8 Advanced Mistakes Students Make in Mathematics Board Exams (With Examples & Solutions)

Mathematics is known as a scoring subject for board exams, but students end up dropping marks not due to insufficient knowledge, but due to repeated silly errors that could have been easily avoided. Mistakes vary from minor calculation errors to misinterpreting concepts or omitting critical steps in multi-part answers. We have put a spotlight on the 8 most common mistakes that students make in Mathematics, with clear examples and solutions to these have been proven to assist students in making the most out of their marks. At Global NextGen Academia, we have specialized teachers who teach structured online classes with a special focus on conceptual clarity, step-wise solving of problems, along practice-based corrections to help students bring out their best during the board exams.

1. Misreading the Question

• The simplest yet most common mistake is not understanding what the question is asking.
• Students tend to fly through problems and miss important information.

Example: Question: Solve for x if 3x + 5 = 20 Student Mistake: Writes x = 20 ÷ 3 + 5 = 11.67

Where is the mistake? The student divided 20 by 3 without first subtracting 5.

Correct Solution: 3x + 5 = 20 3x = 20 – 5 = 15 x = 15 ÷ 3 = 5

Tips:

• Read each question carefully
• Identify exactly what is asked
• Highlight keywords such as “simplify,” “factor,” “solve,” or “find.”

2. Calculation Errors

• Students often perform simple arithmetic incorrectly, which affects the entire solution.

Example: Solve 25 × 36 Student Mistake: Writes 25 × 36 = 950 Error: Miscalculation of multiplication

Correct Solution: 25 × 36 = 900

Tips:

• Double-check calculations
• Use stepwise multiplication
• When possible, use estimation to verify

3. Incorrect Application of Formulas

• A lot of students know the formulas but apply them incorrectly to the wrong situations.

Example: Area of a triangle = ½ × base × height. Question: Find the area when only sides are given. Mistake: Uses ½ × side × side without height. Error: Formula is misapplied.

Correct Solution: Use Heron’s formula: s = (a + b + c)/2 Area = √[s(s–a)(s–b)(s–c)]

Tips:

• Know when each formula applies
• Practice multiple examples
• Write down the given values clearly before substitution

4. Ignoring Units or Signs

• Error in calculation! Students often ignore minus signs, exponents, or units, and this results in errors in their final answer.

Example: Simplify: –5 × (–2) Mistake: Writes –10

Correct Solution: –5 × (–2) = 10

Tips:

• Check negative signs carefully
• Include units in word problems
• Verify after each step

5. Skipping Steps in Multi-Step Problems

• In questions involving complex algebra, geometry, or calculus, students frequently omit intermediate working and thus miss out on marks for the method.

Example: Differentiate y = 3x² + 5x Mistake: Writes derivative as 3x² only

Correct Solution: dy/dx = 6x + 5

Tips:

• Write each step
• Show substitution and simplification
• Markers award points for method, not just the final answer

6. Misinterpreting Graphs and Data

• Students frequently interpret graphs, tables, or charts incorrectly in questions.

Example: A Bar graph shows sales of 5 companies. Mistake: Reads the wrong bar or miscalculates values.

Correct Solution:

• Check axes labels carefully
• Double-check scale and intervals
• Write calculations clearly

7. Confusing Similar Concepts

• In mathematics, many concepts appear similar but have different rules.

Examples: Students often misread graphs or tables, or charts in questions.

Correct Solution:

• Memorize formulas with examples
• Practice concept comparison tables
• Solve multiple past-paper problems

8. Rushing to Final Answer Without Verification

• Many students calculate quickly and write an answer without verifying.
• This leads to avoidable errors.

Example: Solve 7/8 + 5/12 Mistake: Writes 12/20

Correct Solution: LCM of 8 and 12 = 24 7/8 = 21/24, 5/12 = 10/24 Sum = 31/24

Tips:

• Always check answers
• Convert fractions, decimals, or units back to the original
• Estimate to see if the answer is reasonable

Summary

Mathematics can be made among the highest scoring subjects if such errors are avoided, like questions being read wrongly, mistakes in calculations, using the wrong formula, not considering units or negative signs, leaving steps while solving questions, misreading graphs, mixing up concepts, or rushing towards final answers. At Global NextGen Academia, students enjoy the best of both worlds through meticulously planned online sessions where the stalwart educators impart concept-centric lectures, stepwise methodology of solving problems, and practice worksheets that ensure better understanding and fewer errors. With repeated exercises, illustrative examples, and techniques based on examination, the students face board exams with confidence and gain in accuracy with a better score. Regular study, systematic working, and going over answers over and over again are the keys to getting good results in Maths.