Foundation Mathematics

JEE Foundation Maths for Class 8-10

Class 11 physics and maths punish shaky algebra. This course is where the algebra stops being shaky.

12 months (48 weeks) Class 8 to 10 students, batched by class 2 live classes/week + 3-4 hours of problem sets Course-completion certificate from Modern Age Coders
JEE Foundation Maths Class 8-10: Proofs & Problem Solving

Flexible course duration

Duration depends on the student's background and pace. Beginners (kids / teens): typically 6 to 9 months. Adults with prior knowledge: often shorter, with an accelerated path.

Standard pace6 to 9 months
AcceleratedAdd class frequency to finish faster

For personalised duration planning, call +91 91233 66161 and we'll map a schedule to your goals.

Ready to Master JEE Foundation Maths Class 8-10: Proofs & Problem Solving?

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₹1,499/month

2 Classes per Week · Up to 10 students

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₹4,999/month

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Program Overview

Most students who struggle in JEE preparation do not struggle with Class 11 topics; they struggle with Class 8 to 10 topics that were never made solid. Fractions handled nervously, identities half-remembered, geometry never actually proved. A foundation course exists to fix that before it costs anything, and this one does it honestly: no rank promises, no 'future IITian' theatre, just the school syllabus taught deeper than school goes, plus the problem-solving habits that entrance exams eventually demand.

The 12-month plan runs in four phases. First, numbers and algebra at real depth: divisibility and remainders, exponents and surds, identities and factorisation, equations and inequalities. Second, geometry as a proof discipline, congruence, similarity, circles, because writing a correct proof is the closest a school student comes to real mathematical thinking. Third, mensuration, introductory trigonometry and coordinate geometry, the toolkit chapters. Fourth, the part school never teaches: problem-solving heuristics, olympiad-style questions, and a full timed MCQ phase in the style of NTSE-type talent exams and entrance papers, with error logs and review clinics.

Content is NCERT-aligned and batched by class, so a Class 8 student and a Class 10 student meet the same ideas at different depths. School marks tend to improve as a side effect; the actual product is a student who reaches Class 11 with nothing to repair.

What Makes This Program Different

  • NCERT-aligned but deeper: every chapter is taken past the textbook stopping point, into the why and the harder problem forms
  • Proof skills taught deliberately: given, to prove, construction, proof, drilled until writing a geometry argument feels normal
  • A genuine problem-solving phase: heuristics like working backwards, small cases and clean diagrams, practised on olympiad-style questions
  • A full timed MCQ phase with error logs: elimination, option testing and time budgeting, the craft entrance exams actually test
  • Honest positioning: this is foundation, not JEE coaching, and we say plainly that nobody can promise selections or ranks
  • Batched by class: Class 8, 9 and 10 groups meet the same arc at the right depth, so nobody is drowned or bored

Your Learning Journey

Phase 1
Numbers and algebra at depth: divisibility and remainders, exponents and surds, identities, factorisation, equations and inequalities
Phase 2
Geometry as a proof discipline: angles, congruence, similarity, quadrilaterals and circle theorems, with proof writing drilled throughout
Phase 3
The toolkit chapters: mensuration in 2D and 3D, introductory trigonometry with heights and distances, and coordinate geometry
Phase 4
Problem-solving heuristics and olympiad-style questions, then a timed MCQ and mock phase with error clinics and a readiness review

Career Progression

1
Algebra and geometry solid enough that Class 11 maths builds on them instead of exposing them
2
The ability to write a correct mathematical proof, which most students first meet far too late
3
MCQ craft under timing: elimination, option testing and pacing, with a personal error log as evidence
4
Experience with olympiad-style problems, so unfamiliar questions become interesting rather than frightening
5
A documented mock series showing exactly where the student stands before Class 11 begins

Detailed Course Curriculum

Explore the complete week-by-week breakdown of what you'll learn in this comprehensive program.

Topics Covered
  • Diagnostic paper: arithmetic, fractions, basic algebra and geometry from earlier classes
  • Integers, rationals and irrationals, and how to prove a number belongs where it does
  • Decimal expansions: terminating, recurring, and converting recurring decimals to fractions
  • Representing surds on the number line
  • Density: finding rationals and irrationals between any two numbers
  • Comparing numbers cleverly: without calculators, by squaring or bounding
Projects You Build
  • Number-line dossier: one page classifying 20 assorted numbers with a one-line justification each
Practice & Assignments

30 classification and conversion problems, including 5 recurring-decimal conversions written out in full

Topics Covered
  • Divisibility rules for 2 through 11, proved rather than just stated
  • Primes, composites and prime factorisation as the master tool
  • HCF and LCM: computation, the product relationship, and word problems
  • Remainder thinking: what is left when powers are divided, kept concrete
  • Digit problems: unit digits of large powers, digit sums
  • First olympiad-style flavour: divisibility puzzles with small numbers
Projects You Build
  • Divisibility rule proof sheet: the rules for 3, 9 and 11 explained in the student's own words with examples
Practice & Assignments

25 divisibility and HCF-LCM problems plus 5 unit-digit puzzles, hardest two attempted before class discussion

Assessment

Month 1 test: a 25-mark paper on number systems mixing standard questions with two puzzle-style problems

Topics Covered
  • Laws of exponents for integer and rational powers, with the proofs sketched
  • Negative and fractional exponents handled without fear
  • Surds: simplifying, adding, and rationalising denominators including two-term denominators
  • Comparing surds and exponential expressions by clever bounding
  • Scientific notation and orders of magnitude
  • Exam forms: simplify-this-monster questions and how to dismantle them
Projects You Build
  • Simplification gauntlet: 10 layered exponent-surd expressions reduced step by step, each step justified
Practice & Assignments

35 exponent and surd problems including 8 rationalisations and 5 comparison questions without a calculator

Topics Covered
  • The square and cube identities, derived, visualised, and drilled
  • Sum and difference of cubes, and the three-variable identity for a cubed sum
  • Factorisation strategy: common factors, grouping, splitting the middle term, identities
  • The remainder theorem and factor theorem, introduced with numeric checks
  • Evaluating expressions cleverly: 99 squared, 101 cubed via identities
  • Identity-based olympiad-style problems: finding values without finding variables
Projects You Build
  • Identity map: every identity in the phase on one sheet with a numeric example and one exam use each
Practice & Assignments

30 factorisations across all five strategies plus 8 evaluate-cleverly problems, strategy named before each

Assessment

Month 2 test: a 30-mark paper on exponents, surds and identities including two multi-step simplifications

Topics Covered
  • Linear equations in one variable, including fractional and bracketed forms
  • Word-problem craft: translating ages, digits, mixtures and motion into equations
  • Pairs of linear equations: substitution and elimination done cleanly
  • Consistency: when systems have one, many or no solutions, seen graphically
  • Parameter questions: for what value of k does the system break
  • Checking solutions as a habit, not an afterthought
Projects You Build
  • Translation drill sheet: 12 word problems converted to equations before any are solved
Practice & Assignments

25 equations and systems plus 8 word problems, with the check step written for every answer

Topics Covered
  • Linear inequalities: solving, representing on the number line, and the sign-flip rule proved
  • Compound conditions: and versus or, read carefully
  • Quadratic equations by factorisation: the bridge from identities to solving
  • The idea of a discriminant, previewed for the Class 10 batch
  • Absolute value as distance, kept geometric and gentle
  • Phase consolidation: mixed algebra sets that do not announce their chapter
Projects You Build
  • Personal error log opened: every phase 1 test miss classified as concept, method or slip, used all year
Practice & Assignments

20 inequalities and 15 factorisation-solved quadratics, plus one mixed set of 15 unannounced problems

Assessment

Phase 1 milestone: a 40-mark numbers-and-algebra paper, one third of it in MCQ format as a preview of phase 4

Topics Covered
  • Angles on a line, vertically opposite angles, and angles with parallel lines
  • The triangle angle-sum result and exterior angle theorem, proved
  • What a proof is: statements, reasons, and why 'it looks true' is not enough
  • The four-part format: given, to prove, construction, proof
  • Angle chasing: finding unknown angles in layered figures
  • Drawing honest figures: large, labelled, and not misleadingly special
Projects You Build
  • First proof portfolio entries: angle-sum and exterior-angle proofs written in full four-part format
Practice & Assignments

20 angle-chasing figures of rising difficulty plus 2 proofs, every figure redrawn by hand before solving

Topics Covered
  • Congruence criteria: SAS, ASA, AAS, SSS and RHS, and why AAA fails
  • Choosing the right criterion: reading the figure for what is actually given
  • Isosceles triangle results, proved both directions
  • Inequalities in a triangle: bigger side, bigger angle, and the triangle inequality
  • Multi-step congruence proofs: proving parts equal via congruent triangles
  • Common proof errors: assuming the conclusion, circular reasoning, unstated steps
Projects You Build
  • Criterion sorting sheet: 12 figures matched to their congruence criterion with the given parts marked
Practice & Assignments

15 congruence problems including 5 full proofs, each proof peer-checked against the four-part format

Assessment

Month 4 test: a 25-mark geometry paper with two full proofs marked strictly on structure and justification

Topics Covered
  • Similar triangles: the AA, SSS and SAS similarity criteria
  • The basic proportionality theorem and its converse
  • How similarity scales lengths and areas differently, seen with numbers first
  • The Pythagoras theorem proved by similarity, and its converse
  • Applications: heights via shadows, distances across rivers, ladders and slopes
  • Pythagorean triples and spotting them fast in MCQs
Projects You Build
  • Proof portfolio extended: BPT and the similarity proof of Pythagoras written in full
Practice & Assignments

20 similarity and Pythagoras problems including 3 proofs and 5 real-setting applications

Topics Covered
  • The parallelogram theorems: sides, angles and diagonals, proved and reversed
  • Tests for a parallelogram: which minimal facts force the shape
  • Rectangle, rhombus and square as parallelograms with extra conditions
  • The midpoint theorem and its converse, with applications
  • Multi-step figures: midpoints inside triangles inside parallelograms
  • Proof strategy: what to construct when the figure refuses to yield
Projects You Build
  • Quadrilateral family tree: the shapes and the exact conditions separating them, made by the student
Practice & Assignments

18 quadrilateral problems including 4 proofs, plus 5 midpoint-theorem applications

Assessment

Month 5 test: a 25-mark paper on similarity and quadrilaterals with two proofs and one construction-strategy question

Topics Covered
  • Chords: equal chords, distances from the centre, the perpendicular from the centre
  • The central angle theorem: the angle at the centre doubles the angle at the arc
  • Angles in the same segment, and the angle in a semicircle
  • Cyclic quadrilaterals and their opposite angles
  • Tangents: perpendicularity to the radius and equal tangents from an external point
  • Angle chasing in circle figures, the entrance-exam favourite
Projects You Build
  • Circle theorem atlas: every theorem drawn, stated and proved or justified on the student's own pages
Practice & Assignments

20 circle problems from single-theorem to three-theorem figures, plus 2 full proofs

Topics Covered
  • Hard multi-step figures mixing congruence, similarity, quadrilaterals and circles
  • Auxiliary constructions: when and what to draw, taught as a decision, not magic
  • Working backwards from what must be proved
  • Olympiad-style geometry: problems where the figure is the puzzle
  • Timed geometry MCQs: answering from the figure without full proofs
  • Phase review: the proof portfolio completed and audited
Projects You Build
  • Workshop set: 6 multi-step geometry problems solved with the construction decision written out for each
Practice & Assignments

One timed 15-question geometry MCQ set plus 4 workshop problems, error log updated with figure-reading misses

Assessment

Phase 2 milestone: a 40-mark geometry paper, half proofs and half timed MCQs, with a one-on-one proof review

Topics Covered
  • Areas of triangles: half base times height, and Heron's formula for when heights hide
  • Areas of parallelograms, trapeziums and rhombuses, derived not memorised
  • Circles, sectors and segments, with arc lengths
  • Composite figures: decomposing shaded regions cleanly
  • Same base, same parallels: area relationships without any measuring
  • Estimation checks: is that area plausible for that figure
Projects You Build
  • Decomposition sheet: 8 shaded-region problems with the cut lines drawn and named before any formula is used
Practice & Assignments

22 area problems including 5 Heron applications and 5 composite figures, decomposition stated in one line each

Topics Covered
  • Surface areas and volumes: cube, cuboid, cylinder, cone, sphere, hemisphere
  • Combined solids and which surfaces vanish at the joins
  • Melting and recasting problems: volume as the conserved quantity
  • Scaling laws: double the length, four times the area, eight times the volume
  • Unit discipline across centimetres, metres and litres
  • MCQ forms: ratio-based mensuration questions solved without computing either quantity
Projects You Build
  • Scaling experiment write-up: one solid scaled by 2 and by 3, with areas and volumes tabulated and the pattern stated
Practice & Assignments

18 solid problems including 4 recasting and 4 ratio questions, units checked on every line

Assessment

Month 7 test: a 25-mark mensuration paper mixing computation, ratio reasoning and one composite figure

Topics Covered
  • The six trigonometric ratios in a right triangle and the naming logic
  • Exact values at 0, 30, 45, 60 and 90 degrees, rebuilt from two triangles rather than memorised
  • Finding all ratios from one, with Pythagoras doing the work
  • The fundamental identity and its rearrangements
  • Proving simple identities with a fixed strategy list
  • Ratio MCQs at speed: value questions in under a minute
Projects You Build
  • Two-triangle derivation page: the 30-60-90 and 45-45-90 triangles built and every standard value read off them
Practice & Assignments

30 ratio evaluations and 6 identity proofs, plus one 10-question timed MCQ set on values

Topics Covered
  • Angles of elevation and depression on honest, labelled figures
  • Single-triangle problems: towers, poles, kites and slopes
  • Two-triangle problems: two observation points and moving observers
  • Choosing the ratio that solves in one step
  • Rounding sensibly and sanity-checking against the figure
  • Where trigonometry goes in Class 11: a preview, not a syllabus
Projects You Build
  • Figure-first set: 8 heights and distances problems where the marked figure is drawn and approved before solving
Practice & Assignments

15 heights and distances problems including 4 two-triangle setups, every figure labelled with the given angle

Assessment

Month 8 test: a 25-mark trigonometry paper of ratios, identities and applications, one third MCQ

Topics Covered
  • The Cartesian plane: plotting, quadrants and reading coordinates fluently
  • The distance formula from Pythagoras, derived and drilled
  • Classifying triangles and quadrilaterals by computed distances
  • The section formula and midpoints, with internal division problems
  • Ratios from coordinates: where the axes cut a segment
  • Sketch-first habit: every coordinate problem starts with a drawing
Projects You Build
  • Coordinate gallery: 6 figures plotted, classified and verified by distances, presented on graph paper
Practice & Assignments

25 distance and section formula problems, each with a labelled sketch, plus 5 classification questions

Topics Covered
  • Slope as steepness: computing it and reading it from a sketch
  • Parallel and perpendicular slopes, kept concrete
  • Collinearity by slope and by distance, two roads to one answer
  • Coordinate proofs: choosing axes cleverly to make geometry easy
  • Mixed coordinate MCQs under time
  • Phase review: the toolkit chapters consolidated onto revision sheets
Projects You Build
  • Coordinate proof piece: one classical geometry fact proved by placing coordinates well, written up in full
Practice & Assignments

20 slope and collinearity problems plus one timed 12-question coordinate MCQ set, error log updated

Assessment

Phase 3 milestone: a 40-mark paper across mensuration, trigonometry and coordinates, half MCQ, fully reviewed

Topics Covered
  • Understand, plan, execute, check: the honest version of problem solving
  • Trying small cases and looking for the pattern that survives
  • Working backwards from what is asked
  • Drawing the right diagram, and redrawing when it misleads
  • Parity and simple invariants: what cannot change no matter the moves
  • Olympiad-style number and algebra problems using the heuristics, difficulty honest but humane
Projects You Build
  • Solution journal opened: every hard problem written up with the heuristic used and the dead ends kept, not erased
Practice & Assignments

8 problems for the week, chosen to need different heuristics; write-ups matter more than answer counts

Topics Covered
  • Systematic listing: counting without missing and without double-counting
  • The multiplication principle and simple arrangements
  • Combinations kept concrete: choosing teams and handshakes
  • The pigeonhole principle through puzzles
  • Logic puzzles: knights, liars and truth tables lite
  • Where these ideas reappear: Class 11 permutations and combinations, and reasoning sections of talent exams
Projects You Build
  • Counting problem set write-up: 5 counting problems solved twice, once by listing and once by principle, results reconciled
Practice & Assignments

12 counting and logic problems with full write-ups in the solution journal

Assessment

Month 10 checkpoint: a 20-mark problem-solving paper where method write-ups earn marks alongside answers

Topics Covered
  • How MCQ setters build wrong options, and what that tells the solver
  • Elimination: discarding options by sign, size, units or parity
  • Option testing: substituting answers back instead of solving forwards
  • Special values: choosing convenient numbers for variable-heavy questions
  • Estimation as a weapon: bounding the answer before computing it
  • When to solve honestly: questions where shortcuts are traps
Projects You Build
  • Technique tally: 30 MCQs solved with the technique noted per question, then tallied to see each student's habits
Practice & Assignments

Three 15-question topic-wise MCQ sets under time, error log updated with technique choices, not just misses

Topics Covered
  • Time budgeting: marks per minute and the discipline of moving on
  • Sectional MCQ sets across algebra, geometry, mensuration, trigonometry and coordinates
  • The two-pass strategy: bank the easy questions first
  • Guessing policy: when unanswered beats wrong, and reading the paper's rules
  • Error log analytics: which topic, which technique, which minute of the section
  • Building each student's personal weak-topic drill plan for the mock month
Projects You Build
  • Error log analysis report: the student's own two-page summary of their MCQ patterns going into the mocks
Practice & Assignments

Four timed sectional sets across the fortnight, each reviewed the same week, drill plan agreed with the teacher

Assessment

Month 11 checkpoint: one full-length topic-mixed MCQ paper under exam timing, fully debriefed

Topics Covered
  • Full-length foundation mocks in the style of NTSE-type talent exams and entrance papers
  • Exam-day routine rehearsed: instructions, bubbling, rough-work discipline
  • Review clinic after every mock: every miss classified and assigned a fix
  • Score movement read honestly: trends matter, single papers do not
  • Targeted drills between mocks from each student's plan
  • Stamina: holding accuracy in the last quarter of a long paper
Projects You Build
  • Mock file: each paper filed with its marked script, error classification and one-line fix per miss
Practice & Assignments

One additional mock at home under honest timing, self-marked and brought to the review clinic

Topics Covered
  • Two final mocks under strict conditions, spaced for recovery
  • The readiness map: every topic rated from the year's evidence, no vibes
  • The solution journal and proof portfolio reviewed as a body of work
  • What Class 11 changes: pace, abstraction, and how this foundation meets it
  • Keeping the edge: a weekly problem habit for the months after the course
  • Course close: one-on-one review with each family
Projects You Build
  • Personal readiness map: topic-by-topic strengths and fixes, built from the error log and mock file
  • Completed solution journal: a year of hard problems with the student's own write-ups
Practice & Assignments

Light targeted drills only, set individually from the final error log

Assessment

Course milestone: final full-length mock and readiness review with the family, plus certificate review

Projects You'll Build

Build a professional portfolio with A year-long body of work: proof portfolio, solution journal, error log, mock file and readiness map real-world projects.

A proof portfolio every major theorem of the course written in full four-part format
A solution journal hard problems written up with heuristics and honest dead ends
A personal error log maintained from phase 1 and analysed before the mock phase
The identity map and circle theorem atlas, built by the student
A coordinate proof piece classical geometry proved by clever axis placement
A scaling experiment write-up connecting length, area and volume
The technique tally and error log analysis report from the MCQ phase
A mock file with marked scripts and a final topic-by-topic readiness map

Weekly Learning Structure

Live Classes
2 live one-hour classes per week; mock sittings in month 12 run longer for full papers
Practice
3-4 hours weekly of problem sets, proofs and journal write-ups between classes
Review
Problem sets marked with written feedback; proofs and journal entries reviewed line by line each month

Certification & Recognition

Completion
Course-completion certificate from Modern Age Coders, alongside the student's readiness map and mock file

Technologies & Skills You'll Master

Comprehensive coverage of the entire modern web development stack.

Number theory basics
divisibility, primes, HCF-LCM and remainder thinking
Algebra at depth
exponents, surds, identities, factorisation, equations and inequalities
Proof writing across congruence, similarity, quadrilaterals and circle theorems
Mensuration, introductory trigonometry and coordinate geometry to entrance-exam standard
Problem-solving heuristics
small cases, working backwards, invariants and clean diagrams
Timed MCQ craft
elimination, option testing, time budgeting and error-log-driven improvement

Support & Resources

Doubt Support
WhatsApp doubt support between classes, with worked solutions for stuck problems
Progress Updates
Monthly progress notes to parents with test scores, error-log trends and the current readiness picture

Career Outcomes & Opportunities

Transform your career with industry-ready skills and job placement support.

Prerequisites

Maths Level
Comfortable with the previous class's school maths. The week 1 diagnostic finds the gaps and the early weeks patch them
Class
Class 8, 9 or 10. Batches are separated by class so depth and pace fit the student
Equipment
The student's NCERT maths textbook, a geometry box, graph paper, notebooks, and a device with stable internet
Mindset
Willingness to write solutions out in full. This course grades reasoning, not just answers

Who Is This Course For?

Future Jee Aspirants
Students in Class 8 to 10 who intend to attempt JEE or similar entrances and want the base built before Class 11 raises the stakes
Strong Students Underfed
Students who find school maths easy and are bored, and need harder problems rather than more of the same
Proof Never Taught
Students who can compute but have never been taught to prove, which is most students
Mcq First Timers
Students who have only ever written school papers and need timed MCQ craft before any talent or entrance exam
Families Avoiding Hype
Parents who want serious foundation work without rank promises and future-topper theatre

Career Paths After Completion

Class 11 maths in the science stream, entered with algebra and geometry that do not need repair
Formal JEE preparation from Class 11, with the foundation layer already done
Olympiad tracks such as IOQM for students who discover they enjoy the hard problems
School exams along the way: the depth here makes board-level questions feel routine
Our data science and programming courses, where the same structured thinking transfers directly

Course Guarantees

Live Classes
Live, interactive classes with a real instructor, never pre-recorded videos.
Small Batches
Small batches only: group classes are capped at 10 students, with mini-batch (3 to 4 students) and personal 1-on-1 options.
Structured Curriculum
A structured, well-paced curriculum taught step by step, with hands-on practice in every session.
Doubt Support
Doubt support between classes over WhatsApp, so you are never left stuck.
Certificate
A course-completion certificate you can share.
Free Demo
A free demo class before you enrol, so you can decide with no pressure.

What Families Say

Real feedback from the parents and students who learn with us.

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"Modern Age Coders has wonderful teachers who teach in a clear, easy and practical way. My son looks forward to every single class."

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"Modern Age Coders has been a game-changer for me. I struggled to grasp IT concepts before, and now they finally click, and I actually look forward to learning."

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