Every Single Chapter & Definitive Formula Blueprint Matrix • Grades 1 to 10 Complete
| Spatial Layouts | Inside, Outside, Bigger, Smaller, Top, Bottom, Nearer, Farther |
| Solid Shapes | Spherical (Rolls), Cylindrical/Cuboid (Slides) |
| Number Set | Count: 1, 2, 3, 4, 5, 6, 7, 8, 9 |
| Addition (+) | Combining groups together. E.g., 3 + 2 = 5 |
| Subtraction (-) | Taking away elements from a group. E.g., 5 - 2 = 3 |
| Zero Property | X + 0 = X and X - 0 = X |
| Place Value | 10 = 1 Ten + 0 Ones; 15 = 1 Ten + 5 Ones |
| Time Sequences | Morning → Afternoon → Evening → Night |
| Measurement Metrics | Length estimation via Span, Foot-print, Pace length comparisons |
| Weight Scales | Heavier vs Lighter elements |
| Sequence Pattern | Incremental skip steps and structural block shapes tracking |
| Currency Notes | Indian coins/notes valid currency units: ₹1, ₹2, ₹5, ₹10, ₹20, ₹50 |
| Grouping Units | Counting pairs (2s), bundles of tens (10s) |
| 2-Digit Partition | Number = (Tens × 10) + Ones |
| Geometric Traces | Circle (Coins), Rectangle (Boxes), Triangle (Cones) |
| Currency Split | Breaking double-digit integers into configurations of ₹10 notes & ₹1 coins |
| Calendar Cycle | 7 Days in Week, 12 Months in Year (365 Days standard) |
| Capacity Scale | Volume units matching relative sizing: Litres vs Millilitres |
| Carryover Add | Regrouping 10 Ones into a single 1 Ten shift unit |
| Borrowing Sub | Decomposing 1 Ten into 10 structural Ones units |
| View Perspectives | Top View, Side View, Front View spatial offsets |
| 3-Digit Base | Value = (H × 100) + (T × 10) + O |
| Century Bounds | 1 Century = 100 Runs / Units |
| Edges & Corners | Square/Rectangle = 4 Edges, 4 Corners. Circle = 0 Corners |
| Length Scaling | 1 Metre (m) = 100 Centimetres (cm) |
| Distance Scale | 1 Kilometre (km) = 1000 Metres (m) |
| Multiplication | Repeated addition array logic |
| Weight Equation | 1 Kilogram (kg) = 1000 Grams (g) |
| Volume Metrics | 1 Litre (L) = 1000 Millilitres (mL) |
| Division Inverse | If A × B = C, then C ÷ B = A and C ÷ A = B |
| Data Pictograms | Tracking item repeat counts via symbol icons or tally checkmarks |
| Brick Geometry | 6 rectangular faces, 12 edges, 8 vertices (Cuboid layout) |
| Time Calculation | 1 Hour = 60 Mins, 1 Min = 60 Secs |
| 24-Hour Switch | Time PM = 12-Hour Time + 12. (E.g., 4 PM = 16:00) |
| Circle Anatomy | Center point, Radius, Diameter line spacing |
| Diameter Factor | Diameter = 2 × Radius |
| Fraction Blocks | Half = 1/2, Quarter = 1/4, Three-Quarters = 3/4 |
| Whole Assembly | 1/4 + 1/4 + 1/4 + 1/4 = 1 |
| Division Theorem | Dividend = (Divisor × Quotient) + Remainder |
| Perimeter Formula | Sum total boundary line path length around flat geometric arrays |
| Square Perimeter | Perimeter = 4 × Side |
| Rect. Perimeter | Perimeter = 2 × (Length + Breadth) |
| Speed Equation | Speed = Distance / Time |
| Angle Classes | Right Angle = 90°, Acute Angle < 90°, Obtuse Angle > 90° |
| Fraction Multi | Fraction value of a collection = (Numerator × Total Collection) / Denominator |
| Symmetry Check | Mirror half reflections, 1/2 turns (180°), 1/4 turns (90°) layouts |
| Factors & Multiples | Common factors matrix, Least Common Multiple matching bounds |
| Net Formations | 2D foldable templates assembly maps into 3D structural cubes |
| Decimal Base | 1/10 = 0.1 (Tenths place), 1/100 = 0.01 (Hundredths place) |
| Area of Rectangle | Area = Length × Breadth |
| Area of Square | Area = Side × Side |
| Tally System | Vertical strokes grouped with diagonal crossing lines at every 5th count element |
| Volume of Cube | Volume = Side × Side × Side |
| Volume of Cuboid | Volume = Length × Breadth × Height |
| Large Numbers | 1 Lakh = 100,000; 1 Crore = 10,000,000 |
| HCF & LCM Rule | HCF(a,b) × LCM(a,b) = a × b |
| Divisibility 3 / 9 | Sum of individual digits must be divisible by 3 or 9 |
| Divisibility 6 | Must pass both Divisibility by 2 (Even) and Divisibility by 3 rules |
| Divisibility 11 | |Sum of odd digits - Sum of even digits| = 0 or multiple of 11 |
| Polygon Basics | Triangle (3 sides), Quadrilateral (4 sides), Pentagon (5 sides) |
| Integers Axis | Negative Integers (...) < -2 < -1 < 0 < +1 < +2 < (...) |
| Equivalent Frac. | a / b = (a × k) / (b × k) |
| Decimal Convers. | x cm = x/100 m; y g = y/1000 kg |
| Area of Triangle | Area = 0.5 × Base × Height |
| Equi. Triangle Per. | Perimeter = 3 × Side |
| Variable Logic | General expression tracking rules: e.g., Matchstick patterns = 2n |
| Ratio Form | Comparison layout: a : b = a / b |
| Proportion Identity | If a, b, c, d are in proportion, then a × d = b × c |
| Unitary Method | Calculate 1 unit value first → multiply by target count |
| Sign Matrix | (-) × (-) = (+), (-) × (+) = (-), (+) × (-) = (-) |
| Fraction Division | (a/b) ÷ (c/d) = (a/b) × (d/c) |
| Arithmetic Mean | Mean = Sum of observations / Number of observations |
| Data Range | Range = Maximum Value - Minimum Value |
| Median | Middle value of organized datasets arranged in ascending/descending order |
| Angle Pairs | Complementary = 90°, Supplementary = 180° |
| Transversal Cross | Alternate Interior angles match, Corresponding angles match |
| Triangle Sum | Angle A + Angle B + Angle C = 180° |
| Exterior Angle | Exterior Angle = Sum of 2 Interior Opposite Angles |
| Pythagoras Theorem | In a right-angled triangle: Hypotenuse² = Base² + Perpendicular² |
| Congruence Tests | SSS, SAS, ASA, RHS congruence parameters |
| Unitary Change | Profit% = (Profit / Cost Price) × 100 |
| Simple Interest | SI = (P × R × T) / 100 |
| Total Maturity | Amount = Principal (P) + Interest (SI) |
| Parallelogram Area | Area = Base × Height |
| Circle Metrics | Circumference = 2πr; Area = πr² |
| Exponent Power 1 | aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ ÷ aⁿ = aᵐ⁻ⁿ |
| Exponent Power 2 | (aᵐ)ⁿ = aᵐⁿ; a⁰ = 1 |
| Rational Axioms | Identity: Addition = 0, Multiplication = 1 |
| Linear Form | Standard shape configuration: ax + b = c |
| Polygon Interior | Sum of Interior Angles = (n - 2) × 180° |
| Exterior Sum | Sum of all Exterior Angles for any polygon = 360° |
| Parallelogram rules | Opposite sides match, opposite interior angles match, diagonals bisect |
| Pie Chart Angle | Central Sector Angle = (Component Value / Total) × 360° |
| Probability | P(E) = Outcomes / Total Samples |
| Pythagorean Triple | Configured via integers array: 2m, m²-1, m²+1 |
| Compound Interest | A = P(1 + R/100)ⁿ |
| Identity 1 & 2 | (a±b)² = a² ± 2ab + b² |
| Identity 3 | a² - b² = (a - b)(a + b) |
| Euler's Formula | For 3D polyhedrons: Faces (F) + Vertices (V) - Edges (E) = 2 |
| Trapezium Area | Area = 0.5 × (a + b) × h |
| Rhombus Area | Area = 0.5 × d₁ × d₂ |
| TSA Cylinder | Surface Area = 2πr(r + h); Volume = πr²h |
| Direct Proportion | Ratio stays constant: x / y = k |
| Inverse Proportion | Product stays constant: x × y = k |
| Rationalizing | Multiplier for denominator: 1/(√a+b) × (√a-b)/(√a-b) |
| Identity 4 | (x+a)(x+b) = x² + (a+b)x + ab |
| Identity 5 | (a+b+c)² = a²+b²+c²+2ab+2bc+2ca |
| Identity 6 & 7 | (a±b)³ = a³ ± b³ ± 3ab(a±b) |
| Identity 8 | a³+b³+c³-3abc = (a+b+c)(a²+b²+c²-ab-bc-ca) |
| Conditional Rule | If a + b + c = 0, then a³ + b³ + c³ = 3abc |
| Linear Graph | Standard two-variable line configuration: ax + by + c = 0 |
| Euclid Axiom | Things equal to the same thing are equal to each other |
| Lines & Angles | Vertically opposite angles match; Interior angles on same side sum to 180° |
| Triangle Criteria | SAS, ASA, SSS, RHS congruence, and AAS variation rules |
| Quad Angle Sum | Total interior sum = 360° |
| Mid-Point Theorem | Segment joining midpoints of 2 sides is parallel to 3rd side and = 0.5 × 3rd Side |
| Circle Angles | Angle subtended at center = 2 × Angle subtended at any point on circumference |
| Heron's Formula | Area = √[s(s-a)(s-b)(s-c)] where semiperimeter s = (a+b+c)/2 |
| Cone Metrics | Slant height l = √(r² + h²); CSA = πrl; Volume = 1/3 πr²h |
| Sphere Metrics | Surface Area = 4πr²; Volume = 4/3 πr³ |
| Hemisphere CSA | Curved Surface Area = 2πr²; Total Surface Area = 3πr² |
| Fundamental Th. | Composite Number = Product of Unique Prime Factors |
| Zeros Quadratic | Sum α + β = -b/a; Product α · β = c/a |
| Lines Intersect | Unique solution if a₁/a₂ ≠ b₁/b₂ |
| Lines Parallel | No solution if a₁/a₂ = b₁/b₂ ≠ c₁/c₂ (Inconsistent) |
| Lines Coincident | Infinite solutions if a₁/a₂ = b₁/b₂ = c₁/c₂ (Dependent) |
| Discriminant | D = b² - 4ac (Real distinct if D > 0, Real equal if D = 0) |
| Quadratic Root | Roots equation: x = [-b ± √D] / 2a |
| AP n-th Term | aₙ = a + (n - 1)d |
| AP Term Sum | Sₙ = (n/2)[2a + (n - 1)d] or Sₙ = (n/2)[a + l] |
| Thales Theorem | If DE || BC in triangle ABC, then AD/DB = AE/EC |
| Distance Formula | d = √[(x₂ - x₁)² + (y₂ - y₁)²] |
| Section Formula | Internal split: P(x,y) = ((m₁x₂ + m₂x₁)/(m₁+m₂), (m₁y₂ + m₂y₁)/(m₁+m₂)) |
| Trig Ratios | sinθ = P/H, cosθ = B/H, tanθ = P/B |
| Trig Identity 1 | sin²θ + cos²θ = 1 |
| Trig Identity 2 | 1 + tan²θ = sec²θ |
| Correct Identity | 1 + cot²θ = cosec²θ |
| Tangent Length | Tangents drawn from an external point to a circle are equal in length |
| Sector Area | Area = (θ/360°) × πr²; Arc Length = (θ/360°) × 2πr |
| Mean Calculation | Direct Method: Mean = Σfᵢxᵢ / Σfᵢ |
| Mode Equation | Mode = l + [(f₁ - f₀)/(2f₁ - f₀ - f₂)] × h |
| Median Equation | Median = l + [(n/2 - CF)/f] × h |
| Empirical Law | Crucial link: 3 × Median = Mode + 2 × Mean |