ICSE Class 9 maths solutions explained simply. Learn step-by-step to understand algebra, geometry, and other maths topics.
Maths can be tricky sometimes, but with a little help, it becomes much easier to understand. For ICSE Class 9 students, solving maths problems can feel overwhelming. However, with practice and the right approach, even the most complex problems can be solved. This guide provides solutions to various types of questions from the Class 9 ICSE maths syllabus. Whether it’s algebra, geometry, or arithmetic, the explanations are simple and easy to follow. By working through these questions and answers, students will get better at tackling maths problems and improve their skills.
Question 1
Question: What is the sum of the first 10 natural numbers?
Answer: The sum of the first 10 natural numbers is 55. This can be calculated using the formula for the sum of an arithmetic series: S = n(n+1)/2.
Question 2
Question: What is the value of x in the equation 3x + 5 = 20?
Answer: To solve for x, subtract 5 from both sides: 3x = 15. Then divide both sides by 3: x = 5.
Question 3
Question: What is the product of 8 and 12?
Answer: The product of 8 and 12 is 96.
Question 4
Question: Find the area of a rectangle with length 5 cm and width 3 cm.
Answer: The area of a rectangle is found using the formula: Area = length × width. So, Area = 5 × 3 = 15 cm².
Question 5
Question: What is the perimeter of a square with a side of 7 cm?
Answer: The perimeter of a square is calculated using the formula: Perimeter = 4 × side. So, Perimeter = 4 × 7 = 28 cm.
Question 6
Question: Solve for x in the equation 4x - 3 = 13.
Answer: Add 3 to both sides: 4x = 16. Then divide both sides by 4: x = 4.
Question 7
Question: What is the product of -3 and 6?
Answer: The product of -3 and 6 is -18.
Question 8
Question: If a triangle has a base of 10 cm and height of 6 cm, what is its area?
Answer: The area of a triangle is given by the formula: Area = (base × height) / 2. So, Area = (10 × 6) / 2 = 30 cm².
Question 9
Question: Solve for y in the equation 2y + 7 = 15.
Answer: Subtract 7 from both sides: 2y = 8. Then divide both sides by 2: y = 4.
Question 10
Question: What is the square root of 144?
Answer: The square root of 144 is 12.
Question 11
Question: Find the value of x if 5x - 4 = 21.
Answer: Add 4 to both sides: 5x = 25. Then divide both sides by 5: x = 5.
Question 12
Question: What is the area of a circle with a radius of 7 cm?
Answer: The area of a circle is given by the formula: Area = π × radius². So, Area = 3.14 × 7² = 153.86 cm².
Question 13
Question: What is the perimeter of a rectangle with length 8 cm and width 5 cm?
Answer: The perimeter of a rectangle is calculated as: Perimeter = 2 × (length + width). So, Perimeter = 2 × (8 + 5) = 26 cm.
Question 14
Question: Simplify the expression: 3x + 2x.
Answer: The simplified expression is 5x.
Question 15
Question: Solve for x in the equation 2x/3 = 6.
Answer: Multiply both sides by 3: 2x = 18. Then divide both sides by 2: x = 9.
Question 16
Question: What is the area of a square with a side of 4 cm?
Answer: The area of a square is calculated as: Area = side². So, Area = 4² = 16 cm².
Question 17
Question: Find the volume of a cube with a side of 3 cm.
Answer: The volume of a cube is calculated as: Volume = side³. So, Volume = 3³ = 27 cm³.
Question 18
Question: What is the perimeter of a triangle with sides 5 cm, 6 cm, and 7 cm?
Answer: The perimeter of a triangle is the sum of its sides. So, Perimeter = 5 + 6 + 7 = 18 cm.
Question 19
Question: What is the value of 4³?
Answer: The value of 4³ is 64.
Question 20
Question: Solve for y in the equation 3y + 9 = 18.
Answer: Subtract 9 from both sides: 3y = 9. Then divide both sides by 3: y = 3.
Question 21
Question: What is the LCM of 6 and 8?
Answer: The LCM of 6 and 8 is 24.
Question 22
Question: Find the area of a trapezium with parallel sides of 10 cm and 6 cm, and height of 4 cm.
Answer: The area of a trapezium is given by: Area = ½ × (sum of parallel sides) × height. So, Area = ½ × (10 + 6) × 4 = 32 cm².
Question 23
Question: What is the square of 9?
Answer: The square of 9 is 81.
Question 24
Question: Solve for z in the equation 3z - 8 = 16.
Answer: Add 8 to both sides: 3z = 24. Then divide both sides by 3: z = 8.
Question 25
Question: What is the difference between 100 and 45?
Answer: The difference between 100 and 45 is 55.
Question 26
Question: Solve for x in the equation 2(x + 3) = 14.
Answer: First expand the equation: 2x + 6 = 14. Then subtract 6 from both sides: 2x = 8. Finally, divide by 2: x = 4.
Question 27
Question: What is the area of a parallelogram with base 12 cm and height 5 cm?
Answer: The area of a parallelogram is given by: Area = base × height. So, Area = 12 × 5 = 60 cm².
Question 28
Question: What is the cube of 2?
Answer: The cube of 2 is 8.
Question 29
Question: Solve for x in the equation x/4 + 3 = 7.
Answer: Subtract 3 from both sides: x/4 = 4. Then multiply both sides by 4: x = 16.
Question 30
Question: Find the perimeter of a rectangle with length 10 cm and width 2 cm.
Answer: The perimeter of a rectangle is calculated as: Perimeter = 2 × (length + width). So, Perimeter = 2 × (10 + 2) = 24 cm.
Question 31
Question: What is the value of 5²?
Answer: The value of 5² is 25.
Question 32
Question: Solve for y in the equation y/3 = 5.
Answer: Multiply both sides by 3: y = 15.
Question 33
Question: What is the area of a circle with a radius of 10 cm?
Answer: The area of a circle is calculated as: Area = π × radius². So, Area = 3.14 × 10² = 314 cm².
Question 34
Question: Find the square root of 225.
Answer: The square root of 225 is 15.
Question 35
Question: What is the perimeter of a triangle with sides 6 cm, 8 cm, and 10 cm?
Answer: The perimeter of a triangle is the sum of its sides. So, Perimeter = 6 + 8 + 10 = 24 cm.
Question 36
Question: What is the cube of 3?
Answer: The cube of 3 is 27.
Question 37
Question: Solve for x in the equation 7x + 2 = 30.
Answer: Subtract 2 from both sides: 7x = 28. Then divide both sides by 7: x = 4.
Question 38
Question: What is the area of a rhombus with diagonals 6 cm and 8 cm?
Answer: The area of a rhombus is given by: Area = ½ × diagonal1 × diagonal2. So, Area = ½ × 6 × 8 = 24 cm².
Question 39
Question: What is the value of 3²?
Answer: The value of 3² is 9.
Question 40
Question: Solve for y in the equation 4y + 5 = 25.
Answer: Subtract 5 from both sides: 4y = 20. Then divide both sides by 4: y = 5.
Question 41
Question: Find the area of a rectangle with length 7 cm and width 5 cm.
Answer: The area of a rectangle is calculated as: Area = length × width. So, Area = 7 × 5 = 35 cm².
Question 42
Question: What is the perimeter of a square with a side of 8 cm?
Answer: The perimeter of a square is calculated as: Perimeter = 4 × side. So, Perimeter = 4 × 8 = 32 cm.
Question 43
Question: Solve for x in the equation 2x - 6 = 12.
Answer: Add 6 to both sides: 2x = 18. Then divide both sides by 2: x = 9.
Question 44
Question: What is the sum of the angles in a triangle?
Answer: The sum of the angles in a triangle is always 180°.
Question 45
Question: What is the square root of 169?
Answer: The square root of 169 is 13.
Question 46
Question: Solve for x in the equation 5(x - 2) = 20.
Answer: First expand the equation: 5x - 10 = 20. Then add 10 to both sides: 5x = 30. Finally, divide both sides by 5: x = 6.
Question 47
Question: What is the perimeter of a rectangle with length 15 cm and width 6 cm?
Answer: The perimeter of a rectangle is calculated as: Perimeter = 2 × (length + width). So, Perimeter = 2 × (15 + 6) = 42 cm.
Question 48
Question: What is the volume of a cylinder with radius 3 cm and height 7 cm?
Answer: The volume of a cylinder is calculated as: Volume = π × radius² × height. So, Volume = 3.14 × 3² × 7 = 197.82 cm³.
Question 49
Question: What is the difference between 85 and 32?
Answer: The difference between 85 and 32 is 53.
Question 50
Question: What is the value of 7³?
Answer: The value of 7³ is 343.
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