Detailed ICSE Class 10 Maths Solutions for All Topics

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Maths is one of the core subjects in the ICSE Class 10 curriculum. It covers a wide range of topics that require a solid understanding of various concepts and methods. The subject can be tricky for some students, but with the right approach, it becomes easier to grasp. By solving problems from each chapter, students can enhance their understanding and prepare effectively for exams. This guide provides solutions to common types of questions that appear in ICSE Class 10 Maths, offering detailed answers that will help in boosting your performance and confidence.

 

Topic	Key Concepts	Formulae/Method	Importance in Exam
Algebra	Linear equations, quadratic equations, polynomials, factorization	$ax+b=0$, x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}x=2a−b±b2−4ac​​	Frequently asked in both theoretical and problem-solving sections.
Geometry	Perimeter, area, volume, surface area of different shapes, properties of triangles and quadrilaterals	Area of circle: πr2\pi r^2πr2, Volume of cube: a3a^3a3	Crucial for problem-solving and application-based questions.
Trigonometry	Trigonometric ratios, identities, heights and distances, angles of elevation and depression	$\sin \theta ,\cos \theta ,\tan \theta$, sin⁡2θ+cos⁡2θ=1\sin^2 \theta + \cos^2 \theta = 1sin2θ+cos2θ=1	Important for derivations and real-world application problems.
Mensuration	Areas and volumes of 2D and 3D shapes like circles, cones, spheres, cylinders	Volume of cone: 13πr2h\frac{1}{3} \pi r^2 h31​πr2h, Surface Area of sphere: 4πr24\pi r^24πr2	Often appears in applications and word problems in exams.
Statistics	Mean, median, mode, range, standard deviation, frequency distribution	Mean = ∑xn\frac{\sum x}{n}n∑x​, Range = $\text{max}-\text{min}$	Key topic for understanding data and analyzing distributions.

This table covers the main topics in ICSE Class 10 Maths, along with important formulae and methods, highlighting their relevance and frequency in exams.

Chapter 1: Algebra

Question: What is the value of x in the equation 2x + 5 = 15?

Answer: To solve for x, subtract 5 from both sides:
2x = 15 - 5
2x = 10
Now divide both sides by 2:
x = 10/2 = 5.

Question: Solve for y in the equation 3y - 8 = 16.

Answer: Add 8 to both sides of the equation:
3y = 16 + 8
3y = 24
Now divide both sides by 3:
y = 24/3 = 8.

Question: Solve the quadratic equation x² - 5x + 6 = 0.

Answer: Factor the equation:
(x - 2)(x - 3) = 0
Now set each factor to zero:
x - 2 = 0 or x - 3 = 0
Thus, x = 2 or x = 3.

Question: Find the value of x in the equation x² - 4x - 12 = 0.

Answer: Factor the equation:
(x - 6)(x + 2) = 0
Now set each factor to zero:
x - 6 = 0 or x + 2 = 0
Thus, x = 6 or x = -2.

Question: Solve for p in the equation 4p + 7 = 23.

Answer: Subtract 7 from both sides:
4p = 23 - 7
4p = 16
Now divide both sides by 4:
p = 16/4 = 4.

Chapter 2: Geometry

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(l + w)
= 2(8 + 5)
= 2 × 13 = 26 cm.

Question: What is the area of a triangle with base 6 cm and height 4 cm?

Answer: The area of a triangle is calculated as:
Area = (1/2) × base × height
= (1/2) × 6 × 4
= 12 cm².

Question: Find the volume of a cube with side length 3 cm.

Answer: The volume of a cube is calculated as:
Volume = side³
= 3³ = 27 cm³.

Question: What is the surface area of a sphere with radius 7 cm?

Answer: The surface area of a sphere is calculated as:
Surface Area = 4πr²
= 4 × 3.14 × 7²
= 4 × 3.14 × 49
= 615.44 cm².

Question: Calculate the circumference of a circle with radius 6 cm.

Answer: The circumference of a circle is calculated as:
Circumference = 2πr
= 2 × 3.14 × 6
= 37.68 cm.

Chapter 3: Trigonometry

Question: Find sin 30°.

Answer: The value of sin 30° is 1/2.

Question: Find cos 45°.

Answer: The value of cos 45° is √2/2.

Question: Find tan 60°.

Answer: The value of tan 60° is √3.

Question: If tan θ = 1, what is the value of θ?

Answer: tan θ = 1 implies θ = 45°.

Question: Find the value of cos 90°.

Answer: The value of cos 90° is 0.

Chapter 4: Mensuration

Question: What is the area of a circle with radius 10 cm?

Answer: The area of a circle is calculated as:
Area = πr²
= 3.14 × 10²
= 314 cm².

Question: Find the volume of a cone with radius 5 cm and height 12 cm.

Answer: The volume of a cone is calculated as:
Volume = (1/3)πr²h
= (1/3) × 3.14 × 5² × 12
= 314 × 25 × 12 / 3
= 314 × 100
= 31400 cm³.

Question: Find the surface area of a cylinder with radius 4 cm and height 10 cm.

Answer: The surface area of a cylinder is calculated as:
Surface Area = 2πr(h + r)
= 2 × 3.14 × 4 × (10 + 4)
= 2 × 3.14 × 4 × 14
= 350.24 cm².

Question: What is the perimeter of a square with side 6 cm?

Answer: The perimeter of a square is calculated as:
Perimeter = 4 × side
= 4 × 6
= 24 cm.

Question: Find the area of a rectangle with length 7 cm and width 3 cm.

Answer: The area of a rectangle is calculated as:
Area = length × width
= 7 × 3
= 21 cm².

Chapter 5: Statistics

Question: Find the mean of the numbers 10, 12, 14, 16, and 18.

Answer: The mean is calculated as:
Mean = (sum of all numbers) / number of numbers
= (10 + 12 + 14 + 16 + 18) / 5
= 70 / 5
= 14.

Question: Find the median of the numbers 5, 8, 12, 15, and 20.

Answer: To find the median, arrange the numbers in ascending order:
5, 8, 12, 15, 20.
The median is the middle number, so the median is 12.

Question: Find the mode of the numbers 4, 6, 8, 8, 10, 12.

Answer: The mode is the number that appears most frequently.
Here, 8 appears twice, so the mode is 8.

Question: Calculate the range of the numbers 2, 7, 10, 15, and 20.

Answer: The range is calculated as:
Range = highest number - lowest number
= 20 - 2
= 18.

Question: Find the standard deviation of the numbers 2, 4, 6, 8, and 10.

Answer: First, find the mean:
Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.
Then calculate the squared differences from the mean:
(2 - 6)² = 16, (4 - 6)² = 4, (6 - 6)² = 0, (8 - 6)² = 4, (10 - 6)² = 16.
Now, find the variance:
Variance = (16 + 4 + 0 + 4 + 16) / 5 = 40 / 5 = 8.
Finally, the standard deviation is the square root of the variance:
√8 ≈ 2.83.

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