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ACADIFY · FREE MATHEMATICS CHALLENGE

Class 10
Mathematics.

Go beyond memorising formulas. Test your mathematical reasoning, problem-solving ability, and understanding through application-based questions.

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Challenge your mathematical thinking.

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📐 10 Questions ⏱️ About 20 Minutes 🧠 Problem-Solving Challenge

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1. If α and β are the zeroes of 2x² − 7x + 3 = 0, find α² + β².
2. The pair of linear equations 2x + 3y = 7 and 4x + ky = 14 has infinitely many solutions. Find k.
3. The 5th term of an arithmetic progression is 18 and its 11th term is 42. Find the sum of its first 20 terms.
4. The points A(2, 3), B(4, k), and C(6, 7) lie on the same straight line. Find k.
5. From an external point P, a tangent PA is drawn to a circle with centre O. If OP = 13 cm and the radius OA = 5 cm, find PA.
6. If tan θ = 3/4, where θ is an acute angle, find (sin θ + cos θ)/(sin θ − cos θ).
7. From a point on the ground, the angle of elevation of the top of a vertical tower is 30°. If the point is 20√3 metres from the foot of the tower, find the tower's height.
8. A solid sphere of radius 6 cm is melted and recast into smaller spheres of radius 2 cm. How many smaller spheres are formed?
9. Two fair six-sided dice are rolled simultaneously. What is the probability that their sum is 9?
10. The values xᵢ and their frequencies fᵢ are shown below. Find the missing frequency x if the arithmetic mean is 2.5.

xᵢ: 1, 2, 3, 4
fᵢ: 2, x, 4, 2

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