Class 10 Maths: The Most Common Board-Exam Mistakes and How to Avoid Them

Every year, after the Class 10 Maths board exam, the same story repeats. A student walks out confident, then the result shows 8 or 10 marks fewer than expected.

When we go through mock papers with students, the lost marks rarely come from questions they "didn't know". They come from small, avoidable mistakes made under time pressure.

Here are the most common ones, chapter by chapter, with simple fixes. They apply to both Mathematics Standard and Mathematics Basic.

Mistake 1: Skipping steps

CBSE marking schemes award marks to key steps. If you jump straight to the answer, the examiner has nothing to give marks for, and if the answer is wrong you get zero.

Fix:

• Write each step on a new line.
• State the formula before substituting into it.
• For 3- and 5-mark questions, write a one-line conclusion ("Hence, the required number is 24.").

Mistake 2: Sign errors in quadratic equations

Solve 2x² − 7x + 3 = 0.

Here a = 2, b = −7, c = 3.

D = b² − 4ac = (−7)² − 4(2)(3) = 49 − 24 = 25

x = (−b ± √D) / 2a = (7 ± 5) / 4

So x = 3 or x = 1/2.

The common mistake is writing −b as −7 instead of +7, which gives x = −3 and x = −1/2.

Fix: write a, b and c with their signs before using the formula. Then substitute both roots back into the equation. It takes 20 seconds and catches most errors.

Mistake 3: HCF × LCM for three numbers

HCF × LCM = product of the numbers is true only for two numbers.

Check with 2, 4 and 6: HCF = 2, LCM = 12, so HCF × LCM = 24. But 2 × 4 × 6 = 48.

Fix: for three numbers, find the HCF and LCM by prime factorisation. Never use the product shortcut.

Mistake 4: Inventing trigonometric identities

Students under pressure write things like sin(A + B) = sin A + sin B. It is false.

Check: sin 30° + sin 60° = 0.5 + 0.866 = 1.366, but sin 90° = 1.

Fix:

• Learn the three identities in your syllabus: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ.
• In "prove that" questions, work on one side only (usually the more complicated one) until it equals the other side. Don't move terms across the equals sign.
• Learn the table of values for 0°, 30°, 45°, 60° and 90°, and rewrite it at the top of your rough work in the exam.

Mistake 5: Using the wrong cumulative frequency in the median

The median of grouped data is:

Median = l + [(n/2 − cf) / f] × h

where:

• l = lower limit of the median class
• n = total frequency
• cf = cumulative frequency of the class before the median class
• f = frequency of the median class
• h = class width

The most common mistake is using the cumulative frequency of the median class.

Similarly, for the mode:

Mode = l + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h

where f₁ is the frequency of the modal class, f₀ the class before it and f₂ the class after it.

Fix: always make a table with a cf column, mark the median class with an arrow, and write out what each letter equals before substituting.

Mistake 6: Probability greater than 1

A probability can never be more than 1 or less than 0. If you get 7/5, something went wrong.

Other frequent slips:

• Forgetting that a standard deck has 52 cards, with 26 red and 26 black, and 12 face cards (Jack, Queen and King of each suit).
• Miscounting the outcomes for two dice: there are 36, not 12.

Fix: list the sample space when it is small. Use P(not E) = 1 − P(E) when it is easier to count the opposite event.

Mistake 7: Units and conversions in mensuration

• Writing area in cm³ or volume in cm².
• Mixing metres and centimetres in the same calculation.
• Using π = 3.14 when the question says "use π = 22/7" (or the other way round).

In melting and recasting questions, remember that volume stays the same, not surface area.

Example: a metal sphere is melted and recast into smaller spheres. Number of small spheres = volume of big sphere ÷ volume of one small sphere.

Fix: convert all lengths to one unit at the start, and write the unit with every final answer.

Mistake 8: Misreading arithmetic progression questions

• nth term: aₙ = a + (n − 1)d
• Sum of first n terms: Sₙ = (n/2)[2a + (n − 1)d]

Students often confuse "the 10th term" with "the sum of the first 10 terms", or take d as a₁ − a₂ instead of a₂ − a₁.

Fix: underline what the question asks for before you start. Write a, d and n clearly.

Mistake 9: Section formula in the wrong order

If P divides the join of A(x₁, y₁) and B(x₂, y₂) in the ratio m : n, then:

P = ((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n))

Note that m pairs with B's coordinates. Swapping them is a common error.

Fix: draw a quick line with A, P and B marked and the ratio written above it.

Mistake 10: Poor time management

Spending 25 minutes on one tough question can cost three easy ones at the end.

Fix:

• Read the whole paper in the first 15 minutes (the reading time).
• Attempt the sections you are most confident in first, but label each answer with the correct question number.
• Keep 10–15 minutes at the end to recheck calculations, especially in long-answer questions.

Build your own mistakes list

The mistakes above are common, but your own pattern matters most. After every test, write each lost mark in a notebook under one of three headings: concept, calculation, or misread. Before the board exam, read that notebook twice.

For a full revision timeline, see our 90-day Class 10 revision plan.

Get step-by-step feedback

Most of these mistakes disappear with regular, properly checked practice. Our Class 10 Maths programme includes weekly step-marked tests in the CBSE pattern for both Standard and Basic. Students who need a final push before the boards can join the Board Exam Crash Course.

Next step: after the boards, students moving into Class 11 can take ASCAT, our scholarship-cum-admission test for a scholarship on Class 11 Physics tuition.