how many of you are Indians and are about to appear for the board exams this year?
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Maths Class 10 Chapter 13 Surface Areas and Volume : Important Formulas ...
Remainder and Factor theorem | Mathematics class 10
Factor and Remainder theorem
1. Remainder theorem
If a polynomial f(x) is divided by (x – α) then remainder = f(α)
Example: Find the remainder (Without division) on dividing f(x) by (x + 3) where f(x) = 2x2 – 7x – 1
Solution:-
X + 3 = 0 or, x = -3
put x = -3 in f(x)
f(-3) = 2(-3)(-3) – (-3) – 1 = 20
Hence, remainder is 20.
2. Factor theorem
(x- α) is a factor of the polynomial f(x) if and only if f(α) = 0
Example: Show that (x – 5) is factors of f(x) where f(x) = 2x2 – 11x + 5.
Solution:-
x – 5 = 0 or, x = 5
put x = 5 in f(x)
f(5) = 2(5)(5) – 11(5) + 5 = 50 – 50 = 0
Hence (x – 5) is the factor.
for more formulas click here
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Class 10 Board Strategy: Navigating the February and May Exam Options
To maximize your scores and protect your Class 11 preparation, you must target the February exam as your main attempt. Treat the new May exam strictly as an optional safety net. Finish your entire syllabus by December. Delaying your preparation until May will create massive academic panic and ruin your high school foundation timeline.
The National Education Policy (NEP) 2020 has officially changed the rules of the game. For the first time, CBSE Class 10 students have the option of a bi-annual board exam system. You now have two chances to prove yourself: one exam in February, and a second exam in May.
At first glance, this sounds like a massive relief. Two chances mean less pressure, right?
Unfortunately, this new system is creating a dangerous psychological trap. Thousands of students are completely misunderstanding how to use these two dates. They are relaxing their study habits, assuming they have extra time. This mistake will cost them their board percentages and their Class 11 academic head start.
If you want to conquer the 2026 board exams without burning out, you need a strict CBSE Class 10 two board exams strategy. Here is exactly how to navigate the February and May options.
The Trap of the New System: Killing the "Extra Time" Myth
When a Class 10 student hears the phrase "exams in February and May," their brain translates it into a very dangerous thought: "I do not need to finish my syllabus by December anymore. I can finish it in April."
You must kill this myth immediately.
If you delay your syllabus completion, you will experience a domino effect of academic disasters. Your school will still hold pre-boards in December and January. If you are only 60% done with your syllabus by December, you will fail your pre-boards. Failing pre-boards destroys your confidence.
Furthermore, you will lose the crucial "Revision Buffer." Board exams are not cracked by reading a chapter once. They are cracked by solving 10 years of past papers. If you are still learning new theory in April, you have zero time for mock tests. You are setting yourself up for average marks.
The Core Strategy: February is the Main Event, May is the Safety Net
The only way to win this bi-annual system is to pretend the May exam does not exist until March.
You must walk into the February examination hall intending to score your peak 95%+. Treat February as the ultimate finish line. Give it 100% of your energy, focus, and revision time.
So, what is the point of the May exam?
The May exam is your Safety Net. The CBSE uses a "Best of Two" grading system. This means you do not have to retake the entire board exam in May. You only use May to selectively rewrite specific subjects.
Imagine you take all five subjects in February. You score brilliantly in Science, English, SST, and Hindi. But the Mathematics paper was unusually tough, and you made silly calculation errors, dropping your score to a 75%.
Under the old system, you were stuck with that 75%. Under the new system, you simply register to take only the Mathematics exam in May. You spend March and April focusing entirely on Math. If you score a 95% in May, CBSE takes your new Math score and combines it with your excellent February scores for your final report card.
That is how you use the system strategically. You do not delay your prep; you use May to fix isolated mistakes.
The Ultimate Month-by-Month Syllabus Timeline
To make this strategy work, you must know exactly when to finish class 10 syllabus chapters. You cannot leave your pacing to chance. Print out this exact timeline and stick it above your study desk.
If needed, write the improvement exam for 1 or 2 specific subjects only.
By locking your syllabus in December, you give yourself a massive 60-day revision buffer. This buffer is where average students turn into school toppers.
Why Delaying Until May Ruins Your Class 11 Prep
There is a massive hidden cost to procrastinating until May that nobody talks about: It ruins your high school transition.
Class 11 is universally known as the hardest academic jump in a student’s life. The syllabus volume triples. Whether you are aiming for JEE, NEET, or a rigorous Commerce track, Class 11 foundation batches begin in the first week of April.
Competitive exam timelines wait for no one. If you treat May as your main Class 10 board exam, you will spend April and May reading basic Class 10 Science and Math. Meanwhile, the students who finished their Class 10 boards in February have already started mastering Class 11 Kinematics and Mole Concept.
By the time you finally finish your May exams, you will be two full months behind your peers in Class 11. Catching up on a two-month backlog in Class 11 is nearly impossible and leads to severe burnout.
By executing a strict February and May board exams CBSE plan, you finish early. You get to rest in March, and you start Class 11 in April with a fresh, focused mind.
Quick Summary: The 2026 Board Exam Master Plan
Lock the Syllabus: Complete 100% of your NCERT syllabus by the end of December.
Target February: Treat the February exam as your primary, 100% effort attempt.
Leverage the Best-of-Two: Use the May exam only to improve scores in 1 or 2 specific subjects where you underperformed.
Protect Your Future: Finishing in February ensures you do not miss the crucial April start date for Class 11 prep.
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Master Your Timeline with Expert Guidance
Sticking to an aggressive syllabus timeline requires discipline, structured learning, and concept clarity. You cannot afford to waste weeks trying to understand difficult chapters on your own. If you want to finish your syllabus early and transition smoothly into higher-level academics, explore our Class 10 foundation timeline. We provide the exact structured pacing you need to conquer your boards in February and launch successfully into Class 11.
Every Small Step Today Creates Bigger Success Tomorrow
Preparing for Class 10 can feel like standing at the beginning of an important journey. There are assignments to complete, concepts to understand, regular tests to prepare for, and eventually the board examinations. For many students, this year feels different because it demands not only hard work but also consistency and confidence.
The good news is that success doesn't come from studying all day. It comes from building smart habits that make learning easier and more enjoyable over time.
Learning Is More Than Scoring Marks
Many students believe that high marks should be the only goal. While good grades certainly matter, understanding concepts is even more valuable. When students truly understand a topic, they remember it longer and can apply it in different situations instead of simply recalling memorized answers.
Subjects like mathematics and science especially reward logical thinking and conceptual clarity. Once the basics become strong, advanced chapters also become easier to understand.
Small Daily Efforts Make a Big Difference
Instead of waiting until examinations are only a few weeks away, students should make studying a daily habit. Even one focused hour every day often produces better results than trying to study for several hours at the last minute.
A simple routine could include:
Revising classroom notes
Solving a few practice questions
Reviewing mistakes from previous tests
Reading one difficult topic again
Planning the next day's study goals
Following a schedule also reduces stress because students always know what needs to be completed.
Confidence Comes From Practice
Nobody becomes good at mathematics by reading solutions alone. Confidence develops through solving problems independently.
Practice helps students:
Improve calculation speed
Reduce careless mistakes
Understand different question patterns
Strengthen logical thinking
Prepare for application-based questions
Every incorrect answer should be viewed as an opportunity to learn something new rather than as a failure.
Everyone Learns Differently
One of the biggest misconceptions about education is that every student learns at the same speed. In reality, some students understand concepts quickly, while others require additional explanations and repeated practice.
Because classrooms must follow a common teaching pace, individual doubts may not always receive enough attention. This is one reason many parents look for tuition classes in Bangalore for class 10 that provide focused guidance based on each student's learning style.
Personalized support allows students to ask questions comfortably, revisit difficult chapters, and improve steadily without feeling rushed.
Managing Exam Pressure
Board examinations naturally create anxiety, but proper preparation can significantly reduce that pressure.
Students should remember that examinations test preparation, not perfection. Solving sample papers under timed conditions helps build familiarity with the exam format while improving time management.
Another useful habit is preparing short revision notes. These become extremely valuable during the final weeks before examinations because students can quickly revise important formulas, definitions, and concepts.
Don't Ignore Health While Studying
Academic performance depends on more than books and notebooks.
Students should also focus on:
Getting enough sleep every night
Eating balanced meals
Drinking enough water
Taking regular breaks
Spending some time outdoors or exercising
A healthy body supports better concentration, stronger memory, and improved productivity during study sessions.
Support Makes Learning Easier
Parents and teachers both play an important role during Class 10. Encouragement often motivates students far more effectively than criticism. Celebrating small improvements builds confidence and creates a positive attitude toward learning.
Students should never hesitate to ask questions whenever they feel confused. Clarifying doubts early prevents small misunderstandings from becoming larger academic problems later.
Looking Ahead
Class 10 is not simply about passing examinations. It is about developing study habits, discipline, confidence, and problem-solving skills that remain useful throughout higher education.
Many students benefit from structured guidance, regular assessments, and consistent practice, which is why families often consider tuition classes in Bangalore for class 10 as an additional learning resource alongside school education. Combined with dedication and daily effort, the right support can help students perform to the best of their abilities.
Every chapter completed, every question solved, and every concept understood brings students one step closer to their goals. Progress may happen gradually, but consistent learning always creates lasting success.
The Right Way to Make Notes for Class 10 Social Science (Without Copying the Textbook)
The secret to how to make notes for class 10 SST is abandoning paragraph writing. Copying the NCERT textbook wastes time and creates false confidence. Instead, use chronological flowcharts for History, spatial mind maps for Geography, and comparison tables for Civics and Economics. This visual system cuts study time in half and prepares you directly for competency-based questions.
Ask any Class 10 student which subject takes the most time to study, and the answer is almost always Social Science (SST).
The NCERT SST textbooks are dense. They are packed with dates, treaties, soil types, and political systems. When students sit down to make notes, they panic. They end up highlighting every single line. Then, they copy those highlighted lines into a notebook. They write page after page of long, boring paragraphs.
This is a massive waste of time. It drains your energy and leaves you with zero time for Math or Science. Worse, when you sit in the exam hall, you forget everything.
If you want to score 95+ in the 2026 board exams, you must completely change your strategy. Here is the exact, subject-by-subject framework for class 10 social science notes making.
The Biggest Mistake: Why "Highlighting" and "Rewriting" Fails
Before we look at the right way to make notes, we must kill the wrong way.
Writing textbook paragraphs into a notebook creates the Illusion of Competence. When you copy a paragraph about the Non-Cooperation Movement, your hand is moving, and your eyes are reading. You feel like you are studying hard. But your brain is actually turned off. It is a passive activity.
The 2026 CBSE board exams feature 50% competency-based questions. The examiner will not ask you to simply "Write a note on the Non-Cooperation Movement." They will ask you to analyze why different social groups joined the movement and how their goals differed.
If your notes are just copied textbook sentences, you will fail to answer these analytical questions. You need a system that forces your brain to understand causes, effects, and connections.
History: The Chronological Flowchart Method
History is not a list of random dates. History is a movie. Every single event happens as a direct reaction to the event before it.
The biggest question students ask is how to remember history dates class 10. The answer is the Flowchart Method for Social Science. You must stop writing paragraphs and start drawing cause-and-effect chains.
When you read a chapter like Nationalism in India, use this exact format on a blank A4 sheet:
1. The Margin Rule
Draw a line down the left side of your page. Dates belong strictly in this margin. Never bury a date in the middle of a sentence. When dates are isolated on the left, your eyes can scan a 20-year timeline in three seconds.
2. The Trigger Method (Cause $\rightarrow$ Event $\rightarrow$ Impact)
In the center of the page, write the event in a box. Above it, write the Cause. Below it, draw an arrow to the Impact.
Here is how a flowchart for the year 1919 should look in your notes:
[Margin: 1919]
Cause: British government passes strict laws to crush Indian political activity.
THE EVENT: Rowlatt Act Passed. (Allows arrest without trial for 2 years).
The Impact (Reaction): Gandhi organizes a nationwide Hartal on April 6. Peaceful protests begin.
The Escalation: British declare Martial Law in Amritsar. General Dyer takes command.
[Margin: April 13, 1919]
THE EVENT: Jallianwala Bagh Massacre.
Do you see the power of this method? You just condensed two full pages of the NCERT textbook into five clear, logical steps. When an exam question asks about the consequences of the Rowlatt Act, your brain simply reads the flowchart arrows.
Geography: Spatial Mind Maps and Map-Based Notes
History flows in a straight line through time. Geography does not. Geography is about space, locations, and categories. If you use a flowchart for Geography, you will get confused.
For chapters like Resources and Development or Agriculture, you must use Spatial Mind Maps.
Do not write bulleted lists of soil types. Your brain struggles to memorize lists. Instead, put the main topic in a circle in the center of your page. Draw branches outward for each category.
For example, if the center circle is Black Soil:
Branch 1 (Location): Maharashtra, Saurashtra, Malwa.
Branch 2 (Characteristics): Holds moisture, rich in calcium carbonate, poor in phosphoric contents.
Branch 3 (Crops): Ideal for growing Cotton.
The Map Trick: Do not make Geography notes in a standard notebook. Buy a pack of 50 blank political maps of India. If you are making notes on Major Crops, draw the mind map directly onto the blank map. Shade the states that grow wheat and write the temperature requirements right next to the shaded area. This instantly prepares you for the 5-mark map-pointing section of the board exam.
Civics & Economics: The Power of Comparison Tables
Civics (Democratic Politics) and Economics are completely different from History and Geography. These subjects are highly analytical. They explain systems, rules, and power structures.
The best way to study these subjects is by forcing the information into Comparison Tables.
Chapters like Power Sharing, Federalism, and Sectors of the Indian Economy are built entirely on contrasts. The board exam loves to ask 3-mark and 5-mark "Differentiate between X and Y" questions. If your notes are already formatted as tables, you have practically pre-written your board exam answers.
Whenever you spot two opposing concepts in the textbook, immediately draw a table.
Here is a sample table for the Federalism chapter:
When you review this table, you instantly understand the core concept of the chapter. You did not have to read five pages of text to grasp the difference between India and the USA.
How to Review Your Notes for Competency-Based Questions
Making visual notes is only step one. Step two is using them correctly.
Never just "read" your flowcharts or tables. You must practice Active Recall.
When you sit down to revise your History flowchart, cover the bottom half of the page with your hand. Look at the "Cause" and force yourself to speak the "Event" and the "Impact" out loud. If you cannot explain the impact without looking at the paper, you have not learned it yet.
This active recall method forces your brain to generate answers from scratch. This is exactly what you must do during the board exam. By testing yourself daily with these visual triggers, you train your brain to retrieve facts instantly. You will never blank out in an exam hall again.
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Quick Summary: The SST Note-Making Checklist
Stop Copying: Do not rewrite NCERT paragraphs. It wastes time and does not build memory.
History: Use chronological flowcharts. Put dates in the left margin and draw arrows to show cause and effect.
Geography: Use spatial mind maps. Draw your notes directly onto blank political maps of India.
Civics & Economics: Force concepts into comparison tables to prepare for 5-mark differentiation questions.
Master Your Class 10 Board Preparation
Smart study methods are the secret to balancing your school scores with early competitive exam prep. If you want to stop wasting hours on rote memorization and start learning concepts deeply, explore our Class 10 board preparation strategy. We teach you the exact frameworks needed to master the syllabus quickly, giving you a massive advantage in both boards and foundation learning.
How to Write Board-Perfect Answers in Class 10 Science (Competency-Based Guide)
CBSE Science board exams now demand application over memorization. To score full marks, stop writing long, rambling paragraphs. Use the "Keyword-Explain-Apply" formula: anchor your answer with a specific scientific keyword, explain the theory briefly, and apply it to the scenario in the question.
Every year, thousands of brilliant Class 10 students walk out of the Science exam room feeling confident. They knew the answers. They studied the NCERT textbook until they could recite it. Yet, when the results come out, they find their scores capped at 70% or 80%.
They blame the teacher, the marking scheme, or the "toughness" of the paper. But the truth is usually simpler: They knew the content, but they did not know how to write it for the board.
In 2026, the CBSE board exam is fundamentally different. With 50% of the paper now dedicated to competency-based questions, examiners are not looking for your ability to memorize a definition. They are testing your ability to apply science to real-world scenarios. If you write like a textbook, you will lose marks. If you write like a scientist, you will win them.
Here is how to write board-perfect answers that satisfy the examiner’s marking scheme.
The New Reality: Why "Paragraphs" Are Killing Your Score
The biggest mistake a Class 10 student makes is writing long, fluffy paragraphs.
When an examiner sits down to grade 50 to 100 papers a day, they do not read every word you write. They scan for keywords.
If your answer is five lines long but misses the one specific keyword the marking scheme demands, you will get zero or half-marks. The new competency-based structure prioritizes precision. If a question asks you to explain the Refraction of Light, the examiner is hunting for terms like "bending of light," "medium," "change in speed," and "optical density." If those aren't there, your beautifully written, three-paragraph explanation is worthless.
To score full marks, you must shift your writing style from "narrative" to "structured."
The Anatomy of a Perfect Answer: The 3-Step Formula
For every single theory-based question—whether it is worth 2 marks or 5 marks—use this structural formula. It forces your brain to be concise and accurate.
The Keyword (The Anchor): Start with the scientific term that is essential to the marking scheme.
The Explanation (The Logic): Write one clear sentence explaining the "Why" or "How."
The Application (The Competency): Connect this concept back to the specific scenario provided in the question.
Good vs. Bad Answer Example
Question: Why does a pencil appear bent when dipped in a glass of water?
Bad Answer (Amateur)
Board-Perfect Answer (Pro)
"The pencil looks bent because light changes direction in water. This makes it look like it's broken, but it's just an illusion that happens when you look at it from the side of the glass."
"The pencil appears bent due to the refraction of light. When light travels from a denser medium (water) to a rarer medium (air), it bends away from the normal. This change in the path of light rays causes the virtual image of the pencil to appear raised."
Why the "Pro" answer wins: It uses the keyword (refraction), identifies the medium change (denser to rarer), and explains the visual result (virtual image). The amateur answer is just a descriptive guess.
Physics: The "GIVEN-FORMULA-SOLUTION" Method
Physics numericals are not about getting the right answer at the end; they are about showing the right process along the way. If you arrive at the correct numerical answer but skip the formula step, you will lose marks.
Follow this strict layout for every Physics calculation:
GIVEN: List all knowns (e.g., $u = 0$, $t = 5s$, $a = 2 m/s^2$). Always convert units to SI (meters, seconds, Amperes) before you start.
FORMULA: Write the exact formula you are about to use (e.g., $v = u + at$).
SOLUTION: Plug in the numbers and solve.
THE UNIT: This is where most students fail. If you calculate the distance but forget to write "meters" or "m" next to the final answer, you will lose 0.5 marks.
Pro-Tip: If the question is a derivation (like the Mirror Formula), draw the diagram first, label it clearly, and then state the assumptions you are making before starting the math. The diagram is part of your answer, not just decoration.
Chemistry: Balancing Equations & Scientific Terminology
In Chemistry, your answer is only as good as the reaction you provide.
If a question asks you to explain Displacement Reactions, do not just describe them. You must write a balanced chemical equation. If your equation is not balanced, the examiner considers the whole reaction scientifically incorrect.
When describing chemical processes, use "Action-Result" language.
Bad: "When you put iron in copper sulfate, it changes color."
Board-Perfect: "When Iron (Fe) is dipped in Copper Sulfate ($CuSO_4$) solution, a displacement reaction occurs because Iron is more reactive than Copper. The solution turns from blue to green as Ferrous Sulfate ($FeSO_4$) is formed."
Note the use of specific terms: Displacement reaction, reactive, blue to green. This is the language of the marking scheme.
Biology: The Power of Flowcharts and Labeled Diagrams
Biology questions are often about processes, not definitions. A paragraph about how a cell works is inferior to a simple flowchart.
When a question asks for a process (like The Journey of Food in the Alimentary Canal), stop writing sentences.
Draw a Flowchart: Mouth $\rightarrow$ Esophagus $\rightarrow$ Stomach $\rightarrow$ Small Intestine $\rightarrow$ Large Intestine.
Label the Diagram: If a question asks about the Human Heart, draw it, label the four chambers, and use arrows to show blood flow direction.
Explain with Bullets: Once the diagram and flowchart are done, add 3-4 bullet points to explain any high-level details that weren't obvious in the drawing.
Examiners love flowcharts because they prove you understand the order of events. If your diagram is well-labeled, it acts as a shorthand for the entire explanation.
Tackling Case-Based Questions (CBQs)
The new 50% competency requirement means case-based questions are now the most important part of your paper.
The Strategy:
Read the Questions First: Do not read the passage first! Read the questions so you know exactly what information you are looking for.
Highlight the Keyword: Scan the passage for the scientific topic the question is asking about (e.g., Respiration).
Apply Logic, Not Quotes: Do not just copy-paste sentences from the passage. The examiner wants to see if you can use the information in the passage to answer a deeper "Why" question.
Final Checklist Before You Submit
Before the bell rings, check your paper for these three "Easy-Mark" errors:
Did I underline the keywords? (This makes it impossible for an examiner to miss them).
Are all diagrams labeled? (A diagram without a label is just a doodle).
Are the SI units present? (If the answer is a measurement, it must have a unit).
Board exams are not tests of how much you know; they are tests of how well you can communicate what you know. If you follow this structured approach, you stop leaving your marks to chance. You start taking full control of your score.
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Build a Foundation for Full Marks
Writing perfect answers is a skill that comes from understanding concepts at a deep, application-based level. If you struggle to connect the theory you read in your textbook to the real-world questions you see on exams, explore our Class 10 Foundation Program. We don't just teach you the content; we teach you how to apply it, structure it, and ace every question with total confidence.