Class 9 is where the foundations for the board years are laid. The concepts introduced here, from number systems to coordinate geometry and the first real proofs in geometry, carry straight through to Class 10 and beyond. Students who practise a steady mix of problems from every chapter build the fluency that makes Class 10 far less daunting. Maths Daily Helper gives you unlimited fresh Class 9 questions, matched to the NCERT chapters, each with a full worked solution so you learn the method, not just the answer.
Chapters covered
- Number Systems (rational and irrational numbers, real numbers)
- Polynomials (identities, factorisation, remainder theorem)
- Coordinate Geometry
- Linear Equations in Two Variables
- Introduction to Euclid's Geometry
- Lines and Angles
- Triangles (congruence)
- Quadrilaterals
- Circles
- Heron's Formula
- Surface Areas and Volumes
- Statistics and Probability
Try a few Class 9 problems
Work each one out first, then check your steps.
Using an identity, expand (x + 5)².
1. Use the identity (a + b)² = a² + 2ab + b², with a = x and b = 5.
2. = x² + 2(x)(5) + 5² = x² + 10x + 25.
Answer: x² + 10x + 25.
Simplify √50 into its simplest surd form.
1. Factor 50 into a perfect square times another factor: 50 = 25 × 2.
2. √50 = √25 × √2 = 5√2.
Answer: 5√2.
Find the remainder when p(x) = x³ − 2x² + x + 1 is divided by (x − 1).
1. By the remainder theorem, the remainder is p(1).
2. p(1) = 1³ − 2(1²) + 1 + 1 = 1 − 2 + 1 + 1 = 1.
Answer: 1.
Find the area of a triangle with sides 3 cm, 4 cm and 5 cm.
1. Semi-perimeter s = (3 + 4 + 5)/2 = 6.
2. Area = √[s(s−a)(s−b)(s−c)] = √[6 × 3 × 2 × 1] = √36.
Answer: 6 cm².
If x = 2 and y = 3 is a solution of 2x + ky = 13, find k.
1. Substitute x = 2, y = 3: 2(2) + k(3) = 13, so 4 + 3k = 13.
2. 3k = 9, so k = 3.
Answer: k = 3.
In which quadrant does the point (−4, 5) lie?
1. The x-coordinate is negative and the y-coordinate is positive.
2. Negative x with positive y is the second quadrant.
Answer: Second quadrant.
Find the volume of a cube of side 6 cm.
1. Volume of a cube = side³.
2. = 6³ = 216.
Answer: 216 cm³.
Find the mean of the first five natural numbers: 1, 2, 3, 4, 5.
1. Sum = 1 + 2 + 3 + 4 + 5 = 15.
2. Mean = sum ÷ count = 15 ÷ 5 = 3.
Answer: 3.
Practise every chapter, unlimited
Choose Class 9 and any chapter. Get a fresh question each time, with hints and full solutions.
Open Maths Daily Helper →Building good habits in Class 9
Class 9 is the year to build the daily practice habit before the board pressure of Class 10. Ten questions a day across two or three chapters, rotating so nothing goes cold, is plenty. Use hints before solutions so you learn to find the next step yourself. Pay special attention to the geometry proofs and the algebraic identities, since these underpin much of what comes next.