More Practice / Class 8

Class 8 Math Practice Test Online

Class 8 Math is CBSE's own 'bridge curriculum,' connecting middle-school arithmetic to real algebra: compound interest and profit-loss calculations on one side, factorisation and standard identities like (a+b)² on the other.

Class 8Math

Browse all classes

Reviewed by Hari Narayana · Maths Faculty, GV Academy · 14+ years teaching Class 6-10 Math, reviewed for curriculum & exam alignment.Linear equations, algebraic identities, and profit-loss problems double-checked for age-appropriate problem-solving methods.

Last reviewed: August 2026

📘 NCERT curriculum alignmentThis practice test follows NCERT Class 8 Mathematics, India's national curriculum board.▶

Topics covered

Rational Numbers
Linear Equations in One Variable
Understanding Quadrilaterals
Data Handling
Squares and Square Roots
Cubes and Cube Roots
Comparing Quantities
Algebraic Expressions and Identities
Mensuration
Exponents and Powers
Direct and Inverse Proportions
Factorisation
Introduction to Graphs

View official NCERT textbooks →

⚡ Quick quiz

Test yourself in under a minute: Class 8 Math Practice Test

Factorisation using standard identities and compound-interest word problems make up most of these questions.

1. What is the multiplicative inverse (reciprocal) of -9/14?
2. Express 3^-3 as a simplified fraction.
3. Solve for z: 5z - 8 = 27.
4. Expand (y + 6)(y - 6) using a standard identity.
5. A book marked at 800 rupees is sold for 680 rupees. What is the discount percentage?
6. If one interior angle of a parallelogram measures 70 degrees, what is the measure of its adjacent interior angle?
7. If 6 workers take 10 hours to build a wall, how many hours will 15 workers take to finish the same job at the same speed?

💭 Think about this

Can you apply A = P(1 + r/100)ⁿ to a real profit-and-loss word problem, not just recite it?

Questions below are grouped by topic, pick the Math topics you want to practice, or swap in your own worksheet, notebook, or textbook questions any time.

Rational Numbers, Squares & Roots

Tests additive and multiplicative inverses of rational numbers, square roots and cube roots by prime factorization, and squaring a decimal.

📋 Quick referenceInverses, Squares & Roots▶

Additive inverse: the number that adds to zero (add the opposite sign).
Multiplicative inverse (reciprocal): the number that multiplies to 1 (flip numerator and denominator).
Square root by prime factorization: group prime factors into pairs, take one from each pair.
Cube root by prime factorization: group prime factors into triplets, take one from each triplet.

Sign Rules for Inverses

For Students

Check your multiplicative inverse by multiplying it with the original fraction, only a correct, sign-preserving flip gives exactly 1.

For Teachers

Common mistake: finding the multiplicative inverse of a negative fraction like -7/11, students flip the fraction but also flip the sign. Ask them to check that two negative factors multiply to a positive result.

1. What is the additive inverse of the rational number -5/8?
▶Reveal answer
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. Find the multiplicative inverse of the rational number -13/19.
▶Reveal answer
-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. Find the square root of the number 729 using prime factorization.
▶Reveal answer
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) = 3² × 3² × 3². Taking one digit from each matching pair yields 3 × 3 × 3 = 27.
4. What is the smallest natural number by which 72 must be multiplied to make it a perfect square?
▶Reveal answer
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 (12²).
5. Calculate the cube root of the number 512.
▶Reveal answer
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.
6. Find the square of the decimal number 2.5.
▶Reveal answer
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. A quick check on the decimal placement: squaring a number with 1 decimal place always gives a result with 2 decimal places, which is a fast way to catch a misplaced decimal point.

Exponents & Powers

Covers laws of exponents, powers of zero, solving for an unknown exponent, and scientific notation.

📋 Quick referenceExponent Rules & Scientific Notation▶

aᵐ × aⁿ = aᵐ⁺ⁿ. Any non-zero number raised to the power 0 equals 1.
Scientific notation: write a very large or small number as a decimal between 1 and 10, multiplied by a power of 10.
To solve for an unknown exponent, first write both sides with the same base, then compare the exponents directly.

Zero Power Is Not Always One

For Students

Any non-zero number raised to the power 0 equals 1, but 0 to the power 0 itself is undefined at this level, don't assume the same rule applies.

1. Find the value of 5³ × 5⁻¹.
▶Reveal answer
25
Using exponent rules for a shared base, we sum the powers: aᵐ × aⁿ = aᵐ⁺ⁿ. Here, we add the exponents 3 and -1, which gives 5², since 3 + (-1) = 2. This gives a simple final value of 5 × 5 = 25.
2. What is the value of (2⁰ + 3⁰) × 5¹?
▶Reveal answer
10
Any non-zero base raised to the power of 0 equals 1, so 2⁰ = 1 and 3⁰ = 1. The sum inside the parentheses is 1 + 1 = 2. Multiplying this by 5¹ (which is 5) gives 2 × 5 = 10.
3. Find the value of x when 2^(3x) = 64.
▶Reveal answer
x = 2
First express both sides of the balance with a matching base of 2: 64 = 2⁶. This transforms the problem to 2^(3x) = 2⁶. Comparing powers directly gives 3x = 6, so x = 6/3 = 2.
4. Express the small number 0.000035 in standard scientific notation.
▶Reveal answer
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.

Equations, Expressions & Factorisation

Tests solving single-variable linear equations, expanding and multiplying algebraic expressions, factorisation using standard identities, and identifying coefficients.

📋 Quick referenceAlgebra Formulas & Identities▶

Solving for a variable: undo addition/subtraction first, then multiplication/division, doing the same to both sides.
Standard Identities
- Difference of squares: a² − b² = (a − b)(a + b).
- Perfect square trinomial: a² − 2ab + b² = (a − b)².
The coefficient is the number multiplied with a variable term (in 5x², the coefficient is 5); a lone number with no variable attached is a constant, not a coefficient.

Factoring Stops When the Question Says So

For Teachers

Grading note: if a student factors y² - 16 correctly as (y - 4)(y + 4) but then adds an unnecessary '= 0' and solves for y, mark it as an error, not a bonus.
The question asks for factorisation, not the roots of an equation, worth stating that boundary explicitly before a test.

1. Solve the equation for the variable x: 3x - 7 = 14.
▶Reveal answer
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.
2. Solve the algebraic simplification: (2x + 5)(3x - 4).
▶Reveal answer
6x² + 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 6x² - 8x + 15x - 20, which simplifies to 6x² + 7x - 20.
3. Factorize the algebraic expression: x² - 9.
▶Reveal answer
(x - 3)(x + 3)
This expression follows the classical difference of squares identity: a² - b² = (a - b)(a + b). Writing 9 as the perfect square 3², the term x² - 3² factorizes directly into (x - 3)(x + 3).
4. Factorize the expression: p² - 10p + 25.
▶Reveal answer
(p - 5)² (or (p-5)(p-5))
This looks like a perfect square trinomial matching the identity (a - b)² = a² - 2ab + b². Writing 10p as 2(p)(5) and 25 as 5², we simplify the expression directly to (p - 5)².
5. Solve for y: 5y/3 - 4 = 11.
▶Reveal answer
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.
6. Find the product of the monomials: -4p and 7pq.
▶Reveal answer
-28p²q
Multiply coefficients and variables separately: (-4 × 7) × (p × pq) = -28 × p¹⁺¹q = -28p²q. Keep in mind the negative sign is retained in the result. Multiplying like variables adds their exponents (p × pq means p¹ × p¹ × q, giving p²q), the same rule used for any exponent multiplication.
7. State the coefficient of the variable x² in the algebraic expression: 5 - 4x² + 7x.
▶Reveal answer
-4
The coefficient is the multiplying factor in front of the variable. Looking closely at the term -4x², the coefficient of x² is -4. A common mistake is leaving out the negative sign.

Comparing Quantities: Ratios, Percentages & Probability

Covers converting percentages to fractions, discount and GST calculations, direct and inverse proportion, and basic probability.

📋 Quick referenceRatio, Percentage & Probability Formulas▶

To turn a part-to-whole comparison into a percentage, divide the part by the whole and multiply by 100.
Inverse proportion: x₁ × y₁ = x₂ × y₂ (more of one means less of the other).
To find the probability of an event, count how many outcomes count as a 'win' and divide by how many outcomes are possible altogether.
Discount = Marked Price − Selling Price. GST is added on top of the selling price at the given rate to get the final bill amount.

Base of a Discount Is the Marked Price

For Students

Underline 'marked price' in the question before touching the calculator, that word decides which number goes in the denominator.

1. Express the percentage 15% in its simplest fraction terms.
▶Reveal answer
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.
2. If an item priced at 120 rupees is sold for 96 rupees, what is the discount percentage?
▶Reveal answer
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%.
3. If 15 workers can build a wall in 48 hours, how many workers will be required to do the same work in 30 hours?
▶Reveal answer
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.
4. If the selling price of an article is 250 rupees with a GST rate of 12%, find the total amount including tax.
▶Reveal answer
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.
5. 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?
▶Reveal answer
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.
6. If x and y are in inverse proportion, and x = 8 when y = 6, find the value of y when x = 12.
▶Reveal answer
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.

Geometry: Angles & Coordinates

Covers the interior and exterior angle sums of polygons, adjacent angles in a parallelogram, and coordinates of the origin. The exterior-angle rule is the more surprising one: it stays fixed at 360 degrees no matter how many sides the polygon has, since walking once around any closed shape always turns you through exactly one full rotation.

📋 Quick referenceAngle & Coordinate Rules▶

Use the interior-angle formula for a polygon's inside angles. For exterior angles, imagine walking once around the shape and record the total turn before returning to the starting direction.
The origin (0, 0) is the fixed point where the x-axis and y-axis intersect.
Interior and exterior angles at the same vertex always add up to 180 degrees (they form a straight line), which is why knowing one lets you find the other without a separate formula.

Testing the Formula Against a Shape You Know

For Students

Check any new polygon formula against a shape you already know, like confirming (n - 2) × 180 gives 360 degrees for a square (n = 4).
If a question asks for the exterior angle sum, don't reach for (n - 2) × 180 at all, that formula is only for interior angles.

For Teachers

Fast diagnostic: ask what (n - 2) × 180 gives for n = 4. A student who can't instantly connect the result to a square's known 360 degrees has memorized the formula without understanding what it counts.
Grading note: adjacent angles in a parallelogram being supplementary (summing to 180 degrees) comes from the parallel sides acting like a transversal-cut pair, not from a separate parallelogram-specific rule, worth connecting back to co-interior angles from Class 7.

1. Determine the sum of all interior angles of a regular pentagon.
▶Reveal answer
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.
2. In a parallelogram, two adjacent angles are in the ratio 2:3. Find the measure of the smaller angle.
▶Reveal answer
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.
3. Find the value of the coordinates (x, y) where the horizontal x-axis and vertical y-axis intersect on a cartesian plane.
▶Reveal answer
(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. Every other point's position is measured relative to this fixed reference point, which is why it never moves regardless of where a graph's data actually lies.
4. What is the sum of the exterior angles of any convex polygon?
▶Reveal answer
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.

Introduction to Graphs

Covers the x-axis and y-axis, identifying a point's quadrant, reading constant speed from a straight-line distance-time graph, and choosing a line graph for continuously changing data. A coordinate pair is always read in the same order, horizontal position first, then vertical, which is exactly what makes (3, -2) and (-2, 3) different points despite using the same two numbers.

📋 Quick referenceReading the Cartesian Plane▶

Quadrant sign rules
- Quadrant I: x positive, y positive.
- Quadrant II: x negative, y positive.
- Quadrant III: x negative, y negative.
- Quadrant IV: x positive, y negative.
Compare equal time intervals on a distance-time graph and check whether the distance rises by the same amount each time.
Line graphs suit continuously changing data (temperature, growth); bar graphs suit separate categories.
On a distance-time graph, a flat (horizontal) segment means the object has stopped, zero distance is being covered even though time is still passing.

Sign of Each Coordinate Decides the Quadrant

For Students

Check the sign of x first, then the sign of y, to find the quadrant, don't just guess from the numbers' size.
For distance-time graphs, compare equal time intervals and calculate how much distance is added in each one before deciding whether the speed changes.

For Teachers

Common mistake: students remember quadrant I is 'top right' but forget the sign pattern itself, so they struggle the moment a point isn't neatly plotted first.
Fast check: ask what a perfectly flat (horizontal) line on a distance-time graph means. Students who answer 'very slow' instead of 'stopped' haven't yet connected the graph's shape to the physical situation it represents.

1. On a Cartesian plane, what do we call the horizontal and vertical number lines used to locate a point?
▶Reveal answer
The x-axis (horizontal) and y-axis (vertical)
Every point on a Cartesian plane is located using its distance from these two perpendicular reference lines: how far along the x-axis, then how far along the y-axis.
2. In which quadrant does the point (3, -2) lie on a Cartesian plane?
▶Reveal answer
Fourth quadrant
The four quadrants are defined by the sign of each coordinate: quadrant I has both positive, II has x negative and y positive, III has both negative, and IV has x positive and y negative. Since (3, -2) has a positive x and a negative y, it lies in the fourth quadrant.
3. A line graph shows a car's distance travelled over time as a perfectly straight line passing through the origin. What does this tell you about the car's speed?
▶Reveal answer
The car is travelling at a constant (uniform) speed
A straight line on a distance-time graph means the distance increases by the same amount for every equal time interval, which is exactly what constant speed means. A curved line would instead mean the car's speed was changing over time.
4. What type of graph is best suited to show how one changing quantity, like temperature, varies continuously over time?
▶Reveal answer
A line graph
A line graph is built for showing a continuous trend, since points are joined by a line that reflects the value at every moment in between, not just at the marked points. A bar graph fits separate categories much better than a continuously changing quantity like temperature.

Data Handling

Tests frequency in a data table, reading and constructing a pie chart, distinguishing a histogram from a bar graph, and reading a grouped frequency table. Grouping data always trades some detail for a clearer overall pattern: a grouped frequency table shows how many students scored between 20 and 30, but not each individual student's exact mark within that range.

📋 Quick referenceOrganizing & Charting Data▶

Frequency = how many times a value appears in the data.
To build a pie-chart slice, first find how much of the whole one item represents, then convert that share into an angle.
Before choosing a graph, decide whether the values form continuous intervals or separate named categories.
A pie chart's slices must always add up to exactly 360 degrees in total, since together they represent the whole (100%) of the data, which is a quick way to check a finished pie chart for errors.

Count First, Chart Second

For Students

For pie-chart questions, find degrees-per-item first (360 / total), then multiply by each category's count.
Before choosing histogram or bar graph, check whether the data is a continuous range (like marks or heights) or separate categories (like favourite subjects).
Grouping data into class intervals makes a large data set easier to read at a glance, but it also means some individual detail is lost, a real tradeoff, not a shortcut without cost.

1. In a frequency distribution table, what do we call the number of times a particular observation occurs in the data?
▶Reveal answer
Frequency
Frequency simply counts how often a specific value or observation shows up in a data set. Organizing raw data into a frequency table is usually the first step before drawing any chart from it, whether a bar graph, histogram, or pie chart.
2. A survey of 36 students shows favourite subjects as: Math 9, Science 12, English 8, Art 7. In a pie chart of this data, which subject's slice measures exactly 90 degrees (one-quarter of the circle)?
▶Reveal answer
Math
Each student's share of the full circle is 360 / 36 = 10 degrees. Math has 9 students, so its slice measures 9 x 10 = 90 degrees, exactly one-quarter of the full 360-degree circle.
3. Which type of graph uses adjoining (touching) bars to represent grouped, continuous numerical data, unlike a bar graph, which uses separated bars for different categories?
▶Reveal answer
Histogram
A histogram's bars touch because the data is continuous, each class interval flows directly into the next with no natural gap. A bar graph represents separate, unrelated categories instead, so its bars are drawn with gaps on purpose.
4. In a grouped frequency table, the marks of 10 students fall into class intervals 0-10 (frequency 2), 10-20 (frequency 5), and 20-30 (frequency 3). How many students scored below 20?
▶Reveal answer
7
'Below 20' includes the 0-10 and 10-20 intervals. Adding their frequencies: 2 + 5 = 7 students scored below 20.

Mensuration: Area, Volume & Surface Area

Covers the area of a trapezium, the volume of a cylinder, and the total surface area of a cube.

📋 Quick referenceMensuration Formulas▶

Area of a trapezium = ½ × (sum of parallel sides) × height.
Volume of a cylinder = π × r² × height.
Total surface area of a cube = 6 × side².

Circle Radius Before Reaching for the Formula

For Students

Circle the word 'radius' or 'diameter' in the question before starting any calculation, this catches a diameter-instead-of-radius mistake before it reaches the working.
Remember to halve the diameter before squaring it in a cylinder volume formula, plugging the diameter straight into r² is the most common error here.

1. Calculate the area of a trapezium whose parallel sides measure 12 cm and 20 cm, and the perpendicular height is 8 cm.
▶Reveal answer
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.
2. Find the volume of a cylinder with a base radius of 7 cm and a height of 10 cm. Take pi = 22/7.
▶Reveal answer
1540 cubic centimeters (cm³)
The volume of a cylinder is calculated via V = pi × r² × 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.
3. Calculate the total surface area of a cube whose edge length is 5 cm.
▶Reveal answer
150 square centimeters (cm²)
A cube has six identical square faces. The surface area is given by the formula 6s², where s is the side length. Substituting gives 6 × 5² = 6 × 25 = 150 cm².

∑

Worked example: two methods, side by side

A sum of Rs. 10,000 is invested for 2 years at 10% per annum. Find the difference between the amounts under Simple Interest and Compound Interest.

Simple Interest (direct formula plug-in)

1. SI = P x r x t / 100 = 10000 x 10 x 2 / 100 = Rs. 2000.
2. Amount = P + SI = 10000 + 2000 = Rs. 12,000.

Compound Interest (A = P(1 + r/100)ⁿ)

1. A = 10000 x (1 + 10/100)² = 10000 x 1.21 = Rs. 12,100.
2. CI = A - P = Rs. 2,100.
3. Difference between CI and SI = 2100 - 2000 = Rs. 100, the extra 'interest on interest' that compounding adds.

Where board-exam marks are actually lost

Students often skip writing the formula itself and jump straight to plugging in numbers. If a calculation error creeps in, there is no working shown to earn partial credit.
Approximate steps or skipped units often still earn partial marks at this level. Precision expectations rise sharply the next year.
Treating this as 'still arithmetic' instead of practicing the standard identities (like (a+b)²) leaves students unprepared for Class 9 factorisation.

Frequently asked questions

What is the hardest part of Class 8 Math for most students?

Commercial Math (compound interest, profit & loss) and Algebra/Factorisation (standard identities), both marked as the 'bridge curriculum' units connecting middle-school arithmetic to high-school algebra.

Is Class 8 Math the same difficulty as Class 9?

No. Class 8 uses direct formula application on concrete problems, while Class 9 requires multi-step algebraic manipulation and formal proof-writing, a noticeably harder jump.

Explore more for Class 8

Class 8 English practice test Class 8 Science practice test

Move between subjects in the same class to build a fuller revision routine.

Math learning ladder — Middle (Class 6-8)

See where Class 8 Math fits in the middle (class 6-8) years, and jump straight to the next step.

Class 6
Integers, Ratios & Introductory Algebra
The jump from Class 5: introduces negative numbers, ratio and the unitary method, and the first algebraic variables and equations, the first year of middle-school math.
Open test →
Class 7
Rational Numbers, Exponents & Algebraic Expressions
Extends Class 6 further: integers become rational numbers, exponents and algebraic expressions enter the picture, and triangle geometry and proportional comparison bring in multi-step problems in place of single-step arithmetic.
Open test →
📍 You are here
Class 8
Roots, Factorisation & Applied Percentages
Class 7's algebra and geometry get real-world application here: square/cube roots, algebraic factorisation, and percentage-based problems like profit/loss and simple interest, the last middle-school milestone before Class 9 board-prep math.

The comfort with percentages and factorisation built here is what makes Class 9's algebra feel like a continuation, not a restart.

Was this page helpful?