What to revise before Class 10 Quadratic Equations

Quadratic Equations is one of the highest-scoring chapters in CBSE Class 10 Maths, and one where students lose marks they were fully capable of earning. The reason is rarely the quadratic formula. It is almost always something from Class 8 that nobody went back to check.

Here are the four things this chapter silently assumes your child already owns.

1. Factorisation, from Class 8

This is the big one. A student who cannot factorise fluently will find every single part of this chapter harder than it needs to be, because factorisation is the fastest route to the roots and the fallback when the formula gets messy.

The specific skill is finding two numbers with a given product and a given sum. Students who say they “cannot see the factors” usually believe that strong students simply spot them. They do not. They search, and the search is short.

2. Rearranging into standard form

Board questions almost never hand over a tidy equation. They give things like $x(x+3)=10$ or $\frac{1}{x}+\frac{1}{x+2}=\frac{3}{4}$, and the first job is to reach:

That needs comfortable expansion of brackets, moving terms across the equals sign with the correct sign change, and clearing denominators without losing a term. All Class 7 and 8 algebra. None of it is taught again in Class 10.

3. Square roots and surds, from Class 8

The moment the discriminant is not a perfect square, the answer contains a surd. Students need to simplify $\sqrt{48}$ to $4\sqrt{3}$ without hesitating, and to leave an answer in exact form rather than reaching for a decimal.

They also need to be sure that $\sqrt{b^2-4ac}$ is one single quantity to be computed before anything else happens to it.

The sign trap inside the formula

In $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$, when $b$ is already negative, $-b$ becomes positive. A student who is shaky on negative numbers loses the question here, having understood quadratics perfectly.

4. Turning a story into an equation

The application questions are where the marks concentrate and where students lose them. The maths is not the hard part. Choosing what $x$ stands for is.

The skills assumed here go back to Class 7:

• Naming the unknown deliberately, and writing down what it represents.
• Expressing everything else in terms of that unknown, so a number that is “3 more than” becomes $x+3$ rather than a new letter.
• Standard relationships: speed, distance and time; area of a rectangle; consecutive integers; ages now versus ages later.

The checklist

• Can they find two numbers with a given product and sum, quickly and without panic?
• Can they expand brackets and clear denominators to reach standard form?
• Can they simplify a surd and handle a negative $b$ inside the formula?
• Can they name an unknown and express the rest of a story in terms of it?
• Do they check whether each root makes sense before writing the final answer?

A no anywhere in that list will present itself as “I am bad at quadratic equations”. It is not. It is one specific earlier skill, and it is usually repairable in days rather than months.