calculation speed needed for final board outcomes.

  • Solving step-by-step questions for composite areas, trapeziums, and 3D cylinder volumes prevents standard measurement formula application mistakes.

  • Working through coordinates, angles, and variables equations helps students construct clear, well-structured math papers.

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. Calculate the additive inverse of the rational number negative 8/13.

    8/13

    The additive inverse of a number is the value we add to it to get zero. For a negative fraction negative a/b, the additive inverse is positive a/b. Adding negative 8/13 and positive 8/13 equals zero.

  2. 2. State the multiplicative inverse of the rational number negative 17/25.

    -25/17 (or -1 8/17)

    The multiplicative inverse, or reciprocal, of a number is what we multiply it by to get exactly 1. For a fraction, we invert the numerator and denominator without changing the sign, yielding negative 25/17.

  3. 3. Solve the linear balance for the variable x: 4x - 11 = 25.

    x = 9

    First, add 11 to both sides of the equation to isolate the variable term: 4x = 25 + 11, which gives 4x = 36. Now, dividing both sides by 4 gives x = 36/4 = 9.

  4. 4. Determine the sum of all interior angles of a regular heptagon (7 sides).

    900 degrees

    The sum of the interior angles of any polygon is found using the formula (n - 2) × 180 degrees. A heptagon has 7 sides, so substituting n = 7 gives (7 - 2) × 180 = 5 × 180 = 900 degrees.

  5. 5. In a parallelogram, two adjacent angles are in the ratio 4:5. Find the degree measure of the smaller angle.

    80 degrees

    The adjacent angles of any parallelogram are supplementary, meaning they add up to 180 degrees. Let the angles be represented by 4x and 5x: 4x + 5x = 180, which means 9x = 180 and x = 20. The smaller angle is 4 × 20 = 80 degrees.

  6. 6. Find the square root of the number 1600 using prime factorization.

    40

    The prime factorization of 1600 yields 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5. Grouping them into matching duplicate pairs gives (2 × 2) × (2 × 2) × (2 × 2) × (5 × 5). Selecting one factor from each pair gives 2 × 2 × 2 × 5 = 40.

  7. 7. What is the smallest natural number by which 18 must be multiplied to make it a perfect square?

    2

    The prime factorization of 18 is 2 × 3 × 3. Grouping into duplicate pairs gives 2 × (3 × 3). The prime factor 2 remains unpaired, so multiplying 18 by 2 forms a complete pair, yielding the perfect square 36 (6 × 6).

  8. 8. Calculate the cube root of the integer 729.

    9

    To find the cube root of 729, we look for a number that multiplied by itself three times equals 729. Since 9 × 9 × 9 = 81 × 9 = 729, the cube root is exactly 9.

  9. 9. Express the percentage 28% in its simplest fraction terms.

    7/25

    Convert a percentage directly into a fraction by placing the value over 100, which gives 28/100. Dividing both the top and bottom by their greatest common factor, which is 4, simplifies the fraction to 7/25.

  10. 10. If an article priced at 150 rupees is sold for 120 rupees, what is the discount percentage?

    20%

    The discount value is marked price minus sales price: 150 - 120 = 30 rupees. The discount percentage is this discount divided by the marked price, multiplied by 100: (30 / 150) × 100 = 0.2 × 100 = 20%.

  11. 11. Solve the algebraic simplification: (3x + 4) × (2x - 3).

    6x^2 - x - 12

    Multiply each term in the first binomial by each term in the second: (3x × 2x) + (3x × negative 3) + (4 × 2x) + (4 × negative 3). This expands to 6x^2 - 9x + 8x - 12, which simplifies to 6x^2 - x - 12.

  12. 12. Find the value of 6 raised to the power of 3 × 6 raised to the power of negative 1.

    36

    Using exponent rules for a shared base, we sum the powers: 6 raised to the power of (3 + negative 1) = 6 raised to the power of 2. This gives a final value of 6 × 6 = 36.

  13. 13. If 12 workers can build a stone wall in 30 hours, how many workers are needed to do the same work in 20 hours?

    18 workers

    This is an inverse proportion because adding more workers reduces the total hours needed. The total work remains constant: 12 × 30 = 360 worker-hours. Dividing this by the required 20 hours yields 360 / 20 = 18 workers.

  14. 14. Factorize the algebraic expression: x square - 25.

    (x - 5)(x + 5)

    This expression follows the classical difference of squares identity: a square - b square = (a - b)(a + b). Writing 25 as the perfect square 5 square, the binominal factors directly to (x - 5)(x + 5).

  15. 15. Calculate the area of a trapezium whose parallel sides measure 15 cm and 25 cm, and the perpendicular height is 10 cm.

    200 square centimeters (cm2)

    The area formula for any trapezium is (1/2) × (a + b) × h, where a and b are the parallel sides. Substituting our values gives (1/2) × (15 + 25) × 10 = (1/2) × 40 × 10 = 20 × 10 = 200 square centimeters.

  16. 16. Find the volume of a cylinder with a base radius of 7 cm and a height of 15 cm. Take the value of pi as 22/7.

    2310 cubic centimeters (cm3)

    The volume of a cylinder is given by the formula V = pi × r square × h. Substituting our parameters: V = (22/7) × 7 × 7 × 15. Canceling the 7 in the denominator with one in the numerator yields 22 × 7 × 15 = 154 × 15 = 2310 cubic centimeters.

  17. 17. What is the value of the expression: (3 raised to the power of 0 + 4 raised to the power of 0) × 6 raised to the power of 1?

    12

    Any non-zero base raised to the power of 0 equals 1, so 3 raised to the power of 0 is 1 and 4 raised to the power of 0 is 1. The sum inside the parentheses is 1 + 1 = 2. Multiplying this by 6 raised to the power of 1 (which is 6) gives 2 × 6 = 12.

  18. 18. Find the coordinates of the central origin on a cartesian grid.

    (0, 0) (or origin)

    The meeting point of the horizontal x-axis and the vertical y-axis is defined as the origin. Its coordinates are always represented as (0, 0) on any cartesian reference plane.

  19. 19. Factorize the expression: p square - 14p + 49.

    (p - 7)^2 (or (p-7)(p-7))

    This looks like a perfect square trinomial matching the identity (a - b) square = a square - 2ab + b square. Writing 14p as 2 × p × 7 and 49 as 7 square, the expression simplifies directly to (p - 7) square.

  20. 20. Solve for y: 3y/4 - 5 = 10.

    y = 20

    First, add 5 to both sides of the equation to isolate the fraction term: 3y/4 = 10 + 5, which gives 3y/4 = 15. Now multiply both sides by 4 to remove the denominator: 3y = 60. Dividing both sides by 3 yields y = 60/3 = 20.

  21. 21. What is the sum of the exterior angles of any convex polygon in degrees?

    360 degrees

    The sum of the exterior angles of any convex polygon is always a constant 360 degrees, regardless of how many sides the polygon has, representing one complete circular turn.

  22. 22. If the printed price of an article is 400 rupees with an additional GST of 18%, calculate the final bill total including tax.

    472 rupees

    The tax is calculated over the printed price: 18% of 400 rupees = (18/100) × 400 = 18 × 4 = 72 rupees. Adding this tax value to our base cost gives a final customer total of 400 + 72 = 472 rupees.

  23. 23. Calculate the square of the decimal number 3.5.

    12.25

    To square a decimal, it can be helpful to treat it as a fraction: (35/10) square = 1225/100. Converting back to standard decimal format yields 12.25.

  24. 24. A bag contains 7 red balls and 5 blue balls. If a ball is drawn at random, what is the probability of getting a red ball?

    7/12

    Probability represents favorable outcomes divided by total outcomes. The number of red balls is 7, and the total count of balls is 7 + 5 = 12. Thus, the probability is 7/12.

  25. 25. Find the value of x when 2 raised to the power of 5x = 128.

    x = 1.4 (or 7/5)

    Express 128 as a power with a base of 2, which gives 128 = 2 raised to the power of 7. Comparing exponents directly: 5x = 7, which gives x = 7/5 = 1.4.

  26. 26. Express the small number 0.000072 in standard scientific notation.

    7.2 x 10^-5 (or 7.2 * 10^-5)

    To write 0.000072 in scientific notation, slide the decimal point 5 spaces to the right, placing it between 7 and 2. Because the original value is less than 1, we use a negative exponent: 7.2 × 10 raised to the power of negative 5.

  27. 27. Calculate the total surface area of a cube whose side edge length measures 5 cm.

    150 square centimeters (cm2)

    A cube has six identical square faces. The total surface area is given by the formula 6 × s square. Substituting our values gives 6 × 5 square = 6 × 25 = 150 square centimeters.

  28. 28. Find the product of the monomials: negative 3p and 8pq.

    -24p^2q

    Multiply coefficients and variables separately: (negative 3 × 8) × (p × pq) = negative 24 × p raised to the power of (1 + 1) × q = negative 24p square q.

  29. 29. If x and y are in inverse proportion, and x = 6 when y = 8, find the value of y when x = 12.

    4

    In an inverse proportion, the product of the variables remains constant: x1 × y1 = x2 × y2. Substituting our values gives 6 × 8 = 12 × y2, which means 48 = 12y2. Dividing both sides by 12 yields y = 48/12 = 4.

  30. 30. State the coefficient of the variable term x square in the algebraic expression: 8 - 9x square + 12x.

    -9

    The coefficient is the multiplier factor in front of the variable. Looking closely at the term negative 9x square, the coefficient of x square is negative 9. A common student trap is omitting the negative sign.

Curriculum Mapping & Learning Guide

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

Algebra, Roots & Sequences (Questions 1-10)

Tests polynomial factorization, quadratic equations, and finding terms/sums in arithmetic progressions.

Equations, Proportions & Coordinate Systems (Questions 11-20)

Checks coordinate markers, direct and inverse ratios, percentage changes, and evaluating variables.

Geometry, Mensuration & Probability (Questions 21-30)

Reviews interior polygon sum formulas, circle radius and cylinder volumes, triangle areas, and simple probability.

Class 10 Math chapters covered

  1. Chapter 1: Mastering rational boundaries, decimals representation, and real number divisions.
  2. Chapter 2: Solving linear equations, balancing equations, and solving multi-step word problems.
  3. Chapter 3: Calculating interior angles, adjacent sides, and perimeters of polygons.
  4. Chapter 4: Factoring perfect squares, evaluating cube roots, and using exponent laws.
  5. Chapter 5: Using formulas for trapeziums, cylinder volumes, and coordinates on Cartesian axes.
  6. Chapter 6: Comparing ratios, percentage changes, and simple probability events.
  7. Chapter 7: Expanding binomials, finding perfect square factors, and identifying coefficients.

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