7 Common Class 10 Maths Mistakes | Rahnuma Academy

You recognise the question, remember the formula and start solving. A few lines later, your answer is different from the one in the book.

Before starting the whole question again, check your working. A negative sign, an incomplete division or a missing root may explain the difference.

The examples below focus on quadratic equations. Compare them with your own notebook and make a short checklist of the mistakes you need to watch for.

1. Identifying coefficients before writing standard form

A quadratic equation is usually written as:

ax² + bx + c = 0, where a ≠ 0.

Suppose the question gives you:

2x² + 5 = 7x

First bring all the terms to one side:

2x² − 7x + 5 = 0

Now you can identify:

• a = 2

• b = −7

• c = 5

The coefficient b is −7, including the negative sign. Write the coefficients separately before substituting them into a formula.

2. Losing brackets around a negative number

For the equation:

x² − 6x + 5 = 0

the value of b is −6. Therefore:

b² = (−6)² = 36

Writing −6² without brackets means −(6²) under the usual order of operations, giving −36.

This difference can change the discriminant and the rest of your answer. Whenever you substitute a negative coefficient, put it in brackets.

Also check the value of −b. When b = −6, then −b = 6.

3. Dividing only part of the quadratic formula

The quadratic formula is:

x = (−b ± √(b² − 4ac)) / (2a)

The entire numerator must be divided by 2a.

For x² − 4x + 1 = 0, substitution gives:

x = (4 ± √12) / 2

Since √12 = 2√3:

x = (4 ± 2√3) / 2 = 2 ± √3

A common mistake is dividing the 4 by 2 while leaving the square-root term unchanged.

When writing by hand, draw a fraction bar long enough to show everything being divided. On a calculator, use brackets around the complete numerator and denominator.

4. Forgetting the second root

From:

x² = 16

you get:

x = 4 or x = −4

Both values give 16 when squared.

The ± symbol in the quadratic formula also requires you to consider both branches. Write the plus result and the minus result separately if that helps you keep track.

Before finishing, check whether your method has produced every root.

5. Dividing by a variable that could be zero

Consider:

x² − 5x = 0

Dividing both sides by x gives x − 5 = 0, leading to x = 5. But dividing by x assumes that x is not zero, so this step loses a valid solution.

Factor instead:

x(x − 5) = 0

Therefore:

x = 0 or x = 5

Whenever you cancel a variable expression, check whether setting that expression equal to zero could satisfy the original equation.

6. Solving for something the question did not ask

A question may ask for the discriminant or the nature of the roots rather than the roots themselves.

For:

x² + 4x + 4 = 0

the discriminant is:

D = b² − 4ac = 16 − 16 = 0

So the equation has a repeated real root.

Read the instruction before starting, then read it again before finishing. Your final statement should answer the actual request.

7. Skipping the substitution check

If you obtain x = 2 for:

x² − 5x + 6 = 0

substitute it into the original equation:

2² − 5(2) + 6 = 4 − 10 + 6 = 0

The root works. Check the other root too.

If the original question contains a denominator, also check any restrictions. A value that makes a denominator zero cannot be accepted, even if it appears during later algebraic steps.

Build a checking routine from your own mistakes

Choose two or three checks that address errors you actually make. For example:

1. Did I keep the signs of the coefficients?

2. Did I divide the whole numerator?

3. Did I include and check every valid root?

Keep an error notebook with the question, the incorrect step and a corrected example. Return to a similar question later and solve it independently.

Try this question before you leave

Solve:

2x² − 7x + 3 = 0

Factorisation gives:

(2x − 1)(x − 3) = 0

Therefore:

x = 1/2 or x = 3

Substitute both values into the original equation to check them.

If you keep getting stuck at the same step, show your working to a teacher. Finding the exact error gives you something specific to practise. Contact Rahnuma Academy if you would like to discuss Class 10 Mathematics tuition.

Does every quadratic equation have two different real roots?

No. For real coefficients, a positive discriminant gives two distinct real roots, zero gives a repeated real root and a negative discriminant gives no real roots.

Should I always use factorisation?

Use it when suitable factors are easy to identify. The quadratic formula is another method. Follow any method specifically required by the question.