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Class 8 Math Practice Test Online

Equations are just scales waiting to be balanced! Instead of memorizing formulas, let's explore how exponents, square roots, and variable balances actually interact. Each question here is a puzzle designed to show you the 'why' behind the math, helping you build core problem-solving habits that take the stress out of exam day.

Class 8MathAI practice test
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About this Class 8 Math practice test

Struggling to visualize how 3D shapes unfold or why algebra feels like a game with hidden rules? Moving from everyday arithmetic to abstract variables is one of the most exciting shifts in middle school mathematics. This practice set provides the mental gym you need to turn tricky algebraic structures into simple, step-by-step logical victories.

Class 8 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. What is the additive inverse of the rational number -5/8?

  2. 2. Find the multiplicative inverse of the rational number -13/19.

  3. 3. Solve the equation for the variable x: 3x - 7 = 14.

  4. 4. Determine the sum of all interior angles of a regular pentagon.

  5. 5. In a parallelogram, two adjacent angles are in the ratio 2:3. Find the measure of the smaller angle.

  6. 6. Find the square root of the number 729 using prime factorization.

  7. 7. What is the smallest natural number by which 72 must be multiplied to make it a perfect square?

  8. 8. Calculate the cube root of the number 512.

  9. 9. Express the percentage 15% in its simplest fraction terms.

  10. 10. If an item priced at 120 rupees is sold for 96 rupees, what is the discount percentage?

  11. 11. Solve the algebraic simplification: (2x + 5)(3x - 4).

  12. 12. Find the value of 5^3 × 5^-1.

  13. 13. If 15 workers can build a wall in 48 hours, how many workers will be required to do the same work in 30 hours?

  14. 14. Factorize the algebraic expression: x^2 - 9.

  15. 15. Calculate the area of a trapezium whose parallel sides measure 12 cm and 20 cm, and the perpendicular height is 8 cm.

  16. 16. Find the volume of a cylinder with a base radius of 7 cm and a height of 10 cm. Take pi = 22/7.

  17. 17. What is the value of (2^0 + 3^0) × 5^1?

  18. 18. Find the value of the coordinates (x, y) where the horizontal x-axis and vertical y-axis intersect on a cartesian plane.

  19. 19. Factorize the expression: p^2 - 10p + 25.

  20. 20. Solve for y: 5y/3 - 4 = 11.

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

  22. 22. If the selling price of an article is 250 rupees with a GST rate of 12%, find the total amount including tax.

  23. 23. Find the square of the decimal number 2.5.

  24. 24. A bag contains 5 red balls and 3 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^(3x) = 64.

  26. 26. Express the small number 0.000035 in standard scientific notation.

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

  28. 28. Find the product of the monomials: -4p and 7pq.

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

  30. 30. State the coefficient of the variable x^2 in the algebraic expression: 5 - 4x^2 + 7x.

Syllabus & Core Topics

Rational number properties, additive and multiplicative identitiesLinear equations with variables on one or both sidesAngle sums, polygons, and properties of quadrilateralsSquare roots, cube roots, and exponent base operationsMensuration formulas for 2D trapeziums and 3D cylindersCore algebra expansion, factorization patterns, and coordinates

Every mathematical rule you lock in during Class 8 becomes a tool for the future. From calculating interest rates on home savings to figuring out coordinates in a game, these numbers guide real-life engineering. Mastering them now gives you an incredible head-start for Class 9 algebra.

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Why this practice page is useful

  • Direct practice with linear equations and algebraic identities builds a stable foundation for high-school mathematics.

  • Comparing surface areas, composite shapes, and 3D volumes helps students apply measurement formulas confidently.

  • Practicing clear steps for square roots, percentages, and exponents reduces arithmetic mistakes on exams.

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. What is the additive inverse of the rational number -5/8?

    5/8

    The additive inverse of a number is the value we add to it to get zero as the sum. For a rational number -a/b, the additive inverse is a/b. Thus, the additive inverse of -5/8 is indeed 5/8, as -5/8 + 5/8 = 0.

  2. 2. Find the multiplicative inverse of the rational number -13/19.

    -19/13 (or -1 6/13)

    The multiplicative inverse, or reciprocal, of a number is what we multiply it by to get exactly 1. The reciprocal of -13/19 is -19/13 because (-13/19) × (-19/13) = 1. Keep in mind that the sign of the fraction does not change.

  3. 3. Solve the equation for the variable x: 3x - 7 = 14.

    x = 7

    To find the unknown variable x, first add 7 to both sides of the equation to balance it: 3x = 14 + 7, which means 3x = 21. Now, dividing both sides by 3 gives x = 21/3 = 7.

  4. 4. Determine the sum of all interior angles of a regular pentagon.

    540 degrees

    We use the interior angle sum formula for any n-sided polygon: (n - 2) × 180 degrees. A regular pentagon features 5 sides, so substituting n = 5 gives (5 - 2) × 180 degrees = 3 × 180 degrees = 540 degrees.

  5. 5. In a parallelogram, two adjacent angles are in the ratio 2:3. Find the measure of the smaller angle.

    72 degrees

    The adjacent angles in any parallelogram are supplementary, meaning they add up to exactly 180 degrees. Let the two parts represent 2x and 3x, meaning 2x + 3x = 180 degrees, which leads to 5x = 180 degrees, and x = 36 degrees. The smaller adjacent angle measures 2 × 36 degrees = 72 degrees.

  6. 6. Find the square root of the number 729 using prime factorization.

    27

    Let us factorize the number: 729 = 3 × 3 × 3 × 3 × 3 × 3. Grouping these prime factors into pairs of duplicates, we have (3 × 3) × (3 × 3) × (3 × 3) = 3^2 × 3^2 × 3^2. Taking one digit from each matching pair yields 3 × 3 × 3 = 27.

  7. 7. What is the smallest natural number by which 72 must be multiplied to make it a perfect square?

    2

    The prime factorization of 72 is 2 × 2 × 2 × 3 × 3. Grouping them into matching pairs gives (2 × 2) × 2 × (3 × 3). The factor 2 remains unpaired, so multiplying 72 by another 2 forms a complete pair, yielding the perfect square 144 (12^2).

  8. 8. Calculate the cube root of the number 512.

    8

    To calculate the cube root, look for a number that multiplied by itself three times equals 512. If we write 8 × 8 × 8, the result is 64 × 8 = 512. Thus, the cube root of 512 is exactly 8, written as cube root of 512 = 8.

  9. 9. Express the percentage 15% in its simplest fraction terms.

    3/20

    To convert a percentage directly into a fraction, write the value over 100 and reduce: 15/100. Dividing both the numerator and the denominator by their biggest common factor (5) reduces the expression to 3/20.

  10. 10. If an item priced at 120 rupees is sold for 96 rupees, what is the discount percentage?

    20%

    The discount amount is calculated first: 120 - 96 = 24 rupees. The discount percentage represents this reduction over the marked price: (Discount / Marked Price) × 100. This matches (24 / 120) × 100 = 0.2 × 100 = 20%.

  11. 11. Solve the algebraic simplification: (2x + 5)(3x - 4).

    6x^2 + 7x - 20

    We use the FOIL method to multiply the binomial expressions step-by-step: (2x × 3x) + (2x × -4) + (5 × 3x) + (5 × -4). This expands to 6x^2 - 8x + 15x - 20, which simplifies to 6x^2 + 7x - 20.

  12. 12. Find the value of 5^3 × 5^-1.

    25

    Using exponent rules for a shared base, we sum the powers: a^m × a^n = a^(m+n). Here, we calculate 5^(3 + (-1)) = 5^(3-1) = 5^2. This gives a simple final value of 5 × 5 = 25.

  13. 13. If 15 workers can build a wall in 48 hours, how many workers will be required to do the same work in 30 hours?

    24 workers

    This represents an inverse proportion because more workers reduce the total time needed. The total work remains constant: x_1 × y_1 = x_2 × y_2, which means 15 × 48 = x_2 × 30, which leads to 720 = 30x_2. Dividing gives x_2 = 720/30 = 24 workers.

  14. 14. Factorize the algebraic expression: x^2 - 9.

    (x - 3)(x + 3)

    This expression follows the classical difference of squares identity: a^2 - b^2 = (a - b)(a + b). Writing 9 as the perfect square 3^2, the term x^2 - 3^2 factorizes directly into (x - 3)(x + 3).

  15. 15. Calculate the area of a trapezium whose parallel sides measure 12 cm and 20 cm, and the perpendicular height is 8 cm.

    128 square centimeters (cm2)

    The formula for the area of a trapezium is (1/2) × (a + b) × h. Substituting the values we have, the calculation is (1/2) × (12 + 20) × 8 = (1/2) × 32 × 8 = 16 × 8 = 128 cm2.

  16. 16. Find the volume of a cylinder with a base radius of 7 cm and a height of 10 cm. Take pi = 22/7.

    1540 cubic centimeters (cm3)

    The volume of a cylinder is calculated via V = pi × r^2 × h. Substituting our values: V = (22/7) × 7 × 7 × 10. The 7 in the denominator cancels one 7 in the numerator, yielding 22 × 7 × 10 = 154 × 10 = 1540 cm3.

  17. 17. What is the value of (2^0 + 3^0) × 5^1?

    10

    Any non-zero base raised to the power of 0 equals 1, so 2^0 = 1 and 3^0 = 1. The sum inside the parentheses is 1 + 1 = 2. Multiplying this by 5^1 (which is 5) gives 2 × 5 = 10.

  18. 18. Find the value of the coordinates (x, y) where the horizontal x-axis and vertical y-axis intersect on a cartesian plane.

    (0, 0) (or origin)

    The exact crossing point of the two axis reference lines is called the origin. Its coordinates are always designated as (0, 0), representing the baseline starting coordinates on any cartesian grid.

  19. 19. Factorize the expression: p^2 - 10p + 25.

    (p - 5)^2 (or (p-5)(p-5))

    This looks like a perfect square trinomial matching the identity (a - b)^2 = a^2 - 2ab + b^2. Writing 10p as 2(p)(5) and 25 as 5^2, we simplify the expression directly to (p - 5)^2.

  20. 20. Solve for y: 5y/3 - 4 = 11.

    y = 9

    First, add 4 to both sides to begin isolating the fraction term: 5y/3 = 11 + 4, which means 5y/3 = 15. Now multiply both sides by 3 to remove the denominator: 5y = 45. Dividing both sides by 5 gives y = 45/5 = 9.

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

    360 degrees

    The sum of the exterior angles of any convex polygon is always 360 degrees, regardless of its total number of sides. This occurs because traveling around the perimeter completes a single full turn.

  22. 22. If the selling price of an article is 250 rupees with a GST rate of 12%, find the total amount including tax.

    280 rupees

    The tax is calculated over the price: 12% of 250 = (12/100) × 250 = 30 rupees. Adding this tax value to the base cost gives the final customer invoice total of 250 + 30 = 280 rupees.

  23. 23. Find the square of the decimal number 2.5.

    6.25

    To square a decimal, it can be helpful to treat it as a fraction first: (25/10)^2 = 625/100. Converting back to standard decimal format yields 6.25.

  24. 24. A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability of getting a red ball?

    5/8

    Probability represents favorable outcomes divided by total outcomes. The number of red balls is 5, and the total count of balls is 5 + 3 = 8. Thus, the probability is 5/8.

  25. 25. Find the value of x when 2^(3x) = 64.

    x = 2

    First express both sides of the balance with a matching base of 2: 64 = 2^6. This transforms the problem to 2^(3x) = 2^6. Comparing powers directly gives 3x = 6, so x = 6/3 = 2.

  26. 26. Express the small number 0.000035 in standard scientific notation.

    3.5 x 10^-5 (or 3.5 * 10^-5)

    To rewrite 0.000035 in scientific notation, we slide the decimal point five spaces to the right, placing it between the 3 and the 5. Because the original number is less than one, we use a negative exponent: 3.5 × 10^-5.

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

    150 square centimeters (cm2)

    A cube has six identical square faces. The surface area is given by the formula 6s^2, where s is the side length. Substituting gives 6 × 5^2 = 6 × 25 = 150 cm2.

  28. 28. Find the product of the monomials: -4p and 7pq.

    -28p^2q

    Multiply coefficients and variables separately: (-4 × 7) × (p × pq) = -28 × p^(1+1)q = -28p^2q. Keep in mind the negative sign is retained in the result.

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

    4

    In an inverse proportion, the product of the variables remains constant: x_1 * y_1 = x_2 * y_2. Here, 8 × 6 = 12 × y_2, which means 48 = 12y_2. Dividing both sides by 12 yields y = 48/12 = 4.

  30. 30. State the coefficient of the variable x^2 in the algebraic expression: 5 - 4x^2 + 7x.

    -4

    The coefficient is the multiplying factor in front of the variable. Looking closely at the term -4x^2, the coefficient of x^2 is -4. A common mistake is leaving out the negative sign.

Curriculum Mapping & Learning Guide

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

Rational Numbers, Roots & Exponents (Questions 1-10)

Tests rational identities, prime factorization for square or cube roots, laws of exponents, and basic fractions.

Equations, Ratios & Percentages (Questions 11-20)

Checks single-variable equations, direct and inverse proportions, percentage changes, and compound interest calculations.

Geometry, Mensuration & Factorisation (Questions 21-30)

Covers parallel lines, trapezium or cylinder formulas, simple coordinates, and algebraic factorization.

Class 8 Math chapters covered

  1. Chapter 1: Understanding rational numbers, reciprocals, and additive properties.
  2. Chapter 2: Balancing simple linear equations and solving multi-step word problems.
  3. Chapter 3: Exploring polygons, parallel lines, angles, and quadrilateral properties.
  4. Chapter 4: Calculating square roots, cube roots, and applying laws of exponents.
  5. Chapter 5: Using formulas for trapeziums, cylinder volumes, and 3D surface areas.
  6. Chapter 6: Comparing quantities using percentage changes, compound interest, and direct/inverse proportions.
  7. Chapter 7: Practicing algebraic factorization, expanding brackets, and finding variables coefficients.

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