NOTES FOR YOUR NEXT STUDY SESSION

The study blog

Useful routines, worked examples and small ideas that make learning feel more manageable.

CHOOSE YOUR NEXT GUIDE

Which average problem are you solving?

Choose the method that matches your question, then work through the examples.

सवाल में गलत मान है, दो ग्रुप हैं या कोई संख्या जोड़नी है? सही तरीका यहाँ चुनो।

Maths

Use HCF × LCM = product for two positive integers, then verify the candidate. Learn why the product equation alone is not sufficient.

Maths

Build a quadratic polynomial from two zeroes or their sum and product, check signs and understand why the polynomial is not unique.

Maths

Count ordered outcomes for two fair dice to find the probability of sum 7, compare other sums and avoid treating sums as equally likely.

Maths

Calculate the probability of at least one head in fair coin tosses using the complement, and distinguish at least one from exactly one.

Maths

Turn a product of consecutive integers into a quadratic equation, solve both roots and use the wording to choose valid integer pairs.

Maths

Set the discriminant to zero to find a parameter for equal roots, then verify the equation is still quadratic and check the repeated root.

Maths

Find the common difference and first term of an AP from two known positions, with subtraction, substitution and independent checks.

Maths

Use a strict inequality to find the first negative term of a decreasing AP. See why zero is not negative and check the neighbouring terms.

Maths

Find the position of a number in an arithmetic progression, check whether it belongs to the AP, and avoid negative or fractional term numbers.

Maths

Distinguish semicircle perimeter from curved arc length. Calculate with a radius or diameter and check compound-shape boundaries.