Important Questions Class 8 Maths With Answers For CBSE 2026

Important Questions Class 8 Maths are solved practice questions from the updated NCERT Ganita Prakash syllabus for CBSE 2026.
These questions test squares, cubes, exponents, quadrilaterals, algebra, proportional reasoning, percentages, Pythagoras theorem, data handling, line graphs, and area.

Class 8 Maths in 2026 needs careful practice because the updated NCERT Ganita Prakash book is split into Part-I and Part-II. Important Questions Class 8 Maths help students revise squares, cubes, powers, number systems, quadrilaterals, algebra, proportional reasoning, percentages, the Baudhayana-Pythagoras theorem, 3D geometry, graphs, and area. The 2026 books use stories, puzzles, activities, and proof-based thinking to build stronger mathematical reasoning. This article updates the earlier draft by keeping the numbered list focused on actual exam-style Maths questions instead of study-advice questions.

Key Takeaways

• Ganita Prakash 2026: Class 8 Maths has Part-I with 7 chapters and Part-II with 7 chapters.
• Part-I Focus: Students practise squares, cubes, powers, number systems, quadrilaterals, algebra, and proportional reasoning.
• Part-II Focus: Students practise percentages, Pythagoras theorem, inverse proportion, 3D geometry, line graphs, algebra, and area.
• School Exam Pattern: Class 8 Maths tests formulas, reasoning, diagrams, word problems, and step-by-step calculations.

Important Questions Class 8 Maths Structure 2026

Class 8 Maths Important Questions With Answers

These Class 8 Maths important questions with answers follow one continuous numbering pattern. The questions are exam-focused and include direct sums, reasoning questions, diagram-based topics, algebraic simplification, word problems, and data interpretation.

1. Find the square of 25 using the identity (a + b)².

The square of 25 is 625.

Write:

25 = 20 + 5

Formula Used:

(a + b)² = a² + 2ab + b²

Calculation:

25² = (20 + 5)²
= 20² + 2 × 20 × 5 + 5²
= 400 + 200 + 25
= 625

Final Answer: 25² = 625

2. Is 729 a cube number?

Yes, 729 is a cube number.

Check:

9³ = 9 × 9 × 9
= 81 × 9
= 729

So, 729 is the cube of 9.

Final Answer: 729 = 9³

3. Simplify 10³ × 10².

Use the exponent rule:

aᵐ × aⁿ = aᵐ⁺ⁿ

Calculation:

10³ × 10² = 10³⁺²
= 10⁵

10⁵ = 100000

Final Answer: 10³ × 10² = 10⁵ = 100000

Class 8 Maths Important Questions Chapter Wise For Ganita Prakash Part-I

Part-I builds the base for advanced arithmetic, algebra, geometry, and proportional thinking. Class 8 Maths important questions chapter wise should start with squares, cubes, powers, quadrilaterals, distributive law, and ratio-based reasoning.

4. What is a square number?

A square number is a number obtained by multiplying a number by itself.

If n is a whole number, then:

Square of n = n × n

Example:

7² = 7 × 7 = 49

So, 49 is a square number.

Final Answer: A square number is of the form n².

5. Find the square of 16.

The square of 16 is 256.

Given Data:

Number = 16

Formula Used:

Square of n = n × n

Calculation:

16² = 16 × 16
16² = 256

Final Answer: 16² = 256

6. What is a cube number?

A cube number is a number obtained by multiplying a number by itself three times.

If n is a whole number, then:

Cube of n = n × n × n

Example:

5³ = 5 × 5 × 5 = 125

So, 125 is a cube number.

Final Answer: A cube number is of the form n³.

7. Find the cube of 8.

The cube of 8 is 512.

Given Data:

Number = 8

Formula Used:

Cube of n = n × n × n

Calculation:

8³ = 8 × 8 × 8
= 64 × 8
= 512

Final Answer: 8³ = 512

8. What is an exponent?

An exponent shows how many times a base is multiplied by itself.

In aⁿ, a is the base and n is the exponent.

Example:

2⁵ = 2 × 2 × 2 × 2 × 2
= 32

Final Answer: An exponent tells how many times the base is used as a factor.

9. Simplify 3⁴.

3⁴ = 81

Given Data:

3⁴

Rule Used:

Multiply 3 by itself 4 times.

Calculation:

3⁴ = 3 × 3 × 3 × 3
= 81

Final Answer: 3⁴ = 81

10. What is the distributive law in algebra?

The distributive law states that multiplication can be distributed over addition or subtraction.

Formula:

a × (b + c) = a × b + a × c

Example:

5(x + 3) = 5x + 15

This idea appears in algebra and helps students expand expressions quickly.

Final Answer: The distributive law is a(b + c) = ab + ac.

NCERT Class 8 Maths Ganita Prakash Questions From Squares, Cubes And Powers

Squares, cubes, and powers help students write repeated multiplication in short form. NCERT Class 8 Maths Ganita Prakash questions from this area often test identities, exponent laws, and number patterns.

11. Find 12² using multiplication.

12² = 144

Given Data:

Number = 12

Formula Used:

n² = n × n

Calculation:

12² = 12 × 12
= 144

Final Answer: 12² = 144

12. Find 15² using the identity (a + b)².

15² = 225

Given Data:

15 = 10 + 5

Formula Used:

(a + b)² = a² + 2ab + b²

Calculation:

15² = (10 + 5)²
= 10² + 2 × 10 × 5 + 5²
= 100 + 100 + 25
= 225

Final Answer: 15² = 225

13. Find 6³.

6³ = 216

Given Data:

Number = 6

Formula Used:

n³ = n × n × n

Calculation:

6³ = 6 × 6 × 6
= 36 × 6
= 216

Final Answer: 6³ = 216

14. Write 100000 as a power of 10.

100000 = 10⁵

Given Data:

Number = 100000

Rule Used:

Count the number of zeros after 1.

Calculation:

100000 has 5 zeros.

So:

100000 = 10⁵

Final Answer: 100000 = 10⁵

15. Simplify 2³ × 2⁴.

2³ × 2⁴ = 128

Given Data:

2³ × 2⁴

Formula Used:

aᵐ × aⁿ = aᵐ⁺ⁿ

Calculation:

2³ × 2⁴ = 2³⁺⁴
= 2⁷
= 128

Final Answer: 128

16. Simplify 5⁶ ÷ 5².

5⁶ ÷ 5² = 625

Given Data:

5⁶ ÷ 5²

Formula Used:

aᵐ ÷ aⁿ = aᵐ⁻ⁿ

Calculation:

5⁶ ÷ 5² = 5⁶⁻²
= 5⁴
= 625

Final Answer: 625

Class 8 Maths Geometry Questions From Quadrilaterals And Pythagoras Theorem

Geometry in Class 8 connects shape properties with logical proof. Class 8 Maths geometry questions include quadrilaterals, right triangles, solids, and shortest-path reasoning.

17. What is a quadrilateral?

A quadrilateral is a closed figure with four sides.

It has:

1. Four sides
2. Four vertices
3. Four angles

Examples include square, rectangle, rhombus, parallelogram, and trapezium.

The sum of interior angles of a quadrilateral is:

360°

Final Answer: A quadrilateral is a closed four-sided figure.

18. Find the missing angle of a quadrilateral with angles 80°, 90°, and 110°.

The missing angle is 80°.

Given Data:

Three angles = 80°, 90°, 110°

Formula Used:

Sum of angles of a quadrilateral = 360°

Calculation:

Missing angle = 360° – (80° + 90° + 110°)
= 360° – 280°
= 80°

Final Answer: Missing angle = 80°

19. What is a parallelogram?

A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

Properties:

1. Opposite sides are equal.
2. Opposite angles are equal.
3. Diagonals bisect each other.

Final Answer: A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

20. What is the Baudhayana-Pythagoras theorem?

The Baudhayana-Pythagoras theorem states that in a right triangle:

Hypotenuse² = Base² + Height²

Formula:

c² = a² + b²

Here, c is the hypotenuse.

It applies only to right-angled triangles.

Final Answer: In a right triangle, c² = a² + b².

21. Find the hypotenuse if the two shorter sides are 6 cm and 8 cm.

The hypotenuse is 10 cm.

Given Data:

a = 6 cm
b = 8 cm

Formula Used:

c² = a² + b²

Calculation:

c² = 6² + 8²
c² = 36 + 64
c² = 100
c = 10 cm

Final Answer: Hypotenuse = 10 cm

22. Find the missing side if the hypotenuse is 13 cm and one side is 5 cm.

The missing side is 12 cm.

Given Data:

c = 13 cm
a = 5 cm

Formula Used:

c² = a² + b²

Calculation:

13² = 5² + b²
169 = 25 + b²
b² = 144
b = 12 cm

Final Answer: Missing side = 12 cm

Class 8 Maths Algebra Questions With Step-By-Step Solutions

Algebra turns number patterns into general rules. Class 8 Maths algebra questions usually test expansion, simplification, like terms, distributive law, and simple equations.

23. Simplify 4(x + 7).

4(x + 7) = 4x + 28

Given Data:

4(x + 7)

Formula Used:

a(b + c) = ab + ac

Calculation:

4(x + 7) = 4 × x + 4 × 7
= 4x + 28

Final Answer: 4x + 28

24. Simplify 3a + 5a – 2a.

3a + 5a – 2a = 6a

Given Data:

3a + 5a – 2a

Rule Used:

Add or subtract like terms.

Calculation:

3a + 5a = 8a
8a – 2a = 6a

Final Answer: 6a

25. Expand 5(2x – 3).

5(2x – 3) = 10x – 15

Given Data:

5(2x – 3)

Formula Used:

a(b – c) = ab – ac

Calculation:

5(2x – 3) = 5 × 2x – 5 × 3
= 10x – 15

Final Answer: 10x – 15

26. Solve x + 9 = 20.

x = 11

Given Data:

x + 9 = 20

Rule Used:

Subtract 9 from both sides.

Calculation:

x + 9 – 9 = 20 – 9
x = 11

Final Answer: x = 11

27. Solve 3x = 24.

x = 8

Given Data:

3x = 24

Rule Used:

Divide both sides by 3.

Calculation:

3x ÷ 3 = 24 ÷ 3
x = 8

Final Answer: x = 8

28. Solve 2x + 5 = 17.

x = 6

Given Data:

2x + 5 = 17

Rule Used:

Subtract 5, then divide by 2.

Calculation:

2x + 5 – 5 = 17 – 5
2x = 12
x = 6

Final Answer: x = 6

Class 8 Maths Proportional Reasoning Questions With Answers

Proportional reasoning helps students compare quantities through ratios, rates, percentages, and inverse variation. Class 8 Maths proportional reasoning questions appear in both Part-I and Part-II of Ganita Prakash.

29. What is a ratio?

A ratio compares two quantities of the same kind.

It shows how one quantity relates to another.

Example:

If there are 3 red balls and 5 blue balls, the ratio is:

3 : 5

Final Answer: A ratio compares two quantities of the same kind.

30. Simplify the ratio 18 : 24.

18 : 24 = 3 : 4

Given Data:

Ratio = 18 : 24

Rule Used:

Divide both terms by their HCF.

Calculation:

HCF of 18 and 24 = 6

18 ÷ 6 = 3
24 ÷ 6 = 4

Final Answer: 18 : 24 = 3 : 4

31. If 4 notebooks cost ₹80, what is the cost of 7 notebooks?

The cost of 7 notebooks is ₹140.

Given Data:

Cost of 4 notebooks = ₹80

Formula Used:

Cost of 1 notebook = Total cost ÷ Number of notebooks

Calculation:

Cost of 1 notebook = 80 ÷ 4 = ₹20

Cost of 7 notebooks = 7 × 20 = ₹140

Final Answer: ₹140

32. What is inverse proportion?

Inverse proportion means one quantity increases when the other quantity decreases in the same ratio.

The product of the two quantities remains constant.

Example:

More workers take fewer days for the same work.

If workers double, days become half.

Final Answer: In inverse proportion, one quantity increases while the other decreases.

33. If 6 workers complete work in 10 days, how many days will 12 workers take?

12 workers will complete the work in 5 days.

Given Data:

6 workers take 10 days.
12 workers take x days.

Rule Used:

Workers and days are in inverse proportion.

Calculation:

6 × 10 = 12 × x
60 = 12x
x = 5

Final Answer: 5 days

34. Convert 35% into a fraction.

35% = 7/20

Given Data:

35%

Formula Used:

x% = x/100

Calculation:

35% = 35/100
= 7/20

Final Answer: 35% = 7/20

35. Find 20% of 250.

20% of 250 is 50.

Given Data:

20% of 250

Formula Used:

x% of y = (x/100) × y

Calculation:

20% of 250 = (20/100) × 250
= 50

Final Answer: 50

Class 8 Maths Data Handling Questions With Line Graphs And Mean

Data questions test reading, organising, and interpreting values. Class 8 Maths data handling questions should include mean, trends, tables, and graph interpretation. Class 8 Maths line graph questions often ask students to read increases, decreases, and constant values.

36. What is arithmetic mean?

Arithmetic mean is the sum of observations divided by the number of observations.

Formula:

Mean = Sum of observations ÷ Number of observations

It gives one representative value for the data.

Final Answer: Arithmetic mean is the average of all observations.

37. Find the mean of 6, 8, 10, 12, 14.

The mean is 10.

Given Data:

Numbers = 6, 8, 10, 12, 14

Formula Used:

Mean = Sum of observations ÷ Number of observations

Calculation:

Sum = 6 + 8 + 10 + 12 + 14 = 50

Number of observations = 5

Mean = 50 ÷ 5 = 10

Final Answer: Mean = 10

38. Find the mean of 15, 20, 25, 40.

The mean is 25.

Given Data:

Numbers = 15, 20, 25, 40

Formula Used:

Mean = Sum ÷ Number of observations

Calculation:

Sum = 15 + 20 + 25 + 40 = 100

Number of observations = 4

Mean = 100 ÷ 4 = 25

Final Answer: Mean = 25

39. What does an upward line graph show?

An upward line graph shows an increase in value over time.

It means the quantity rises from left to right.

Example:

If temperature values rise each hour, the line graph moves upward.

Final Answer: An upward line graph shows an increasing trend.

40. What does a flat line in a line graph show?

A flat line in a line graph shows no change in value.

The quantity remains constant.

Example:

If water level stays at 50 cm for 3 hours, the graph stays horizontal.

Final Answer: A flat line shows a constant value.

Class 8 Maths Area Questions With Formulas And Solutions

Area questions need the correct formula before calculation. Class 8 Maths area questions should always include square units in the final answer.

41. What is the area of a rectangle?

The area of a rectangle is:

Length × Breadth

Formula:

Area = length × breadth

The answer uses square units such as cm², m², or km².

Final Answer: Area of rectangle = length × breadth

42. Find the area of a rectangle with length 12 cm and breadth 7 cm.

The area is 84 cm².

Given Data:

Length = 12 cm
Breadth = 7 cm

Formula Used:

Area = length × breadth

Calculation:

Area = 12 × 7
Area = 84 cm²

Final Answer: 84 cm²

43. What is the area of a triangle?

The area of a triangle is:

1/2 × base × height

Formula:

Area = 1/2 × base × height

The base and height must be perpendicular.

Final Answer: Area of triangle = 1/2 × base × height

44. Find the area of a triangle with base 10 cm and height 6 cm.

The area is 30 cm².

Given Data:

Base = 10 cm
Height = 6 cm

Formula Used:

Area = 1/2 × base × height

Calculation:

Area = 1/2 × 10 × 6
Area = 30 cm²

Final Answer: 30 cm²

45. What is the area of a parallelogram?

The area of a parallelogram is:

Base × Height

Formula:

Area = base × height

The height must be perpendicular to the base.

Final Answer: Area of parallelogram = base × height

46. Find the area of a parallelogram with base 14 cm and height 5 cm.

The area is 70 cm².

Given Data:

Base = 14 cm
Height = 5 cm

Formula Used:

Area = base × height

Calculation:

Area = 14 × 5
Area = 70 cm²

Final Answer: 70 cm²

Class 8 Maths Extra Questions With Solutions For Mixed Practice

Mixed practice helps students connect formulas across chapters. Class 8 Maths extra questions with solutions should include one-step, two-step, and word-problem formats.

47. A number is multiplied by 5 and the result is 45. Find the number.

The number is 9.

Given Data:

5x = 45

Rule Used:

Divide both sides by 5.

Calculation:

x = 45 ÷ 5
x = 9

Final Answer: x = 9

48. Find 25% of ₹640.

25% of ₹640 is ₹160.

Given Data:

25% of 640

Formula Used:

x% of y = (x/100) × y

Calculation:

25% of 640 = 25/100 × 640
= 160

Final Answer: ₹160

49. A square has side 9 cm. Find its area.

The area is 81 cm².

Given Data:

Side = 9 cm

Formula Used:

Area of square = side × side

Calculation:

Area = 9 × 9
Area = 81 cm²

Final Answer: 81 cm²

50. A line graph shows sales increased from 40 to 65. Find the increase.

The increase is 25 units.

Given Data:

Initial value = 40
Final value = 65

Formula Used:

Increase = Final value – Initial value

Calculation:

Increase = 65 – 40
Increase = 25

Final Answer: 25 units

51. A shopkeeper marks an item at ₹800 and gives a 15% discount. Find the selling price.

The selling price is ₹680.

Given Data:

Marked price = ₹800
Discount = 15%

Discount:

15% of 800 = 15/100 × 800
= 120

Selling price:

800 – 120 = 680

Final Answer: ₹680

52. A car travels 180 km in 3 hours. Find its speed.

The speed is 60 km/h.

Formula Used:

Speed = Distance ÷ Time

Calculation:

Speed = 180 ÷ 3
= 60 km/h

Final Answer: 60 km/h

53. The angles of a quadrilateral are 70°, 95°, 110°, and x°. Find x.

x = 85°

Formula Used:

Sum of angles of a quadrilateral = 360°

Calculation:

70° + 95° + 110° + x = 360°
275° + x = 360°
x = 85°

Final Answer: x = 85°

54. A right triangle has hypotenuse 17 cm and one side 8 cm. Find the other side.

The other side is 15 cm.

Use the Baudhayana-Pythagoras theorem:

c² = a² + b²

Given:

c = 17 cm
a = 8 cm

Calculation:

17² = 8² + b²
289 = 64 + b²
b² = 225
b = 15 cm

Final Answer: 15 cm

55. The marks of five students are 12, 16, 18, 20, 24. Find the mean.

The mean is 18.

Formula Used:

Mean = Sum of observations ÷ Number of observations

Calculation:

Sum = 12 + 16 + 18 + 20 + 24 = 90

Number of observations = 5

Mean = 90 ÷ 5 = 18

Final Answer: 18

Class 8 Maths Important Questions Chapter-Wise

This chapter-wise list helps students organise Important Questions Class 8 Maths across Ganita Prakash Part-I and Part-II.

How To Practise Important Questions Class 8 Maths For CBSE 2026

Important Questions Class 8 Maths should be practised by chapter and by skill. First, revise formula-based topics like squares, cubes, exponents, area, and Pythagoras theorem. Then solve reasoning-based topics like quadrilaterals, proportional reasoning, line graphs, algebra, and word problems.

A useful practice order is:

1. Number Round: Squares, cubes, exponents, powers, and number patterns.
2. Geometry Round: Quadrilaterals, Pythagoras theorem, 3D geometry, and area.
3. Algebra Round: Distributive law, like terms, expansion, and equations.
4. Application Round: Percentages, ratios, inverse proportion, mean, and line graphs.

This makes Important Questions Class 8 Maths useful for both quick revision and full school-exam preparation.

Class 8 Maths Important Questions Chapter-Wise