Can You Solve These 20 Tricky Math Problems for Classes IX and X CBSE ICSE

📚 20 Mathematical Challenges – CBSE, ICSE

Welcome! This slider shows two problems side by side on each page. Use Previous / Next buttons (or left/right arrow keys) to navigate through the 10 slides. Each problem has its own “Show hint” button – click to reveal a subtle nudge.

✨ Covers rational proofs, surd simplifications, Diophantine equations, and more. Suitable for grades 9–12 and competitive exams. Featuring 20 hand-picked problems covering everything from rational, irrational numbers to algebra and number theory. Whether you are prepping for a competitive exam or just love a good brain-teaser, this is for you. Suitable for students of IX and X of CBSE and ICSE. If these problems feel a bit intimidating, don't worry—they are designed to be! While standard high school mathematics focuses heavily on rote memorization and applying standard formulas to straightforward questions, this problem set bridges the gap between the regular classroom and competitive mathematics (like the AMC, math Olympiads, or advanced entrance exams). Instead of just asking you to "solve for x," these questions require creative algebraic manipulation, pattern recognition, and proof-based logical reasoning. They test whether you can combine multiple mathematical concepts to find an elegant solution, rather than just grinding through a standard algorithm. Key Mathematical Areas Covered This set of 20 problems targets several advanced domains: Advanced Algebra & Identities: Moving beyond basic factoring to use conditional identities (like the sum of cubes) and symmetric functions. Number Theory: Exploring the properties of prime numbers, divisibility rules, and solving basic Diophantine equations (finding integer solutions to polynomial equations). Complex Radicals & Surds: Tackling nested square roots, cube roots of binomial surds, and rationalizing multi-term denominators. Telescoping Series: Recognizing patterns in sequences that cancel each other out to reveal a clean, simple answer. Introductory Complex Numbers & Logarithms: Understanding the cyclical nature of imaginary numbers and manipulating logarithmic bases.

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✨ 20 problems, 10 slides, 2 per slide. Click "Show hint" for each problem individually. Left/right arrow keys navigate. Good luck! © Vinod Singh

Algebra Problem on the Concept of Odd and Even Numbers

 Let m, n, p and q be four positive integers such that m+n+p+q = 200. If S = (-1)^m+(-1)^n+(-1)^p+(-1)^q, then what is the number of possible values of S? #algebra #ProblemSolving #schoolmathematics

Surds Practice Problem Set

In Mathematics, surds are the values in square root that cannot be further simplified into whole numbers or integers. Surds are irrational numbers. The examples of surds are √2, √3, √5, etc., as these values cannot be further simplified. If we further simply them, we get decimal values, such as:

√2  = 1.4142135…

√3 = 1.7320508…

√5 = 2.2360679…

Surds Definition

Surds are the square roots  (√) of numbers that cannot be simplified into a whole or rational number. It cannot be accurately represented in a fraction. In other words, a surd is a root of the whole number that has an irrational value. Consider an example, √2 ≈ 1.414213. It is more accurate if we leave it as a surd √2.

Surds Worksheet

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Surd-Practice-II

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Surd-Practice-III

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Term of a sequence 1,2,2,3,3,3,4,4,4,4....

Can you solve this problem? In #mathematics, a #sequence is an enumerated collection of objects in which repetitions are allowed and order does matter. Like a set, it contains members (also called elements, or terms).
#Solution https://t.me/PrimeMaths/50
#PrimeMaths #Algebra

Powers of 2

A #Number #Theory gem based on #PigeonHole principle.

Prove that there exist two powers of 2 which differ by a multiple of 2020.

#PrimeMaths #Integers #Divisibility

More Problems for Practice:

Problem 1. Prove that of any 52 integers, two can always be found such that the difference of their squares is divisible by 100.

Problem 2. 15 boys gathered 100 nuts. Prove that some pair of buys gathered an identical number of nuts.

Problem 3. Given 11 different natural numbers, none greater than 20. Prove that two of these can be chosen, on of which divides the other.

Factorisation of n^5+n^4+1

To show a given expression not a prime we have to simply factor it into at least two factors with each factor greater than 1. Here is a #problem from #NumberTheory which uses this technique of proving not a #prime.
#PrimeMaths

Binomial Coefficients

An elegant problem from #Binomial Coefficients. Try this out or else see our solution.
#Algebra #Mathematics #CBSE #ISC #IIT #ISI #Learning #practicemakesperfect

Solution: https://t.me/PrimeMaths/24

Area of a Triangle

Solution:

Solving a system of in-equations: A problem form High School

In this video, I have solve a system of in-equations, using elementary ideas of high school mathematics. Using the fact that, square of any real number is always greater than equal to zero, we can at the same time frame and solve unique problems. Watch the full video, to learn.

Algebra Problem: Can you Solve it?

Using elementary identity from middle school, his problem can be solved. But it's really challenging and tricky if you don't hit the right idea. Check out the video to learn something new and interesting.

Let x,y,z be distinct real
numbers.

Prove that

∛(x-y)+∛(y-z)+∛(z-x)  ≠0