15-Day Exam Plan
This page turns the NIOS past-paper analysis into a low-disruption exam-prep layer for Lemu: high-yield chapter rankings, repeated-question heatmaps, in-lesson priority signals, and a subject-based crash schedule that assumes very limited prep time.
Cover only the most repeated chapters first. Equal coverage is a trap when the time window is short.
Each study day is built as learn, solve past-paper questions, then compress the chapter into one short sheet.
The last phase removes new learning and keeps only timed recall, formulas, dates, formats and error-log revision.
Quick Index
Every major panel is listed here first. Jump directly to the section you want instead of scrolling through the whole page.
Generator + Schedule
Choose subjects, set days left, and jump into the daily 15-day plan.
High-Yield Ranking
See the strongest chapters by subject before spending time on low-return units.
Question Bank
Use pattern-based important questions instead of brittle OCR repeats, then switch to the mixed overall list later.
Repeat Heatmaps
Get a fast overview of which chapters are blazing, hot, warm, or steady.
Personalized Generator
Select the subjects being written and the days left. The schedule keeps high-yield coverage first.
Subjects
6 selected
10
coverage
3
practice
2
revision
Data Entry Operations: DEO is based on only 2023-2024 papers and some regional PDFs remain locked, so confidence is limited.
English: English analysis has fewer usable years than the major theory subjects, so treat the ranking as directional rather than exhaustive.
Generated Schedule
The first phase is always high-yield chapters. Lower-return content only shows up if time remains.
Day 1
Lock two repeated chapters before moving on: Trigonometry + Acids, Bases and Salts.
Block 1
Open chapterMathematics: Trigonometry
Shows up across every analysed year and mixes direct scoring identities with application problems. Learn the concept, solve 4-6 previous-year questions, then write a one-page sheet.
Block 2
Open chapterScience & Technology: Acids, Bases and Salts
Reactions, indicators and salts repeat heavily and are easy to drill from a compact sheet. Focus on solved examples first, then mirror the question format from past papers.
Block 3
Past-paper drill + one-page revision
Attempt only previous-year questions from Trigonometry and Acids, Bases and Salts. End with a one-page recall sheet and a five-minute oral recap.
Day 2
Lock two repeated chapters before moving on: Word Processing + Democracy and Civics.
Block 1
Open chapterData Entry Operations: Word Processing
Word processing dominates the available DEO papers and includes direct commands, formatting and mail-merge steps. Learn the concept, solve 4-6 previous-year questions, then write a one-page sheet.
Block 2
Open chapterSocial Science: Democracy and Civics
Democracy, institutions, rights and governance dominate the paper and reward structured answers. Focus on solved examples first, then mirror the question format from past papers.
Block 3
Past-paper drill + one-page revision
Attempt only previous-year questions from Word Processing and Democracy and Civics. End with a one-page recall sheet and a five-minute oral recap.
Day 3
Lock two repeated chapters before moving on: Food, Nutrition and Health + Writing.
Block 1
Open chapterHome Science: Food, Nutrition and Health
Nutrition, deficiency and preservation questions appear in every analysed year and are very memory-friendly. Learn the concept, solve 4-6 previous-year questions, then write a one-page sheet.
Block 2
Open chapterEnglish: Writing
Formal/informal writing formats are the fastest marks in the paper once the structure is memorised. Focus on solved examples first, then mirror the question format from past papers.
Block 3
Past-paper drill + one-page revision
Attempt only previous-year questions from Food, Nutrition and Health and Writing. End with a one-page recall sheet and a five-minute oral recap.
Day 4
Lock two repeated chapters before moving on: Circle Geometry + Metals and Non-metals.
Block 1
Open chapterMathematics: Circle Geometry
Circle theorems, tangents and cyclic quadrilateral patterns repeat with small value changes. Learn the concept, solve 4-6 previous-year questions, then write a one-page sheet.
Block 2
Open chapterScience & Technology: Metals and Non-metals
Properties, reactivity and uses appear across most years with very similar framing. Focus on solved examples first, then mirror the question format from past papers.
Block 3
Past-paper drill + one-page revision
Attempt only previous-year questions from Circle Geometry and Metals and Non-metals. End with a one-page recall sheet and a five-minute oral recap.
Day 5
Lock two repeated chapters before moving on: Spreadsheets + Indian History and Freedom Struggle.
Block 1
Open chapterData Entry Operations: Spreadsheets
Spreadsheet formatting and formula work are the next most repeated practical tasks. Learn the concept, solve 4-6 previous-year questions, then write a one-page sheet.
Block 2
Open chapterSocial Science: Indian History and Freedom Struggle
Freedom struggle chronology and reform movements are repeatedly asked as explain-in-points answers. Focus on solved examples first, then mirror the question format from past papers.
Block 3
Past-paper drill + one-page revision
Attempt only previous-year questions from Spreadsheets and Indian History and Freedom Struggle. End with a one-page recall sheet and a five-minute oral recap.
Day 6
Lock two repeated chapters before moving on: Family Health and Hygiene + Grammar.
Block 1
Open chapterHome Science: Family Health and Hygiene
Hygiene, sanitation, diseases and first-aid are among the most repeated and most direct scoring units. Learn the concept, solve 4-6 previous-year questions, then write a one-page sheet.
Block 2
Open chapterEnglish: Grammar
Tenses, voice and reported speech produce repeatable transformation questions. Focus on solved examples first, then mirror the question format from past papers.
Block 3
Past-paper drill + one-page revision
Attempt only previous-year questions from Family Health and Hygiene and Grammar. End with a one-page recall sheet and a five-minute oral recap.
Day 7
Lock two repeated chapters before moving on: Statistics and Probability + Force and Motion.
Block 1
Open chapterMathematics: Statistics and Probability
Mean/median/mode and basic probability are fast to revise and repeatedly tested. Learn the concept, solve 4-6 previous-year questions, then write a one-page sheet.
Block 2
Open chapterScience & Technology: Force and Motion
Definitions, Newton-style reasoning and numericals repeat with light variation. Focus on solved examples first, then mirror the question format from past papers.
Block 3
Past-paper drill + one-page revision
Attempt only previous-year questions from Statistics and Probability and Force and Motion. End with a one-page recall sheet and a five-minute oral recap.
Day 8
Lock two repeated chapters before moving on: Presentations + Renaissance and Industrial Revolution.
Block 1
Open chapterData Entry Operations: Presentations
Presentation basics appear, but the available past-paper coverage is lighter than word processing and spreadsheets. Learn the concept, solve 4-6 previous-year questions, then write a one-page sheet.
Block 2
Open chapterSocial Science: Renaissance and Industrial Revolution
Industrial Revolution and modern world movements recur as short and long theory answers. Focus on solved examples first, then mirror the question format from past papers.
Block 3
Past-paper drill + one-page revision
Attempt only previous-year questions from Presentations and Renaissance and Industrial Revolution. End with a one-page recall sheet and a five-minute oral recap.
Day 9
Lock two repeated chapters before moving on: Home Management and Consumer Education + Prose and Reading.
Block 1
Open chapterHome Science: Home Management and Consumer Education
Resource management, budgeting and household organisation repeat often and respond well to point-wise revision. Learn the concept, solve 4-6 previous-year questions, then write a one-page sheet.
Block 2
Open chapterEnglish: Prose and Reading
Reading comprehension and prose answers recur with similar answer structures even when passages change. Focus on solved examples first, then mirror the question format from past papers.
Block 3
Past-paper drill + one-page revision
Attempt only previous-year questions from Home Management and Consumer Education and Prose and Reading. End with a one-page recall sheet and a five-minute oral recap.
Day 10
Lock two repeated chapters before moving on: Mensuration + Periodic Table.
Block 1
Open chapterMathematics: Mensuration
Formula-based questions make this one of the fastest scoring chapters once the sheet is memorised. Learn the concept, solve 4-6 previous-year questions, then write a one-page sheet.
Block 2
Open chapterScience & Technology: Periodic Table
Periodic trends are common medium-effort marks once the table logic is clear. Focus on solved examples first, then mirror the question format from past papers.
Block 3
Past-paper drill + one-page revision
Attempt only previous-year questions from Mensuration and Periodic Table. End with a one-page recall sheet and a five-minute oral recap.
Day 11
Shift from chapter study to exam-style retrieval across Mathematics and Science & Technology.
Block 1
Open chapterMathematics timed set
Solve a 60-90 minute mixed set from Trigonometry first, then add one medium-priority chapter if time remains.
Block 2
Open chapterScience & Technology recovery set
Redo weak questions from Metals and Non-metals. Write full answers, not loose points, and mark where you lost steps.
Block 3
Error log and same-day correction
Rewrite every wrong answer, note the exact trigger of the mistake, and revise only that error log before bed.
Day 12
Shift from chapter study to exam-style retrieval across Science & Technology and Data Entry Operations.
Block 1
Open chapterScience & Technology timed set
Solve a 60-90 minute mixed set from Acids, Bases and Salts first, then add one medium-priority chapter if time remains.
Block 2
Open chapterData Entry Operations recovery set
Redo weak questions from Spreadsheets. Write full answers, not loose points, and mark where you lost steps.
Block 3
Error log and same-day correction
Rewrite every wrong answer, note the exact trigger of the mistake, and revise only that error log before bed.
Day 13
Shift from chapter study to exam-style retrieval across Data Entry Operations and Social Science.
Block 1
Open chapterData Entry Operations timed set
Solve a 60-90 minute mixed set from Word Processing first, then add one medium-priority chapter if time remains.
Block 2
Open chapterSocial Science recovery set
Redo weak questions from Indian History and Freedom Struggle. Write full answers, not loose points, and mark where you lost steps.
Block 3
Error log and same-day correction
Rewrite every wrong answer, note the exact trigger of the mistake, and revise only that error log before bed.
Day 14
Compress the syllabus into formulas, formats, definitions and repeated mistakes only.
Block 1
Rapid-sheet revision
Use one-page sheets only. Revise formulas, key dates, grammar formats, diagrams and named laws without reopening full chapters.
Block 2
Repeat-pattern recall
Pick only the question patterns that showed up across years. Answer them aloud or in bullet form from memory.
Block 3
Light mock and correction
Do one short timed section, then spend the rest of the block correcting mistakes rather than taking another paper.
Day 15
No new learning. Run only fast recall for Mathematics, Science & Technology, Data Entry Operations, Social Science, Home Science, English.
Block 1
Formula + fact sweep
Use one-page sheets only. Revise formulas, key dates, grammar formats, diagrams and named laws without reopening full chapters.
Block 2
Most-missed questions only
Pick only the question patterns that showed up across years. Answer them aloud or in bullet form from memory.
Block 3
Sleep-protecting shutdown
Stop early, pack materials, and avoid heavy new study. Sleep beats last-minute panic.
Subject-Wise High-Yield Ranking
Ranked from the past-paper report and mapped to the exact Lemu chapters already in the app.
Mathematics
31 papers analysed · 2017, 2019, 2021, 2022, 2023, 2024
Finish trigonometry, circle geometry, statistics, mensuration and commercial maths before spending time on lower-frequency chapters.
Trigonometry
Must Do30/31 papers · 6 years · 117 tagged question units
Shows up across every analysed year and mixes direct scoring identities with application problems.
Circle Geometry
Must Do26/31 papers · 6 years · 120 tagged question units
Circle theorems, tangents and cyclic quadrilateral patterns repeat with small value changes.
Statistics and Probability
Must Do28/31 papers · 6 years · 107 tagged question units
Mean/median/mode and basic probability are fast to revise and repeatedly tested.
Mensuration
High Yield27/31 papers · 6 years · 70 tagged question units
Formula-based questions make this one of the fastest scoring chapters once the sheet is memorised.
Commercial Mathematics
High Yield26/31 papers · 6 years · 57 tagged question units
Profit-loss, interest, GST and installment patterns keep returning in predictable formats.
Arithmetic Progression
Worth A Pass27/31 papers · 6 years · 66 tagged question units
Usually appears as one direct nth-term or sum question.
Science & Technology
28 papers analysed · 2017, 2019, 2021, 2022, 2023, 2024
Split time between physics and chemistry. Light, acids/bases, measurement and force/motion should be done before lower-yield biology chapters.
Acids, Bases and Salts
Must Do27/28 papers · 6 years · 93 tagged question units
Reactions, indicators and salts repeat heavily and are easy to drill from a compact sheet.
Metals and Non-metals
High Yield26/28 papers · 5 years · 49 tagged question units
Properties, reactivity and uses appear across most years with very similar framing.
Force and Motion
High Yield21/28 papers · 6 years · 45 tagged question units
Definitions, Newton-style reasoning and numericals repeat with light variation.
Periodic Table
Worth A Pass26/28 papers · 6 years · 49 tagged question units
Periodic trends are common medium-effort marks once the table logic is clear.
Chemical Bonding
Worth A Pass27/28 papers · 6 years · 42 tagged question units
Bond types and valency questions recur, but a smaller share than the core four chapters.
Data Entry Operations
6 papers analysed · 2021, 2023, 2024
Start with word processing, then spreadsheets. Presentations should be the final polish chapter once the core operations are comfortable.
Word Processing
Must Do3/6 papers · 2 years · 18 tagged question units
Word processing dominates the available DEO papers and includes direct commands, formatting and mail-merge steps.
Spreadsheets
High Yield5/6 papers · 2 years · 15 tagged question units
Spreadsheet formatting and formula work are the next most repeated practical tasks.
Presentations
Worth A Pass2/6 papers · 1 year · 11 tagged question units
Presentation basics appear, but the available past-paper coverage is lighter than word processing and spreadsheets.
Social Science
27 papers analysed · 2017, 2019, 2021, 2022, 2023, 2024
Prioritise civics and national-movement history first, then geography chapters like agriculture and water resources.
Democracy and Civics
Must Do27/27 papers · 6 years · 130 tagged question units
Democracy, institutions, rights and governance dominate the paper and reward structured answers.
Indian History and Freedom Struggle
Must Do27/27 papers · 6 years · 71 tagged question units
Freedom struggle chronology and reform movements are repeatedly asked as explain-in-points answers.
Renaissance and Industrial Revolution
High Yield11/27 papers · 5 years · 17 tagged question units
Industrial Revolution and modern world movements recur as short and long theory answers.
Agriculture and Resources
High Yield15/27 papers · 5 years · 23 tagged question units
Crop belts, seasons, soil-resource links and conservation keep repeating in direct forms.
Water Resources
High Yield13/27 papers · 5 years · 31 tagged question units
Water distribution, rivers, irrigation and conservation are frequent map-style and descriptive questions.
Panchayati Raj and Local Governance
Worth A Pass10/27 papers · 4 years · 19 tagged question units
Often appears as a direct short-answer civics chapter and is quick to finish once basics are clear.
Home Science
29 papers analysed · 2017, 2019, 2021, 2022, 2023, 2024
Do food/nutrition and family-health chapters first, then move to textiles and home-management once the high-return health material is locked.
Food, Nutrition and Health
Must Do29/29 papers · 6 years · 124 tagged question units
Nutrition, deficiency and preservation questions appear in every analysed year and are very memory-friendly.
Family Health and Hygiene
Must Do29/29 papers · 6 years · 142 tagged question units
Hygiene, sanitation, diseases and first-aid are among the most repeated and most direct scoring units.
Home Management and Consumer Education
High Yield28/29 papers · 6 years · 85 tagged question units
Resource management, budgeting and household organisation repeat often and respond well to point-wise revision.
Human Development
High Yield15/29 papers · 6 years · 27 tagged question units
Human development and family life chapters show up consistently in medium and long answers.
Textiles and Clothing
High Yield28/29 papers · 6 years · 106 tagged question units
Textiles questions repeat in practical, definition-heavy formats that are efficient to memorise.
English
13 papers analysed · 2017, 2019, 2021, 2022, 2023, 2024
Secure writing formats first, then grammar transformations, then reading/prose. Poetry can wait until the final pass.
Writing
Must Do13/13 papers · 6 years · 114 tagged question units
Formal/informal writing formats are the fastest marks in the paper once the structure is memorised.
Grammar
High Yield13/13 papers · 6 years · 70 tagged question units
Tenses, voice and reported speech produce repeatable transformation questions.
Prose and Reading
High Yield10/13 papers · 5 years · 43 tagged question units
Reading comprehension and prose answers recur with similar answer structures even when passages change.
Poetry
Worth A Pass8/13 papers · 4 years · 11 tagged question units
Poetry still appears, but it is lower-return than writing, grammar and comprehension in a short prep window.
Important Question Bank
Best default: study question patterns chapter-wise while covering the syllabus, then switch to an overall mixed list during the practice phase.
Chapter-wise is the recommended view for days 1-8 because it reduces context-switching while a student is still learning the chapter. After that, the overall list becomes more useful because mixed retrieval is closer to exam conditions. For scanned maths and science papers, exact OCR wording is not reliable enough, so this bank groups recurring exam patterns instead of showing broken literal question text.
Trigonometry
Must DoHeat 10030/31 papers · 6 years
Shows up across every analysed year and mixes direct scoring identities with application problems.
Find unknown side or height using a trig ratio
Typical question: Use sin, cos, tan or heights-and-distances to find a missing side, building height, or distance.
Example: A tree casts a 10 m shadow. If the angle of elevation of the sun is 60°, find the height of the tree.
Step 1: Draw a right triangle and let the height of the tree be h metres. The shadow is the side adjacent to the 60° angle, so its length is 10 m.
Step 2: For this question we use tan because tan theta = opposite / adjacent.
Step 3: Substitute the values: tan 60° = h / 10.
Step 4: From the standard trigonometric table, tan 60° = √3. Here √3 means the square root of 3.
Step 5: So √3 = h / 10. Multiply both sides by 10 to isolate h.
Final answer: h = 10 × √3 m, so the height of the tree is 10 × √3 metres.
Exam shortcut
Draw the situation as a right triangle and label the known side, unknown side, and given angle. Then decide which trigonometric ratio fits the two sides involved: sin, cos, or tan.
Solve angle relations from identities or combined expressions
Typical question: Questions involving sin(A - B), cos(A + B), complementary angles, or standard-value identities.
Example: If sin(A - B) = 1/2 and cos(A + B) = √3/2, where 0° < A + B < 90° and A > B, find A and B.
Step 1: Use standard trigonometric values. Since sin x = 1/2, the acute angle × is 30°. So A - B = 30°.
Step 2: Also, cos y = √3/2 for the acute angle y = 30°. So A + B = 30°.
Step 3: Now add the two equations: (A - B) + (A + B) = 30° + 30°.
Step 4: This gives 2A = 60°, so A = 30°.
Step 5: Substitute A = 30° into A + B = 30°. Then 30° + B = 30°, so B = 0°.
Final answer: A = 30° and B = 0°.
Exam shortcut
Convert each trigonometric expression into a known standard value such as 1/2, √3/2, or 1. Then write separate equations for the angle combinations, for example A - B and A + B.
Circle Geometry
Must DoHeat 10026/31 papers · 6 years
Circle theorems, tangents and cyclic quadrilateral patterns repeat with small value changes.
Angle-in-circle and cyclic quadrilateral proofs
Typical question: Find an unknown angle using same-segment, opposite-angle, or cyclic-quadrilateral rules.
Example: In a cyclic quadrilateral ABCD, angle A = 72°. Find angle C and state the theorem used.
Step 1: Recall the theorem: opposite angles of a cyclic quadrilateral are supplementary.
Step 2: So angle A + angle C = 180°.
Step 3: Substitute angle A = 72°. Then 72° + angle C = 180°.
Step 4: Subtract 72° from 180°.
Final answer: Angle C = 108°. The theorem used is: opposite angles of a cyclic quadrilateral are supplementary.
Exam shortcut
List the theorem being used first, mark equal angles on the diagram, then substitute into the target angle.
Tangent, secant and power-of-point questions
Typical question: Use tangent properties or PT² = PA × PB style relations.
Example: From an external point P, PT is tangent and PAB is a secant to a circle. If PA = 4 cm and PB = 9 cm, find PT.
Step 1: Use the tangent-secant theorem: PT² = PA × PB.
Step 2: Substitute the given values: PT² = 4 × 9 = 36.
Step 3: Take the positive square root because a length cannot be negative.
Final answer: PT = 6 cm.
Exam shortcut
Identify the circle theorem, write the direct relation, and solve the resulting linear or quadratic step cleanly.
Statistics and Probability
Must DoHeat 10028/31 papers · 6 years
Mean/median/mode and basic probability are fast to revise and repeatedly tested.
Find mean, median or mode from data
Typical question: Ungrouped or grouped table questions asking for central tendency or a missing value.
Example: The marks 12, 15, 18, 15, 10, 20, 15 are given. Find the mean and the mode.
Step 1: Add all the observations: 12 + 15 + 18 + 15 + 10 + 20 + 15 = 105.
Step 2: There are 7 observations, so mean = total sum / number of observations = 105 / 7 = 15.
Step 3: Now check which value appears most often. The number 15 appears three times.
Final answer: Mean = 15 and mode = 15.
Exam shortcut
Write the observations or frequency table neatly before starting the calculation. Then find the required totals such as sum of values, sum of frequencies, or cumulative frequency.
Basic probability from favourable outcomes
Typical question: Cards, coins, dice, or event-count questions asking for simple probability.
Example: Two dice are thrown together. Find the probability of getting an even number on both dice.
Step 1: On one die, the even numbers are 2, 4 and 6. So favourable outcomes = 3 out of 6.
Step 2: Therefore, probability of getting an even number on one die = 3/6 = 1/2.
Step 3: The two dice are independent, so multiply the probabilities.
Step 4: Required probability = 1/2 × 1/2 = 1/4.
Final answer: The probability of getting an even number on both dice is 1/4.
Exam shortcut
List the total number of possible outcomes. Then count only the favourable outcomes that satisfy the question.
Mensuration
High YieldHeat 10027/31 papers · 6 years
Formula-based questions make this one of the fastest scoring chapters once the sheet is memorised.
Volume or surface area from radius-height data
Typical question: Cylinder, cone, sphere or ratio-of-volumes questions.
Example: A cylinder has radius 7 cm and height 10 cm. Find its curved surface area and volume.
Step 1: Write the given values first: radius r = 7 cm and height h = 10 cm.
Step 2: Curved surface area of a cylinder = 2pi rh.
Step 3: Substitute the values: 2 x π x 7 × 10 = 140pi cm². Using π = 22/7, this becomes 440 cm².
Step 4: Volume of a cylinder = π r² h.
Step 5: Substitute the values: π x 7 × 7 x 10 = 490pi cm³. Using π = 22/7, this becomes 1540 cm³.
Final answer: Curved surface area = 440 cm² and volume = 1540 cm³.
Exam shortcut
Write the formula before substituting, align units, and only simplify once the full expression is set up.
Composite area or sector/arc problems
Typical question: Questions mixing circles with rectangles, sectors, semicircles or path-width areas.
Example: A rectangular garden 20 m × 14 m has a semicircular flower bed of radius 7 m on one side. Find the total area.
Step 1: Break the figure into two simple parts: one rectangle and one semicircle.
Step 2: Area of the rectangle = length × breadth = 20 × 14 = 280 m².
Step 3: Area of the semicircle = 1/2 x π x r² = 1/2 x π x 7² = 77 m², using π = 22/7.
Step 4: Add the two areas to get the total area.
Final answer: Total area = 280 + 77 = 357 m².
Exam shortcut
Break the figure into smaller known shapes, compute each piece, then add or subtract in the final line.
Commercial Mathematics
High YieldHeat 10026/31 papers · 6 years
Profit-loss, interest, GST and installment patterns keep returning in predictable formats.
Profit-loss or selling-price change questions
Typical question: Watch sold at profit, discount change, marked price, or price difference after percentage change.
Example: A shopkeeper marks an article 20% above cost price and gives a discount of 10%. Find the profit percent.
Step 1: Assume the cost price is Rs 100. This makes the percentage calculation easy.
Step 2: If the article is marked 20% above cost price, the marked price becomes Rs 120.
Step 3: A discount of 10% on Rs 120 means discount = Rs 12.
Step 4: So selling price = 120 - 12 = Rs 108.
Step 5: Profit = selling price - cost price = 108 - 100 = Rs 8.
Final answer: Profit percent = 8%.
Exam shortcut
Convert every percentage into cost-price or marked-price equations and solve the system instead of guessing.
Interest, GST and installment calculations
Typical question: Simple interest, compound interest, tax, GST, or installment-buying word problems.
Example: Find the simple interest on Rs 5,000 at 8% per annum for 3 years.
Step 1: Write the values clearly: P = 5000, R = 8% per year, T = 3 years.
Step 2: Use the formula for simple interest: SI = PRT / 100.
Step 3: Substitute the values: SI = 5000 × 8 x 3 / 100 = 1200.
Step 4: Add the interest to the principal to find the amount.
Final answer: Simple interest = Rs 1,200 and amount = Rs 6,200.
Exam shortcut
Identify the money formula first, define the known variables, then calculate principal, rate, or amount in order.
Arithmetic Progression
Worth A PassHeat 10027/31 papers · 6 years
Usually appears as one direct nth-term or sum question.
Nth term using a_n = a + (n - 1)d
Typical question: Find the 20th term, first term, or common difference from one or two given AP terms.
Example: The 5th term of an AP is 23 and the 12th term is 37. Find the first term and common difference.
Step 1: Use the nth term formula: a_n = a + (n - 1)d.
Step 2: For the 5th term, 23 = a + 4d.
Step 3: For the 12th term, 37 = a + 11d.
Step 4: Subtract the first equation from the second: 37 - 23 = (a + 11d) - (a + 4d). This gives 14 = 7d, so d = 2.
Step 5: Substitute d = 2 into a + 4d = 23. Then a + 8 = 23, so a = 15.
Final answer: First term a = 15 and common difference d = 2.
Exam shortcut
Start with the AP formula a_n = a + (n - 1)d. Then translate every given term into an equation in a and d.
Sum of first n terms using S_n formulas
Typical question: Find the sum of an AP, number of terms, or an unknown term from the total sum.
Example: Find the sum of the first 20 terms of the AP 3, 7, 11, ...
Step 1: First identify the values: a = 3, common difference d = 4, and n = 20.
Step 2: Use the formula S_n = n/2 [2a + (n - 1)d].
Step 3: Substitute the values: S_20 = 20/2 [2 × 3 + 19 × 4].
Step 4: Simplify the bracket: 2 × 3 = 6 and 19 × 4 = 76, so the bracket becomes 82.
Step 5: Now S_20 = 10 × 82 = 820.
Final answer: The sum of the first 20 terms is 820.
Exam shortcut
Identify a, d and n from the AP first. Then choose the correct sum formula. Use S_n = n/2[2a + (n - 1)d] when the last term is not directly given.
Repeated-Question Heatmaps
Heat is based on paper coverage, year coverage and total repeat volume. Use this for overview, then use the Question Bank above for the actual pattern list.
Mathematics
Heatmap from 31 analysed papers
Trigonometry
10030/31 papers · 6 years
117 repeat-tagged units
Circle Geometry
10026/31 papers · 6 years
120 repeat-tagged units
Statistics and Probability
10028/31 papers · 6 years
107 repeat-tagged units
Mensuration
10027/31 papers · 6 years
70 repeat-tagged units
Commercial Mathematics
10026/31 papers · 6 years
57 repeat-tagged units
Arithmetic Progression
10027/31 papers · 6 years
66 repeat-tagged units
Open the Question Bank for the chapter-wise and overall important-pattern lists.
Science & Technology
Heatmap from 28 analysed papers
Acids, Bases and Salts
10027/28 papers · 6 years
93 repeat-tagged units
Metals and Non-metals
10026/28 papers · 5 years
49 repeat-tagged units
Force and Motion
10021/28 papers · 6 years
45 repeat-tagged units
Periodic Table
10026/28 papers · 6 years
49 repeat-tagged units
Chemical Bonding
10027/28 papers · 6 years
42 repeat-tagged units
Open the Question Bank for the chapter-wise and overall important-pattern lists.
Data Entry Operations
Heatmap from 6 analysed papers
Word Processing
1003/6 papers · 2 years
18 repeat-tagged units
Spreadsheets
1005/6 papers · 2 years
15 repeat-tagged units
Presentations
1002/6 papers · 1 year
11 repeat-tagged units
Open the Question Bank for the chapter-wise and overall important-pattern lists.
Social Science
Heatmap from 27 analysed papers
Democracy and Civics
10027/27 papers · 6 years
130 repeat-tagged units
Indian History and Freedom Struggle
10027/27 papers · 6 years
71 repeat-tagged units
Renaissance and Industrial Revolution
10011/27 papers · 5 years
17 repeat-tagged units
Agriculture and Resources
10015/27 papers · 5 years
23 repeat-tagged units
Water Resources
10013/27 papers · 5 years
31 repeat-tagged units
Panchayati Raj and Local Governance
10010/27 papers · 4 years
19 repeat-tagged units
Open the Question Bank for the chapter-wise and overall important-pattern lists.
Home Science
Heatmap from 29 analysed papers
Food, Nutrition and Health
10029/29 papers · 6 years
124 repeat-tagged units
Family Health and Hygiene
10029/29 papers · 6 years
142 repeat-tagged units
Home Management and Consumer Education
10028/29 papers · 6 years
85 repeat-tagged units
Human Development
10015/29 papers · 6 years
27 repeat-tagged units
Textiles and Clothing
10028/29 papers · 6 years
106 repeat-tagged units
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English
Heatmap from 13 analysed papers
Writing
10013/13 papers · 6 years
114 repeat-tagged units
Grammar
10013/13 papers · 6 years
70 repeat-tagged units
Prose and Reading
10010/13 papers · 5 years
43 repeat-tagged units
Poetry
1008/13 papers · 4 years
11 repeat-tagged units
Open the Question Bank for the chapter-wise and overall important-pattern lists.